1.1.1 pi
1.1.2 Euler number
1.1.3 natural logarithm of 2
1.1.4 natural logarithm of 10
1.1.5 base-2 logarithm of e
1.1.6 base-10 logarithm of e
1.1.7 square root of 2
1.1.8 square root of 0.5
1.1.9 Random
1.1.10 largest positive finite value of the number type
| Expression | Number.MAX_VALUE |
1.1.11 smallest positive nonzero value of the number type
| Expression | Number.MIN_VALUE |
1.1.12 positive infinite value
| Expression | Number.POSITIVE_INFINITY |
1.1.13 negative infinite value
| Expression | Number.NEGATIVE_INFINITY |
1.1.14 non-numeric
1.2.1 absoluate
| Variables | x |
| Expression | Math.abs(x) |
1.2.2.1 convert angle to radian
| Variables | angle |
| Expression | angle * Math.PI / 180 |
1.2.2.2 convert radian to angle
| Variables | radian |
| Expression | radian * 180 / Math.PI |
1.2.2.3 cosine_radian
| Variables | radian |
| Expression | Math.cos(radian) |
1.2.2.4 sine_radian
| Variables | radian |
| Expression | Math.sin(radian) |
1.2.2.5 tangent_radian
| Variables | radian |
| Expression | Math.tan(radian) |
| Function domain | ( radian - Math.PI / 2 ) % Math.PI != 0 |
1.2.2.6 arcCosine_radian
| Variables | x |
| Expression | Math.acos(x) |
| Function domain | x >= -1 && x <= 1 |
1.2.2.7 arcSine_radian
| Variables | x |
| Expression | Math.asin(x) |
| Function domain | x >= -1 && x <= 1 |
1.2.2.8 arcTangent_radian
| Variables | x |
| Expression | Math.atan(x) |
1.2.2.9 cosine_angle
| Variables | angle |
| Expression | Math.cos( angle * Math.PI / 180) |
1.2.2.10 sine_angle
| Variables | angle |
| Expression | Math.sin( angle * Math.PI / 180) |
1.2.2.11 tangent_angle
| Variables | angle |
| Expression | Math.tan( angle * Math.PI / 180) |
| Function domain | ( angle - 90 ) % 180 != 0 |
1.2.2.12 arcCosine_ angle
| Variables | x |
| Expression | Math.acos(x) * 180 / Math.PI |
| Function domain | x >= -1 && x <= 1 |
1.2.2.13 arcSine_angle
| Variables | x |
| Expression | Math.asin(x) * 180 / Math.PI |
| Function domain | x >= -1 && x <= 1 |
1.2.2.14 arcTangent_angle
| Variables | x |
| Expression | Math.atan(x) * 180 / Math.PI |
1.2.3.1 area of circle - radius
| Variables | radius |
| Expression | Math.PI * radius * radius |
| Function domain | radius > 0 |
1.2.3.2 area of circle - diameter
| Variables | diameter |
| Expression | var r = diameter / 2.0;
Math.PI * r * r |
| Function domain | diameter > 0 |
1.2.3.3 area of sphere - radius
| Variables | radius |
| Expression | 4 * Math.PI * radius * radius |
| Function domain | radius > 0 |
1.2.3.4 area of sphere - diameter
| Variables | diameter |
| Expression | Math.PI * diameter * diameter |
| Function domain | diameter > 0 |
1.2.3.5 volume of sphere - radius
| Variables | radius |
| Expression | 4 * Math.PI * Math.pow(radius,3) / 3 |
| Function domain | radius > 0 |
1.2.3.6 volume of sphere - diameter
| Variables | diameter |
| Expression | Math.PI * Math.pow(diameter,3) / 6 |
| Function domain | diameter > 0 |
1.2.4.1 square
| Variables | x |
| Expression | Math.pow(x,2) |
1.2.4.2 cubic
| Variables | x |
| Expression | Math.pow(x,3) |
1.2.4.3 quartic
| Variables | x |
| Expression | Math.pow(x,4) |
1.2.4.4 quintic
| Variables | x |
| Expression | Math.pow(x,5) |
1.2.4.5 square_root
| Variables | x |
| Expression | Math.sqrt(x) |
| Function domain | x >= 0 |
1.2.4.6 cubic_root
| Variables | x |
| Expression | Math.pow(x,1/3) |
| Function domain | x >= 0 |
1.2.4.7 quartic_root
| Variables | x |
| Expression | Math.pow(x,1/4) |
| Function domain | x >= 0 |
1.2.4.8 quintic_root
| Variables | x |
| Expression | Math.pow(x,1/5) |
| Function domain | x >= 0 |
1.2.4.9 reciprocal
| Variables | x |
| Expression | Math.pow(x,-1) |
| Function domain | x != 0 |
1.2.4.10 quadratic_reciprocal
| Variables | x |
| Expression | Math.pow(x,-2) |
| Function domain | x != 0 |
1.2.4.11 cubic_reciprocal
| Variables | x |
| Expression | Math.pow(x,-3) |
| Function domain | x != 0 |
1.2.5.1 exponential_of_e
| Variables | x |
| Expression | Math.exp(x + 5) |
1.2.5.2 exponential_base_greater_than_1
| Variables | x |
| Expression | Math.pow(5.9,x) |
1.2.5.3 exponential_base_less_than_1
| Variables | x |
| Expression | Math.pow(0.7,x) |
1.2.6.1 natural_logarithm
| Variables | x |
| Expression | Math.log(x) |
| Function domain | x > 0 |
1.2.7.1 round_up
| Variables | x |
| Expression | Math.ceil(x) |
1.2.7.2 round_down
| Variables | x |
| Expression | Math.floor(x) |
1.2.7.3 round
| Variables | x |
| Expression | Math.round(x) |
1.2.7.4 trunc
| Variables | x |
| Expression | Math.trunc(x) |
1.2.8.1 unitary_linear_function
| Variables | x |
| Expression | 5 * x + 9 |
1.2.8.2 unitary_quadratic_function
| Variables | x |
| Expression | 5 * Math.pow(x,2) + 3 * x + 9 |
1.2.8.3 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
| 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
| 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 |
1.2.9.1 direct values
| 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
| 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); |
1.2.10.1 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
| Variables | x |
| Expression | Math.exp(- x * x / 2) / Math.sqrt(2 * Math.PI) |
1.2.10.3 sigmoid
| Variables | x |
| Expression | 1 / (1 + Math.exp(-x)) |
1.2.10.4 derivative of sigmoid
| Variables | x |
| Expression | var s = 1 / (1 + Math.exp(-x));
s * (1 - s); |
1.3.1.1 univariate linear polynomial
| Variables | x,y |
| Expression | 5 * x + 9 * y - 4 |
1.3.1.2 univariate quadratic polynomial
| Variables | x,y |
| Expression | 5 * x * x + 3 * y * y + y + 9 |
1.3.1.3 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
| 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
| 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 |
1.3.2.1 volume of cylinder
| Variables | radius,height |
| Expression | Math.PI * radius * radius * height |
1.3.2.2 area of ellipse - half_axle
| 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
| 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
1.3.4.1 univariate linear trigonometry
| Variables | x,y |
| Expression | 5 * Math.sin(x) + 3 * y + 9 |
1.3.4.2 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
| Variables | x,y |
| Expression | 5 * Math.tan(x * x * x) + 3 * Math.cos(x) * Math.sin(y) + 9 |
1.3.5.1 univariate exponential
| Variables | x,y |
| Expression | 5 * Math.exp(x - 2 * y) + 3 * x - y + 9 |
1.3.6.1 univariate logarithmic
| Variables | x,y |
| Expression | 5 * Math.log(x * y) - 9 |
| Function domain | x * y > 0 |
1.3.7.1 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
| 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 |
1.4.1.1 law of sines - for angle(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)
| 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)
| 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)
| 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)
| 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)
| 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)
| 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)
| 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 |
1.4.2.1 area of ellipsoid - half_axie
| 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
| 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
| 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
| 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
| 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
| Variables | length,width,height |
| Expression | length * width * height |
| Function domain | length > 0 && width > 0 && height > 0 |