Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A

Percentage Accurate: 98.5% → 98.5%

Time: 21.4s

Alternatives: 16

Speedup: 1.0×

• 48.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x * exp((((y * log(z)) + ((t - 1.0d0) * log(a))) - b))) / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x * Math.exp((((y * Math.log(z)) + ((t - 1.0) * Math.log(a))) - b))) / y;
}

Python

def code(x, y, z, t, a, b):
	return (x * math.exp((((y * math.log(z)) + ((t - 1.0) * math.log(a))) - b))) / y

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) + Float64(Float64(t - 1.0) * log(a))) - b))) / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] + N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Initial Program: 98.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x * exp((((y * log(z)) + ((t - 1.0d0) * log(a))) - b))) / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x * Math.exp((((y * Math.log(z)) + ((t - 1.0) * Math.log(a))) - b))) / y;
}

Python

def code(x, y, z, t, a, b):
	return (x * math.exp((((y * math.log(z)) + ((t - 1.0) * math.log(a))) - b))) / y

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) + Float64(Float64(t - 1.0) * log(a))) - b))) / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] + N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Alternative 1: 98.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot e^{\left(y \cdot \log z + \left(t + -1\right) \cdot \log a\right) - b}}{y} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (* x (exp (- (+ (* y (log z)) (* (+ t -1.0) (log a))) b))) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * exp((((y * log(z)) + ((t + -1.0) * log(a))) - b))) / y;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x * exp((((y * log(z)) + ((t + (-1.0d0)) * log(a))) - b))) / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x * Math.exp((((y * Math.log(z)) + ((t + -1.0) * Math.log(a))) - b))) / y;
}

Python

def code(x, y, z, t, a, b):
	return (x * math.exp((((y * math.log(z)) + ((t + -1.0) * math.log(a))) - b))) / y

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) + Float64(Float64(t + -1.0) * log(a))) - b))) / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x * exp((((y * log(z)) + ((t + -1.0) * log(a))) - b))) / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] + N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 91.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+110} \lor \neg \left(y \leq 4.25 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.1e+110) (not (<= y 4.25e-38)))
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.1e+110) || !(y <= 4.25e-38)) {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	} else {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.1d+110)) .or. (.not. (y <= 4.25d-38))) then
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y
    else
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.1e+110) || !(y <= 4.25e-38)) {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	} else {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.1e+110) or not (y <= 4.25e-38):
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	else:
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.1e+110) || !(y <= 4.25e-38))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.1e+110) || ~((y <= 4.25e-38)))
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	else
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.1e+110], N[Not[LessEqual[y, 4.25e-38]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 88.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+110} \lor \neg \left(y \leq 7.1 \cdot 10^{+31}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8.2e+110) (not (<= y 7.1e+31)))
   (/ (* x (/ (pow z y) y)) a)
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.2e+110) || !(y <= 7.1e+31)) {
		tmp = (x * (pow(z, y) / y)) / a;
	} else {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-8.2d+110)) .or. (.not. (y <= 7.1d+31))) then
        tmp = (x * ((z ** y) / y)) / a
    else
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.2e+110) || !(y <= 7.1e+31)) {
		tmp = (x * (Math.pow(z, y) / y)) / a;
	} else {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -8.2e+110) or not (y <= 7.1e+31):
		tmp = (x * (math.pow(z, y) / y)) / a
	else:
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -8.2e+110) || !(y <= 7.1e+31))
		tmp = Float64(Float64(x * Float64((z ^ y) / y)) / a);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -8.2e+110) || ~((y <= 7.1e+31)))
		tmp = (x * ((z ^ y) / y)) / a;
	else
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -8.2e+110], N[Not[LessEqual[y, 7.1e+31]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 81.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+58} \lor \neg \left(y \leq 3.2 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{\frac{{a}^{t}}{a}}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.3e+58) (not (<= y 3.2e+30)))
   (/ (* x (/ (pow z y) y)) a)
   (/ (* x (/ (/ (pow a t) a) (exp b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.3e+58) || !(y <= 3.2e+30)) {
		tmp = (x * (pow(z, y) / y)) / a;
	} else {
		tmp = (x * ((pow(a, t) / a) / exp(b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.3d+58)) .or. (.not. (y <= 3.2d+30))) then
        tmp = (x * ((z ** y) / y)) / a
    else
        tmp = (x * (((a ** t) / a) / exp(b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.3e+58) || !(y <= 3.2e+30)) {
		tmp = (x * (Math.pow(z, y) / y)) / a;
	} else {
		tmp = (x * ((Math.pow(a, t) / a) / Math.exp(b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.3e+58) or not (y <= 3.2e+30):
		tmp = (x * (math.pow(z, y) / y)) / a
	else:
		tmp = (x * ((math.pow(a, t) / a) / math.exp(b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.3e+58) || !(y <= 3.2e+30))
		tmp = Float64(Float64(x * Float64((z ^ y) / y)) / a);
	else
		tmp = Float64(Float64(x * Float64(Float64((a ^ t) / a) / exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.3e+58) || ~((y <= 3.2e+30)))
		tmp = (x * ((z ^ y) / y)) / a;
	else
		tmp = (x * (((a ^ t) / a) / exp(b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.3e+58], N[Not[LessEqual[y, 3.2e+30]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x * N[(N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 74.7% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ t_2 := \frac{x \cdot \frac{{z}^{y}}{y}}{a}\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-160}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;y \leq 1.48 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* a (* y (exp b))))) (t_2 (/ (* x (/ (pow z y) y)) a)))
   (if (<= y -1.6e+98)
     t_2
     (if (<= y -2.6e-137)
       t_1
       (if (<= y 2.5e-160)
         (/ (* x (pow a (+ t -1.0))) y)
         (if (<= y 1.48e+29) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * (y * exp(b)));
	double t_2 = (x * (pow(z, y) / y)) / a;
	double tmp;
	if (y <= -1.6e+98) {
		tmp = t_2;
	} else if (y <= -2.6e-137) {
		tmp = t_1;
	} else if (y <= 2.5e-160) {
		tmp = (x * pow(a, (t + -1.0))) / y;
	} else if (y <= 1.48e+29) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (a * (y * exp(b)))
    t_2 = (x * ((z ** y) / y)) / a
    if (y <= (-1.6d+98)) then
        tmp = t_2
    else if (y <= (-2.6d-137)) then
        tmp = t_1
    else if (y <= 2.5d-160) then
        tmp = (x * (a ** (t + (-1.0d0)))) / y
    else if (y <= 1.48d+29) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * (y * Math.exp(b)));
	double t_2 = (x * (Math.pow(z, y) / y)) / a;
	double tmp;
	if (y <= -1.6e+98) {
		tmp = t_2;
	} else if (y <= -2.6e-137) {
		tmp = t_1;
	} else if (y <= 2.5e-160) {
		tmp = (x * Math.pow(a, (t + -1.0))) / y;
	} else if (y <= 1.48e+29) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a * (y * math.exp(b)))
	t_2 = (x * (math.pow(z, y) / y)) / a
	tmp = 0
	if y <= -1.6e+98:
		tmp = t_2
	elif y <= -2.6e-137:
		tmp = t_1
	elif y <= 2.5e-160:
		tmp = (x * math.pow(a, (t + -1.0))) / y
	elif y <= 1.48e+29:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a * Float64(y * exp(b))))
	t_2 = Float64(Float64(x * Float64((z ^ y) / y)) / a)
	tmp = 0.0
	if (y <= -1.6e+98)
		tmp = t_2;
	elseif (y <= -2.6e-137)
		tmp = t_1;
	elseif (y <= 2.5e-160)
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y);
	elseif (y <= 1.48e+29)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a * (y * exp(b)));
	t_2 = (x * ((z ^ y) / y)) / a;
	tmp = 0.0;
	if (y <= -1.6e+98)
		tmp = t_2;
	elseif (y <= -2.6e-137)
		tmp = t_1;
	elseif (y <= 2.5e-160)
		tmp = (x * (a ^ (t + -1.0))) / y;
	elseif (y <= 1.48e+29)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[y, -1.6e+98], t$95$2, If[LessEqual[y, -2.6e-137], t$95$1, If[LessEqual[y, 2.5e-160], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 1.48e+29], t$95$1, t$95$2]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 74.7% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ t_2 := \frac{x \cdot \frac{{z}^{y}}{y}}{a}\\ \mathbf{if}\;y \leq -1.26 \cdot 10^{+98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-158}:\\ \;\;\;\;\frac{\frac{x}{\frac{a}{{a}^{t}}}}{y}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* a (* y (exp b))))) (t_2 (/ (* x (/ (pow z y) y)) a)))
   (if (<= y -1.26e+98)
     t_2
     (if (<= y -1.08e-136)
       t_1
       (if (<= y 2.3e-158)
         (/ (/ x (/ a (pow a t))) y)
         (if (<= y 2.25e+29) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * (y * exp(b)));
	double t_2 = (x * (pow(z, y) / y)) / a;
	double tmp;
	if (y <= -1.26e+98) {
		tmp = t_2;
	} else if (y <= -1.08e-136) {
		tmp = t_1;
	} else if (y <= 2.3e-158) {
		tmp = (x / (a / pow(a, t))) / y;
	} else if (y <= 2.25e+29) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (a * (y * exp(b)))
    t_2 = (x * ((z ** y) / y)) / a
    if (y <= (-1.26d+98)) then
        tmp = t_2
    else if (y <= (-1.08d-136)) then
        tmp = t_1
    else if (y <= 2.3d-158) then
        tmp = (x / (a / (a ** t))) / y
    else if (y <= 2.25d+29) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * (y * Math.exp(b)));
	double t_2 = (x * (Math.pow(z, y) / y)) / a;
	double tmp;
	if (y <= -1.26e+98) {
		tmp = t_2;
	} else if (y <= -1.08e-136) {
		tmp = t_1;
	} else if (y <= 2.3e-158) {
		tmp = (x / (a / Math.pow(a, t))) / y;
	} else if (y <= 2.25e+29) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a * (y * math.exp(b)))
	t_2 = (x * (math.pow(z, y) / y)) / a
	tmp = 0
	if y <= -1.26e+98:
		tmp = t_2
	elif y <= -1.08e-136:
		tmp = t_1
	elif y <= 2.3e-158:
		tmp = (x / (a / math.pow(a, t))) / y
	elif y <= 2.25e+29:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a * Float64(y * exp(b))))
	t_2 = Float64(Float64(x * Float64((z ^ y) / y)) / a)
	tmp = 0.0
	if (y <= -1.26e+98)
		tmp = t_2;
	elseif (y <= -1.08e-136)
		tmp = t_1;
	elseif (y <= 2.3e-158)
		tmp = Float64(Float64(x / Float64(a / (a ^ t))) / y);
	elseif (y <= 2.25e+29)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a * (y * exp(b)));
	t_2 = (x * ((z ^ y) / y)) / a;
	tmp = 0.0;
	if (y <= -1.26e+98)
		tmp = t_2;
	elseif (y <= -1.08e-136)
		tmp = t_1;
	elseif (y <= 2.3e-158)
		tmp = (x / (a / (a ^ t))) / y;
	elseif (y <= 2.25e+29)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[y, -1.26e+98], t$95$2, If[LessEqual[y, -1.08e-136], t$95$1, If[LessEqual[y, 2.3e-158], N[(N[(x / N[(a / N[Power[a, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 2.25e+29], t$95$1, t$95$2]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 72.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -760000000 \lor \neg \left(b \leq 4.5 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{{z}^{y}}{y} \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -760000000.0) (not (<= b 4.5e-16)))
   (/ x (* a (* y (exp b))))
   (* (/ (pow z y) y) (/ x a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -760000000.0) || !(b <= 4.5e-16)) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = (pow(z, y) / y) * (x / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-760000000.0d0)) .or. (.not. (b <= 4.5d-16))) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = ((z ** y) / y) * (x / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -760000000.0) || !(b <= 4.5e-16)) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = (Math.pow(z, y) / y) * (x / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -760000000.0) or not (b <= 4.5e-16):
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = (math.pow(z, y) / y) * (x / a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -760000000.0) || !(b <= 4.5e-16))
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(Float64((z ^ y) / y) * Float64(x / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -760000000.0) || ~((b <= 4.5e-16)))
		tmp = x / (a * (y * exp(b)));
	else
		tmp = ((z ^ y) / y) * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -760000000.0], N[Not[LessEqual[b, 4.5e-16]], $MachinePrecision]], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 74.0% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+98} \lor \neg \left(y \leq 2.1 \cdot 10^{+29}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.35e+98) (not (<= y 2.1e+29)))
   (/ (* x (/ (pow z y) y)) a)
   (/ x (* a (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.35e+98) || !(y <= 2.1e+29)) {
		tmp = (x * (pow(z, y) / y)) / a;
	} else {
		tmp = x / (a * (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.35d+98)) .or. (.not. (y <= 2.1d+29))) then
        tmp = (x * ((z ** y) / y)) / a
    else
        tmp = x / (a * (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.35e+98) || !(y <= 2.1e+29)) {
		tmp = (x * (Math.pow(z, y) / y)) / a;
	} else {
		tmp = x / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.35e+98) or not (y <= 2.1e+29):
		tmp = (x * (math.pow(z, y) / y)) / a
	else:
		tmp = x / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.35e+98) || !(y <= 2.1e+29))
		tmp = Float64(Float64(x * Float64((z ^ y) / y)) / a);
	else
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.35e+98) || ~((y <= 2.1e+29)))
		tmp = (x * ((z ^ y) / y)) / a;
	else
		tmp = x / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.35e+98], N[Not[LessEqual[y, 2.1e+29]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 9: 59.1% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \frac{x}{a \cdot \left(y \cdot e^{b}\right)} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x (* a (* y (exp b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / (a * (y * exp(b)));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / (a * (y * exp(b)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / (a * (y * Math.exp(b)));
}

Python

def code(x, y, z, t, a, b):
	return x / (a * (y * math.exp(b)))

Julia

function code(x, y, z, t, a, b)
	return Float64(x / Float64(a * Float64(y * exp(b))))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / (a * (y * exp(b)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 10: 40.0% accurate, 20.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{-41}:\\ \;\;\;\;\frac{\frac{b}{a}}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+131} \lor \neg \left(b \leq 9.6 \cdot 10^{+302}\right):\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.1e-41)
   (* (/ (/ b a) y) (- x))
   (if (<= b 1.1e+23)
     (/ x (* y a))
     (if (or (<= b 4.5e+131) (not (<= b 9.6e+302)))
       (/ (/ x (* a b)) y)
       (/ x (* a (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.1e-41) {
		tmp = ((b / a) / y) * -x;
	} else if (b <= 1.1e+23) {
		tmp = x / (y * a);
	} else if ((b <= 4.5e+131) || !(b <= 9.6e+302)) {
		tmp = (x / (a * b)) / y;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.1d-41)) then
        tmp = ((b / a) / y) * -x
    else if (b <= 1.1d+23) then
        tmp = x / (y * a)
    else if ((b <= 4.5d+131) .or. (.not. (b <= 9.6d+302))) then
        tmp = (x / (a * b)) / y
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.1e-41) {
		tmp = ((b / a) / y) * -x;
	} else if (b <= 1.1e+23) {
		tmp = x / (y * a);
	} else if ((b <= 4.5e+131) || !(b <= 9.6e+302)) {
		tmp = (x / (a * b)) / y;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.1e-41:
		tmp = ((b / a) / y) * -x
	elif b <= 1.1e+23:
		tmp = x / (y * a)
	elif (b <= 4.5e+131) or not (b <= 9.6e+302):
		tmp = (x / (a * b)) / y
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.1e-41)
		tmp = Float64(Float64(Float64(b / a) / y) * Float64(-x));
	elseif (b <= 1.1e+23)
		tmp = Float64(x / Float64(y * a));
	elseif ((b <= 4.5e+131) || !(b <= 9.6e+302))
		tmp = Float64(Float64(x / Float64(a * b)) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.1e-41)
		tmp = ((b / a) / y) * -x;
	elseif (b <= 1.1e+23)
		tmp = x / (y * a);
	elseif ((b <= 4.5e+131) || ~((b <= 9.6e+302)))
		tmp = (x / (a * b)) / y;
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.1e-41], N[(N[(N[(b / a), $MachinePrecision] / y), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[b, 1.1e+23], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 4.5e+131], N[Not[LessEqual[b, 9.6e+302]], $MachinePrecision]], N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 11: 40.0% accurate, 23.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{-40}:\\ \;\;\;\;\frac{\frac{b}{a}}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+131}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+302}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.4e-40)
   (* (/ (/ b a) y) (- x))
   (if (<= b 4.4e+131)
     (/ (/ x (+ a (* a b))) y)
     (if (<= b 7.5e+302) (/ x (* a (* y b))) (/ (/ x (* a b)) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.4e-40) {
		tmp = ((b / a) / y) * -x;
	} else if (b <= 4.4e+131) {
		tmp = (x / (a + (a * b))) / y;
	} else if (b <= 7.5e+302) {
		tmp = x / (a * (y * b));
	} else {
		tmp = (x / (a * b)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-5.4d-40)) then
        tmp = ((b / a) / y) * -x
    else if (b <= 4.4d+131) then
        tmp = (x / (a + (a * b))) / y
    else if (b <= 7.5d+302) then
        tmp = x / (a * (y * b))
    else
        tmp = (x / (a * b)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.4e-40) {
		tmp = ((b / a) / y) * -x;
	} else if (b <= 4.4e+131) {
		tmp = (x / (a + (a * b))) / y;
	} else if (b <= 7.5e+302) {
		tmp = x / (a * (y * b));
	} else {
		tmp = (x / (a * b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5.4e-40:
		tmp = ((b / a) / y) * -x
	elif b <= 4.4e+131:
		tmp = (x / (a + (a * b))) / y
	elif b <= 7.5e+302:
		tmp = x / (a * (y * b))
	else:
		tmp = (x / (a * b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.4e-40)
		tmp = Float64(Float64(Float64(b / a) / y) * Float64(-x));
	elseif (b <= 4.4e+131)
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	elseif (b <= 7.5e+302)
		tmp = Float64(x / Float64(a * Float64(y * b)));
	else
		tmp = Float64(Float64(x / Float64(a * b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5.4e-40)
		tmp = ((b / a) / y) * -x;
	elseif (b <= 4.4e+131)
		tmp = (x / (a + (a * b))) / y;
	elseif (b <= 7.5e+302)
		tmp = x / (a * (y * b));
	else
		tmp = (x / (a * b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5.4e-40], N[(N[(N[(b / a), $MachinePrecision] / y), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[b, 4.4e+131], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 7.5e+302], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 12: 39.1% accurate, 23.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{-277}:\\ \;\;\;\;\frac{\frac{x}{y} - b \cdot \frac{x}{y}}{a}\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+131}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+302}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2e-277)
   (/ (- (/ x y) (* b (/ x y))) a)
   (if (<= b 4.4e+131)
     (/ (/ x (+ a (* a b))) y)
     (if (<= b 6.8e+302) (/ x (* a (* y b))) (/ (/ x (* a b)) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2e-277) {
		tmp = ((x / y) - (b * (x / y))) / a;
	} else if (b <= 4.4e+131) {
		tmp = (x / (a + (a * b))) / y;
	} else if (b <= 6.8e+302) {
		tmp = x / (a * (y * b));
	} else {
		tmp = (x / (a * b)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2d-277)) then
        tmp = ((x / y) - (b * (x / y))) / a
    else if (b <= 4.4d+131) then
        tmp = (x / (a + (a * b))) / y
    else if (b <= 6.8d+302) then
        tmp = x / (a * (y * b))
    else
        tmp = (x / (a * b)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2e-277) {
		tmp = ((x / y) - (b * (x / y))) / a;
	} else if (b <= 4.4e+131) {
		tmp = (x / (a + (a * b))) / y;
	} else if (b <= 6.8e+302) {
		tmp = x / (a * (y * b));
	} else {
		tmp = (x / (a * b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2e-277:
		tmp = ((x / y) - (b * (x / y))) / a
	elif b <= 4.4e+131:
		tmp = (x / (a + (a * b))) / y
	elif b <= 6.8e+302:
		tmp = x / (a * (y * b))
	else:
		tmp = (x / (a * b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2e-277)
		tmp = Float64(Float64(Float64(x / y) - Float64(b * Float64(x / y))) / a);
	elseif (b <= 4.4e+131)
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	elseif (b <= 6.8e+302)
		tmp = Float64(x / Float64(a * Float64(y * b)));
	else
		tmp = Float64(Float64(x / Float64(a * b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2e-277)
		tmp = ((x / y) - (b * (x / y))) / a;
	elseif (b <= 4.4e+131)
		tmp = (x / (a + (a * b))) / y;
	elseif (b <= 6.8e+302)
		tmp = x / (a * (y * b));
	else
		tmp = (x / (a * b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2e-277], N[(N[(N[(x / y), $MachinePrecision] - N[(b * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, 4.4e+131], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 6.8e+302], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 13: 39.7% accurate, 23.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{-281}:\\ \;\;\;\;\frac{\frac{x}{y} - \frac{x \cdot b}{y}}{a}\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+131}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+302}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.5e-281)
   (/ (- (/ x y) (/ (* x b) y)) a)
   (if (<= b 4.5e+131)
     (/ (/ x (+ a (* a b))) y)
     (if (<= b 7.5e+302) (/ x (* a (* y b))) (/ (/ x (* a b)) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.5e-281) {
		tmp = ((x / y) - ((x * b) / y)) / a;
	} else if (b <= 4.5e+131) {
		tmp = (x / (a + (a * b))) / y;
	} else if (b <= 7.5e+302) {
		tmp = x / (a * (y * b));
	} else {
		tmp = (x / (a * b)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.5d-281)) then
        tmp = ((x / y) - ((x * b) / y)) / a
    else if (b <= 4.5d+131) then
        tmp = (x / (a + (a * b))) / y
    else if (b <= 7.5d+302) then
        tmp = x / (a * (y * b))
    else
        tmp = (x / (a * b)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.5e-281) {
		tmp = ((x / y) - ((x * b) / y)) / a;
	} else if (b <= 4.5e+131) {
		tmp = (x / (a + (a * b))) / y;
	} else if (b <= 7.5e+302) {
		tmp = x / (a * (y * b));
	} else {
		tmp = (x / (a * b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.5e-281:
		tmp = ((x / y) - ((x * b) / y)) / a
	elif b <= 4.5e+131:
		tmp = (x / (a + (a * b))) / y
	elif b <= 7.5e+302:
		tmp = x / (a * (y * b))
	else:
		tmp = (x / (a * b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.5e-281)
		tmp = Float64(Float64(Float64(x / y) - Float64(Float64(x * b) / y)) / a);
	elseif (b <= 4.5e+131)
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	elseif (b <= 7.5e+302)
		tmp = Float64(x / Float64(a * Float64(y * b)));
	else
		tmp = Float64(Float64(x / Float64(a * b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.5e-281)
		tmp = ((x / y) - ((x * b) / y)) / a;
	elseif (b <= 4.5e+131)
		tmp = (x / (a + (a * b))) / y;
	elseif (b <= 7.5e+302)
		tmp = x / (a * (y * b));
	else
		tmp = (x / (a * b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.5e-281], N[(N[(N[(x / y), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, 4.5e+131], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 7.5e+302], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 14: 28.8% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 5.7 \cdot 10^{-236}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 5.7e-236) (/ x (* a (* y b))) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 5.7e-236) {
		tmp = x / (a * (y * b));
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 5.7d-236) then
        tmp = x / (a * (y * b))
    else
        tmp = x / (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 5.7e-236) {
		tmp = x / (a * (y * b));
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 5.7e-236:
		tmp = x / (a * (y * b))
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 5.7e-236)
		tmp = Float64(x / Float64(a * Float64(y * b)));
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 5.7e-236)
		tmp = x / (a * (y * b));
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 5.7e-236], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 15: 30.4% accurate, 44.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{-182}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.22e-182) (/ (/ x y) a) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.22e-182) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.22d-182)) then
        tmp = (x / y) / a
    else
        tmp = x / (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.22e-182) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.22e-182:
		tmp = (x / y) / a
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.22e-182)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.22e-182)
		tmp = (x / y) / a;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.22e-182], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 16: 30.6% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot a} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x (* y a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / (y * a)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Python

def code(x, y, z, t, a, b):
	return x / (y * a)

Julia

function code(x, y, z, t, a, b)
	return Float64(x / Float64(y * a))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / (y * a);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Developer target: 71.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t - 1\right)}\\ t_2 := \frac{x \cdot \frac{t_1}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{if}\;t < -0.8845848504127471:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < 852031.2288374073:\\ \;\;\;\;\frac{\frac{x}{y} \cdot t_1}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (- t 1.0)))
        (t_2 (/ (* x (/ t_1 y)) (- (+ b 1.0) (* y (log z))))))
   (if (< t -0.8845848504127471)
     t_2
     (if (< t 852031.2288374073)
       (/ (* (/ x y) t_1) (exp (- b (* (log z) y))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a ** (t - 1.0d0)
    t_2 = (x * (t_1 / y)) / ((b + 1.0d0) - (y * log(z)))
    if (t < (-0.8845848504127471d0)) then
        tmp = t_2
    else if (t < 852031.2288374073d0) then
        tmp = ((x / y) * t_1) / exp((b - (log(z) * y)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * Math.log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / Math.exp((b - (Math.log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, (t - 1.0))
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * math.log(z)))
	tmp = 0
	if t < -0.8845848504127471:
		tmp = t_2
	elif t < 852031.2288374073:
		tmp = ((x / y) * t_1) / math.exp((b - (math.log(z) * y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = a ^ Float64(t - 1.0)
	t_2 = Float64(Float64(x * Float64(t_1 / y)) / Float64(Float64(b + 1.0) - Float64(y * log(z))))
	tmp = 0.0
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = Float64(Float64(Float64(x / y) * t_1) / exp(Float64(b - Float64(log(z) * y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a ^ (t - 1.0);
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	tmp = 0.0;
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] / N[(N[(b + 1.0), $MachinePrecision] - N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -0.8845848504127471], t$95$2, If[Less[t, 852031.2288374073], N[(N[(N[(x / y), $MachinePrecision] * t$95$1), $MachinePrecision] / N[Exp[N[(b - N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024008 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (if (< t -0.8845848504127471) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z)))) (if (< t 852031.2288374073) (/ (* (/ x y) (pow a (- t 1.0))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))