Unfold Hierarchy number Tags Values
      Math Function
        1  Examples
            1.1  Constants
                1.1.1  pi 
Math.PI
                1.1.2  Euler number 
Math.E
                1.1.3  natural logarithm of 2 
Math.LN2
                1.1.4  natural logarithm of 10 
Math.LN10
                1.1.5  base-2 logarithm of e 
Math.LOG2E
                1.1.6  base-10 logarithm of e 
Math.LOG10E
                1.1.7  square root of 2 
Math.SQRT2
                1.1.8  square root of 0.5 
Math.SQRT1_2
                1.1.9  Random 
Math.random()
                1.1.10  largest positive finite value of the number type 
Number.MAX_VALUE
                1.1.11  smallest positive nonzero value of the number type 
Number.MIN_VALUE
                1.1.12  positive infinite value 
Number.POSITIVE_INFINITY
                1.1.13  negative infinite value 
Number.NEGATIVE_INFINITY
                1.1.14  non-numeric 
Number.NaN
            1.2  Unary Function
                1.2.1  absoluate
Function name 
absoluate
Variables 
x
Expression 
Math.abs(x)
                1.2.2  Trigonometry
                    1.2.2.1  convert angle to radian
Function name 
radian
Variables 
angle
Expression 
angle  * Math.PI / 180
                    1.2.2.2  convert radian to angle
Function name 
angle
Variables 
radian
Expression 
radian  * 180 / Math.PI
                    1.2.2.3  cosine_radian
Function name 
cosine
Variables 
radian
Expression 
Math.cos(radian)
                    1.2.2.4  sine_radian
Function name 
sine
Variables 
radian
Expression 
Math.sin(radian)
                    1.2.2.5  tangent_radian
Function name 
tangent
Variables 
radian
Expression 
Math.tan(radian)
Function domain 
(  radian  - Math.PI / 2 ) % Math.PI != 0
                    1.2.2.6  arcCosine_radian
Function name 
arcCosine_radian
Variables 
x
Expression 
Math.acos(x)
Function domain 
x >= -1 && x <= 1
                    1.2.2.7  arcSine_radian
Function name 
arcSine_radian
Variables 
x
Expression 
Math.asin(x)
Function domain 
x >= -1 && x <= 1
                    1.2.2.8  arcTangent_radian
Function name 
arcTangent_radian
Variables 
x
Expression 
Math.atan(x)
                    1.2.2.9  cosine_angle
Function name 
cosine_angle
Variables 
angle
Expression 
Math.cos( angle  * Math.PI / 180)
                    1.2.2.10  sine_angle
Function name 
sine_angle
Variables 
angle
Expression 
Math.sin( angle  * Math.PI / 180)
                    1.2.2.11  tangent_angle
Function name 
tangent_angle
Variables 
angle
Expression 
Math.tan( angle  * Math.PI / 180)
Function domain 
(  angle  - 90 ) % 180 != 0
                    1.2.2.12  arcCosine_ angle
Function name 
arcCosine_  angle
Variables 
x
Expression 
Math.acos(x) * 180 / Math.PI
Function domain 
x >= -1 && x <= 1
                    1.2.2.13  arcSine_angle
Function name 
arcSine_angle
Variables 
x
Expression 
Math.asin(x) * 180 / Math.PI
Function domain 
x >= -1 && x <= 1
                    1.2.2.14  arcTangent_angle
Function name 
arcTangent_angle
Variables 
x
Expression 
Math.atan(x) * 180 / Math.PI
                1.2.3  Geometry
                    1.2.3.1  area of circle - radius
Function name 
area_of_circle
Variables 
radius
Expression 
Math.PI * radius * radius
Function domain 
radius > 0
                    1.2.3.2  area of circle - diameter
Function name 
area_of_circle
Variables 
diameter
Expression 
var r = diameter / 2.0;
Math.PI * r * r
Function domain 
diameter > 0
                    1.2.3.3  area of sphere - radius
Function name 
area of sphere
Variables 
radius
Expression 
4 * Math.PI * radius * radius
Function domain 
radius > 0
                    1.2.3.4  area of sphere - diameter
Function name 
area of sphere
Variables 
diameter
Expression 
Math.PI * diameter * diameter
Function domain 
diameter > 0
                    1.2.3.5  volume of sphere - radius
Function name 
volume of sphere
Variables 
radius
Expression 
4 * Math.PI * Math.pow(radius,3) / 3
Function domain 
radius > 0
                    1.2.3.6  volume of sphere - diameter
Function name 
volume of sphere
Variables 
diameter
Expression 
Math.PI * Math.pow(diameter,3) / 6
Function domain 
diameter > 0
                1.2.4  Power Function
                    1.2.4.1  square
Function name 
square
Variables 
x
Expression 
Math.pow(x,2)
                    1.2.4.2  cubic
Function name 
cubic
Variables 
x
Expression 
Math.pow(x,3)
                    1.2.4.3  quartic
Function name 
quartic
Variables 
x
Expression 
Math.pow(x,4)
                    1.2.4.4  quintic
Function name 
quintic
Variables 
x
Expression 
Math.pow(x,5)
                    1.2.4.5  square_root
Function name 
square_root
Variables 
x
Expression 
Math.sqrt(x)
Function domain 
x >= 0
                    1.2.4.6  cubic_root
Function name 
cubic_root
Variables 
x
Expression 
Math.pow(x,1/3)
Function domain 
x >= 0
                    1.2.4.7  quartic_root
Function name 
quartic_root
Variables 
x
Expression 
Math.pow(x,1/4)
Function domain 
x >= 0
                    1.2.4.8  quintic_root
Function name 
quintic_root
Variables 
x
Expression 
Math.pow(x,1/5)
Function domain 
x >= 0
                    1.2.4.9  reciprocal
Function name 
reciprocal
Variables 
x
Expression 
Math.pow(x,-1)
Function domain 
x != 0
                    1.2.4.10  quadratic_reciprocal
Function name 
quadratic_reciprocal
Variables 
x
Expression 
Math.pow(x,-2)
Function domain 
x != 0
                    1.2.4.11  cubic_reciprocal
Function name 
cubic_reciprocal
Variables 
x
Expression 
Math.pow(x,-3)
Function domain 
x != 0
                1.2.5  Exponential Function
                    1.2.5.1  exponential_of_e
Function name 
exponential_of_e
Variables 
x
Expression 
Math.exp(x + 5)
                    1.2.5.2  exponential_base_greater_than_1
Function name 
exponential_5.9
Variables 
x
Expression 
Math.pow(5.9,x)
                    1.2.5.3  exponential_base_less_than_1
Function name 
exponential_0.7
Variables 
x
Expression 
Math.pow(0.7,x)
                1.2.6  Logarithmic Function
                    1.2.6.1  natural_logarithm
Function name 
natural_logarithm
Variables 
x
Expression 
Math.log(x)
Function domain 
x > 0
                1.2.7  Intercept Function
                    1.2.7.1  round_up
Function name 
round_up
Variables 
x
Expression 
Math.ceil(x)
                    1.2.7.2  round_down
Function name 
round_down
Variables 
x
Expression 
Math.floor(x)
                    1.2.7.3  round
Function name 
round
Variables 
x
Expression 
Math.round(x)
                    1.2.7.4  trunc
Function name 
trunc
Variables 
x
Expression 
Math.trunc(x)
                1.2.8  Unitary Polynomial
                    1.2.8.1  unitary_linear_function
Function name 
unitary_linear_function
Variables 
x
Expression 
5 * x + 9
                    1.2.8.2  unitary_quadratic_function
Function name 
unitary_quadratic_function
Variables 
x
Expression 
5 * Math.pow(x,2)  + 3 * x + 9
                    1.2.8.3  unitary_cubic_function
Function name 
unitary_cubic_function
Variables 
x
Expression 
6 * Math.pow(x,3)  + 5 * Math.pow(x,2)  + 3 * x + 9
                    1.2.8.4  unitary_quartic_function
Function name 
unitary_quartic_function
Variables 
x
Expression 
7 * Math.pow(x,4)  + 6 * Math.pow(x,3)  + 5 * Math.pow(x,2)  + 3 * x + 9
                    1.2.8.5  unitary_quintic_function
Function name 
unitary_quintic_function
Variables 
x
Expression 
8 * Math.pow(x,5)  +7 * Math.pow(x,4)  + 6 * Math.pow(x,3)  + 5 * Math.pow(x,2)  + 3 * x + 9
                1.2.9  piecewise values
                    1.2.9.1  direct values
Function name 
piecewise_direct
Variables 
x
Expression 
if ( x > 1 ) 
    6 * x - 5.9;
else if ( x == 1)
    38; 
else 
    Math.pow(x, 2) + 2.7;
                    1.2.9.2  define functions
Function name 
piecewise_functions
Variables 
x
Expression 
function f1(x) {
    var multiply = 1;
    for (var i = 1; i <= Math.abs(x); i++) {
        multiply = multiply * i;
    }
    return multiply ;
}
function f2(x) {
    var sum = 0;
    for (var i = 1; i > x; i--) {
        sum += f1(i);
    }
    return sum;
}
if ( x > 1 ) 
    f1(x);
else if ( x == 1)
    38; 
else 
    f2(x);
                1.2.10  Numerical Analysis
                    1.2.10.1  Unary Normal probability density function
Function name 
Unary Normal probability density function
Variables 
x
Expression 
var mean = 1; 
var stdDeviation = 2; 
var dx = x - mean;
var expP = - dx * dx / ( 2 * stdDeviation * stdDeviation );
var div = Math.sqrt(2 * Math.PI) * stdDeviation;
Math.exp(expP) / div
                    1.2.10.2  Unary Standard normal probability density function
Function name 
Unary Standard normal probability density function
Variables 
x
Expression 
Math.exp(- x * x / 2) / Math.sqrt(2 * Math.PI)
                    1.2.10.3  sigmoid
Function name 
sigmoid
Variables 
x
Expression 
1 / (1 + Math.exp(-x))
                    1.2.10.4  derivative of sigmoid
Function name 
derivative of sigmoid
Variables 
x
Expression 
var s = 1 / (1 + Math.exp(-x));
s * (1 - s);
            1.3  Binary Function
                1.3.1  Univariate Polynomial
                    1.3.1.1  univariate linear polynomial
Function name 
univariate linear polynomial
Variables 
x,y
Expression 
5 * x + 9 * y - 4
                    1.3.1.2  univariate quadratic polynomial
Function name 
univariate quadratic polynomial
Variables 
x,y
Expression 
5 * x * x  + 3 * y * y + y + 9
                    1.3.1.3  univariate cubic polynomial
Function name 
univariate cubic polynomial
Variables 
x,y
Expression 
6 * Math.pow(x,3)  + 5 * Math.pow(y,2)  + 3 * y + 9
                    1.3.1.4  univariate quartic polynomial
Function name 
univariate quartic polynomial
Variables 
x,y
Expression 
7 * Math.pow(x,4)  + 6 * Math.pow(y,3)  + 5 * Math.pow(x,2)  + 3 * y + 9
                    1.3.1.5  univariate quintic polynomial
Function name 
univariate quintic polynomial
Variables 
x,y
Expression 
8 * Math.pow(x,5)  +7 * Math.pow(y,5)  + 6 * Math.pow(x,3)  + 5 * Math.pow(y,2)  + 3 * x + 9
                1.3.2  Geometry
                    1.3.2.1  volume of cylinder
Function name 
volume of cylinder
Variables 
radius,height
Expression 
Math.PI * radius * radius * height
                    1.3.2.2  area of ellipse - half_axle
Function name 
area of ellipse
Variables 
long_half_axle,short_half_axle
Expression 
Math.PI * long_half_axle * short_half_axle
Function domain 
long_half_axle > 0 && short_half_axle > 0
                    1.3.2.3  area of ellipse - axle
Function name 
area of ellipse
Variables 
long_axle,short_axle
Expression 
Math.PI * long_axle * short_axle / 4
Function domain 
long_axle > 0 && short_axle > 0
                1.3.3  Quadric Surface
                1.3.4  Trigonometry
                    1.3.4.1  univariate linear trigonometry
Function name 
univariate linear trigonometry
Variables 
x,y
Expression 
5 * Math.sin(x) + 3 * y + 9
                    1.3.4.2  univariate quadratic trigonometry
Function name 
univariate quadratic trigonometry
Variables 
x,y
Expression 
5 * Math.cos(x * x) + 3 * Math.sin(y) * Math.sin(y) + 9
                    1.3.4.3  univariate cubic trigonometry
Function name 
univariate cubic trigonometry
Variables 
x,y
Expression 
5 * Math.tan(x * x * x) + 3 * Math.cos(x) * Math.sin(y) + 9
                1.3.5  Exponential Function
                    1.3.5.1  univariate exponential
Function name 
univariate exponential
Variables 
x,y
Expression 
5 * Math.exp(x - 2 * y) + 3 * x - y + 9
                1.3.6  Logarithmic Function
                    1.3.6.1  univariate logarithmic
Function name 
univariate logarithmic
Variables 
x,y
Expression 
5 * Math.log(x  * y) - 9
Function domain 
x * y > 0
                1.3.7  Numerical Analysis
                    1.3.7.1  Univariate Normal probability density function
Function name 
Univariate Normal probability density function
Variables 
x,y
Expression 
var xMean = 1;
var xStd = 2; 
var yMean = 2;
var yStd = 1; 
var coefficient = 0.2; 
var dx = x - xMean;
var dy = y - yMean;
var xyStd = xStd * yStd;
var dco = 1 - coefficient * coefficient;
var px = dx * dx / ( xStd * xStd );
var py = dy * dy / ( yStd * yStd );
var pxy = 2 * coefficient * dx * dy / xyStd;
var expP = - (px + py - pxy) / ( 2 * dco)
var div = 2 * Math.PI * xyStd * Math.sqrt(dco);
Math.exp(expP) / div
                    1.3.7.2  Univariate Standard normal probability density function
Function name 
Univariate Standard normal probability density function
Variables 
x,y
Expression 
var xMean = 1;
var xStd = 2; 
var yMean = 2;
var yStd = 1; 
var dx = x - xMean;
var dy = y - yMean;
var xyStd = xStd * yStd;
var px = dx * dx / ( xStd * xStd );
var py = dy * dy / ( yStd * yStd );
var expP = - (px + py) / 2
var div = 2 * Math.PI * xyStd;
Math.exp(expP) / div
            1.4  Ternary Function
                1.4.1  Trigonometry
                    1.4.1.1  law of sines - for angle(radian)
Function name 
angleB_radian
Variables 
angleA_radian ,edge_a,edge_b
Expression 
var sinB = Math.sin(angleA_radian ) * edge_b / edge_a;
Math.asin(sinB)
Function domain 
angleA_radian  > 0 && edge_a > 0 && edge_b > 0
                    1.4.1.2  law of sines - for angle(angle)
Function name 
angleB_angle
Variables 
angleA_angle ,edge_a,edge_b
Expression 
var sinA = Math.sin(angleA_angle  * Math.PI / 180);
var sinB = sinA * edge_b / edge_a;
Math.asin(sinB) * 180 / Math.PI
Function domain 
angleA_angle  > 0 && edge_a > 0 && edge_b > 0
                    1.4.1.3  law of sines - for edge(radian)
Function name 
edge_b
Variables 
angleA_radian ,edge_a,angleB_radian
Expression 
edge_a * Math.sin(angleB_radian ) / Math.sin(angleA_radian )
Function domain 
angleA_radian  > 0 && angleB_radian  > 0 && edge_a > 0
                    1.4.1.4  law of sines - for edge(angle)
Function name 
edge_b
Variables 
angleA_angle ,edge_a,angleB_angle
Expression 
var sinA = Math.sin(angleA_angle  * Math.PI / 180);
var sinB = Math.sin(angleB_angle  * Math.PI / 180);
edge_a * sinB / sinA
Function domain 
angleA_angle  > 0 && angleB_angle  > 0 && edge_a > 0
                    1.4.1.5  law of cosines - for edge(radian)
Function name 
edge_a
Variables 
angleA_radian ,edge_b,edge_c
Expression 
Math.sqrt(edge_b * edge_b + edge_c * edge_c - 2 * edge_b * edge_c * Math.cos(angleA_radian ))
Function domain 
angleA_radian  > 0 && edge_b > 0 && edge_c > 0
                    1.4.1.6  law of cosines - for edge(angle)
Function name 
edge_a
Variables 
angleA_angle ,edge_b,edge_c
Expression 
var cosA = Math.cos(angleA_angle  * Math.PI / 180);
Math.sqrt(edge_b * edge_b + edge_c * edge_c - 2 * edge_b * edge_c * cosA)
Function domain 
angleA_angle  > 0 && edge_b > 0 && edge_c > 0
                    1.4.1.7  law of cosines - for angle(radian)
Function name 
angleA_radian
Variables 
edge_a,edge_b,edge_c
Expression 
var cosA = (edge_b * edge_b + edge_c * edge_c - edge_a * edge_a) / (2 * edge_b * edge_c);
Math.acos( cosA )
Function domain 
edge_a > 0 && edge_b > 0 && edge_c > 0
                    1.4.1.8  law of cosines - for angle(angle)
Function name 
angleA_angle
Variables 
edge_a,edge_b,edge_c
Expression 
var cosA = (edge_b * edge_b + edge_c * edge_c - edge_a * edge_a) / (2 * edge_b * edge_c);
Math.acos( cosA ) * 180 / Math.PI
Function domain 
edge_a > 0 && edge_b > 0 && edge_c > 0
                1.4.2  Geometry
                    1.4.2.1  area of ellipsoid - half_axie
Function name 
area of ellipsoid
Variables 
half_axie_a,half_axie_b,half_axie_c
Expression 
4 * Math.PI * ( half_axie_a * half_axie_b + half_axie_a * half_axie_c + half_axie_b * half_axie_c )/ 3
Function domain 
half_axie_a > 0 && half_axie_b > 0 && half_axie_c > 0
                    1.4.2.2  area of ellipsoid - axie
Function name 
area of ellipsoid
Variables 
axie_a,axie_b,axie_c
Expression 
Math.PI * ( axie_a * axie_b + axie_a * axie_c + axie_b * axie_c )/ 3
Function domain 
axie_a > 0 && axie_b > 0 && _axie_c > 0
                    1.4.2.3  volumn of ellipsoid - half_axie
Function name 
volumn of ellipsoid
Variables 
half_axie_a,half_axie_b,half_axie_c
Expression 
4 * Math.PI * half_axie_a * half_axie_b * half_axie_c / 3
Function domain 
half_axie_a > 0 && half_axie_b > 0 && half_axie_c > 0
                    1.4.2.4  volumn of ellipsoid - axie
Function name 
volumn of ellipsoid
Variables 
axie_a,axie_b,axie_c
Expression 
Math.PI * axie_a * axie_b * axie_c / 6
Function domain 
axie_a > 0 && axie_b > 0 && axie_c > 0
                    1.4.2.5  area of cube
Function name 
area of cube
Variables 
length,width,height
Expression 
2 * ( length * width + length * height + width * height )
Function domain 
length > 0 && width > 0 && height > 0
                    1.4.2.6  volumn of cube
Function name 
volumn of cube
Variables 
length,width,height
Expression 
length * width * height
Function domain 
length > 0 && width > 0 && height > 0
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