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

Percentage Accurate: 98.3% → 98.3%

Time: 27.8s

Alternatives: 23

Speedup: 1.0×

• 48.8% 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: 98.3% 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: 98.3% 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: 91.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.007 \lor \neg \left(y \leq 1.15 \cdot 10^{-54}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -0.007) (not (<= y 1.15e-54)))
   (/ (* 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 <= -0.007) || !(y <= 1.15e-54)) {
		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 <= (-0.007d0)) .or. (.not. (y <= 1.15d-54))) 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 <= -0.007) || !(y <= 1.15e-54)) {
		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 <= -0.007) or not (y <= 1.15e-54):
		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 <= -0.007) || !(y <= 1.15e-54))
		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 <= -0.007) || ~((y <= 1.15e-54)))
		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, -0.007], N[Not[LessEqual[y, 1.15e-54]], $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: 73.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot e^{b}\\ t_2 := \frac{\frac{x}{t_1}}{y}\\ t_3 := \frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -3.3 \cdot 10^{+109}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-154}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-108}:\\ \;\;\;\;\frac{{a}^{t}}{t_1} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+23}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (exp b)))
        (t_2 (/ (/ x t_1) y))
        (t_3 (/ (* x (/ (pow z y) a)) y)))
   (if (<= y -3.3e+109)
     t_3
     (if (<= y 7e-154)
       t_2
       (if (<= y 3.6e-108)
         (* (/ (pow a t) t_1) (/ x y))
         (if (<= y 2.9e+23) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * exp(b);
	double t_2 = (x / t_1) / y;
	double t_3 = (x * (pow(z, y) / a)) / y;
	double tmp;
	if (y <= -3.3e+109) {
		tmp = t_3;
	} else if (y <= 7e-154) {
		tmp = t_2;
	} else if (y <= 3.6e-108) {
		tmp = (pow(a, t) / t_1) * (x / y);
	} else if (y <= 2.9e+23) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = a * exp(b)
    t_2 = (x / t_1) / y
    t_3 = (x * ((z ** y) / a)) / y
    if (y <= (-3.3d+109)) then
        tmp = t_3
    else if (y <= 7d-154) then
        tmp = t_2
    else if (y <= 3.6d-108) then
        tmp = ((a ** t) / t_1) * (x / y)
    else if (y <= 2.9d+23) then
        tmp = t_2
    else
        tmp = t_3
    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 = a * Math.exp(b);
	double t_2 = (x / t_1) / y;
	double t_3 = (x * (Math.pow(z, y) / a)) / y;
	double tmp;
	if (y <= -3.3e+109) {
		tmp = t_3;
	} else if (y <= 7e-154) {
		tmp = t_2;
	} else if (y <= 3.6e-108) {
		tmp = (Math.pow(a, t) / t_1) * (x / y);
	} else if (y <= 2.9e+23) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * math.exp(b)
	t_2 = (x / t_1) / y
	t_3 = (x * (math.pow(z, y) / a)) / y
	tmp = 0
	if y <= -3.3e+109:
		tmp = t_3
	elif y <= 7e-154:
		tmp = t_2
	elif y <= 3.6e-108:
		tmp = (math.pow(a, t) / t_1) * (x / y)
	elif y <= 2.9e+23:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * exp(b))
	t_2 = Float64(Float64(x / t_1) / y)
	t_3 = Float64(Float64(x * Float64((z ^ y) / a)) / y)
	tmp = 0.0
	if (y <= -3.3e+109)
		tmp = t_3;
	elseif (y <= 7e-154)
		tmp = t_2;
	elseif (y <= 3.6e-108)
		tmp = Float64(Float64((a ^ t) / t_1) * Float64(x / y));
	elseif (y <= 2.9e+23)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * exp(b);
	t_2 = (x / t_1) / y;
	t_3 = (x * ((z ^ y) / a)) / y;
	tmp = 0.0;
	if (y <= -3.3e+109)
		tmp = t_3;
	elseif (y <= 7e-154)
		tmp = t_2;
	elseif (y <= 3.6e-108)
		tmp = ((a ^ t) / t_1) * (x / y);
	elseif (y <= 2.9e+23)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / t$95$1), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -3.3e+109], t$95$3, If[LessEqual[y, 7e-154], t$95$2, If[LessEqual[y, 3.6e-108], N[(N[(N[Power[a, t], $MachinePrecision] / t$95$1), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e+23], t$95$2, t$95$3]]]]]]]

Derivation

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

Alternative 4: 88.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+138} \lor \neg \left(y \leq 1.05 \cdot 10^{+98}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.45e+138) (not (<= y 1.05e+98)))
   (/ (* x (/ (pow z y) a)) 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 <= -1.45e+138) || !(y <= 1.05e+98)) {
		tmp = (x * (pow(z, y) / a)) / 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 <= (-1.45d+138)) .or. (.not. (y <= 1.05d+98))) then
        tmp = (x * ((z ** y) / a)) / 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 <= -1.45e+138) || !(y <= 1.05e+98)) {
		tmp = (x * (Math.pow(z, y) / a)) / 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 <= -1.45e+138) or not (y <= 1.05e+98):
		tmp = (x * (math.pow(z, y) / a)) / 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 <= -1.45e+138) || !(y <= 1.05e+98))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / 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 <= -1.45e+138) || ~((y <= 1.05e+98)))
		tmp = (x * ((z ^ y) / a)) / 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, -1.45e+138], N[Not[LessEqual[y, 1.05e+98]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $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 5: 81.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+66} \lor \neg \left(y \leq 2.7 \cdot 10^{+23}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.6e+66) (not (<= y 2.7e+23)))
   (/ (* x (/ (pow z y) a)) y)
   (/ (* x (/ (pow a (+ t -1.0)) (exp b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.6e+66) || !(y <= 2.7e+23)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = (x * (pow(a, (t + -1.0)) / 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 <= (-1.6d+66)) .or. (.not. (y <= 2.7d+23))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = (x * ((a ** (t + (-1.0d0))) / 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 <= -1.6e+66) || !(y <= 2.7e+23)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = (x * (Math.pow(a, (t + -1.0)) / Math.exp(b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.6e+66) or not (y <= 2.7e+23):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = (x * (math.pow(a, (t + -1.0)) / math.exp(b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.6e+66) || !(y <= 2.7e+23))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(Float64(x * Float64((a ^ Float64(t + -1.0)) / exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.6e+66) || ~((y <= 2.7e+23)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = (x * ((a ^ (t + -1.0)) / exp(b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.6e+66], N[Not[LessEqual[y, 2.7e+23]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

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

Alternative 6: 73.5% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{a \cdot e^{b}}}{y}\\ t_2 := \frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+108}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-112}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot a}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x (* a (exp b))) y)) (t_2 (/ (* x (/ (pow z y) a)) y)))
   (if (<= y -2.2e+108)
     t_2
     (if (<= y 7.6e-144)
       t_1
       (if (<= y 5.2e-112)
         (/ (* x (pow a t)) (* y a))
         (if (<= y 6.2e+22) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / (a * exp(b))) / y;
	double t_2 = (x * (pow(z, y) / a)) / y;
	double tmp;
	if (y <= -2.2e+108) {
		tmp = t_2;
	} else if (y <= 7.6e-144) {
		tmp = t_1;
	} else if (y <= 5.2e-112) {
		tmp = (x * pow(a, t)) / (y * a);
	} else if (y <= 6.2e+22) {
		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 * exp(b))) / y
    t_2 = (x * ((z ** y) / a)) / y
    if (y <= (-2.2d+108)) then
        tmp = t_2
    else if (y <= 7.6d-144) then
        tmp = t_1
    else if (y <= 5.2d-112) then
        tmp = (x * (a ** t)) / (y * a)
    else if (y <= 6.2d+22) 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 * Math.exp(b))) / y;
	double t_2 = (x * (Math.pow(z, y) / a)) / y;
	double tmp;
	if (y <= -2.2e+108) {
		tmp = t_2;
	} else if (y <= 7.6e-144) {
		tmp = t_1;
	} else if (y <= 5.2e-112) {
		tmp = (x * Math.pow(a, t)) / (y * a);
	} else if (y <= 6.2e+22) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / (a * math.exp(b))) / y
	t_2 = (x * (math.pow(z, y) / a)) / y
	tmp = 0
	if y <= -2.2e+108:
		tmp = t_2
	elif y <= 7.6e-144:
		tmp = t_1
	elif y <= 5.2e-112:
		tmp = (x * math.pow(a, t)) / (y * a)
	elif y <= 6.2e+22:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / Float64(a * exp(b))) / y)
	t_2 = Float64(Float64(x * Float64((z ^ y) / a)) / y)
	tmp = 0.0
	if (y <= -2.2e+108)
		tmp = t_2;
	elseif (y <= 7.6e-144)
		tmp = t_1;
	elseif (y <= 5.2e-112)
		tmp = Float64(Float64(x * (a ^ t)) / Float64(y * a));
	elseif (y <= 6.2e+22)
		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 * exp(b))) / y;
	t_2 = (x * ((z ^ y) / a)) / y;
	tmp = 0.0;
	if (y <= -2.2e+108)
		tmp = t_2;
	elseif (y <= 7.6e-144)
		tmp = t_1;
	elseif (y <= 5.2e-112)
		tmp = (x * (a ^ t)) / (y * a);
	elseif (y <= 6.2e+22)
		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[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -2.2e+108], t$95$2, If[LessEqual[y, 7.6e-144], t$95$1, If[LessEqual[y, 5.2e-112], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e+22], t$95$1, t$95$2]]]]]]

Derivation

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

Alternative 7: 73.7% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{+108} \lor \neg \left(y \leq 1.85 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8.4e+108) (not (<= y 1.85e+22)))
   (/ (* x (/ (pow z y) a)) y)
   (/ (/ x (* a (exp b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.4e+108) || !(y <= 1.85e+22)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = (x / (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 <= (-8.4d+108)) .or. (.not. (y <= 1.85d+22))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = (x / (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 <= -8.4e+108) || !(y <= 1.85e+22)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = (x / (a * Math.exp(b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -8.4e+108) or not (y <= 1.85e+22):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = (x / (a * math.exp(b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -8.4e+108) || !(y <= 1.85e+22))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -8.4e+108) || ~((y <= 1.85e+22)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = (x / (a * exp(b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -8.4e+108], N[Not[LessEqual[y, 1.85e+22]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

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

Alternative 8: 71.8% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+34}:\\ \;\;\;\;\frac{x}{\frac{y}{e^{-b}}}\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{-42}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4e+34)
   (/ x (/ y (exp (- b))))
   (if (<= b 3.3e-42) (* (/ x a) (/ (pow z y) y)) (/ (/ x (* a (exp b))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4e+34) {
		tmp = x / (y / exp(-b));
	} else if (b <= 3.3e-42) {
		tmp = (x / a) * (pow(z, y) / y);
	} else {
		tmp = (x / (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 (b <= (-4d+34)) then
        tmp = x / (y / exp(-b))
    else if (b <= 3.3d-42) then
        tmp = (x / a) * ((z ** y) / y)
    else
        tmp = (x / (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 (b <= -4e+34) {
		tmp = x / (y / Math.exp(-b));
	} else if (b <= 3.3e-42) {
		tmp = (x / a) * (Math.pow(z, y) / y);
	} else {
		tmp = (x / (a * Math.exp(b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4e+34:
		tmp = x / (y / math.exp(-b))
	elif b <= 3.3e-42:
		tmp = (x / a) * (math.pow(z, y) / y)
	else:
		tmp = (x / (a * math.exp(b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4e+34)
		tmp = Float64(x / Float64(y / exp(Float64(-b))));
	elseif (b <= 3.3e-42)
		tmp = Float64(Float64(x / a) * Float64((z ^ y) / y));
	else
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -4e+34)
		tmp = x / (y / exp(-b));
	elseif (b <= 3.3e-42)
		tmp = (x / a) * ((z ^ y) / y);
	else
		tmp = (x / (a * exp(b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4e+34], N[(x / N[(y / N[Exp[(-b)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.3e-42], N[(N[(x / a), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

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

Alternative 9: 58.3% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.1 \cdot 10^{-8} \lor \neg \left(b \leq 9.2 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{x}{\frac{y}{e^{-b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5.1e-8) (not (<= b 9.2e-7)))
   (/ x (/ y (exp (- b))))
   (/ 1.0 (* y (/ a x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.1e-8) || !(b <= 9.2e-7)) {
		tmp = x / (y / exp(-b));
	} else {
		tmp = 1.0 / (y * (a / x));
	}
	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 <= (-5.1d-8)) .or. (.not. (b <= 9.2d-7))) then
        tmp = x / (y / exp(-b))
    else
        tmp = 1.0d0 / (y * (a / x))
    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 <= -5.1e-8) || !(b <= 9.2e-7)) {
		tmp = x / (y / Math.exp(-b));
	} else {
		tmp = 1.0 / (y * (a / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -5.1e-8) or not (b <= 9.2e-7):
		tmp = x / (y / math.exp(-b))
	else:
		tmp = 1.0 / (y * (a / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -5.1e-8) || !(b <= 9.2e-7))
		tmp = Float64(x / Float64(y / exp(Float64(-b))));
	else
		tmp = Float64(1.0 / Float64(y * Float64(a / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -5.1e-8) || ~((b <= 9.2e-7)))
		tmp = x / (y / exp(-b));
	else
		tmp = 1.0 / (y * (a / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -5.1e-8], N[Not[LessEqual[b, 9.2e-7]], $MachinePrecision]], N[(x / N[(y / N[Exp[(-b)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 10: 59.2% 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 11: 58.8% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 12: 40.6% accurate, 14.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.86 \cdot 10^{+133}:\\ \;\;\;\;\frac{\frac{x}{y} - \frac{x}{\frac{y}{b}}}{a}\\ \mathbf{elif}\;b \leq -4.3 \cdot 10^{-159}:\\ \;\;\;\;\frac{a \cdot \left(\frac{x \cdot y}{y} - x \cdot b\right)}{a \cdot \left(y \cdot a\right)}\\ \mathbf{elif}\;b \leq -2.55 \cdot 10^{-294}:\\ \;\;\;\;\frac{\frac{x}{y}}{a} - \frac{b}{\frac{y}{\frac{x}{a}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.86e+133)
   (/ (- (/ x y) (/ x (/ y b))) a)
   (if (<= b -4.3e-159)
     (/ (* a (- (/ (* x y) y) (* x b))) (* a (* y a)))
     (if (<= b -2.55e-294)
       (- (/ (/ x y) a) (/ b (/ y (/ x a))))
       (/ x (* y (+ a (* a b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.86e+133) {
		tmp = ((x / y) - (x / (y / b))) / a;
	} else if (b <= -4.3e-159) {
		tmp = (a * (((x * y) / y) - (x * b))) / (a * (y * a));
	} else if (b <= -2.55e-294) {
		tmp = ((x / y) / a) - (b / (y / (x / a)));
	} else {
		tmp = x / (y * (a + (a * 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 <= (-1.86d+133)) then
        tmp = ((x / y) - (x / (y / b))) / a
    else if (b <= (-4.3d-159)) then
        tmp = (a * (((x * y) / y) - (x * b))) / (a * (y * a))
    else if (b <= (-2.55d-294)) then
        tmp = ((x / y) / a) - (b / (y / (x / a)))
    else
        tmp = x / (y * (a + (a * 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 <= -1.86e+133) {
		tmp = ((x / y) - (x / (y / b))) / a;
	} else if (b <= -4.3e-159) {
		tmp = (a * (((x * y) / y) - (x * b))) / (a * (y * a));
	} else if (b <= -2.55e-294) {
		tmp = ((x / y) / a) - (b / (y / (x / a)));
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.86e+133:
		tmp = ((x / y) - (x / (y / b))) / a
	elif b <= -4.3e-159:
		tmp = (a * (((x * y) / y) - (x * b))) / (a * (y * a))
	elif b <= -2.55e-294:
		tmp = ((x / y) / a) - (b / (y / (x / a)))
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.86e+133)
		tmp = Float64(Float64(Float64(x / y) - Float64(x / Float64(y / b))) / a);
	elseif (b <= -4.3e-159)
		tmp = Float64(Float64(a * Float64(Float64(Float64(x * y) / y) - Float64(x * b))) / Float64(a * Float64(y * a)));
	elseif (b <= -2.55e-294)
		tmp = Float64(Float64(Float64(x / y) / a) - Float64(b / Float64(y / Float64(x / a))));
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.86e+133)
		tmp = ((x / y) - (x / (y / b))) / a;
	elseif (b <= -4.3e-159)
		tmp = (a * (((x * y) / y) - (x * b))) / (a * (y * a));
	elseif (b <= -2.55e-294)
		tmp = ((x / y) / a) - (b / (y / (x / a)));
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.86e+133], N[(N[(N[(x / y), $MachinePrecision] - N[(x / N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, -4.3e-159], N[(N[(a * N[(N[(N[(x * y), $MachinePrecision] / y), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.55e-294], N[(N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision] - N[(b / N[(y / N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 13: 39.5% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{+59}:\\ \;\;\;\;\frac{x \cdot \left(-\frac{b}{a}\right)}{y}\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+16}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+86}:\\ \;\;\;\;\frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -9.2e+59)
   (/ (* x (- (/ b a))) y)
   (if (<= b 1.45e+16)
     (/ 1.0 (* y (/ a x)))
     (if (<= b 2.15e+86) (/ (* x a) y) (/ x (* y (+ a (* a b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.2e+59) {
		tmp = (x * -(b / a)) / y;
	} else if (b <= 1.45e+16) {
		tmp = 1.0 / (y * (a / x));
	} else if (b <= 2.15e+86) {
		tmp = (x * a) / y;
	} else {
		tmp = x / (y * (a + (a * 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 <= (-9.2d+59)) then
        tmp = (x * -(b / a)) / y
    else if (b <= 1.45d+16) then
        tmp = 1.0d0 / (y * (a / x))
    else if (b <= 2.15d+86) then
        tmp = (x * a) / y
    else
        tmp = x / (y * (a + (a * 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 <= -9.2e+59) {
		tmp = (x * -(b / a)) / y;
	} else if (b <= 1.45e+16) {
		tmp = 1.0 / (y * (a / x));
	} else if (b <= 2.15e+86) {
		tmp = (x * a) / y;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -9.2e+59:
		tmp = (x * -(b / a)) / y
	elif b <= 1.45e+16:
		tmp = 1.0 / (y * (a / x))
	elif b <= 2.15e+86:
		tmp = (x * a) / y
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -9.2e+59)
		tmp = Float64(Float64(x * Float64(-Float64(b / a))) / y);
	elseif (b <= 1.45e+16)
		tmp = Float64(1.0 / Float64(y * Float64(a / x)));
	elseif (b <= 2.15e+86)
		tmp = Float64(Float64(x * a) / y);
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -9.2e+59)
		tmp = (x * -(b / a)) / y;
	elseif (b <= 1.45e+16)
		tmp = 1.0 / (y * (a / x));
	elseif (b <= 2.15e+86)
		tmp = (x * a) / y;
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -9.2e+59], N[(N[(x * (-N[(b / a), $MachinePrecision])), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 1.45e+16], N[(1.0 / N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.15e+86], N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 14: 40.0% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{\frac{x}{y} - \frac{x}{\frac{y}{b}}}{a}\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+16}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+85}:\\ \;\;\;\;\frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.5e+58)
   (/ (- (/ x y) (/ x (/ y b))) a)
   (if (<= b 1.55e+16)
     (/ 1.0 (* y (/ a x)))
     (if (<= b 4.5e+85) (/ (* x a) y) (/ x (* y (+ a (* a b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.5e+58) {
		tmp = ((x / y) - (x / (y / b))) / a;
	} else if (b <= 1.55e+16) {
		tmp = 1.0 / (y * (a / x));
	} else if (b <= 4.5e+85) {
		tmp = (x * a) / y;
	} else {
		tmp = x / (y * (a + (a * 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 <= (-2.5d+58)) then
        tmp = ((x / y) - (x / (y / b))) / a
    else if (b <= 1.55d+16) then
        tmp = 1.0d0 / (y * (a / x))
    else if (b <= 4.5d+85) then
        tmp = (x * a) / y
    else
        tmp = x / (y * (a + (a * 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 <= -2.5e+58) {
		tmp = ((x / y) - (x / (y / b))) / a;
	} else if (b <= 1.55e+16) {
		tmp = 1.0 / (y * (a / x));
	} else if (b <= 4.5e+85) {
		tmp = (x * a) / y;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.5e+58:
		tmp = ((x / y) - (x / (y / b))) / a
	elif b <= 1.55e+16:
		tmp = 1.0 / (y * (a / x))
	elif b <= 4.5e+85:
		tmp = (x * a) / y
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.5e+58)
		tmp = Float64(Float64(Float64(x / y) - Float64(x / Float64(y / b))) / a);
	elseif (b <= 1.55e+16)
		tmp = Float64(1.0 / Float64(y * Float64(a / x)));
	elseif (b <= 4.5e+85)
		tmp = Float64(Float64(x * a) / y);
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.5e+58)
		tmp = ((x / y) - (x / (y / b))) / a;
	elseif (b <= 1.55e+16)
		tmp = 1.0 / (y * (a / x));
	elseif (b <= 4.5e+85)
		tmp = (x * a) / y;
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.5e+58], N[(N[(N[(x / y), $MachinePrecision] - N[(x / N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, 1.55e+16], N[(1.0 / N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.5e+85], N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 15: 39.3% accurate, 23.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+61}:\\ \;\;\;\;\frac{x \cdot \left(-\frac{b}{a}\right)}{y}\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+15}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \mathbf{elif}\;b \leq 6.3 \cdot 10^{+85}:\\ \;\;\;\;\frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.5e+61)
   (/ (* x (- (/ b a))) y)
   (if (<= b 4.6e+15)
     (/ 1.0 (* y (/ a x)))
     (if (<= b 6.3e+85) (/ (* x a) y) (/ x (* a (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.5e+61) {
		tmp = (x * -(b / a)) / y;
	} else if (b <= 4.6e+15) {
		tmp = 1.0 / (y * (a / x));
	} else if (b <= 6.3e+85) {
		tmp = (x * a) / 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 <= (-3.5d+61)) then
        tmp = (x * -(b / a)) / y
    else if (b <= 4.6d+15) then
        tmp = 1.0d0 / (y * (a / x))
    else if (b <= 6.3d+85) then
        tmp = (x * a) / 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 <= -3.5e+61) {
		tmp = (x * -(b / a)) / y;
	} else if (b <= 4.6e+15) {
		tmp = 1.0 / (y * (a / x));
	} else if (b <= 6.3e+85) {
		tmp = (x * a) / y;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.5e+61:
		tmp = (x * -(b / a)) / y
	elif b <= 4.6e+15:
		tmp = 1.0 / (y * (a / x))
	elif b <= 6.3e+85:
		tmp = (x * a) / y
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.5e+61)
		tmp = Float64(Float64(x * Float64(-Float64(b / a))) / y);
	elseif (b <= 4.6e+15)
		tmp = Float64(1.0 / Float64(y * Float64(a / x)));
	elseif (b <= 6.3e+85)
		tmp = Float64(Float64(x * a) / 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 <= -3.5e+61)
		tmp = (x * -(b / a)) / y;
	elseif (b <= 4.6e+15)
		tmp = 1.0 / (y * (a / x));
	elseif (b <= 6.3e+85)
		tmp = (x * a) / y;
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.5e+61], N[(N[(x * (-N[(b / a), $MachinePrecision])), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 4.6e+15], N[(1.0 / N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.3e+85], N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 16: 40.3% accurate, 24.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.0021:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{1}{a} - \frac{b}{a}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.0021)
   (/ x (/ y (- (/ 1.0 a) (/ b a))))
   (/ x (* y (+ a (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.0021) {
		tmp = x / (y / ((1.0 / a) - (b / a)));
	} else {
		tmp = x / (y * (a + (a * 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 <= (-0.0021d0)) then
        tmp = x / (y / ((1.0d0 / a) - (b / a)))
    else
        tmp = x / (y * (a + (a * 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 <= -0.0021) {
		tmp = x / (y / ((1.0 / a) - (b / a)));
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -0.0021:
		tmp = x / (y / ((1.0 / a) - (b / a)))
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.0021)
		tmp = Float64(x / Float64(y / Float64(Float64(1.0 / a) - Float64(b / a))));
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -0.0021)
		tmp = x / (y / ((1.0 / a) - (b / a)));
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.0021], N[(x / N[(y / N[(N[(1.0 / a), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 17: 37.8% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.35 \cdot 10^{+58}:\\ \;\;\;\;b \cdot \frac{-x}{y \cdot a}\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+61}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.35e+58)
   (* b (/ (- x) (* y a)))
   (if (<= b 5.8e+61) (/ 1.0 (* y (/ a x))) (/ x (* a (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.35e+58) {
		tmp = b * (-x / (y * a));
	} else if (b <= 5.8e+61) {
		tmp = 1.0 / (y * (a / x));
	} 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 <= (-2.35d+58)) then
        tmp = b * (-x / (y * a))
    else if (b <= 5.8d+61) then
        tmp = 1.0d0 / (y * (a / x))
    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 <= -2.35e+58) {
		tmp = b * (-x / (y * a));
	} else if (b <= 5.8e+61) {
		tmp = 1.0 / (y * (a / x));
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.35e+58:
		tmp = b * (-x / (y * a))
	elif b <= 5.8e+61:
		tmp = 1.0 / (y * (a / x))
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.35e+58)
		tmp = Float64(b * Float64(Float64(-x) / Float64(y * a)));
	elseif (b <= 5.8e+61)
		tmp = Float64(1.0 / Float64(y * Float64(a / x)));
	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 <= -2.35e+58)
		tmp = b * (-x / (y * a));
	elseif (b <= 5.8e+61)
		tmp = 1.0 / (y * (a / x));
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.35e+58], N[(b * N[((-x) / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.8e+61], N[(1.0 / N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 18: 35.6% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 3.3:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 3.3) (* (/ x a) (/ 1.0 y)) (/ (* x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 3.3) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = (x * a) / 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 (t <= 3.3d0) then
        tmp = (x / a) * (1.0d0 / y)
    else
        tmp = (x * a) / 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 (t <= 3.3) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = (x * a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 3.3:
		tmp = (x / a) * (1.0 / y)
	else:
		tmp = (x * a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 3.3)
		tmp = Float64(Float64(x / a) * Float64(1.0 / y));
	else
		tmp = Float64(Float64(x * a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 3.3)
		tmp = (x / a) * (1.0 / y);
	else
		tmp = (x * a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 3.3], N[(N[(x / a), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

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

Alternative 19: 35.5% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.8:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 1.8) (/ 1.0 (* y (/ a x))) (/ (* x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1.8) {
		tmp = 1.0 / (y * (a / x));
	} else {
		tmp = (x * a) / 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 (t <= 1.8d0) then
        tmp = 1.0d0 / (y * (a / x))
    else
        tmp = (x * a) / 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 (t <= 1.8) {
		tmp = 1.0 / (y * (a / x));
	} else {
		tmp = (x * a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 1.8:
		tmp = 1.0 / (y * (a / x))
	else:
		tmp = (x * a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 1.8)
		tmp = Float64(1.0 / Float64(y * Float64(a / x)));
	else
		tmp = Float64(Float64(x * a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 1.8)
		tmp = 1.0 / (y * (a / x));
	else
		tmp = (x * a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 1.8], N[(1.0 / N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

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

Alternative 20: 35.0% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 5.8 \cdot 10^{+61}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 5.8e+61) (* (/ x a) (/ 1.0 y)) (/ x (* a (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 5.8e+61) {
		tmp = (x / a) * (1.0 / 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 <= 5.8d+61) then
        tmp = (x / a) * (1.0d0 / 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 <= 5.8e+61) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 5.8e+61:
		tmp = (x / a) * (1.0 / y)
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 5.8e+61)
		tmp = Float64(Float64(x / a) * Float64(1.0 / 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 <= 5.8e+61)
		tmp = (x / a) * (1.0 / y);
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 5.8e+61], N[(N[(x / a), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 21: 34.5% accurate, 44.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.95:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 1.95) (/ x (* y a)) (* a (/ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1.95) {
		tmp = x / (y * a);
	} else {
		tmp = a * (x / 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 (t <= 1.95d0) then
        tmp = x / (y * a)
    else
        tmp = a * (x / 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 (t <= 1.95) {
		tmp = x / (y * a);
	} else {
		tmp = a * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 1.95:
		tmp = x / (y * a)
	else:
		tmp = a * (x / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 1.95)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(a * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 1.95)
		tmp = x / (y * a);
	else
		tmp = a * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 1.95], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 22: 35.7% accurate, 44.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.7:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 1.7) (/ x (* y a)) (/ (* x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1.7) {
		tmp = x / (y * a);
	} else {
		tmp = (x * a) / 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 (t <= 1.7d0) then
        tmp = x / (y * a)
    else
        tmp = (x * a) / 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 (t <= 1.7) {
		tmp = x / (y * a);
	} else {
		tmp = (x * a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 1.7:
		tmp = x / (y * a)
	else:
		tmp = (x * a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 1.7)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(Float64(x * a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 1.7)
		tmp = x / (y * a);
	else
		tmp = (x * a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 1.7], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

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

Alternative 23: 21.8% accurate, 63.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return a * (x / 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 = a * (x / y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Developer target: 72.6% 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 2023350 
(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))