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

Percentage Accurate: 98.5% → 98.5%

Time: 29.0s

Alternatives: 20

Speedup: 1.0×

• 20.9% 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

1. Initial program 98.9%

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

2. Final simplification 98.9%

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

Alternative 2: 88.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+49} \lor \neg \left(y \leq 3.05 \cdot 10^{-12}\right):\\ \;\;\;\;\frac{x}{\frac{y}{e^{\left(y \cdot \log z - \log a\right) - b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot e^{\left(t + -1\right) \cdot \log a - b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -7.5e+49) (not (<= y 3.05e-12)))
   (/ x (/ y (exp (- (- (* y (log z)) (log a)) b))))
   (* (/ x y) (exp (- (* (+ t -1.0) (log a)) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -7.5e+49) || !(y <= 3.05e-12)) {
		tmp = x / (y / exp((((y * log(z)) - log(a)) - b)));
	} else {
		tmp = (x / y) * exp((((t + -1.0) * log(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 ((y <= (-7.5d+49)) .or. (.not. (y <= 3.05d-12))) then
        tmp = x / (y / exp((((y * log(z)) - log(a)) - b)))
    else
        tmp = (x / y) * exp((((t + (-1.0d0)) * log(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 ((y <= -7.5e+49) || !(y <= 3.05e-12)) {
		tmp = x / (y / Math.exp((((y * Math.log(z)) - Math.log(a)) - b)));
	} else {
		tmp = (x / y) * Math.exp((((t + -1.0) * Math.log(a)) - b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -7.5e+49) or not (y <= 3.05e-12):
		tmp = x / (y / math.exp((((y * math.log(z)) - math.log(a)) - b)))
	else:
		tmp = (x / y) * math.exp((((t + -1.0) * math.log(a)) - b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -7.5e+49) || !(y <= 3.05e-12))
		tmp = Float64(x / Float64(y / exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))));
	else
		tmp = Float64(Float64(x / y) * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -7.5e+49) || ~((y <= 3.05e-12)))
		tmp = x / (y / exp((((y * log(z)) - log(a)) - b)));
	else
		tmp = (x / y) * exp((((t + -1.0) * log(a)) - b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -7.5e+49], N[Not[LessEqual[y, 3.05e-12]], $MachinePrecision]], N[(x / N[(y / N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.4999999999999995e49 or 3.0500000000000001e-12 < y

   1. Initial program 99.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.3%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 89.3%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 89.3%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 89.3%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 89.3%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in t around 0 94.3%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}{y}} \]
   5. Step-by-step derivation

      1. associate-/l* 94.3%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}} \]

      2. +-commutative 94.3%

         \[\leadsto \frac{x}{\frac{y}{e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}} \]

      3. mul-1-neg 94.3%

         \[\leadsto \frac{x}{\frac{y}{e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}} \]

      4. unsub-neg 94.3%

         \[\leadsto \frac{x}{\frac{y}{e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}} \]

   6. Simplified 94.3%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\left(y \cdot \log z - \log a\right) - b}}}} \]

   if -7.4999999999999995e49 < y < 3.0500000000000001e-12

   1. Initial program 98.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.4%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 94.4%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 94.4%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 94.4%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 94.4%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around 0 94.4%

      \[\leadsto \frac{x}{y} \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+49} \lor \neg \left(y \leq 3.05 \cdot 10^{-12}\right):\\ \;\;\;\;\frac{x}{\frac{y}{e^{\left(y \cdot \log z - \log a\right) - b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot e^{\left(t + -1\right) \cdot \log a - b}\\ \end{array} \]

Alternative 3: 78.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}\\ \mathbf{if}\;y \leq -2700000000000:\\ \;\;\;\;\frac{x}{y} \cdot e^{y \cdot \log z - b}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-194}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-100}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ x y) (/ (pow a (+ t -1.0)) (exp b)))))
   (if (<= y -2700000000000.0)
     (* (/ x y) (exp (- (* y (log z)) b)))
     (if (<= y 5.4e-194)
       t_1
       (if (<= y 2.8e-100)
         (/ x (* a (* y (exp b))))
         (if (<= y 1.05e+38) t_1 (/ (* x (pow z y)) y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / y) * (pow(a, (t + -1.0)) / exp(b));
	double tmp;
	if (y <= -2700000000000.0) {
		tmp = (x / y) * exp(((y * log(z)) - b));
	} else if (y <= 5.4e-194) {
		tmp = t_1;
	} else if (y <= 2.8e-100) {
		tmp = x / (a * (y * exp(b)));
	} else if (y <= 1.05e+38) {
		tmp = t_1;
	} else {
		tmp = (x * pow(z, y)) / 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) :: t_1
    real(8) :: tmp
    t_1 = (x / y) * ((a ** (t + (-1.0d0))) / exp(b))
    if (y <= (-2700000000000.0d0)) then
        tmp = (x / y) * exp(((y * log(z)) - b))
    else if (y <= 5.4d-194) then
        tmp = t_1
    else if (y <= 2.8d-100) then
        tmp = x / (a * (y * exp(b)))
    else if (y <= 1.05d+38) then
        tmp = t_1
    else
        tmp = (x * (z ** y)) / 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 t_1 = (x / y) * (Math.pow(a, (t + -1.0)) / Math.exp(b));
	double tmp;
	if (y <= -2700000000000.0) {
		tmp = (x / y) * Math.exp(((y * Math.log(z)) - b));
	} else if (y <= 5.4e-194) {
		tmp = t_1;
	} else if (y <= 2.8e-100) {
		tmp = x / (a * (y * Math.exp(b)));
	} else if (y <= 1.05e+38) {
		tmp = t_1;
	} else {
		tmp = (x * Math.pow(z, y)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / y) * (math.pow(a, (t + -1.0)) / math.exp(b))
	tmp = 0
	if y <= -2700000000000.0:
		tmp = (x / y) * math.exp(((y * math.log(z)) - b))
	elif y <= 5.4e-194:
		tmp = t_1
	elif y <= 2.8e-100:
		tmp = x / (a * (y * math.exp(b)))
	elif y <= 1.05e+38:
		tmp = t_1
	else:
		tmp = (x * math.pow(z, y)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / y) * Float64((a ^ Float64(t + -1.0)) / exp(b)))
	tmp = 0.0
	if (y <= -2700000000000.0)
		tmp = Float64(Float64(x / y) * exp(Float64(Float64(y * log(z)) - b)));
	elseif (y <= 5.4e-194)
		tmp = t_1;
	elseif (y <= 2.8e-100)
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	elseif (y <= 1.05e+38)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * (z ^ y)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / y) * ((a ^ (t + -1.0)) / exp(b));
	tmp = 0.0;
	if (y <= -2700000000000.0)
		tmp = (x / y) * exp(((y * log(z)) - b));
	elseif (y <= 5.4e-194)
		tmp = t_1;
	elseif (y <= 2.8e-100)
		tmp = x / (a * (y * exp(b)));
	elseif (y <= 1.05e+38)
		tmp = t_1;
	else
		tmp = (x * (z ^ y)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2700000000000.0], N[(N[(x / y), $MachinePrecision] * N[Exp[N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e-194], t$95$1, If[LessEqual[y, 2.8e-100], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e+38], t$95$1, N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.7e12

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.5%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 94.5%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 94.5%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 94.5%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 94.5%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around inf 86.4%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z} - b} \]

   if -2.7e12 < y < 5.4e-194 or 2.79999999999999995e-100 < y < 1.05e38

   1. Initial program 97.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 95.3%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 95.3%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 95.3%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. exp-sum 93.6%

         \[\leadsto \color{blue}{\left(e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}\right)} \cdot \frac{x}{y} \]

      5. *-commutative 93.6%

         \[\leadsto \left(e^{\color{blue}{\log z \cdot y}} \cdot e^{\left(t - 1\right) \cdot \log a - b}\right) \cdot \frac{x}{y} \]

      6. exp-to-pow 93.6%

         \[\leadsto \left(\color{blue}{{z}^{y}} \cdot e^{\left(t - 1\right) \cdot \log a - b}\right) \cdot \frac{x}{y} \]

      7. exp-diff 87.6%

         \[\leadsto \left({z}^{y} \cdot \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      8. *-commutative 87.6%

         \[\leadsto \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      9. exp-to-pow 88.6%

         \[\leadsto \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      10. sub-neg 88.6%

          \[\leadsto \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      11. metadata-eval 88.6%

          \[\leadsto \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 88.6%

      \[\leadsto \color{blue}{\left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}\right) \cdot \frac{x}{y}} \]

   4. Taylor expanded in y around 0 84.9%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   5. Step-by-step derivation

      1. times-frac 88.6%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}} \]

      2. exp-prod 88.6%

         \[\leadsto \frac{x}{y} \cdot \frac{\color{blue}{{\left(e^{\log a}\right)}^{\left(t - 1\right)}}}{e^{b}} \]

      3. rem-exp-log 89.4%

         \[\leadsto \frac{x}{y} \cdot \frac{{\color{blue}{a}}^{\left(t - 1\right)}}{e^{b}} \]

      4. sub-neg 89.4%

         \[\leadsto \frac{x}{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}} \]

      5. metadata-eval 89.4%

         \[\leadsto \frac{x}{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}} \]

   6. Simplified 89.4%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}} \]

   if 5.4e-194 < y < 2.79999999999999995e-100

   1. Initial program 99.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 83.8%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 83.8%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 83.8%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 83.8%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 83.8%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around 0 99.2%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   5. Step-by-step derivation

      1. associate-/l* 99.2%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\log a \cdot \left(t - 1\right) - b}}}} \]

      2. exp-diff 68.4%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}} \]

      3. exp-prod 68.4%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{\left(e^{\log a}\right)}^{\left(t - 1\right)}}}{e^{b}}}} \]

      4. rem-exp-log 69.1%

         \[\leadsto \frac{x}{\frac{y}{\frac{{\color{blue}{a}}^{\left(t - 1\right)}}{e^{b}}}} \]

      5. sub-neg 69.1%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

      6. metadata-eval 69.1%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

   6. Simplified 69.1%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

   7. Taylor expanded in t around 0 92.3%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   if 1.05e38 < y

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 83.0%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 83.0%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 83.0%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 83.0%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 83.0%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around inf 79.3%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z} - b} \]

   5. Taylor expanded in b around 0 90.7%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2700000000000:\\ \;\;\;\;\frac{x}{y} \cdot e^{y \cdot \log z - b}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-194}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-100}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+38}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y}\\ \end{array} \]

Alternative 4: 84.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.15 \cdot 10^{+152} \lor \neg \left(y \leq 6 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot e^{\left(t + -1\right) \cdot \log a - b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.15e+152) (not (<= y 6e+38)))
   (/ (* x (pow z y)) y)
   (* (/ x y) (exp (- (* (+ t -1.0) (log a)) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.15e+152) || !(y <= 6e+38)) {
		tmp = (x * pow(z, y)) / y;
	} else {
		tmp = (x / y) * exp((((t + -1.0) * log(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 ((y <= (-4.15d+152)) .or. (.not. (y <= 6d+38))) then
        tmp = (x * (z ** y)) / y
    else
        tmp = (x / y) * exp((((t + (-1.0d0)) * log(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 ((y <= -4.15e+152) || !(y <= 6e+38)) {
		tmp = (x * Math.pow(z, y)) / y;
	} else {
		tmp = (x / y) * Math.exp((((t + -1.0) * Math.log(a)) - b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.15e+152) or not (y <= 6e+38):
		tmp = (x * math.pow(z, y)) / y
	else:
		tmp = (x / y) * math.exp((((t + -1.0) * math.log(a)) - b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.15e+152) || !(y <= 6e+38))
		tmp = Float64(Float64(x * (z ^ y)) / y);
	else
		tmp = Float64(Float64(x / y) * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4.15e+152) || ~((y <= 6e+38)))
		tmp = (x * (z ^ y)) / y;
	else
		tmp = (x / y) * exp((((t + -1.0) * log(a)) - b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.15e+152], N[Not[LessEqual[y, 6e+38]], $MachinePrecision]], N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.1500000000000001e152 or 6.0000000000000002e38 < y

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 87.1%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 87.1%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 87.1%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 87.1%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 87.1%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around inf 82.9%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z} - b} \]

   5. Taylor expanded in b around 0 92.6%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{y}} \]

   if -4.1500000000000001e152 < y < 6.0000000000000002e38

   1. Initial program 98.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.7%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 94.7%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 94.7%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 94.7%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 94.7%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around 0 91.2%

      \[\leadsto \frac{x}{y} \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.15 \cdot 10^{+152} \lor \neg \left(y \leq 6 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot e^{\left(t + -1\right) \cdot \log a - b}\\ \end{array} \]

Alternative 5: 82.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{y} \cdot e^{y \cdot \log z - b}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+34}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3e+18)
   (* (/ x y) (exp (- (* y (log z)) b)))
   (if (<= y 1.35e+34)
     (/ x (/ y (/ (pow a (+ t -1.0)) (exp b))))
     (/ (* x (pow z y)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3e+18) {
		tmp = (x / y) * exp(((y * log(z)) - b));
	} else if (y <= 1.35e+34) {
		tmp = x / (y / (pow(a, (t + -1.0)) / exp(b)));
	} else {
		tmp = (x * pow(z, y)) / 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 <= (-3d+18)) then
        tmp = (x / y) * exp(((y * log(z)) - b))
    else if (y <= 1.35d+34) then
        tmp = x / (y / ((a ** (t + (-1.0d0))) / exp(b)))
    else
        tmp = (x * (z ** y)) / 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 <= -3e+18) {
		tmp = (x / y) * Math.exp(((y * Math.log(z)) - b));
	} else if (y <= 1.35e+34) {
		tmp = x / (y / (Math.pow(a, (t + -1.0)) / Math.exp(b)));
	} else {
		tmp = (x * Math.pow(z, y)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3e+18:
		tmp = (x / y) * math.exp(((y * math.log(z)) - b))
	elif y <= 1.35e+34:
		tmp = x / (y / (math.pow(a, (t + -1.0)) / math.exp(b)))
	else:
		tmp = (x * math.pow(z, y)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3e+18)
		tmp = Float64(Float64(x / y) * exp(Float64(Float64(y * log(z)) - b)));
	elseif (y <= 1.35e+34)
		tmp = Float64(x / Float64(y / Float64((a ^ Float64(t + -1.0)) / exp(b))));
	else
		tmp = Float64(Float64(x * (z ^ y)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3e+18)
		tmp = (x / y) * exp(((y * log(z)) - b));
	elseif (y <= 1.35e+34)
		tmp = x / (y / ((a ^ (t + -1.0)) / exp(b)));
	else
		tmp = (x * (z ^ y)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3e+18], N[(N[(x / y), $MachinePrecision] * N[Exp[N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e+34], N[(x / N[(y / N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3e18

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.5%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 94.5%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 94.5%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 94.5%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 94.5%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around inf 86.4%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z} - b} \]

   if -3e18 < y < 1.35e34

   1. Initial program 97.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.2%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 94.2%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 94.2%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 94.2%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 94.2%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around 0 97.1%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   5. Step-by-step derivation

      1. associate-/l* 96.3%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\log a \cdot \left(t - 1\right) - b}}}} \]

      2. exp-diff 87.9%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}} \]

      3. exp-prod 87.9%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{\left(e^{\log a}\right)}^{\left(t - 1\right)}}}{e^{b}}}} \]

      4. rem-exp-log 88.5%

         \[\leadsto \frac{x}{\frac{y}{\frac{{\color{blue}{a}}^{\left(t - 1\right)}}{e^{b}}}} \]

      5. sub-neg 88.5%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

      6. metadata-eval 88.5%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

   6. Simplified 88.5%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

   if 1.35e34 < y

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 83.0%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 83.0%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 83.0%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 83.0%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 83.0%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around inf 79.3%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z} - b} \]

   5. Taylor expanded in b around 0 90.7%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{y} \cdot e^{y \cdot \log z - b}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+34}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y}\\ \end{array} \]

Alternative 6: 71.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{y}{\frac{{a}^{t}}{a}}}\\ \mathbf{if}\;b \leq -5.7 \cdot 10^{-161}:\\ \;\;\;\;\frac{x}{y} \cdot e^{y \cdot \log z - b}\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-136}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y}\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (/ y (/ (pow a t) a)))))
   (if (<= b -5.7e-161)
     (* (/ x y) (exp (- (* y (log z)) b)))
     (if (<= b 1.5e-179)
       t_1
       (if (<= b 1.45e-136)
         (/ (* x (pow z y)) y)
         (if (<= b 1.5e+29) t_1 (/ (/ x (exp b)) y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y / (pow(a, t) / a));
	double tmp;
	if (b <= -5.7e-161) {
		tmp = (x / y) * exp(((y * log(z)) - b));
	} else if (b <= 1.5e-179) {
		tmp = t_1;
	} else if (b <= 1.45e-136) {
		tmp = (x * pow(z, y)) / y;
	} else if (b <= 1.5e+29) {
		tmp = t_1;
	} else {
		tmp = (x / 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) :: t_1
    real(8) :: tmp
    t_1 = x / (y / ((a ** t) / a))
    if (b <= (-5.7d-161)) then
        tmp = (x / y) * exp(((y * log(z)) - b))
    else if (b <= 1.5d-179) then
        tmp = t_1
    else if (b <= 1.45d-136) then
        tmp = (x * (z ** y)) / y
    else if (b <= 1.5d+29) then
        tmp = t_1
    else
        tmp = (x / 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 t_1 = x / (y / (Math.pow(a, t) / a));
	double tmp;
	if (b <= -5.7e-161) {
		tmp = (x / y) * Math.exp(((y * Math.log(z)) - b));
	} else if (b <= 1.5e-179) {
		tmp = t_1;
	} else if (b <= 1.45e-136) {
		tmp = (x * Math.pow(z, y)) / y;
	} else if (b <= 1.5e+29) {
		tmp = t_1;
	} else {
		tmp = (x / Math.exp(b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y / (math.pow(a, t) / a))
	tmp = 0
	if b <= -5.7e-161:
		tmp = (x / y) * math.exp(((y * math.log(z)) - b))
	elif b <= 1.5e-179:
		tmp = t_1
	elif b <= 1.45e-136:
		tmp = (x * math.pow(z, y)) / y
	elif b <= 1.5e+29:
		tmp = t_1
	else:
		tmp = (x / math.exp(b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y / Float64((a ^ t) / a)))
	tmp = 0.0
	if (b <= -5.7e-161)
		tmp = Float64(Float64(x / y) * exp(Float64(Float64(y * log(z)) - b)));
	elseif (b <= 1.5e-179)
		tmp = t_1;
	elseif (b <= 1.45e-136)
		tmp = Float64(Float64(x * (z ^ y)) / y);
	elseif (b <= 1.5e+29)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / exp(b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y / ((a ^ t) / a));
	tmp = 0.0;
	if (b <= -5.7e-161)
		tmp = (x / y) * exp(((y * log(z)) - b));
	elseif (b <= 1.5e-179)
		tmp = t_1;
	elseif (b <= 1.45e-136)
		tmp = (x * (z ^ y)) / y;
	elseif (b <= 1.5e+29)
		tmp = t_1;
	else
		tmp = (x / exp(b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y / N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.7e-161], N[(N[(x / y), $MachinePrecision] * N[Exp[N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.5e-179], t$95$1, If[LessEqual[b, 1.45e-136], N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 1.5e+29], t$95$1, N[(N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.70000000000000022e-161

   1. Initial program 99.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 93.9%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 93.9%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 93.9%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 93.9%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 93.9%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around inf 81.3%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z} - b} \]

   if -5.70000000000000022e-161 < b < 1.50000000000000003e-179 or 1.44999999999999997e-136 < b < 1.5e29

   1. Initial program 97.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.6%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 94.6%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 94.6%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 94.6%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 94.6%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around 0 75.1%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   5. Step-by-step derivation

      1. associate-/l* 76.5%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\log a \cdot \left(t - 1\right) - b}}}} \]

      2. exp-diff 74.4%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}} \]

      3. exp-prod 74.4%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{\left(e^{\log a}\right)}^{\left(t - 1\right)}}}{e^{b}}}} \]

      4. rem-exp-log 75.0%

         \[\leadsto \frac{x}{\frac{y}{\frac{{\color{blue}{a}}^{\left(t - 1\right)}}{e^{b}}}} \]

      5. sub-neg 75.0%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

      6. metadata-eval 75.0%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

   6. Simplified 75.0%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

   7. Taylor expanded in b around 0 76.5%

      \[\leadsto \frac{x}{\color{blue}{\frac{y}{e^{\log a \cdot \left(t - 1\right)}}}} \]
   8. Step-by-step derivation

      1. exp-prod 76.6%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{{\left(e^{\log a}\right)}^{\left(t - 1\right)}}}} \]

      2. sub-neg 76.6%

         \[\leadsto \frac{x}{\frac{y}{{\left(e^{\log a}\right)}^{\color{blue}{\left(t + \left(-1\right)\right)}}}} \]

      3. metadata-eval 76.6%

         \[\leadsto \frac{x}{\frac{y}{{\left(e^{\log a}\right)}^{\left(t + \color{blue}{-1}\right)}}} \]

      4. exp-prod 76.5%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{e^{\log a \cdot \left(t + -1\right)}}}} \]

      5. distribute-lft-in 76.5%

         \[\leadsto \frac{x}{\frac{y}{e^{\color{blue}{\log a \cdot t + \log a \cdot -1}}}} \]

      6. *-commutative 76.5%

         \[\leadsto \frac{x}{\frac{y}{e^{\log a \cdot t + \color{blue}{-1 \cdot \log a}}}} \]

      7. mul-1-neg 76.5%

         \[\leadsto \frac{x}{\frac{y}{e^{\log a \cdot t + \color{blue}{\left(-\log a\right)}}}} \]

      8. sub-neg 76.5%

         \[\leadsto \frac{x}{\frac{y}{e^{\color{blue}{\log a \cdot t - \log a}}}} \]

      9. exp-diff 76.5%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot t}}{e^{\log a}}}}} \]

      10. *-commutative 76.5%

          \[\leadsto \frac{x}{\frac{y}{\frac{e^{\color{blue}{t \cdot \log a}}}{e^{\log a}}}} \]

      11. log-pow 76.6%

          \[\leadsto \frac{x}{\frac{y}{\frac{e^{\color{blue}{\log \left({a}^{t}\right)}}}{e^{\log a}}}} \]

      12. exp-diff 76.5%

          \[\leadsto \frac{x}{\frac{y}{\color{blue}{e^{\log \left({a}^{t}\right) - \log a}}}} \]

      13. log-div 76.5%

          \[\leadsto \frac{x}{\frac{y}{e^{\color{blue}{\log \left(\frac{{a}^{t}}{a}\right)}}}} \]

      14. rem-exp-log 77.3%

          \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{{a}^{t}}{a}}}} \]

   9. Simplified 77.3%

      \[\leadsto \frac{x}{\color{blue}{\frac{y}{\frac{{a}^{t}}{a}}}} \]

   if 1.50000000000000003e-179 < b < 1.44999999999999997e-136

   1. Initial program 99.3%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 82.6%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 82.6%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 82.6%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 82.6%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 82.6%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around inf 67.3%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z} - b} \]

   5. Taylor expanded in b around 0 83.9%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{y}} \]

   if 1.5e29 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 86.9%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 86.9%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 86.9%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 86.9%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 86.9%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around inf 78.8%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z} - b} \]

   5. Taylor expanded in y around 0 83.9%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-b}}{y}} \]

   6. Taylor expanded in b around -inf 83.9%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 83.9%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot b} \cdot x}}{y} \]

      2. mul-1-neg 83.9%

         \[\leadsto \frac{e^{\color{blue}{-b}} \cdot x}{y} \]

      3. exp-neg 83.9%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b}}} \cdot x}{y} \]

      4. associate-/r/ 83.9%

         \[\leadsto \frac{\color{blue}{\frac{1}{\frac{e^{b}}{x}}}}{y} \]

      5. remove-double-div 83.9%

         \[\leadsto \frac{\frac{1}{\frac{e^{b}}{\color{blue}{\frac{1}{\frac{1}{x}}}}}}{y} \]

      6. associate-/r/ 83.9%

         \[\leadsto \frac{\frac{1}{\color{blue}{\frac{e^{b}}{1} \cdot \frac{1}{x}}}}{y} \]

      7. /-rgt-identity 83.9%

         \[\leadsto \frac{\frac{1}{\color{blue}{e^{b}} \cdot \frac{1}{x}}}{y} \]

      8. associate-/l/ 83.9%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{\frac{1}{x}}}{e^{b}}}}{y} \]

      9. remove-double-div 83.9%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b}}}{y} \]

   8. Simplified 83.9%

      \[\leadsto \frac{\color{blue}{\frac{x}{e^{b}}}}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.7 \cdot 10^{-161}:\\ \;\;\;\;\frac{x}{y} \cdot e^{y \cdot \log z - b}\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-179}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{t}}{a}}}\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-136}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y}\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{t}}{a}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \end{array} \]

Alternative 7: 69.6% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot {z}^{y}}{y}\\ t_2 := \frac{x}{y} \cdot \frac{{a}^{t}}{a}\\ t_3 := \frac{\frac{x}{e^{b}}}{y}\\ \mathbf{if}\;b \leq -250000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -5.9 \cdot 10^{-171}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-179}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+30}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (pow z y)) y))
        (t_2 (* (/ x y) (/ (pow a t) a)))
        (t_3 (/ (/ x (exp b)) y)))
   (if (<= b -250000.0)
     t_3
     (if (<= b -5.9e-171)
       t_1
       (if (<= b 1.55e-179)
         t_2
         (if (<= b 5.2e-136) t_1 (if (<= b 8e+30) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * pow(z, y)) / y;
	double t_2 = (x / y) * (pow(a, t) / a);
	double t_3 = (x / exp(b)) / y;
	double tmp;
	if (b <= -250000.0) {
		tmp = t_3;
	} else if (b <= -5.9e-171) {
		tmp = t_1;
	} else if (b <= 1.55e-179) {
		tmp = t_2;
	} else if (b <= 5.2e-136) {
		tmp = t_1;
	} else if (b <= 8e+30) {
		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 = (x * (z ** y)) / y
    t_2 = (x / y) * ((a ** t) / a)
    t_3 = (x / exp(b)) / y
    if (b <= (-250000.0d0)) then
        tmp = t_3
    else if (b <= (-5.9d-171)) then
        tmp = t_1
    else if (b <= 1.55d-179) then
        tmp = t_2
    else if (b <= 5.2d-136) then
        tmp = t_1
    else if (b <= 8d+30) 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 = (x * Math.pow(z, y)) / y;
	double t_2 = (x / y) * (Math.pow(a, t) / a);
	double t_3 = (x / Math.exp(b)) / y;
	double tmp;
	if (b <= -250000.0) {
		tmp = t_3;
	} else if (b <= -5.9e-171) {
		tmp = t_1;
	} else if (b <= 1.55e-179) {
		tmp = t_2;
	} else if (b <= 5.2e-136) {
		tmp = t_1;
	} else if (b <= 8e+30) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.pow(z, y)) / y
	t_2 = (x / y) * (math.pow(a, t) / a)
	t_3 = (x / math.exp(b)) / y
	tmp = 0
	if b <= -250000.0:
		tmp = t_3
	elif b <= -5.9e-171:
		tmp = t_1
	elif b <= 1.55e-179:
		tmp = t_2
	elif b <= 5.2e-136:
		tmp = t_1
	elif b <= 8e+30:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * (z ^ y)) / y)
	t_2 = Float64(Float64(x / y) * Float64((a ^ t) / a))
	t_3 = Float64(Float64(x / exp(b)) / y)
	tmp = 0.0
	if (b <= -250000.0)
		tmp = t_3;
	elseif (b <= -5.9e-171)
		tmp = t_1;
	elseif (b <= 1.55e-179)
		tmp = t_2;
	elseif (b <= 5.2e-136)
		tmp = t_1;
	elseif (b <= 8e+30)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * (z ^ y)) / y;
	t_2 = (x / y) * ((a ^ t) / a);
	t_3 = (x / exp(b)) / y;
	tmp = 0.0;
	if (b <= -250000.0)
		tmp = t_3;
	elseif (b <= -5.9e-171)
		tmp = t_1;
	elseif (b <= 1.55e-179)
		tmp = t_2;
	elseif (b <= 5.2e-136)
		tmp = t_1;
	elseif (b <= 8e+30)
		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[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] * N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -250000.0], t$95$3, If[LessEqual[b, -5.9e-171], t$95$1, If[LessEqual[b, 1.55e-179], t$95$2, If[LessEqual[b, 5.2e-136], t$95$1, If[LessEqual[b, 8e+30], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.5e5 or 8.0000000000000002e30 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.8%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 91.8%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 91.8%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 91.8%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 91.8%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around inf 85.3%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z} - b} \]

   5. Taylor expanded in y around 0 84.7%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-b}}{y}} \]

   6. Taylor expanded in b around -inf 84.7%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 84.7%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot b} \cdot x}}{y} \]

      2. mul-1-neg 84.7%

         \[\leadsto \frac{e^{\color{blue}{-b}} \cdot x}{y} \]

      3. exp-neg 84.7%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b}}} \cdot x}{y} \]

      4. associate-/r/ 84.7%

         \[\leadsto \frac{\color{blue}{\frac{1}{\frac{e^{b}}{x}}}}{y} \]

      5. remove-double-div 84.7%

         \[\leadsto \frac{\frac{1}{\frac{e^{b}}{\color{blue}{\frac{1}{\frac{1}{x}}}}}}{y} \]

      6. associate-/r/ 84.7%

         \[\leadsto \frac{\frac{1}{\color{blue}{\frac{e^{b}}{1} \cdot \frac{1}{x}}}}{y} \]

      7. /-rgt-identity 84.7%

         \[\leadsto \frac{\frac{1}{\color{blue}{e^{b}} \cdot \frac{1}{x}}}{y} \]

      8. associate-/l/ 84.7%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{\frac{1}{x}}}{e^{b}}}}{y} \]

      9. remove-double-div 84.7%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b}}}{y} \]

   8. Simplified 84.7%

      \[\leadsto \frac{\color{blue}{\frac{x}{e^{b}}}}{y} \]

   if -2.5e5 < b < -5.8999999999999998e-171 or 1.5500000000000001e-179 < b < 5.19999999999999993e-136

   1. Initial program 98.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 85.0%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 85.0%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 85.0%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 85.0%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 85.0%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around inf 58.2%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z} - b} \]

   5. Taylor expanded in b around 0 71.9%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{y}} \]

   if -5.8999999999999998e-171 < b < 1.5500000000000001e-179 or 5.19999999999999993e-136 < b < 8.0000000000000002e30

   1. Initial program 97.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 95.6%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 95.6%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 95.6%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 95.6%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 95.6%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around 0 77.7%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   5. Step-by-step derivation

      1. associate-/l* 78.2%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\log a \cdot \left(t - 1\right) - b}}}} \]

      2. exp-diff 76.0%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}} \]

      3. exp-prod 76.0%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{\left(e^{\log a}\right)}^{\left(t - 1\right)}}}{e^{b}}}} \]

      4. rem-exp-log 76.7%

         \[\leadsto \frac{x}{\frac{y}{\frac{{\color{blue}{a}}^{\left(t - 1\right)}}{e^{b}}}} \]

      5. sub-neg 76.7%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

      6. metadata-eval 76.7%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

   6. Simplified 76.7%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

   7. Taylor expanded in b around 0 77.7%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y}} \]
   8. Step-by-step derivation

      1. exp-prod 77.8%

         \[\leadsto \frac{x \cdot \color{blue}{{\left(e^{\log a}\right)}^{\left(t - 1\right)}}}{y} \]

      2. sub-neg 77.8%

         \[\leadsto \frac{x \cdot {\left(e^{\log a}\right)}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y} \]

      3. metadata-eval 77.8%

         \[\leadsto \frac{x \cdot {\left(e^{\log a}\right)}^{\left(t + \color{blue}{-1}\right)}}{y} \]

      4. exp-prod 77.7%

         \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t + -1\right)}}}{y} \]

      5. distribute-lft-in 77.7%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t + \log a \cdot -1}}}{y} \]

      6. *-commutative 77.7%

         \[\leadsto \frac{x \cdot e^{\log a \cdot t + \color{blue}{-1 \cdot \log a}}}{y} \]

      7. mul-1-neg 77.7%

         \[\leadsto \frac{x \cdot e^{\log a \cdot t + \color{blue}{\left(-\log a\right)}}}{y} \]

      8. sub-neg 77.7%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t - \log a}}}{y} \]

      9. exp-diff 77.7%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot t}}{e^{\log a}}}}{y} \]

      10. *-commutative 77.7%

          \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{t \cdot \log a}}}{e^{\log a}}}{y} \]

      11. log-pow 77.8%

          \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log \left({a}^{t}\right)}}}{e^{\log a}}}{y} \]

      12. exp-diff 77.7%

          \[\leadsto \frac{x \cdot \color{blue}{e^{\log \left({a}^{t}\right) - \log a}}}{y} \]

      13. log-div 77.7%

          \[\leadsto \frac{x \cdot e^{\color{blue}{\log \left(\frac{{a}^{t}}{a}\right)}}}{y} \]

      14. rem-exp-log 78.5%

          \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{t}}{a}}}{y} \]

      15. associate-*l/ 78.9%

          \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{a}^{t}}{a}} \]

   9. Simplified 78.9%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{a}^{t}}{a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -250000:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{elif}\;b \leq -5.9 \cdot 10^{-171}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y}\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-179}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{{a}^{t}}{a}\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-136}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y}\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{{a}^{t}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \end{array} \]

Alternative 8: 71.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot {z}^{y}}{y}\\ t_2 := \frac{x}{\frac{y}{\frac{{a}^{t}}{a}}}\\ t_3 := \frac{\frac{x}{e^{b}}}{y}\\ \mathbf{if}\;b \leq -100000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-179}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+29}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (pow z y)) y))
        (t_2 (/ x (/ y (/ (pow a t) a))))
        (t_3 (/ (/ x (exp b)) y)))
   (if (<= b -100000.0)
     t_3
     (if (<= b -8.2e-173)
       t_1
       (if (<= b 1.4e-179)
         t_2
         (if (<= b 1.8e-136) t_1 (if (<= b 1.5e+29) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * pow(z, y)) / y;
	double t_2 = x / (y / (pow(a, t) / a));
	double t_3 = (x / exp(b)) / y;
	double tmp;
	if (b <= -100000.0) {
		tmp = t_3;
	} else if (b <= -8.2e-173) {
		tmp = t_1;
	} else if (b <= 1.4e-179) {
		tmp = t_2;
	} else if (b <= 1.8e-136) {
		tmp = t_1;
	} else if (b <= 1.5e+29) {
		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 = (x * (z ** y)) / y
    t_2 = x / (y / ((a ** t) / a))
    t_3 = (x / exp(b)) / y
    if (b <= (-100000.0d0)) then
        tmp = t_3
    else if (b <= (-8.2d-173)) then
        tmp = t_1
    else if (b <= 1.4d-179) then
        tmp = t_2
    else if (b <= 1.8d-136) then
        tmp = t_1
    else if (b <= 1.5d+29) 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 = (x * Math.pow(z, y)) / y;
	double t_2 = x / (y / (Math.pow(a, t) / a));
	double t_3 = (x / Math.exp(b)) / y;
	double tmp;
	if (b <= -100000.0) {
		tmp = t_3;
	} else if (b <= -8.2e-173) {
		tmp = t_1;
	} else if (b <= 1.4e-179) {
		tmp = t_2;
	} else if (b <= 1.8e-136) {
		tmp = t_1;
	} else if (b <= 1.5e+29) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.pow(z, y)) / y
	t_2 = x / (y / (math.pow(a, t) / a))
	t_3 = (x / math.exp(b)) / y
	tmp = 0
	if b <= -100000.0:
		tmp = t_3
	elif b <= -8.2e-173:
		tmp = t_1
	elif b <= 1.4e-179:
		tmp = t_2
	elif b <= 1.8e-136:
		tmp = t_1
	elif b <= 1.5e+29:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * (z ^ y)) / y)
	t_2 = Float64(x / Float64(y / Float64((a ^ t) / a)))
	t_3 = Float64(Float64(x / exp(b)) / y)
	tmp = 0.0
	if (b <= -100000.0)
		tmp = t_3;
	elseif (b <= -8.2e-173)
		tmp = t_1;
	elseif (b <= 1.4e-179)
		tmp = t_2;
	elseif (b <= 1.8e-136)
		tmp = t_1;
	elseif (b <= 1.5e+29)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * (z ^ y)) / y;
	t_2 = x / (y / ((a ^ t) / a));
	t_3 = (x / exp(b)) / y;
	tmp = 0.0;
	if (b <= -100000.0)
		tmp = t_3;
	elseif (b <= -8.2e-173)
		tmp = t_1;
	elseif (b <= 1.4e-179)
		tmp = t_2;
	elseif (b <= 1.8e-136)
		tmp = t_1;
	elseif (b <= 1.5e+29)
		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[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(y / N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -100000.0], t$95$3, If[LessEqual[b, -8.2e-173], t$95$1, If[LessEqual[b, 1.4e-179], t$95$2, If[LessEqual[b, 1.8e-136], t$95$1, If[LessEqual[b, 1.5e+29], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1e5 or 1.5e29 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.8%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 91.8%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 91.8%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 91.8%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 91.8%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around inf 85.3%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z} - b} \]

   5. Taylor expanded in y around 0 84.7%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-b}}{y}} \]

   6. Taylor expanded in b around -inf 84.7%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 84.7%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot b} \cdot x}}{y} \]

      2. mul-1-neg 84.7%

         \[\leadsto \frac{e^{\color{blue}{-b}} \cdot x}{y} \]

      3. exp-neg 84.7%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b}}} \cdot x}{y} \]

      4. associate-/r/ 84.7%

         \[\leadsto \frac{\color{blue}{\frac{1}{\frac{e^{b}}{x}}}}{y} \]

      5. remove-double-div 84.7%

         \[\leadsto \frac{\frac{1}{\frac{e^{b}}{\color{blue}{\frac{1}{\frac{1}{x}}}}}}{y} \]

      6. associate-/r/ 84.7%

         \[\leadsto \frac{\frac{1}{\color{blue}{\frac{e^{b}}{1} \cdot \frac{1}{x}}}}{y} \]

      7. /-rgt-identity 84.7%

         \[\leadsto \frac{\frac{1}{\color{blue}{e^{b}} \cdot \frac{1}{x}}}{y} \]

      8. associate-/l/ 84.7%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{\frac{1}{x}}}{e^{b}}}}{y} \]

      9. remove-double-div 84.7%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b}}}{y} \]

   8. Simplified 84.7%

      \[\leadsto \frac{\color{blue}{\frac{x}{e^{b}}}}{y} \]

   if -1e5 < b < -8.1999999999999995e-173 or 1.4e-179 < b < 1.7999999999999999e-136

   1. Initial program 98.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 85.0%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 85.0%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 85.0%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 85.0%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 85.0%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around inf 58.2%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z} - b} \]

   5. Taylor expanded in b around 0 71.9%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{y}} \]

   if -8.1999999999999995e-173 < b < 1.4e-179 or 1.7999999999999999e-136 < b < 1.5e29

   1. Initial program 97.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 95.6%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 95.6%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 95.6%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 95.6%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 95.6%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around 0 77.7%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   5. Step-by-step derivation

      1. associate-/l* 78.2%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\log a \cdot \left(t - 1\right) - b}}}} \]

      2. exp-diff 76.0%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}} \]

      3. exp-prod 76.0%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{\left(e^{\log a}\right)}^{\left(t - 1\right)}}}{e^{b}}}} \]

      4. rem-exp-log 76.7%

         \[\leadsto \frac{x}{\frac{y}{\frac{{\color{blue}{a}}^{\left(t - 1\right)}}{e^{b}}}} \]

      5. sub-neg 76.7%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

      6. metadata-eval 76.7%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

   6. Simplified 76.7%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

   7. Taylor expanded in b around 0 78.2%

      \[\leadsto \frac{x}{\color{blue}{\frac{y}{e^{\log a \cdot \left(t - 1\right)}}}} \]
   8. Step-by-step derivation

      1. exp-prod 78.3%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{{\left(e^{\log a}\right)}^{\left(t - 1\right)}}}} \]

      2. sub-neg 78.3%

         \[\leadsto \frac{x}{\frac{y}{{\left(e^{\log a}\right)}^{\color{blue}{\left(t + \left(-1\right)\right)}}}} \]

      3. metadata-eval 78.3%

         \[\leadsto \frac{x}{\frac{y}{{\left(e^{\log a}\right)}^{\left(t + \color{blue}{-1}\right)}}} \]

      4. exp-prod 78.2%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{e^{\log a \cdot \left(t + -1\right)}}}} \]

      5. distribute-lft-in 78.2%

         \[\leadsto \frac{x}{\frac{y}{e^{\color{blue}{\log a \cdot t + \log a \cdot -1}}}} \]

      6. *-commutative 78.2%

         \[\leadsto \frac{x}{\frac{y}{e^{\log a \cdot t + \color{blue}{-1 \cdot \log a}}}} \]

      7. mul-1-neg 78.2%

         \[\leadsto \frac{x}{\frac{y}{e^{\log a \cdot t + \color{blue}{\left(-\log a\right)}}}} \]

      8. sub-neg 78.2%

         \[\leadsto \frac{x}{\frac{y}{e^{\color{blue}{\log a \cdot t - \log a}}}} \]

      9. exp-diff 78.2%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot t}}{e^{\log a}}}}} \]

      10. *-commutative 78.2%

          \[\leadsto \frac{x}{\frac{y}{\frac{e^{\color{blue}{t \cdot \log a}}}{e^{\log a}}}} \]

      11. log-pow 78.3%

          \[\leadsto \frac{x}{\frac{y}{\frac{e^{\color{blue}{\log \left({a}^{t}\right)}}}{e^{\log a}}}} \]

      12. exp-diff 78.2%

          \[\leadsto \frac{x}{\frac{y}{\color{blue}{e^{\log \left({a}^{t}\right) - \log a}}}} \]

      13. log-div 78.2%

          \[\leadsto \frac{x}{\frac{y}{e^{\color{blue}{\log \left(\frac{{a}^{t}}{a}\right)}}}} \]

      14. rem-exp-log 79.1%

          \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{{a}^{t}}{a}}}} \]

   9. Simplified 79.1%

      \[\leadsto \frac{x}{\color{blue}{\frac{y}{\frac{{a}^{t}}{a}}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -100000:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-173}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y}\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-179}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{t}}{a}}}\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-136}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y}\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{t}}{a}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \end{array} \]

Alternative 9: 62.5% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{e^{b}}}{y}\\ t_2 := \frac{x \cdot {z}^{y}}{y}\\ \mathbf{if}\;y \leq -6 \cdot 10^{+147}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{-268}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-219}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x (exp b)) y)) (t_2 (/ (* x (pow z y)) y)))
   (if (<= y -6e+147)
     t_2
     (if (<= y 2.95e-268)
       t_1
       (if (<= y 3.2e-219) (/ (/ x a) y) (if (<= y 1.15e+30) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / exp(b)) / y;
	double t_2 = (x * pow(z, y)) / y;
	double tmp;
	if (y <= -6e+147) {
		tmp = t_2;
	} else if (y <= 2.95e-268) {
		tmp = t_1;
	} else if (y <= 3.2e-219) {
		tmp = (x / a) / y;
	} else if (y <= 1.15e+30) {
		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 / exp(b)) / y
    t_2 = (x * (z ** y)) / y
    if (y <= (-6d+147)) then
        tmp = t_2
    else if (y <= 2.95d-268) then
        tmp = t_1
    else if (y <= 3.2d-219) then
        tmp = (x / a) / y
    else if (y <= 1.15d+30) 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 / Math.exp(b)) / y;
	double t_2 = (x * Math.pow(z, y)) / y;
	double tmp;
	if (y <= -6e+147) {
		tmp = t_2;
	} else if (y <= 2.95e-268) {
		tmp = t_1;
	} else if (y <= 3.2e-219) {
		tmp = (x / a) / y;
	} else if (y <= 1.15e+30) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / math.exp(b)) / y
	t_2 = (x * math.pow(z, y)) / y
	tmp = 0
	if y <= -6e+147:
		tmp = t_2
	elif y <= 2.95e-268:
		tmp = t_1
	elif y <= 3.2e-219:
		tmp = (x / a) / y
	elif y <= 1.15e+30:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / exp(b)) / y)
	t_2 = Float64(Float64(x * (z ^ y)) / y)
	tmp = 0.0
	if (y <= -6e+147)
		tmp = t_2;
	elseif (y <= 2.95e-268)
		tmp = t_1;
	elseif (y <= 3.2e-219)
		tmp = Float64(Float64(x / a) / y);
	elseif (y <= 1.15e+30)
		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 / exp(b)) / y;
	t_2 = (x * (z ^ y)) / y;
	tmp = 0.0;
	if (y <= -6e+147)
		tmp = t_2;
	elseif (y <= 2.95e-268)
		tmp = t_1;
	elseif (y <= 3.2e-219)
		tmp = (x / a) / y;
	elseif (y <= 1.15e+30)
		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[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -6e+147], t$95$2, If[LessEqual[y, 2.95e-268], t$95$1, If[LessEqual[y, 3.2e-219], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 1.15e+30], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.99999999999999987e147 or 1.15e30 < y

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 87.5%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 87.5%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 87.5%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 87.5%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 87.5%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around inf 82.4%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z} - b} \]

   5. Taylor expanded in b around 0 91.8%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{y}} \]

   if -5.99999999999999987e147 < y < 2.94999999999999998e-268 or 3.19999999999999998e-219 < y < 1.15e30

   1. Initial program 98.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 95.0%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 95.0%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 95.0%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 95.0%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 95.0%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around inf 62.6%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z} - b} \]

   5. Taylor expanded in y around 0 61.6%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-b}}{y}} \]

   6. Taylor expanded in b around -inf 61.6%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 61.6%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot b} \cdot x}}{y} \]

      2. mul-1-neg 61.6%

         \[\leadsto \frac{e^{\color{blue}{-b}} \cdot x}{y} \]

      3. exp-neg 61.6%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b}}} \cdot x}{y} \]

      4. associate-/r/ 61.6%

         \[\leadsto \frac{\color{blue}{\frac{1}{\frac{e^{b}}{x}}}}{y} \]

      5. remove-double-div 61.6%

         \[\leadsto \frac{\frac{1}{\frac{e^{b}}{\color{blue}{\frac{1}{\frac{1}{x}}}}}}{y} \]

      6. associate-/r/ 61.6%

         \[\leadsto \frac{\frac{1}{\color{blue}{\frac{e^{b}}{1} \cdot \frac{1}{x}}}}{y} \]

      7. /-rgt-identity 61.6%

         \[\leadsto \frac{\frac{1}{\color{blue}{e^{b}} \cdot \frac{1}{x}}}{y} \]

      8. associate-/l/ 61.6%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{\frac{1}{x}}}{e^{b}}}}{y} \]

      9. remove-double-div 61.6%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b}}}{y} \]

   8. Simplified 61.6%

      \[\leadsto \frac{\color{blue}{\frac{x}{e^{b}}}}{y} \]

   if 2.94999999999999998e-268 < y < 3.19999999999999998e-219

   1. Initial program 98.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 90.8%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 90.8%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 90.8%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. exp-sum 90.8%

         \[\leadsto \color{blue}{\left(e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}\right)} \cdot \frac{x}{y} \]

      5. *-commutative 90.8%

         \[\leadsto \left(e^{\color{blue}{\log z \cdot y}} \cdot e^{\left(t - 1\right) \cdot \log a - b}\right) \cdot \frac{x}{y} \]

      6. exp-to-pow 90.8%

         \[\leadsto \left(\color{blue}{{z}^{y}} \cdot e^{\left(t - 1\right) \cdot \log a - b}\right) \cdot \frac{x}{y} \]

      7. exp-diff 75.4%

         \[\leadsto \left({z}^{y} \cdot \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      8. *-commutative 75.4%

         \[\leadsto \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      9. exp-to-pow 76.8%

         \[\leadsto \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      10. sub-neg 76.8%

          \[\leadsto \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      11. metadata-eval 76.8%

          \[\leadsto \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 76.8%

      \[\leadsto \color{blue}{\left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}\right) \cdot \frac{x}{y}} \]

   5. Applied egg-rr 76.8%

      \[\leadsto \color{blue}{\frac{\frac{{z}^{y} \cdot \left(\frac{{a}^{t}}{a} \cdot x\right)}{e^{b}}}{y}} \]

   6. Taylor expanded in t around 0 47.3%

      \[\leadsto \frac{\frac{{z}^{y} \cdot \color{blue}{\frac{x}{a}}}{e^{b}}}{y} \]

   7. Taylor expanded in y around 0 47.3%

      \[\leadsto \frac{\frac{\color{blue}{\frac{x}{a}}}{e^{b}}}{y} \]

   8. Taylor expanded in b around 0 62.7%

      \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+147}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y}\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{-268}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-219}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+30}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y}\\ \end{array} \]

Alternative 10: 57.7% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{e^{b}}}{y}\\ \mathbf{if}\;b \leq -6.4 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{-156}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{-85}:\\ \;\;\;\;\frac{\frac{x \cdot y}{x} - y \cdot b}{\frac{y}{\frac{x}{y}}}\\ \mathbf{elif}\;b \leq 16200000000000:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x (exp b)) y)))
   (if (<= b -6.4e-24)
     t_1
     (if (<= b 1.95e-156)
       (/ (/ x a) y)
       (if (<= b 1.95e-85)
         (/ (- (/ (* x y) x) (* y b)) (/ y (/ x y)))
         (if (<= b 16200000000000.0) (/ x (* a (+ y (* y b)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / exp(b)) / y;
	double tmp;
	if (b <= -6.4e-24) {
		tmp = t_1;
	} else if (b <= 1.95e-156) {
		tmp = (x / a) / y;
	} else if (b <= 1.95e-85) {
		tmp = (((x * y) / x) - (y * b)) / (y / (x / y));
	} else if (b <= 16200000000000.0) {
		tmp = x / (a * (y + (y * b)));
	} else {
		tmp = t_1;
	}
	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) :: tmp
    t_1 = (x / exp(b)) / y
    if (b <= (-6.4d-24)) then
        tmp = t_1
    else if (b <= 1.95d-156) then
        tmp = (x / a) / y
    else if (b <= 1.95d-85) then
        tmp = (((x * y) / x) - (y * b)) / (y / (x / y))
    else if (b <= 16200000000000.0d0) then
        tmp = x / (a * (y + (y * b)))
    else
        tmp = t_1
    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 / Math.exp(b)) / y;
	double tmp;
	if (b <= -6.4e-24) {
		tmp = t_1;
	} else if (b <= 1.95e-156) {
		tmp = (x / a) / y;
	} else if (b <= 1.95e-85) {
		tmp = (((x * y) / x) - (y * b)) / (y / (x / y));
	} else if (b <= 16200000000000.0) {
		tmp = x / (a * (y + (y * b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / math.exp(b)) / y
	tmp = 0
	if b <= -6.4e-24:
		tmp = t_1
	elif b <= 1.95e-156:
		tmp = (x / a) / y
	elif b <= 1.95e-85:
		tmp = (((x * y) / x) - (y * b)) / (y / (x / y))
	elif b <= 16200000000000.0:
		tmp = x / (a * (y + (y * b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / exp(b)) / y)
	tmp = 0.0
	if (b <= -6.4e-24)
		tmp = t_1;
	elseif (b <= 1.95e-156)
		tmp = Float64(Float64(x / a) / y);
	elseif (b <= 1.95e-85)
		tmp = Float64(Float64(Float64(Float64(x * y) / x) - Float64(y * b)) / Float64(y / Float64(x / y)));
	elseif (b <= 16200000000000.0)
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / exp(b)) / y;
	tmp = 0.0;
	if (b <= -6.4e-24)
		tmp = t_1;
	elseif (b <= 1.95e-156)
		tmp = (x / a) / y;
	elseif (b <= 1.95e-85)
		tmp = (((x * y) / x) - (y * b)) / (y / (x / y));
	elseif (b <= 16200000000000.0)
		tmp = x / (a * (y + (y * b)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -6.4e-24], t$95$1, If[LessEqual[b, 1.95e-156], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 1.95e-85], N[(N[(N[(N[(x * y), $MachinePrecision] / x), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 16200000000000.0], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.40000000000000025e-24 or 1.62e13 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.5%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 91.5%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 91.5%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 91.5%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 91.5%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around inf 84.6%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z} - b} \]

   5. Taylor expanded in y around 0 82.5%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-b}}{y}} \]

   6. Taylor expanded in b around -inf 82.5%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 82.5%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot b} \cdot x}}{y} \]

      2. mul-1-neg 82.5%

         \[\leadsto \frac{e^{\color{blue}{-b}} \cdot x}{y} \]

      3. exp-neg 82.5%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b}}} \cdot x}{y} \]

      4. associate-/r/ 82.5%

         \[\leadsto \frac{\color{blue}{\frac{1}{\frac{e^{b}}{x}}}}{y} \]

      5. remove-double-div 82.5%

         \[\leadsto \frac{\frac{1}{\frac{e^{b}}{\color{blue}{\frac{1}{\frac{1}{x}}}}}}{y} \]

      6. associate-/r/ 82.5%

         \[\leadsto \frac{\frac{1}{\color{blue}{\frac{e^{b}}{1} \cdot \frac{1}{x}}}}{y} \]

      7. /-rgt-identity 82.5%

         \[\leadsto \frac{\frac{1}{\color{blue}{e^{b}} \cdot \frac{1}{x}}}{y} \]

      8. associate-/l/ 82.5%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{\frac{1}{x}}}{e^{b}}}}{y} \]

      9. remove-double-div 82.5%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b}}}{y} \]

   8. Simplified 82.5%

      \[\leadsto \frac{\color{blue}{\frac{x}{e^{b}}}}{y} \]

   if -6.40000000000000025e-24 < b < 1.9500000000000001e-156

   1. Initial program 98.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.2%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 91.2%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 91.2%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. exp-sum 78.4%

         \[\leadsto \color{blue}{\left(e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}\right)} \cdot \frac{x}{y} \]

      5. *-commutative 78.4%

         \[\leadsto \left(e^{\color{blue}{\log z \cdot y}} \cdot e^{\left(t - 1\right) \cdot \log a - b}\right) \cdot \frac{x}{y} \]

      6. exp-to-pow 78.4%

         \[\leadsto \left(\color{blue}{{z}^{y}} \cdot e^{\left(t - 1\right) \cdot \log a - b}\right) \cdot \frac{x}{y} \]

      7. exp-diff 78.4%

         \[\leadsto \left({z}^{y} \cdot \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      8. *-commutative 78.4%

         \[\leadsto \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      9. exp-to-pow 79.5%

         \[\leadsto \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      10. sub-neg 79.5%

          \[\leadsto \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      11. metadata-eval 79.5%

          \[\leadsto \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 79.5%

      \[\leadsto \color{blue}{\left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}\right) \cdot \frac{x}{y}} \]

   5. Applied egg-rr 83.5%

      \[\leadsto \color{blue}{\frac{\frac{{z}^{y} \cdot \left(\frac{{a}^{t}}{a} \cdot x\right)}{e^{b}}}{y}} \]

   6. Taylor expanded in t around 0 71.8%

      \[\leadsto \frac{\frac{{z}^{y} \cdot \color{blue}{\frac{x}{a}}}{e^{b}}}{y} \]

   7. Taylor expanded in y around 0 37.9%

      \[\leadsto \frac{\frac{\color{blue}{\frac{x}{a}}}{e^{b}}}{y} \]

   8. Taylor expanded in b around 0 37.9%

      \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]

   if 1.9500000000000001e-156 < b < 1.94999999999999994e-85

   1. Initial program 92.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 90.8%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 90.8%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 90.8%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 90.8%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 90.8%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around inf 43.5%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z} - b} \]

   5. Taylor expanded in y around 0 29.0%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-b}}{y}} \]
   6. Step-by-step derivation

      1. associate-*l/ 29.0%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{-b}} \]

      2. *-commutative 29.0%

         \[\leadsto \color{blue}{e^{-b} \cdot \frac{x}{y}} \]

   7. Simplified 29.0%

      \[\leadsto \color{blue}{e^{-b} \cdot \frac{x}{y}} \]

   8. Taylor expanded in b around 0 20.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y} + \frac{x}{y}} \]
   9. Step-by-step derivation

      1. +-commutative 20.7%

         \[\leadsto \color{blue}{\frac{x}{y} + -1 \cdot \frac{b \cdot x}{y}} \]

      2. associate-/l* 20.7%

         \[\leadsto \frac{x}{y} + -1 \cdot \color{blue}{\frac{b}{\frac{y}{x}}} \]

      3. associate-*r/ 20.7%

         \[\leadsto \frac{x}{y} + \color{blue}{\frac{-1 \cdot b}{\frac{y}{x}}} \]

      4. neg-mul-1 20.7%

         \[\leadsto \frac{x}{y} + \frac{\color{blue}{-b}}{\frac{y}{x}} \]

      5. frac-add 26.0%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{y}{x} + y \cdot \left(-b\right)}{y \cdot \frac{y}{x}}} \]

      6. associate-*r/ 25.7%

         \[\leadsto \frac{x \cdot \frac{y}{x} + y \cdot \left(-b\right)}{\color{blue}{\frac{y \cdot y}{x}}} \]

   10. Applied egg-rr 25.7%

       \[\leadsto \color{blue}{\frac{x \cdot \frac{y}{x} + y \cdot \left(-b\right)}{\frac{y \cdot y}{x}}} \]
   11. Step-by-step derivation

       1. *-commutative 25.7%

          \[\leadsto \frac{x \cdot \frac{y}{x} + \color{blue}{\left(-b\right) \cdot y}}{\frac{y \cdot y}{x}} \]

       2. cancel-sign-sub-inv 25.7%

          \[\leadsto \frac{\color{blue}{x \cdot \frac{y}{x} - b \cdot y}}{\frac{y \cdot y}{x}} \]

       3. *-commutative 25.7%

          \[\leadsto \frac{x \cdot \frac{y}{x} - \color{blue}{y \cdot b}}{\frac{y \cdot y}{x}} \]

       4. associate-*r/ 50.7%

          \[\leadsto \frac{\color{blue}{\frac{x \cdot y}{x}} - y \cdot b}{\frac{y \cdot y}{x}} \]

       5. associate-/l* 59.3%

          \[\leadsto \frac{\frac{x \cdot y}{x} - y \cdot b}{\color{blue}{\frac{y}{\frac{x}{y}}}} \]

   12. Simplified 59.3%

       \[\leadsto \color{blue}{\frac{\frac{x \cdot y}{x} - y \cdot b}{\frac{y}{\frac{x}{y}}}} \]

   if 1.94999999999999994e-85 < b < 1.62e13

   1. Initial program 99.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.0%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 99.0%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 99.0%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 99.0%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 99.0%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around 0 71.1%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   5. Step-by-step derivation

      1. associate-/l* 71.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\log a \cdot \left(t - 1\right) - b}}}} \]

      2. exp-diff 66.9%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}} \]

      3. exp-prod 66.9%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{\left(e^{\log a}\right)}^{\left(t - 1\right)}}}{e^{b}}}} \]

      4. rem-exp-log 67.4%

         \[\leadsto \frac{x}{\frac{y}{\frac{{\color{blue}{a}}^{\left(t - 1\right)}}{e^{b}}}} \]

      5. sub-neg 67.4%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

      6. metadata-eval 67.4%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

   6. Simplified 67.4%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

   7. Taylor expanded in t around 0 45.2%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 45.4%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   9. Step-by-step derivation

      1. distribute-lft-out 45.4%

         \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

      2. *-commutative 45.4%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot b}\right)} \]

   10. Simplified 45.4%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + y \cdot b\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.4 \cdot 10^{-24}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{-156}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{-85}:\\ \;\;\;\;\frac{\frac{x \cdot y}{x} - y \cdot b}{\frac{y}{\frac{x}{y}}}\\ \mathbf{elif}\;b \leq 16200000000000:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \end{array} \]

Alternative 11: 73.0% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+147} \lor \neg \left(y \leq 1.4 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -6e+147) (not (<= y 1.4e+30)))
   (/ (* x (pow z y)) y)
   (/ x (* a (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6e+147) || !(y <= 1.4e+30)) {
		tmp = (x * pow(z, y)) / y;
	} 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 <= (-6d+147)) .or. (.not. (y <= 1.4d+30))) then
        tmp = (x * (z ** y)) / y
    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 <= -6e+147) || !(y <= 1.4e+30)) {
		tmp = (x * Math.pow(z, y)) / y;
	} else {
		tmp = x / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -6e+147) or not (y <= 1.4e+30):
		tmp = (x * math.pow(z, y)) / y
	else:
		tmp = x / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -6e+147) || !(y <= 1.4e+30))
		tmp = Float64(Float64(x * (z ^ y)) / y);
	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 <= -6e+147) || ~((y <= 1.4e+30)))
		tmp = (x * (z ^ y)) / y;
	else
		tmp = x / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -6e+147], N[Not[LessEqual[y, 1.4e+30]], $MachinePrecision]], N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.99999999999999987e147 or 1.39999999999999992e30 < y

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 87.5%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 87.5%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 87.5%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 87.5%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 87.5%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around inf 82.4%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z} - b} \]

   5. Taylor expanded in b around 0 91.8%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{y}} \]

   if -5.99999999999999987e147 < y < 1.39999999999999992e30

   1. Initial program 98.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.6%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 94.6%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 94.6%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 94.6%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 94.6%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around 0 94.6%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   5. Step-by-step derivation

      1. associate-/l* 94.0%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\log a \cdot \left(t - 1\right) - b}}}} \]

      2. exp-diff 84.6%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}} \]

      3. exp-prod 84.7%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{\left(e^{\log a}\right)}^{\left(t - 1\right)}}}{e^{b}}}} \]

      4. rem-exp-log 85.1%

         \[\leadsto \frac{x}{\frac{y}{\frac{{\color{blue}{a}}^{\left(t - 1\right)}}{e^{b}}}} \]

      5. sub-neg 85.1%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

      6. metadata-eval 85.1%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

   6. Simplified 85.1%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

   7. Taylor expanded in t around 0 71.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+147} \lor \neg \left(y \leq 1.4 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 12: 42.6% accurate, 14.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{+125}:\\ \;\;\;\;\frac{x - x \cdot b}{y} + 0.5 \cdot \frac{b \cdot b}{\frac{y}{x}}\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-72}:\\ \;\;\;\;\frac{\frac{y}{b} - \frac{x \cdot y}{x}}{\frac{y}{x} \cdot \frac{y}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.4e+125)
   (+ (/ (- x (* x b)) y) (* 0.5 (/ (* b b) (/ y x))))
   (if (<= b -6.2e-72)
     (/ (- (/ y b) (/ (* x y) x)) (* (/ y x) (/ y b)))
     (/ x (* a (+ y (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.4e+125) {
		tmp = ((x - (x * b)) / y) + (0.5 * ((b * b) / (y / x)));
	} else if (b <= -6.2e-72) {
		tmp = ((y / b) - ((x * y) / x)) / ((y / x) * (y / b));
	} else {
		tmp = x / (a * (y + (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 <= (-2.4d+125)) then
        tmp = ((x - (x * b)) / y) + (0.5d0 * ((b * b) / (y / x)))
    else if (b <= (-6.2d-72)) then
        tmp = ((y / b) - ((x * y) / x)) / ((y / x) * (y / b))
    else
        tmp = x / (a * (y + (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 <= -2.4e+125) {
		tmp = ((x - (x * b)) / y) + (0.5 * ((b * b) / (y / x)));
	} else if (b <= -6.2e-72) {
		tmp = ((y / b) - ((x * y) / x)) / ((y / x) * (y / b));
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.4e+125:
		tmp = ((x - (x * b)) / y) + (0.5 * ((b * b) / (y / x)))
	elif b <= -6.2e-72:
		tmp = ((y / b) - ((x * y) / x)) / ((y / x) * (y / b))
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.4e+125)
		tmp = Float64(Float64(Float64(x - Float64(x * b)) / y) + Float64(0.5 * Float64(Float64(b * b) / Float64(y / x))));
	elseif (b <= -6.2e-72)
		tmp = Float64(Float64(Float64(y / b) - Float64(Float64(x * y) / x)) / Float64(Float64(y / x) * Float64(y / b)));
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.4e+125)
		tmp = ((x - (x * b)) / y) + (0.5 * ((b * b) / (y / x)));
	elseif (b <= -6.2e-72)
		tmp = ((y / b) - ((x * y) / x)) / ((y / x) * (y / b));
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.4e+125], N[(N[(N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + N[(0.5 * N[(N[(b * b), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.2e-72], N[(N[(N[(y / b), $MachinePrecision] - N[(N[(x * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / N[(N[(y / x), $MachinePrecision] * N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.4e125

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 97.2%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 97.2%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 97.2%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 97.2%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 97.2%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around inf 94.5%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z} - b} \]

   5. Taylor expanded in y around 0 80.9%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-b}}{y}} \]
   6. Step-by-step derivation

      1. *-commutative 80.9%

         \[\leadsto \frac{\color{blue}{e^{-b} \cdot x}}{y} \]

      2. associate-/l* 78.0%

         \[\leadsto \color{blue}{\frac{e^{-b}}{\frac{y}{x}}} \]

      3. associate-/r/ 80.9%

         \[\leadsto \color{blue}{\frac{e^{-b}}{y} \cdot x} \]

   7. Applied egg-rr 80.9%

      \[\leadsto \color{blue}{\frac{e^{-b}}{y} \cdot x} \]

   8. Taylor expanded in b around 0 67.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y} + \left(0.5 \cdot \frac{{b}^{2} \cdot x}{y} + \frac{x}{y}\right)} \]
   9. Step-by-step derivation

      1. +-commutative 67.8%

         \[\leadsto -1 \cdot \frac{b \cdot x}{y} + \color{blue}{\left(\frac{x}{y} + 0.5 \cdot \frac{{b}^{2} \cdot x}{y}\right)} \]

      2. associate-+r+ 67.8%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{b \cdot x}{y} + \frac{x}{y}\right) + 0.5 \cdot \frac{{b}^{2} \cdot x}{y}} \]

      3. +-commutative 67.8%

         \[\leadsto \color{blue}{\left(\frac{x}{y} + -1 \cdot \frac{b \cdot x}{y}\right)} + 0.5 \cdot \frac{{b}^{2} \cdot x}{y} \]

      4. mul-1-neg 67.8%

         \[\leadsto \left(\frac{x}{y} + \color{blue}{\left(-\frac{b \cdot x}{y}\right)}\right) + 0.5 \cdot \frac{{b}^{2} \cdot x}{y} \]

      5. sub-neg 67.8%

         \[\leadsto \color{blue}{\left(\frac{x}{y} - \frac{b \cdot x}{y}\right)} + 0.5 \cdot \frac{{b}^{2} \cdot x}{y} \]

      6. *-commutative 67.8%

         \[\leadsto \left(\frac{x}{y} - \frac{\color{blue}{x \cdot b}}{y}\right) + 0.5 \cdot \frac{{b}^{2} \cdot x}{y} \]

      7. div-sub 67.8%

         \[\leadsto \color{blue}{\frac{x - x \cdot b}{y}} + 0.5 \cdot \frac{{b}^{2} \cdot x}{y} \]

      8. associate-/l* 67.7%

         \[\leadsto \frac{x - x \cdot b}{y} + 0.5 \cdot \color{blue}{\frac{{b}^{2}}{\frac{y}{x}}} \]

      9. unpow2 67.7%

         \[\leadsto \frac{x - x \cdot b}{y} + 0.5 \cdot \frac{\color{blue}{b \cdot b}}{\frac{y}{x}} \]

   10. Simplified 67.7%

       \[\leadsto \color{blue}{\frac{x - x \cdot b}{y} + 0.5 \cdot \frac{b \cdot b}{\frac{y}{x}}} \]

   if -2.4e125 < b < -6.1999999999999996e-72

   1. Initial program 99.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.6%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 91.6%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 91.6%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 91.6%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 91.6%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around inf 76.8%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z} - b} \]

   5. Taylor expanded in y around 0 64.7%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-b}}{y}} \]
   6. Step-by-step derivation

      1. associate-*l/ 59.5%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{-b}} \]

      2. *-commutative 59.5%

         \[\leadsto \color{blue}{e^{-b} \cdot \frac{x}{y}} \]

   7. Simplified 59.5%

      \[\leadsto \color{blue}{e^{-b} \cdot \frac{x}{y}} \]

   8. Taylor expanded in b around 0 6.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y} + \frac{x}{y}} \]
   9. Step-by-step derivation

      1. +-commutative 6.4%

         \[\leadsto \color{blue}{\frac{x}{y} + -1 \cdot \frac{b \cdot x}{y}} \]

      2. mul-1-neg 6.4%

         \[\leadsto \frac{x}{y} + \color{blue}{\left(-\frac{b \cdot x}{y}\right)} \]

      3. unsub-neg 6.4%

         \[\leadsto \color{blue}{\frac{x}{y} - \frac{b \cdot x}{y}} \]

      4. clear-num 6.4%

         \[\leadsto \color{blue}{\frac{1}{\frac{y}{x}}} - \frac{b \cdot x}{y} \]

      5. *-commutative 6.4%

         \[\leadsto \frac{1}{\frac{y}{x}} - \frac{\color{blue}{x \cdot b}}{y} \]

      6. associate-/l* 6.4%

         \[\leadsto \frac{1}{\frac{y}{x}} - \color{blue}{\frac{x}{\frac{y}{b}}} \]

      7. frac-sub 16.0%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{y}{b} - \frac{y}{x} \cdot x}{\frac{y}{x} \cdot \frac{y}{b}}} \]

   10. Applied egg-rr 16.0%

       \[\leadsto \color{blue}{\frac{1 \cdot \frac{y}{b} - \frac{y}{x} \cdot x}{\frac{y}{x} \cdot \frac{y}{b}}} \]
   11. Step-by-step derivation

       1. *-lft-identity 16.0%

          \[\leadsto \frac{\color{blue}{\frac{y}{b}} - \frac{y}{x} \cdot x}{\frac{y}{x} \cdot \frac{y}{b}} \]

       2. *-commutative 16.0%

          \[\leadsto \frac{\frac{y}{b} - \color{blue}{x \cdot \frac{y}{x}}}{\frac{y}{x} \cdot \frac{y}{b}} \]

       3. associate-*r/ 31.2%

          \[\leadsto \frac{\frac{y}{b} - \color{blue}{\frac{x \cdot y}{x}}}{\frac{y}{x} \cdot \frac{y}{b}} \]

   12. Simplified 31.2%

       \[\leadsto \color{blue}{\frac{\frac{y}{b} - \frac{x \cdot y}{x}}{\frac{y}{x} \cdot \frac{y}{b}}} \]

   if -6.1999999999999996e-72 < b

   1. Initial program 98.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.0%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 91.0%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 91.0%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 91.0%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 91.0%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around 0 74.5%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   5. Step-by-step derivation

      1. associate-/l* 75.2%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\log a \cdot \left(t - 1\right) - b}}}} \]

      2. exp-diff 68.6%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}} \]

      3. exp-prod 68.6%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{\left(e^{\log a}\right)}^{\left(t - 1\right)}}}{e^{b}}}} \]

      4. rem-exp-log 69.0%

         \[\leadsto \frac{x}{\frac{y}{\frac{{\color{blue}{a}}^{\left(t - 1\right)}}{e^{b}}}} \]

      5. sub-neg 69.0%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

      6. metadata-eval 69.0%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

   6. Simplified 69.0%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

   7. Taylor expanded in t around 0 54.0%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 34.9%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   9. Step-by-step derivation

      1. distribute-lft-out 37.1%

         \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

      2. *-commutative 37.1%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot b}\right)} \]

   10. Simplified 37.1%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + y \cdot b\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 40.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{+125}:\\ \;\;\;\;\frac{x - x \cdot b}{y} + 0.5 \cdot \frac{b \cdot b}{\frac{y}{x}}\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-72}:\\ \;\;\;\;\frac{\frac{y}{b} - \frac{x \cdot y}{x}}{\frac{y}{x} \cdot \frac{y}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]

Alternative 13: 42.6% accurate, 16.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+78}:\\ \;\;\;\;\frac{x - x \cdot b}{y} + 0.5 \cdot \frac{b \cdot b}{\frac{y}{x}}\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-72}:\\ \;\;\;\;\frac{\frac{x \cdot y}{x} - y \cdot b}{\frac{y}{\frac{x}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.6e+78)
   (+ (/ (- x (* x b)) y) (* 0.5 (/ (* b b) (/ y x))))
   (if (<= b -6.2e-72)
     (/ (- (/ (* x y) x) (* y b)) (/ y (/ x y)))
     (/ x (* a (+ y (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.6e+78) {
		tmp = ((x - (x * b)) / y) + (0.5 * ((b * b) / (y / x)));
	} else if (b <= -6.2e-72) {
		tmp = (((x * y) / x) - (y * b)) / (y / (x / y));
	} else {
		tmp = x / (a * (y + (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 <= (-3.6d+78)) then
        tmp = ((x - (x * b)) / y) + (0.5d0 * ((b * b) / (y / x)))
    else if (b <= (-6.2d-72)) then
        tmp = (((x * y) / x) - (y * b)) / (y / (x / y))
    else
        tmp = x / (a * (y + (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 <= -3.6e+78) {
		tmp = ((x - (x * b)) / y) + (0.5 * ((b * b) / (y / x)));
	} else if (b <= -6.2e-72) {
		tmp = (((x * y) / x) - (y * b)) / (y / (x / y));
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.6e+78:
		tmp = ((x - (x * b)) / y) + (0.5 * ((b * b) / (y / x)))
	elif b <= -6.2e-72:
		tmp = (((x * y) / x) - (y * b)) / (y / (x / y))
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.6e+78)
		tmp = Float64(Float64(Float64(x - Float64(x * b)) / y) + Float64(0.5 * Float64(Float64(b * b) / Float64(y / x))));
	elseif (b <= -6.2e-72)
		tmp = Float64(Float64(Float64(Float64(x * y) / x) - Float64(y * b)) / Float64(y / Float64(x / y)));
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.6e+78)
		tmp = ((x - (x * b)) / y) + (0.5 * ((b * b) / (y / x)));
	elseif (b <= -6.2e-72)
		tmp = (((x * y) / x) - (y * b)) / (y / (x / y));
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.6e+78], N[(N[(N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + N[(0.5 * N[(N[(b * b), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.2e-72], N[(N[(N[(N[(x * y), $MachinePrecision] / x), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.6000000000000002e78

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 97.8%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 97.8%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 97.8%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 97.8%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 97.8%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around inf 91.2%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z} - b} \]

   5. Taylor expanded in y around 0 80.3%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-b}}{y}} \]
   6. Step-by-step derivation

      1. *-commutative 80.3%

         \[\leadsto \frac{\color{blue}{e^{-b} \cdot x}}{y} \]

      2. associate-/l* 78.0%

         \[\leadsto \color{blue}{\frac{e^{-b}}{\frac{y}{x}}} \]

      3. associate-/r/ 80.3%

         \[\leadsto \color{blue}{\frac{e^{-b}}{y} \cdot x} \]

   7. Applied egg-rr 80.3%

      \[\leadsto \color{blue}{\frac{e^{-b}}{y} \cdot x} \]

   8. Taylor expanded in b around 0 57.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y} + \left(0.5 \cdot \frac{{b}^{2} \cdot x}{y} + \frac{x}{y}\right)} \]
   9. Step-by-step derivation

      1. +-commutative 57.3%

         \[\leadsto -1 \cdot \frac{b \cdot x}{y} + \color{blue}{\left(\frac{x}{y} + 0.5 \cdot \frac{{b}^{2} \cdot x}{y}\right)} \]

      2. associate-+r+ 57.3%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{b \cdot x}{y} + \frac{x}{y}\right) + 0.5 \cdot \frac{{b}^{2} \cdot x}{y}} \]

      3. +-commutative 57.3%

         \[\leadsto \color{blue}{\left(\frac{x}{y} + -1 \cdot \frac{b \cdot x}{y}\right)} + 0.5 \cdot \frac{{b}^{2} \cdot x}{y} \]

      4. mul-1-neg 57.3%

         \[\leadsto \left(\frac{x}{y} + \color{blue}{\left(-\frac{b \cdot x}{y}\right)}\right) + 0.5 \cdot \frac{{b}^{2} \cdot x}{y} \]

      5. sub-neg 57.3%

         \[\leadsto \color{blue}{\left(\frac{x}{y} - \frac{b \cdot x}{y}\right)} + 0.5 \cdot \frac{{b}^{2} \cdot x}{y} \]

      6. *-commutative 57.3%

         \[\leadsto \left(\frac{x}{y} - \frac{\color{blue}{x \cdot b}}{y}\right) + 0.5 \cdot \frac{{b}^{2} \cdot x}{y} \]

      7. div-sub 57.3%

         \[\leadsto \color{blue}{\frac{x - x \cdot b}{y}} + 0.5 \cdot \frac{{b}^{2} \cdot x}{y} \]

      8. associate-/l* 55.1%

         \[\leadsto \frac{x - x \cdot b}{y} + 0.5 \cdot \color{blue}{\frac{{b}^{2}}{\frac{y}{x}}} \]

      9. unpow2 55.1%

         \[\leadsto \frac{x - x \cdot b}{y} + 0.5 \cdot \frac{\color{blue}{b \cdot b}}{\frac{y}{x}} \]

   10. Simplified 55.1%

       \[\leadsto \color{blue}{\frac{x - x \cdot b}{y} + 0.5 \cdot \frac{b \cdot b}{\frac{y}{x}}} \]

   if -3.6000000000000002e78 < b < -6.1999999999999996e-72

   1. Initial program 99.3%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.0%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 89.0%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 89.0%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 89.0%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 89.0%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around inf 76.4%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z} - b} \]

   5. Taylor expanded in y around 0 60.6%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-b}}{y}} \]
   6. Step-by-step derivation

      1. associate-*l/ 53.7%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{-b}} \]

      2. *-commutative 53.7%

         \[\leadsto \color{blue}{e^{-b} \cdot \frac{x}{y}} \]

   7. Simplified 53.7%

      \[\leadsto \color{blue}{e^{-b} \cdot \frac{x}{y}} \]

   8. Taylor expanded in b around 0 7.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y} + \frac{x}{y}} \]
   9. Step-by-step derivation

      1. +-commutative 7.4%

         \[\leadsto \color{blue}{\frac{x}{y} + -1 \cdot \frac{b \cdot x}{y}} \]

      2. associate-/l* 7.3%

         \[\leadsto \frac{x}{y} + -1 \cdot \color{blue}{\frac{b}{\frac{y}{x}}} \]

      3. associate-*r/ 7.3%

         \[\leadsto \frac{x}{y} + \color{blue}{\frac{-1 \cdot b}{\frac{y}{x}}} \]

      4. neg-mul-1 7.3%

         \[\leadsto \frac{x}{y} + \frac{\color{blue}{-b}}{\frac{y}{x}} \]

      5. frac-add 19.9%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{y}{x} + y \cdot \left(-b\right)}{y \cdot \frac{y}{x}}} \]

      6. associate-*r/ 19.8%

         \[\leadsto \frac{x \cdot \frac{y}{x} + y \cdot \left(-b\right)}{\color{blue}{\frac{y \cdot y}{x}}} \]

   10. Applied egg-rr 19.8%

       \[\leadsto \color{blue}{\frac{x \cdot \frac{y}{x} + y \cdot \left(-b\right)}{\frac{y \cdot y}{x}}} \]
   11. Step-by-step derivation

       1. *-commutative 19.8%

          \[\leadsto \frac{x \cdot \frac{y}{x} + \color{blue}{\left(-b\right) \cdot y}}{\frac{y \cdot y}{x}} \]

       2. cancel-sign-sub-inv 19.8%

          \[\leadsto \frac{\color{blue}{x \cdot \frac{y}{x} - b \cdot y}}{\frac{y \cdot y}{x}} \]

       3. *-commutative 19.8%

          \[\leadsto \frac{x \cdot \frac{y}{x} - \color{blue}{y \cdot b}}{\frac{y \cdot y}{x}} \]

       4. associate-*r/ 36.5%

          \[\leadsto \frac{\color{blue}{\frac{x \cdot y}{x}} - y \cdot b}{\frac{y \cdot y}{x}} \]

       5. associate-/l* 36.5%

          \[\leadsto \frac{\frac{x \cdot y}{x} - y \cdot b}{\color{blue}{\frac{y}{\frac{x}{y}}}} \]

   12. Simplified 36.5%

       \[\leadsto \color{blue}{\frac{\frac{x \cdot y}{x} - y \cdot b}{\frac{y}{\frac{x}{y}}}} \]

   if -6.1999999999999996e-72 < b

   1. Initial program 98.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.0%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 91.0%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 91.0%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 91.0%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 91.0%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around 0 74.5%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   5. Step-by-step derivation

      1. associate-/l* 75.2%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\log a \cdot \left(t - 1\right) - b}}}} \]

      2. exp-diff 68.6%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}} \]

      3. exp-prod 68.6%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{\left(e^{\log a}\right)}^{\left(t - 1\right)}}}{e^{b}}}} \]

      4. rem-exp-log 69.0%

         \[\leadsto \frac{x}{\frac{y}{\frac{{\color{blue}{a}}^{\left(t - 1\right)}}{e^{b}}}} \]

      5. sub-neg 69.0%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

      6. metadata-eval 69.0%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

   6. Simplified 69.0%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

   7. Taylor expanded in t around 0 54.0%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 34.9%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   9. Step-by-step derivation

      1. distribute-lft-out 37.1%

         \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

      2. *-commutative 37.1%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot b}\right)} \]

   10. Simplified 37.1%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + y \cdot b\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+78}:\\ \;\;\;\;\frac{x - x \cdot b}{y} + 0.5 \cdot \frac{b \cdot b}{\frac{y}{x}}\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-72}:\\ \;\;\;\;\frac{\frac{x \cdot y}{x} - y \cdot b}{\frac{y}{\frac{x}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]

Alternative 14: 38.4% accurate, 22.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.8 \cdot 10^{-69}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot \left(\left(-b\right) - -1\right)\right)}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.8e-69)
   (/ (* y (* x (- (- b) -1.0))) (* y y))
   (/ x (* a (+ y (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.8e-69) {
		tmp = (y * (x * (-b - -1.0))) / (y * y);
	} else {
		tmp = x / (a * (y + (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 <= (-7.8d-69)) then
        tmp = (y * (x * (-b - (-1.0d0)))) / (y * y)
    else
        tmp = x / (a * (y + (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 <= -7.8e-69) {
		tmp = (y * (x * (-b - -1.0))) / (y * y);
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7.8e-69:
		tmp = (y * (x * (-b - -1.0))) / (y * y)
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7.8e-69)
		tmp = Float64(Float64(y * Float64(x * Float64(Float64(-b) - -1.0))) / Float64(y * y));
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -7.8e-69)
		tmp = (y * (x * (-b - -1.0))) / (y * y);
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7.8e-69], N[(N[(y * N[(x * N[((-b) - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.79999999999999961e-69

   1. Initial program 99.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.4%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 94.4%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 94.4%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 94.4%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 94.4%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around inf 86.5%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z} - b} \]

   5. Taylor expanded in y around 0 73.5%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-b}}{y}} \]
   6. Step-by-step derivation

      1. associate-*l/ 69.4%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{-b}} \]

      2. *-commutative 69.4%

         \[\leadsto \color{blue}{e^{-b} \cdot \frac{x}{y}} \]

   7. Simplified 69.4%

      \[\leadsto \color{blue}{e^{-b} \cdot \frac{x}{y}} \]

   8. Taylor expanded in b around 0 21.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y} + \frac{x}{y}} \]
   9. Step-by-step derivation

      1. associate-*r/ 21.2%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(b \cdot x\right)}{y}} + \frac{x}{y} \]

      2. frac-add 37.6%

         \[\leadsto \color{blue}{\frac{\left(-1 \cdot \left(b \cdot x\right)\right) \cdot y + y \cdot x}{y \cdot y}} \]

      3. div-inv 38.9%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(b \cdot x\right)\right) \cdot y + y \cdot x\right) \cdot \frac{1}{y \cdot y}} \]

      4. +-commutative 38.9%

         \[\leadsto \color{blue}{\left(y \cdot x + \left(-1 \cdot \left(b \cdot x\right)\right) \cdot y\right)} \cdot \frac{1}{y \cdot y} \]

      5. *-commutative 38.9%

         \[\leadsto \left(\color{blue}{x \cdot y} + \left(-1 \cdot \left(b \cdot x\right)\right) \cdot y\right) \cdot \frac{1}{y \cdot y} \]

      6. fma-def 38.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \left(-1 \cdot \left(b \cdot x\right)\right) \cdot y\right)} \cdot \frac{1}{y \cdot y} \]

      7. *-commutative 38.9%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\left(\left(b \cdot x\right) \cdot -1\right)} \cdot y\right) \cdot \frac{1}{y \cdot y} \]

      8. associate-*l* 38.9%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\left(b \cdot x\right) \cdot \left(-1 \cdot y\right)}\right) \cdot \frac{1}{y \cdot y} \]

      9. neg-mul-1 38.9%

         \[\leadsto \mathsf{fma}\left(x, y, \left(b \cdot x\right) \cdot \color{blue}{\left(-y\right)}\right) \cdot \frac{1}{y \cdot y} \]

      10. *-commutative 38.9%

          \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\left(x \cdot b\right)} \cdot \left(-y\right)\right) \cdot \frac{1}{y \cdot y} \]

   10. Applied egg-rr 38.9%

       \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \left(x \cdot b\right) \cdot \left(-y\right)\right) \cdot \frac{1}{y \cdot y}} \]
   11. Step-by-step derivation

       1. associate-*r/ 37.6%

          \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, y, \left(x \cdot b\right) \cdot \left(-y\right)\right) \cdot 1}{y \cdot y}} \]

       2. *-rgt-identity 37.6%

          \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, y, \left(x \cdot b\right) \cdot \left(-y\right)\right)}}{y \cdot y} \]

       3. distribute-rgt-neg-out 37.6%

          \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{-\left(x \cdot b\right) \cdot y}\right)}{y \cdot y} \]

       4. fma-neg 37.6%

          \[\leadsto \frac{\color{blue}{x \cdot y - \left(x \cdot b\right) \cdot y}}{y \cdot y} \]

       5. div-sub 30.8%

          \[\leadsto \color{blue}{\frac{x \cdot y}{y \cdot y} - \frac{\left(x \cdot b\right) \cdot y}{y \cdot y}} \]

       6. remove-double-neg 30.8%

          \[\leadsto \frac{\color{blue}{-\left(-x \cdot y\right)}}{y \cdot y} - \frac{\left(x \cdot b\right) \cdot y}{y \cdot y} \]

       7. *-commutative 30.8%

          \[\leadsto \frac{-\left(-\color{blue}{y \cdot x}\right)}{y \cdot y} - \frac{\left(x \cdot b\right) \cdot y}{y \cdot y} \]

       8. distribute-lft-neg-out 30.8%

          \[\leadsto \frac{-\color{blue}{\left(-y\right) \cdot x}}{y \cdot y} - \frac{\left(x \cdot b\right) \cdot y}{y \cdot y} \]

       9. *-commutative 30.8%

          \[\leadsto \frac{-\color{blue}{x \cdot \left(-y\right)}}{y \cdot y} - \frac{\left(x \cdot b\right) \cdot y}{y \cdot y} \]

       10. distribute-lft-neg-out 30.8%

           \[\leadsto \frac{\color{blue}{\left(-x\right) \cdot \left(-y\right)}}{y \cdot y} - \frac{\left(x \cdot b\right) \cdot y}{y \cdot y} \]

       11. div-sub 37.6%

           \[\leadsto \color{blue}{\frac{\left(-x\right) \cdot \left(-y\right) - \left(x \cdot b\right) \cdot y}{y \cdot y}} \]

       12. sub-neg 37.6%

           \[\leadsto \frac{\color{blue}{\left(-x\right) \cdot \left(-y\right) + \left(-\left(x \cdot b\right) \cdot y\right)}}{y \cdot y} \]

       13. distribute-rgt-neg-out 37.6%

           \[\leadsto \frac{\left(-x\right) \cdot \left(-y\right) + \color{blue}{\left(x \cdot b\right) \cdot \left(-y\right)}}{y \cdot y} \]

   12. Simplified 37.6%

       \[\leadsto \color{blue}{\frac{\left(-y\right) \cdot \left(x \cdot \left(-1 + b\right)\right)}{y \cdot y}} \]

   if -7.79999999999999961e-69 < b

   1. Initial program 98.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.0%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 91.0%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 91.0%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 91.0%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 91.0%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around 0 74.5%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   5. Step-by-step derivation

      1. associate-/l* 74.8%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\log a \cdot \left(t - 1\right) - b}}}} \]

      2. exp-diff 68.2%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}} \]

      3. exp-prod 68.3%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{\left(e^{\log a}\right)}^{\left(t - 1\right)}}}{e^{b}}}} \]

      4. rem-exp-log 68.7%

         \[\leadsto \frac{x}{\frac{y}{\frac{{\color{blue}{a}}^{\left(t - 1\right)}}{e^{b}}}} \]

      5. sub-neg 68.7%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

      6. metadata-eval 68.7%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

   6. Simplified 68.7%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

   7. Taylor expanded in t around 0 53.8%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 34.7%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   9. Step-by-step derivation

      1. distribute-lft-out 36.9%

         \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

      2. *-commutative 36.9%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot b}\right)} \]

   10. Simplified 36.9%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + y \cdot b\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.8 \cdot 10^{-69}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot \left(\left(-b\right) - -1\right)\right)}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]

Alternative 15: 38.7% accurate, 24.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+123}:\\ \;\;\;\;x \cdot \frac{-b}{y}\\ \mathbf{elif}\;b \leq -8.8 \cdot 10^{-131}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.35e+123)
   (* x (/ (- b) y))
   (if (<= b -8.8e-131) (/ (/ x a) y) (/ x (* a (+ y (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.35e+123) {
		tmp = x * (-b / y);
	} else if (b <= -8.8e-131) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y + (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 <= (-1.35d+123)) then
        tmp = x * (-b / y)
    else if (b <= (-8.8d-131)) then
        tmp = (x / a) / y
    else
        tmp = x / (a * (y + (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 <= -1.35e+123) {
		tmp = x * (-b / y);
	} else if (b <= -8.8e-131) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.35e+123:
		tmp = x * (-b / y)
	elif b <= -8.8e-131:
		tmp = (x / a) / y
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.35e+123)
		tmp = Float64(x * Float64(Float64(-b) / y));
	elseif (b <= -8.8e-131)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.35e+123)
		tmp = x * (-b / y);
	elseif (b <= -8.8e-131)
		tmp = (x / a) / y;
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.35e+123], N[(x * N[((-b) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -8.8e-131], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.35000000000000007e123

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 97.3%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 97.3%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 97.3%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 97.3%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 97.3%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around inf 94.6%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z} - b} \]

   5. Taylor expanded in y around 0 81.4%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-b}}{y}} \]
   6. Step-by-step derivation

      1. associate-*l/ 78.6%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{-b}} \]

      2. *-commutative 78.6%

         \[\leadsto \color{blue}{e^{-b} \cdot \frac{x}{y}} \]

   7. Simplified 78.6%

      \[\leadsto \color{blue}{e^{-b} \cdot \frac{x}{y}} \]

   8. Taylor expanded in b around 0 35.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y} + \frac{x}{y}} \]

   9. Taylor expanded in b around inf 35.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y}} \]
   10. Step-by-step derivation

       1. mul-1-neg 35.4%

          \[\leadsto \color{blue}{-\frac{b \cdot x}{y}} \]

       2. associate-*l/ 50.8%

          \[\leadsto -\color{blue}{\frac{b}{y} \cdot x} \]

       3. *-commutative 50.8%

          \[\leadsto -\color{blue}{x \cdot \frac{b}{y}} \]

   11. Simplified 50.8%

       \[\leadsto \color{blue}{-x \cdot \frac{b}{y}} \]

   if -1.35000000000000007e123 < b < -8.7999999999999999e-131

   1. Initial program 99.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 90.4%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 90.4%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 90.4%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. exp-sum 79.5%

         \[\leadsto \color{blue}{\left(e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}\right)} \cdot \frac{x}{y} \]

      5. *-commutative 79.5%

         \[\leadsto \left(e^{\color{blue}{\log z \cdot y}} \cdot e^{\left(t - 1\right) \cdot \log a - b}\right) \cdot \frac{x}{y} \]

      6. exp-to-pow 79.5%

         \[\leadsto \left(\color{blue}{{z}^{y}} \cdot e^{\left(t - 1\right) \cdot \log a - b}\right) \cdot \frac{x}{y} \]

      7. exp-diff 73.0%

         \[\leadsto \left({z}^{y} \cdot \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      8. *-commutative 73.0%

         \[\leadsto \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      9. exp-to-pow 73.7%

         \[\leadsto \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      10. sub-neg 73.7%

          \[\leadsto \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      11. metadata-eval 73.7%

          \[\leadsto \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 73.7%

      \[\leadsto \color{blue}{\left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}\right) \cdot \frac{x}{y}} \]

   5. Applied egg-rr 73.9%

      \[\leadsto \color{blue}{\frac{\frac{{z}^{y} \cdot \left(\frac{{a}^{t}}{a} \cdot x\right)}{e^{b}}}{y}} \]

   6. Taylor expanded in t around 0 75.8%

      \[\leadsto \frac{\frac{{z}^{y} \cdot \color{blue}{\frac{x}{a}}}{e^{b}}}{y} \]

   7. Taylor expanded in y around 0 63.3%

      \[\leadsto \frac{\frac{\color{blue}{\frac{x}{a}}}{e^{b}}}{y} \]

   8. Taylor expanded in b around 0 29.8%

      \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]

   if -8.7999999999999999e-131 < b

   1. Initial program 98.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.2%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 91.2%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 91.2%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 91.2%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 91.2%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around 0 75.5%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   5. Step-by-step derivation

      1. associate-/l* 76.3%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\log a \cdot \left(t - 1\right) - b}}}} \]

      2. exp-diff 69.4%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}} \]

      3. exp-prod 69.4%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{\left(e^{\log a}\right)}^{\left(t - 1\right)}}}{e^{b}}}} \]

      4. rem-exp-log 69.8%

         \[\leadsto \frac{x}{\frac{y}{\frac{{\color{blue}{a}}^{\left(t - 1\right)}}{e^{b}}}} \]

      5. sub-neg 69.8%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

      6. metadata-eval 69.8%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

   6. Simplified 69.8%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

   7. Taylor expanded in t around 0 54.0%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 33.8%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   9. Step-by-step derivation

      1. distribute-lft-out 36.2%

         \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

      2. *-commutative 36.2%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot b}\right)} \]

   10. Simplified 36.2%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + y \cdot b\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+123}:\\ \;\;\;\;x \cdot \frac{-b}{y}\\ \mathbf{elif}\;b \leq -8.8 \cdot 10^{-131}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]

Alternative 16: 39.8% accurate, 24.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{-127}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.45e-127)
   (/ (- (/ x a) (/ (* x b) a)) y)
   (/ x (* a (+ y (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.45e-127) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else {
		tmp = x / (a * (y + (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 <= (-1.45d-127)) then
        tmp = ((x / a) - ((x * b) / a)) / y
    else
        tmp = x / (a * (y + (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 <= -1.45e-127) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.45e-127:
		tmp = ((x / a) - ((x * b) / a)) / y
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.45e-127)
		tmp = Float64(Float64(Float64(x / a) - Float64(Float64(x * b) / a)) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.45e-127)
		tmp = ((x / a) - ((x * b) / a)) / y;
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.45e-127], N[(N[(N[(x / a), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.45e-127

   1. Initial program 99.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 93.5%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 93.5%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 93.5%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. exp-sum 76.6%

         \[\leadsto \color{blue}{\left(e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}\right)} \cdot \frac{x}{y} \]

      5. *-commutative 76.6%

         \[\leadsto \left(e^{\color{blue}{\log z \cdot y}} \cdot e^{\left(t - 1\right) \cdot \log a - b}\right) \cdot \frac{x}{y} \]

      6. exp-to-pow 76.6%

         \[\leadsto \left(\color{blue}{{z}^{y}} \cdot e^{\left(t - 1\right) \cdot \log a - b}\right) \cdot \frac{x}{y} \]

      7. exp-diff 65.8%

         \[\leadsto \left({z}^{y} \cdot \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      8. *-commutative 65.8%

         \[\leadsto \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      9. exp-to-pow 66.1%

         \[\leadsto \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      10. sub-neg 66.1%

          \[\leadsto \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      11. metadata-eval 66.1%

          \[\leadsto \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 66.1%

      \[\leadsto \color{blue}{\left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}\right) \cdot \frac{x}{y}} \]

   5. Applied egg-rr 65.0%

      \[\leadsto \color{blue}{\frac{\frac{{z}^{y} \cdot \left(\frac{{a}^{t}}{a} \cdot x\right)}{e^{b}}}{y}} \]

   6. Taylor expanded in t around 0 67.3%

      \[\leadsto \frac{\frac{{z}^{y} \cdot \color{blue}{\frac{x}{a}}}{e^{b}}}{y} \]

   7. Taylor expanded in y around 0 65.3%

      \[\leadsto \frac{\frac{\color{blue}{\frac{x}{a}}}{e^{b}}}{y} \]

   8. Taylor expanded in b around 0 40.2%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]

   if -1.45e-127 < b

   1. Initial program 98.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.2%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 91.2%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 91.2%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 91.2%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 91.2%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around 0 75.5%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   5. Step-by-step derivation

      1. associate-/l* 76.3%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\log a \cdot \left(t - 1\right) - b}}}} \]

      2. exp-diff 69.4%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}} \]

      3. exp-prod 69.4%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{\left(e^{\log a}\right)}^{\left(t - 1\right)}}}{e^{b}}}} \]

      4. rem-exp-log 69.8%

         \[\leadsto \frac{x}{\frac{y}{\frac{{\color{blue}{a}}^{\left(t - 1\right)}}{e^{b}}}} \]

      5. sub-neg 69.8%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

      6. metadata-eval 69.8%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

   6. Simplified 69.8%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

   7. Taylor expanded in t around 0 54.0%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 33.8%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   9. Step-by-step derivation

      1. distribute-lft-out 36.2%

         \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

      2. *-commutative 36.2%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot b}\right)} \]

   10. Simplified 36.2%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + y \cdot b\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{-127}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]

Alternative 17: 32.4% accurate, 25.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1800000:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-57}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{elif}\;t \leq 31:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-b}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1800000.0)
   (/ x (* y a))
   (if (<= t 5.5e-57)
     (/ (/ x y) a)
     (if (<= t 31.0) (/ (/ x a) y) (* x (/ (- b) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1800000.0) {
		tmp = x / (y * a);
	} else if (t <= 5.5e-57) {
		tmp = (x / y) / a;
	} else if (t <= 31.0) {
		tmp = (x / a) / y;
	} else {
		tmp = x * (-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 (t <= (-1800000.0d0)) then
        tmp = x / (y * a)
    else if (t <= 5.5d-57) then
        tmp = (x / y) / a
    else if (t <= 31.0d0) then
        tmp = (x / a) / y
    else
        tmp = x * (-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 (t <= -1800000.0) {
		tmp = x / (y * a);
	} else if (t <= 5.5e-57) {
		tmp = (x / y) / a;
	} else if (t <= 31.0) {
		tmp = (x / a) / y;
	} else {
		tmp = x * (-b / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1800000.0:
		tmp = x / (y * a)
	elif t <= 5.5e-57:
		tmp = (x / y) / a
	elif t <= 31.0:
		tmp = (x / a) / y
	else:
		tmp = x * (-b / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1800000.0)
		tmp = Float64(x / Float64(y * a));
	elseif (t <= 5.5e-57)
		tmp = Float64(Float64(x / y) / a);
	elseif (t <= 31.0)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x * Float64(Float64(-b) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1800000.0)
		tmp = x / (y * a);
	elseif (t <= 5.5e-57)
		tmp = (x / y) / a;
	elseif (t <= 31.0)
		tmp = (x / a) / y;
	else
		tmp = x * (-b / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1800000.0], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e-57], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, 31.0], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x * N[((-b) / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.8e6

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.9%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 94.9%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 94.9%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 94.9%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 94.9%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around 0 93.3%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   5. Step-by-step derivation

      1. associate-/l* 93.3%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\log a \cdot \left(t - 1\right) - b}}}} \]

      2. exp-diff 71.2%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}} \]

      3. exp-prod 71.2%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{\left(e^{\log a}\right)}^{\left(t - 1\right)}}}{e^{b}}}} \]

      4. rem-exp-log 71.2%

         \[\leadsto \frac{x}{\frac{y}{\frac{{\color{blue}{a}}^{\left(t - 1\right)}}{e^{b}}}} \]

      5. sub-neg 71.2%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

      6. metadata-eval 71.2%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

   6. Simplified 71.2%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

   7. Taylor expanded in t around 0 56.7%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 33.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   9. Step-by-step derivation

      1. *-commutative 33.9%

         \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   10. Simplified 33.9%

       \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]

   if -1.8e6 < t < 5.50000000000000011e-57

   1. Initial program 97.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.1%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 89.1%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 89.1%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 89.1%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 89.1%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around 0 67.4%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   5. Step-by-step derivation

      1. associate-/l* 66.6%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\log a \cdot \left(t - 1\right) - b}}}} \]

      2. exp-diff 65.7%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}} \]

      3. exp-prod 65.8%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{\left(e^{\log a}\right)}^{\left(t - 1\right)}}}{e^{b}}}} \]

      4. rem-exp-log 66.4%

         \[\leadsto \frac{x}{\frac{y}{\frac{{\color{blue}{a}}^{\left(t - 1\right)}}{e^{b}}}} \]

      5. sub-neg 66.4%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

      6. metadata-eval 66.4%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

   6. Simplified 66.4%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

   7. Taylor expanded in b around 0 34.8%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y}} \]
   8. Step-by-step derivation

      1. exp-prod 34.9%

         \[\leadsto \frac{x \cdot \color{blue}{{\left(e^{\log a}\right)}^{\left(t - 1\right)}}}{y} \]

      2. sub-neg 34.9%

         \[\leadsto \frac{x \cdot {\left(e^{\log a}\right)}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y} \]

      3. metadata-eval 34.9%

         \[\leadsto \frac{x \cdot {\left(e^{\log a}\right)}^{\left(t + \color{blue}{-1}\right)}}{y} \]

      4. exp-prod 34.8%

         \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t + -1\right)}}}{y} \]

      5. distribute-lft-in 34.9%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t + \log a \cdot -1}}}{y} \]

      6. *-commutative 34.9%

         \[\leadsto \frac{x \cdot e^{\log a \cdot t + \color{blue}{-1 \cdot \log a}}}{y} \]

      7. mul-1-neg 34.9%

         \[\leadsto \frac{x \cdot e^{\log a \cdot t + \color{blue}{\left(-\log a\right)}}}{y} \]

      8. sub-neg 34.9%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t - \log a}}}{y} \]

      9. exp-diff 34.9%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot t}}{e^{\log a}}}}{y} \]

      10. *-commutative 34.9%

          \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{t \cdot \log a}}}{e^{\log a}}}{y} \]

      11. log-pow 34.9%

          \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log \left({a}^{t}\right)}}}{e^{\log a}}}{y} \]

      12. exp-diff 34.9%

          \[\leadsto \frac{x \cdot \color{blue}{e^{\log \left({a}^{t}\right) - \log a}}}{y} \]

      13. log-div 34.9%

          \[\leadsto \frac{x \cdot e^{\color{blue}{\log \left(\frac{{a}^{t}}{a}\right)}}}{y} \]

      14. rem-exp-log 35.9%

          \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{t}}{a}}}{y} \]

      15. associate-*l/ 38.0%

          \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{a}^{t}}{a}} \]

   9. Simplified 38.0%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{a}^{t}}{a}} \]

   10. Taylor expanded in t around 0 31.2%

       \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   11. Step-by-step derivation

       1. *-commutative 31.2%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

       2. associate-/r* 35.8%

          \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]

   12. Simplified 35.8%

       \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]

   if 5.50000000000000011e-57 < t < 31

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 84.2%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 84.2%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 84.2%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. exp-sum 73.7%

         \[\leadsto \color{blue}{\left(e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}\right)} \cdot \frac{x}{y} \]

      5. *-commutative 73.7%

         \[\leadsto \left(e^{\color{blue}{\log z \cdot y}} \cdot e^{\left(t - 1\right) \cdot \log a - b}\right) \cdot \frac{x}{y} \]

      6. exp-to-pow 73.7%

         \[\leadsto \left(\color{blue}{{z}^{y}} \cdot e^{\left(t - 1\right) \cdot \log a - b}\right) \cdot \frac{x}{y} \]

      7. exp-diff 73.7%

         \[\leadsto \left({z}^{y} \cdot \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      8. *-commutative 73.7%

         \[\leadsto \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      9. exp-to-pow 73.7%

         \[\leadsto \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      10. sub-neg 73.7%

          \[\leadsto \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      11. metadata-eval 73.7%

          \[\leadsto \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 73.7%

      \[\leadsto \color{blue}{\left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}\right) \cdot \frac{x}{y}} \]

   5. Applied egg-rr 73.7%

      \[\leadsto \color{blue}{\frac{\frac{{z}^{y} \cdot \left(\frac{{a}^{t}}{a} \cdot x\right)}{e^{b}}}{y}} \]

   6. Taylor expanded in t around 0 73.7%

      \[\leadsto \frac{\frac{{z}^{y} \cdot \color{blue}{\frac{x}{a}}}{e^{b}}}{y} \]

   7. Taylor expanded in y around 0 68.7%

      \[\leadsto \frac{\frac{\color{blue}{\frac{x}{a}}}{e^{b}}}{y} \]

   8. Taylor expanded in b around 0 49.1%

      \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]

   if 31 < t

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 96.8%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 96.8%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 96.8%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 96.8%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 96.8%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around inf 65.5%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z} - b} \]

   5. Taylor expanded in y around 0 41.0%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-b}}{y}} \]
   6. Step-by-step derivation

      1. associate-*l/ 39.3%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{-b}} \]

      2. *-commutative 39.3%

         \[\leadsto \color{blue}{e^{-b} \cdot \frac{x}{y}} \]

   7. Simplified 39.3%

      \[\leadsto \color{blue}{e^{-b} \cdot \frac{x}{y}} \]

   8. Taylor expanded in b around 0 14.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y} + \frac{x}{y}} \]

   9. Taylor expanded in b around inf 26.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y}} \]
   10. Step-by-step derivation

       1. mul-1-neg 26.5%

          \[\leadsto \color{blue}{-\frac{b \cdot x}{y}} \]

       2. associate-*l/ 31.1%

          \[\leadsto -\color{blue}{\frac{b}{y} \cdot x} \]

       3. *-commutative 31.1%

          \[\leadsto -\color{blue}{x \cdot \frac{b}{y}} \]

   11. Simplified 31.1%

       \[\leadsto \color{blue}{-x \cdot \frac{b}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1800000:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-57}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{elif}\;t \leq 31:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-b}{y}\\ \end{array} \]

Alternative 18: 30.6% accurate, 44.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-213}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1e-213) (/ x (* y a)) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1e-213) {
		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 (y <= (-1d-213)) 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 (y <= -1e-213) {
		tmp = x / (y * a);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1e-213:
		tmp = x / (y * a)
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1e-213)
		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 (y <= -1e-213)
		tmp = x / (y * a);
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1e-213], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.9999999999999995e-214

   1. Initial program 98.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 95.4%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. fma-def 95.4%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      3. sub-neg 95.4%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      4. metadata-eval 95.4%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 95.4%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in y around 0 78.2%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   5. Step-by-step derivation

      1. associate-/l* 79.2%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\log a \cdot \left(t - 1\right) - b}}}} \]

      2. exp-diff 70.0%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}} \]

      3. exp-prod 70.0%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{\left(e^{\log a}\right)}^{\left(t - 1\right)}}}{e^{b}}}} \]

      4. rem-exp-log 70.4%

         \[\leadsto \frac{x}{\frac{y}{\frac{{\color{blue}{a}}^{\left(t - 1\right)}}{e^{b}}}} \]

      5. sub-neg 70.4%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

      6. metadata-eval 70.4%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

   6. Simplified 70.4%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

   7. Taylor expanded in t around 0 61.3%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 25.8%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   9. Step-by-step derivation

      1. *-commutative 25.8%

         \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   10. Simplified 25.8%

       \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]

   if -9.9999999999999995e-214 < y

   1. Initial program 99.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.0%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 89.0%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 89.0%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. exp-sum 76.4%

         \[\leadsto \color{blue}{\left(e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}\right)} \cdot \frac{x}{y} \]

      5. *-commutative 76.4%

         \[\leadsto \left(e^{\color{blue}{\log z \cdot y}} \cdot e^{\left(t - 1\right) \cdot \log a - b}\right) \cdot \frac{x}{y} \]

      6. exp-to-pow 76.4%

         \[\leadsto \left(\color{blue}{{z}^{y}} \cdot e^{\left(t - 1\right) \cdot \log a - b}\right) \cdot \frac{x}{y} \]

      7. exp-diff 69.1%

         \[\leadsto \left({z}^{y} \cdot \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      8. *-commutative 69.1%

         \[\leadsto \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      9. exp-to-pow 69.7%

         \[\leadsto \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      10. sub-neg 69.7%

          \[\leadsto \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      11. metadata-eval 69.7%

          \[\leadsto \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 69.7%

      \[\leadsto \color{blue}{\left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}\right) \cdot \frac{x}{y}} \]

   5. Applied egg-rr 72.0%

      \[\leadsto \color{blue}{\frac{\frac{{z}^{y} \cdot \left(\frac{{a}^{t}}{a} \cdot x\right)}{e^{b}}}{y}} \]

   6. Taylor expanded in t around 0 64.0%

      \[\leadsto \frac{\frac{{z}^{y} \cdot \color{blue}{\frac{x}{a}}}{e^{b}}}{y} \]

   7. Taylor expanded in y around 0 52.7%

      \[\leadsto \frac{\frac{\color{blue}{\frac{x}{a}}}{e^{b}}}{y} \]

   8. Taylor expanded in b around 0 33.9%

      \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-213}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]

Alternative 19: 30.9% 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

1. Initial program 98.9%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. associate-*l/ 92.0%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

   2. fma-def 92.0%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

   3. sub-neg 92.0%

      \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

   4. metadata-eval 92.0%

      \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

3. Simplified 92.0%

   \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

4. Taylor expanded in y around 0 78.3%

   \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
5. Step-by-step derivation

   1. associate-/l* 77.9%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\log a \cdot \left(t - 1\right) - b}}}} \]

   2. exp-diff 69.3%

      \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}} \]

   3. exp-prod 69.3%

      \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{\left(e^{\log a}\right)}^{\left(t - 1\right)}}}{e^{b}}}} \]

   4. rem-exp-log 69.6%

      \[\leadsto \frac{x}{\frac{y}{\frac{{\color{blue}{a}}^{\left(t - 1\right)}}{e^{b}}}} \]

   5. sub-neg 69.6%

      \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

   6. metadata-eval 69.6%

      \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

6. Simplified 69.6%

   \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

7. Taylor expanded in t around 0 59.8%

   \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

8. Taylor expanded in b around 0 28.2%

   \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
9. Step-by-step derivation

   1. *-commutative 28.2%

      \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

10. Simplified 28.2%

    \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]

11. Final simplification 28.2%

    \[\leadsto \frac{x}{y \cdot a} \]

Alternative 20: 15.8% accurate, 105.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.9%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. associate-*l/ 92.0%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

   2. fma-def 92.0%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

   3. sub-neg 92.0%

      \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

   4. metadata-eval 92.0%

      \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

3. Simplified 92.0%

   \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

4. Taylor expanded in y around inf 67.8%

   \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z} - b} \]

5. Taylor expanded in y around 0 49.9%

   \[\leadsto \color{blue}{\frac{x \cdot e^{-b}}{y}} \]
6. Step-by-step derivation

   1. associate-*l/ 46.8%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{-b}} \]

   2. *-commutative 46.8%

      \[\leadsto \color{blue}{e^{-b} \cdot \frac{x}{y}} \]

7. Simplified 46.8%

   \[\leadsto \color{blue}{e^{-b} \cdot \frac{x}{y}} \]

8. Taylor expanded in b around 0 15.8%

   \[\leadsto \color{blue}{\frac{x}{y}} \]

9. Final simplification 15.8%

   \[\leadsto \frac{x}{y} \]

Developer target: 71.9% 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 2023297 
(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))