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

Percentage Accurate: 98.3% → 98.3%

Time: 20.7s

Alternatives: 19

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: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Final simplification 99.0%

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

Alternative 2: 93.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -2 \cdot 10^{+42} \lor \neg \left(t + -1 \leq -0.999995\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ t -1.0) -2e+42) (not (<= (+ t -1.0) -0.999995)))
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -2e+42) || !((t + -1.0) <= -0.999995)) {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	} else {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((t + (-1.0d0)) <= (-2d+42)) .or. (.not. ((t + (-1.0d0)) <= (-0.999995d0)))) then
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    else
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -2e+42) || !((t + -1.0) <= -0.999995)) {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	} else {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t + -1.0) <= -2e+42) or not ((t + -1.0) <= -0.999995):
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	else:
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(t + -1.0) <= -2e+42) || !(Float64(t + -1.0) <= -0.999995))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t + -1.0) <= -2e+42) || ~(((t + -1.0) <= -0.999995)))
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	else
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(t + -1.0), $MachinePrecision], -2e+42], N[Not[LessEqual[N[(t + -1.0), $MachinePrecision], -0.999995]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 t 1) < -2.00000000000000009e42 or -0.99999499999999997 < (-.f64 t 1)

   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. Taylor expanded in y around 0 93.7%

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

   if -2.00000000000000009e42 < (-.f64 t 1) < -0.99999499999999997

   1. Initial program 98.1%

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

   2. Taylor expanded in t around 0 97.4%

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

      1. mul-1-neg 97.4%

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

   4. Simplified 97.4%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -2 \cdot 10^{+42} \lor \neg \left(t + -1 \leq -0.999995\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \]

Alternative 3: 82.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{{z}^{y}}{a}\\ t_2 := \frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-46}:\\ \;\;\;\;\frac{x \cdot t_1}{y}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \frac{t_1}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (pow z y) a)) (t_2 (/ (* x (/ (pow a t) a)) y)))
   (if (<= t -2.3e+42)
     t_2
     (if (<= t -2.25e-46)
       (/ (* x t_1) y)
       (if (<= t 6.5e+61) (* x (/ t_1 (* y (exp b)))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(z, y) / a;
	double t_2 = (x * (pow(a, t) / a)) / y;
	double tmp;
	if (t <= -2.3e+42) {
		tmp = t_2;
	} else if (t <= -2.25e-46) {
		tmp = (x * t_1) / y;
	} else if (t <= 6.5e+61) {
		tmp = x * (t_1 / (y * exp(b)));
	} 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 = (z ** y) / a
    t_2 = (x * ((a ** t) / a)) / y
    if (t <= (-2.3d+42)) then
        tmp = t_2
    else if (t <= (-2.25d-46)) then
        tmp = (x * t_1) / y
    else if (t <= 6.5d+61) then
        tmp = x * (t_1 / (y * exp(b)))
    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(z, y) / a;
	double t_2 = (x * (Math.pow(a, t) / a)) / y;
	double tmp;
	if (t <= -2.3e+42) {
		tmp = t_2;
	} else if (t <= -2.25e-46) {
		tmp = (x * t_1) / y;
	} else if (t <= 6.5e+61) {
		tmp = x * (t_1 / (y * Math.exp(b)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(z, y) / a
	t_2 = (x * (math.pow(a, t) / a)) / y
	tmp = 0
	if t <= -2.3e+42:
		tmp = t_2
	elif t <= -2.25e-46:
		tmp = (x * t_1) / y
	elif t <= 6.5e+61:
		tmp = x * (t_1 / (y * math.exp(b)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64((z ^ y) / a)
	t_2 = Float64(Float64(x * Float64((a ^ t) / a)) / y)
	tmp = 0.0
	if (t <= -2.3e+42)
		tmp = t_2;
	elseif (t <= -2.25e-46)
		tmp = Float64(Float64(x * t_1) / y);
	elseif (t <= 6.5e+61)
		tmp = Float64(x * Float64(t_1 / Float64(y * exp(b))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z ^ y) / a;
	t_2 = (x * ((a ^ t) / a)) / y;
	tmp = 0.0;
	if (t <= -2.3e+42)
		tmp = t_2;
	elseif (t <= -2.25e-46)
		tmp = (x * t_1) / y;
	elseif (t <= 6.5e+61)
		tmp = x * (t_1 / (y * exp(b)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -2.3e+42], t$95$2, If[LessEqual[t, -2.25e-46], N[(N[(x * t$95$1), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 6.5e+61], N[(x * N[(t$95$1 / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.3e42 or 6.4999999999999996e61 < 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. Taylor expanded in y around 0 93.6%

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

   3. Taylor expanded in b around 0 86.3%

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

      1. exp-to-pow 86.3%

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

      2. sub-neg 86.3%

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

      3. metadata-eval 86.3%

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

      4. distribute-rgt-in 86.3%

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

      5. mul-1-neg 86.3%

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

      6. sub-neg 86.3%

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

      7. log-pow 86.3%

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

      8. log-div 86.3%

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

      9. rem-exp-log 86.3%

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

   5. Simplified 86.3%

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

   if -2.3e42 < t < -2.25e-46

   1. Initial program 99.4%

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

   2. Taylor expanded in t around 0 96.2%

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

      1. mul-1-neg 96.2%

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

   4. Simplified 96.2%

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

   5. Taylor expanded in b around 0 85.7%

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

      1. div-exp 85.7%

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

      2. *-commutative 85.7%

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

      3. exp-to-pow 85.7%

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

      4. rem-exp-log 86.2%

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

   7. Simplified 86.2%

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

   if -2.25e-46 < t < 6.4999999999999996e61

   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-*r/ 97.0%

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

      2. sub-neg 97.0%

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

      3. exp-sum 84.5%

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

      4. associate-/l* 84.5%

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

      5. associate-/r/ 84.5%

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

      6. exp-neg 84.5%

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

      7. associate-*r/ 84.5%

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

   3. Simplified 82.5%

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

   4. Taylor expanded in t around 0 84.5%

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

      1. associate-/r* 86.2%

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

   6. Simplified 86.2%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+42}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-46}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \end{array} \]

Alternative 4: 87.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+211} \lor \neg \left(y \leq 3.1 \cdot 10^{+26}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.3e+211) (not (<= y 3.1e+26)))
   (/ (* x (/ (pow z y) a)) y)
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.3e+211) || !(y <= 3.1e+26)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.3d+211)) .or. (.not. (y <= 3.1d+26))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.3e+211) || !(y <= 3.1e+26)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.3e+211) or not (y <= 3.1e+26):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.3e+211) || !(y <= 3.1e+26))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.3e+211) || ~((y <= 3.1e+26)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.3e+211], N[Not[LessEqual[y, 3.1e+26]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.30000000000000011e211 or 3.1e26 < 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. Taylor expanded in t around 0 94.8%

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

      1. mul-1-neg 94.8%

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

   4. Simplified 94.8%

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

   5. Taylor expanded in b around 0 89.5%

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

      1. div-exp 89.5%

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

      2. *-commutative 89.5%

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

      3. exp-to-pow 89.5%

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

      4. rem-exp-log 89.5%

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

   7. Simplified 89.5%

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

   if -2.30000000000000011e211 < y < 3.1e26

   1. Initial program 98.4%

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

   2. Taylor expanded in y around 0 90.7%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+211} \lor \neg \left(y \leq 3.1 \cdot 10^{+26}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]

Alternative 5: 73.0% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{{a}^{t}}{a} \cdot \frac{x}{y}\\ t_2 := \frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -13500000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{-213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{-65}:\\ \;\;\;\;\frac{\frac{\frac{x}{a}}{e^{b}}}{y}\\ \mathbf{elif}\;y \leq 58000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (pow a t) a) (/ x y))) (t_2 (/ (* x (/ (pow z y) a)) y)))
   (if (<= y -13500000000.0)
     t_2
     (if (<= y 5.7e-213)
       t_1
       (if (<= y 1.42e-65)
         (/ (/ (/ x a) (exp b)) y)
         (if (<= y 58000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (pow(a, t) / a) * (x / y);
	double t_2 = (x * (pow(z, y) / a)) / y;
	double tmp;
	if (y <= -13500000000.0) {
		tmp = t_2;
	} else if (y <= 5.7e-213) {
		tmp = t_1;
	} else if (y <= 1.42e-65) {
		tmp = ((x / a) / exp(b)) / y;
	} else if (y <= 58000.0) {
		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 = ((a ** t) / a) * (x / y)
    t_2 = (x * ((z ** y) / a)) / y
    if (y <= (-13500000000.0d0)) then
        tmp = t_2
    else if (y <= 5.7d-213) then
        tmp = t_1
    else if (y <= 1.42d-65) then
        tmp = ((x / a) / exp(b)) / y
    else if (y <= 58000.0d0) 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 = (Math.pow(a, t) / a) * (x / y);
	double t_2 = (x * (Math.pow(z, y) / a)) / y;
	double tmp;
	if (y <= -13500000000.0) {
		tmp = t_2;
	} else if (y <= 5.7e-213) {
		tmp = t_1;
	} else if (y <= 1.42e-65) {
		tmp = ((x / a) / Math.exp(b)) / y;
	} else if (y <= 58000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.pow(a, t) / a) * (x / y)
	t_2 = (x * (math.pow(z, y) / a)) / y
	tmp = 0
	if y <= -13500000000.0:
		tmp = t_2
	elif y <= 5.7e-213:
		tmp = t_1
	elif y <= 1.42e-65:
		tmp = ((x / a) / math.exp(b)) / y
	elif y <= 58000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64((a ^ t) / a) * Float64(x / y))
	t_2 = Float64(Float64(x * Float64((z ^ y) / a)) / y)
	tmp = 0.0
	if (y <= -13500000000.0)
		tmp = t_2;
	elseif (y <= 5.7e-213)
		tmp = t_1;
	elseif (y <= 1.42e-65)
		tmp = Float64(Float64(Float64(x / a) / exp(b)) / y);
	elseif (y <= 58000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((a ^ t) / a) * (x / y);
	t_2 = (x * ((z ^ y) / a)) / y;
	tmp = 0.0;
	if (y <= -13500000000.0)
		tmp = t_2;
	elseif (y <= 5.7e-213)
		tmp = t_1;
	elseif (y <= 1.42e-65)
		tmp = ((x / a) / exp(b)) / y;
	elseif (y <= 58000.0)
		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[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -13500000000.0], t$95$2, If[LessEqual[y, 5.7e-213], t$95$1, If[LessEqual[y, 1.42e-65], N[(N[(N[(x / a), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 58000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.35e10 or 58000 < 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. Taylor expanded in t around 0 91.5%

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

      1. mul-1-neg 91.5%

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

   4. Simplified 91.5%

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

   5. Taylor expanded in b around 0 82.3%

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

      1. div-exp 82.3%

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

      2. *-commutative 82.3%

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

      3. exp-to-pow 82.3%

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

      4. rem-exp-log 82.3%

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

   7. Simplified 82.3%

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

   if -1.35e10 < y < 5.69999999999999994e-213 or 1.41999999999999993e-65 < y < 58000

   1. Initial program 97.7%

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

      1. associate-*r/ 97.2%

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

      2. sub-neg 97.2%

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

      3. exp-sum 81.0%

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

      4. associate-/l* 81.0%

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

      5. associate-/r/ 81.0%

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

      6. exp-neg 81.0%

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

      7. associate-*r/ 81.0%

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

   3. Simplified 80.2%

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

   4. Taylor expanded in y around 0 72.9%

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

      1. *-commutative 72.9%

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

      2. associate-*l* 72.9%

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

      3. *-commutative 72.9%

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

      4. times-frac 77.5%

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

   6. Simplified 77.5%

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

   7. Taylor expanded in b around 0 79.6%

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

   if 5.69999999999999994e-213 < y < 1.41999999999999993e-65

   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. Taylor expanded in y around 0 98.2%

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

   3. Taylor expanded in t around 0 83.5%

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

      1. sub-neg 83.5%

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

      2. mul-1-neg 83.5%

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

      3. distribute-neg-in 83.5%

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

      4. +-commutative 83.5%

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

      5. exp-neg 83.5%

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

      6. associate-*l/ 83.5%

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

      7. *-lft-identity 83.5%

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

      8. +-commutative 83.5%

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

      9. exp-sum 83.5%

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

      10. rem-exp-log 85.0%

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

      11. associate-/r* 85.0%

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

   5. Simplified 85.0%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -13500000000:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{-213}:\\ \;\;\;\;\frac{{a}^{t}}{a} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{-65}:\\ \;\;\;\;\frac{\frac{\frac{x}{a}}{e^{b}}}{y}\\ \mathbf{elif}\;y \leq 58000:\\ \;\;\;\;\frac{{a}^{t}}{a} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \end{array} \]

Alternative 6: 75.1% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ t_2 := \frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.05 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-120}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (/ (pow z y) a)) y)) (t_2 (/ (* x (/ (pow a t) a)) y)))
   (if (<= t -3.7e+42)
     t_2
     (if (<= t -3.05e-46)
       t_1
       (if (<= t -9.6e-120)
         (/ x (* y (* a (exp b))))
         (if (<= t 8e+53) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * (pow(z, y) / a)) / y;
	double t_2 = (x * (pow(a, t) / a)) / y;
	double tmp;
	if (t <= -3.7e+42) {
		tmp = t_2;
	} else if (t <= -3.05e-46) {
		tmp = t_1;
	} else if (t <= -9.6e-120) {
		tmp = x / (y * (a * exp(b)));
	} else if (t <= 8e+53) {
		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 * ((z ** y) / a)) / y
    t_2 = (x * ((a ** t) / a)) / y
    if (t <= (-3.7d+42)) then
        tmp = t_2
    else if (t <= (-3.05d-46)) then
        tmp = t_1
    else if (t <= (-9.6d-120)) then
        tmp = x / (y * (a * exp(b)))
    else if (t <= 8d+53) 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.pow(z, y) / a)) / y;
	double t_2 = (x * (Math.pow(a, t) / a)) / y;
	double tmp;
	if (t <= -3.7e+42) {
		tmp = t_2;
	} else if (t <= -3.05e-46) {
		tmp = t_1;
	} else if (t <= -9.6e-120) {
		tmp = x / (y * (a * Math.exp(b)));
	} else if (t <= 8e+53) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * (math.pow(z, y) / a)) / y
	t_2 = (x * (math.pow(a, t) / a)) / y
	tmp = 0
	if t <= -3.7e+42:
		tmp = t_2
	elif t <= -3.05e-46:
		tmp = t_1
	elif t <= -9.6e-120:
		tmp = x / (y * (a * math.exp(b)))
	elif t <= 8e+53:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64((z ^ y) / a)) / y)
	t_2 = Float64(Float64(x * Float64((a ^ t) / a)) / y)
	tmp = 0.0
	if (t <= -3.7e+42)
		tmp = t_2;
	elseif (t <= -3.05e-46)
		tmp = t_1;
	elseif (t <= -9.6e-120)
		tmp = Float64(x / Float64(y * Float64(a * exp(b))));
	elseif (t <= 8e+53)
		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 * ((z ^ y) / a)) / y;
	t_2 = (x * ((a ^ t) / a)) / y;
	tmp = 0.0;
	if (t <= -3.7e+42)
		tmp = t_2;
	elseif (t <= -3.05e-46)
		tmp = t_1;
	elseif (t <= -9.6e-120)
		tmp = x / (y * (a * exp(b)));
	elseif (t <= 8e+53)
		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[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -3.7e+42], t$95$2, If[LessEqual[t, -3.05e-46], t$95$1, If[LessEqual[t, -9.6e-120], N[(x / N[(y * N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+53], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.69999999999999996e42 or 7.9999999999999999e53 < 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. Taylor expanded in y around 0 93.7%

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

   3. Taylor expanded in b around 0 85.7%

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

      1. exp-to-pow 85.7%

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

      2. sub-neg 85.7%

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

      3. metadata-eval 85.7%

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

      4. distribute-rgt-in 85.7%

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

      5. mul-1-neg 85.7%

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

      6. sub-neg 85.7%

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

      7. log-pow 85.7%

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

      8. log-div 85.7%

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

      9. rem-exp-log 85.7%

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

   5. Simplified 85.7%

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

   if -3.69999999999999996e42 < t < -3.05000000000000018e-46 or -9.5999999999999998e-120 < t < 7.9999999999999999e53

   1. Initial program 98.8%

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

   2. Taylor expanded in t around 0 95.3%

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

      1. mul-1-neg 95.3%

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

   4. Simplified 95.3%

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

   5. Taylor expanded in b around 0 82.1%

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

      1. div-exp 82.1%

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

      2. *-commutative 82.1%

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

      3. exp-to-pow 82.1%

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

      4. rem-exp-log 83.1%

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

   7. Simplified 83.1%

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

   if -3.05000000000000018e-46 < t < -9.5999999999999998e-120

   1. Initial program 94.8%

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

      1. associate-*r/ 97.3%

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

      2. sub-neg 97.3%

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

      3. exp-sum 80.6%

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

      4. associate-/l* 80.6%

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

      5. associate-/r/ 80.6%

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

      6. exp-neg 80.6%

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

      7. associate-*r/ 80.6%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in t around 0 77.6%

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

      1. associate-/r* 83.2%

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

   6. Simplified 83.2%

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

   7. Taylor expanded in y around 0 88.9%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+42}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{elif}\;t \leq -3.05 \cdot 10^{-46}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-120}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+53}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \end{array} \]

Alternative 7: 71.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+83} \lor \neg \left(b \leq 3.3 \cdot 10^{+83}\right):\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{t}}{a} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -7e+83) (not (<= b 3.3e+83)))
   (/ x (* y (* a (exp b))))
   (* (/ (pow a t) a) (/ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7e+83) || !(b <= 3.3e+83)) {
		tmp = x / (y * (a * exp(b)));
	} else {
		tmp = (pow(a, t) / a) * (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-7d+83)) .or. (.not. (b <= 3.3d+83))) then
        tmp = x / (y * (a * exp(b)))
    else
        tmp = ((a ** t) / a) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7e+83) || !(b <= 3.3e+83)) {
		tmp = x / (y * (a * Math.exp(b)));
	} else {
		tmp = (Math.pow(a, t) / a) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -7e+83) or not (b <= 3.3e+83):
		tmp = x / (y * (a * math.exp(b)))
	else:
		tmp = (math.pow(a, t) / a) * (x / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -7e+83) || !(b <= 3.3e+83))
		tmp = Float64(x / Float64(y * Float64(a * exp(b))));
	else
		tmp = Float64(Float64((a ^ t) / a) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -7e+83) || ~((b <= 3.3e+83)))
		tmp = x / (y * (a * exp(b)));
	else
		tmp = ((a ^ t) / a) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -7e+83], N[Not[LessEqual[b, 3.3e+83]], $MachinePrecision]], N[(x / N[(y * N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.99999999999999954e83 or 3.29999999999999985e83 < 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-*r/ 100.0%

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

      2. sub-neg 100.0%

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

      3. exp-sum 67.4%

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

      4. associate-/l* 67.4%

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

      5. associate-/r/ 67.4%

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

      6. exp-neg 67.4%

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

      7. associate-*r/ 67.4%

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

   3. Simplified 52.3%

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

   4. Taylor expanded in t around 0 72.2%

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

      1. associate-/r* 72.2%

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

   6. Simplified 72.2%

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

   7. Taylor expanded in y around 0 87.4%

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

   if -6.99999999999999954e83 < b < 3.29999999999999985e83

   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-*r/ 97.8%

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

      2. sub-neg 97.8%

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

      3. exp-sum 86.0%

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

      4. associate-/l* 86.0%

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

      5. associate-/r/ 86.0%

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

      6. exp-neg 86.0%

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

      7. associate-*r/ 86.0%

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

   3. Simplified 75.9%

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

   4. Taylor expanded in y around 0 63.4%

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

      1. *-commutative 63.4%

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

      2. associate-*l* 63.4%

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

      3. *-commutative 63.4%

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

      4. times-frac 65.3%

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

   6. Simplified 65.3%

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

   7. Taylor expanded in b around 0 68.1%

      \[\leadsto \frac{{a}^{t}}{a} \cdot \color{blue}{\frac{x}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+83} \lor \neg \left(b \leq 3.3 \cdot 10^{+83}\right):\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{t}}{a} \cdot \frac{x}{y}\\ \end{array} \]

Alternative 8: 60.2% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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-*r/ 98.5%

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

   2. sub-neg 98.5%

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

   3. exp-sum 79.8%

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

   4. associate-/l* 79.8%

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

   5. associate-/r/ 79.8%

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

   6. exp-neg 79.8%

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

   7. associate-*r/ 79.8%

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

3. Simplified 68.0%

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

4. Taylor expanded in t around 0 65.4%

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

   1. associate-/r* 67.7%

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

6. Simplified 67.7%

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

7. Taylor expanded in y around 0 57.8%

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

8. Final simplification 57.8%

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

Alternative 9: 39.6% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{a}}{y}\\ \mathbf{if}\;b \leq -3.7 \cdot 10^{+126}:\\ \;\;\;\;\frac{b}{y} \cdot \left(-\frac{x}{a}\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+68}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x a) y)))
   (if (<= b -3.7e+126)
     (* (/ b y) (- (/ x a)))
     (if (<= b 8e-95)
       t_1
       (if (<= b 7e+68)
         (/ 1.0 (* a (/ y x)))
         (if (<= b 5.2e+69) t_1 (/ x (* a (* y b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) / y;
	double tmp;
	if (b <= -3.7e+126) {
		tmp = (b / y) * -(x / a);
	} else if (b <= 8e-95) {
		tmp = t_1;
	} else if (b <= 7e+68) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= 5.2e+69) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / a) / y
    if (b <= (-3.7d+126)) then
        tmp = (b / y) * -(x / a)
    else if (b <= 8d-95) then
        tmp = t_1
    else if (b <= 7d+68) then
        tmp = 1.0d0 / (a * (y / x))
    else if (b <= 5.2d+69) then
        tmp = t_1
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) / y;
	double tmp;
	if (b <= -3.7e+126) {
		tmp = (b / y) * -(x / a);
	} else if (b <= 8e-95) {
		tmp = t_1;
	} else if (b <= 7e+68) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= 5.2e+69) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / a) / y
	tmp = 0
	if b <= -3.7e+126:
		tmp = (b / y) * -(x / a)
	elif b <= 8e-95:
		tmp = t_1
	elif b <= 7e+68:
		tmp = 1.0 / (a * (y / x))
	elif b <= 5.2e+69:
		tmp = t_1
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / a) / y)
	tmp = 0.0
	if (b <= -3.7e+126)
		tmp = Float64(Float64(b / y) * Float64(-Float64(x / a)));
	elseif (b <= 8e-95)
		tmp = t_1;
	elseif (b <= 7e+68)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	elseif (b <= 5.2e+69)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / a) / y;
	tmp = 0.0;
	if (b <= -3.7e+126)
		tmp = (b / y) * -(x / a);
	elseif (b <= 8e-95)
		tmp = t_1;
	elseif (b <= 7e+68)
		tmp = 1.0 / (a * (y / x));
	elseif (b <= 5.2e+69)
		tmp = t_1;
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -3.7e+126], N[(N[(b / y), $MachinePrecision] * (-N[(x / a), $MachinePrecision])), $MachinePrecision], If[LessEqual[b, 8e-95], t$95$1, If[LessEqual[b, 7e+68], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.2e+69], t$95$1, N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.6999999999999998e126

   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. Taylor expanded in y around 0 100.0%

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

   3. Taylor expanded in t around 0 94.4%

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

      1. sub-neg 94.4%

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

      2. mul-1-neg 94.4%

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

      3. distribute-neg-in 94.4%

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

      4. +-commutative 94.4%

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

      5. exp-neg 94.4%

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

      6. associate-*l/ 94.4%

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

      7. *-lft-identity 94.4%

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

      8. +-commutative 94.4%

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

      9. exp-sum 94.4%

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

      10. rem-exp-log 94.4%

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

      11. associate-/r* 91.5%

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

   5. Simplified 91.5%

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

   6. Taylor expanded in b around 0 55.9%

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

      1. +-commutative 55.9%

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

      2. mul-1-neg 55.9%

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

      3. unsub-neg 55.9%

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

      4. associate-/l* 45.3%

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

   8. Simplified 45.3%

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

   9. Taylor expanded in b around inf 50.4%

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

       1. mul-1-neg 50.4%

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

       2. times-frac 45.2%

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

   11. Simplified 45.2%

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

   if -3.6999999999999998e126 < b < 7.99999999999999992e-95 or 6.99999999999999955e68 < b < 5.2000000000000004e69

   1. Initial program 98.8%

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

   2. Taylor expanded in t around 0 71.7%

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

      1. mul-1-neg 71.7%

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

   4. Simplified 71.7%

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

   5. Taylor expanded in b around 0 70.3%

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

      1. div-exp 70.4%

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

      2. *-commutative 70.4%

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

      3. exp-to-pow 70.4%

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

      4. rem-exp-log 71.4%

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

   7. Simplified 71.4%

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

   8. Taylor expanded in y around 0 36.5%

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

      1. *-commutative 36.5%

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

      2. associate-/r* 38.5%

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

   10. Simplified 38.5%

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

   if 7.99999999999999992e-95 < b < 6.99999999999999955e68

   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-*r/ 96.8%

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

      2. sub-neg 96.8%

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

      3. exp-sum 77.9%

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

      4. associate-/l* 77.9%

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

      5. associate-/r/ 77.9%

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

      6. exp-neg 77.9%

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

      7. associate-*r/ 77.9%

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

   3. Simplified 70.5%

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

   4. Taylor expanded in t around 0 62.9%

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

      1. associate-/r* 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in b around 0 64.4%

      \[\leadsto \color{blue}{\frac{{z}^{y} \cdot x}{a \cdot y}} \]
   8. Step-by-step derivation

      1. times-frac 77.5%

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

   9. Simplified 77.5%

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

   10. Taylor expanded in y around 0 48.6%

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

       1. *-commutative 48.6%

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

       2. clear-num 48.5%

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

       3. frac-times 48.6%

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

       4. metadata-eval 48.6%

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

   12. Applied egg-rr 48.6%

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

   if 5.2000000000000004e69 < 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-*r/ 100.0%

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

      2. sub-neg 100.0%

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

      3. exp-sum 62.5%

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

      4. associate-/l* 62.5%

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

      5. associate-/r/ 62.5%

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

      6. exp-neg 62.5%

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

      7. associate-*r/ 62.5%

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

   3. Simplified 54.2%

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

   4. Taylor expanded in t around 0 71.0%

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

      1. associate-/r* 71.0%

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

   6. Simplified 71.0%

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

   7. Taylor expanded in y around 0 77.4%

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

   8. Taylor expanded in b around 0 46.5%

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

   9. Taylor expanded in b around inf 52.3%

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

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{+126}:\\ \;\;\;\;\frac{b}{y} \cdot \left(-\frac{x}{a}\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-95}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+68}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+69}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]

Alternative 10: 39.6% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{a}}{y}\\ \mathbf{if}\;b \leq -1.05 \cdot 10^{+83}:\\ \;\;\;\;\frac{b \cdot \left(-\frac{x}{a}\right)}{y}\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+68}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq 2.65 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x a) y)))
   (if (<= b -1.05e+83)
     (/ (* b (- (/ x a))) y)
     (if (<= b 1.45e-94)
       t_1
       (if (<= b 6.2e+68)
         (/ 1.0 (* a (/ y x)))
         (if (<= b 2.65e+69) t_1 (/ x (* a (* y b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) / y;
	double tmp;
	if (b <= -1.05e+83) {
		tmp = (b * -(x / a)) / y;
	} else if (b <= 1.45e-94) {
		tmp = t_1;
	} else if (b <= 6.2e+68) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= 2.65e+69) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / a) / y
    if (b <= (-1.05d+83)) then
        tmp = (b * -(x / a)) / y
    else if (b <= 1.45d-94) then
        tmp = t_1
    else if (b <= 6.2d+68) then
        tmp = 1.0d0 / (a * (y / x))
    else if (b <= 2.65d+69) then
        tmp = t_1
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) / y;
	double tmp;
	if (b <= -1.05e+83) {
		tmp = (b * -(x / a)) / y;
	} else if (b <= 1.45e-94) {
		tmp = t_1;
	} else if (b <= 6.2e+68) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= 2.65e+69) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / a) / y
	tmp = 0
	if b <= -1.05e+83:
		tmp = (b * -(x / a)) / y
	elif b <= 1.45e-94:
		tmp = t_1
	elif b <= 6.2e+68:
		tmp = 1.0 / (a * (y / x))
	elif b <= 2.65e+69:
		tmp = t_1
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / a) / y)
	tmp = 0.0
	if (b <= -1.05e+83)
		tmp = Float64(Float64(b * Float64(-Float64(x / a))) / y);
	elseif (b <= 1.45e-94)
		tmp = t_1;
	elseif (b <= 6.2e+68)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	elseif (b <= 2.65e+69)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / a) / y;
	tmp = 0.0;
	if (b <= -1.05e+83)
		tmp = (b * -(x / a)) / y;
	elseif (b <= 1.45e-94)
		tmp = t_1;
	elseif (b <= 6.2e+68)
		tmp = 1.0 / (a * (y / x));
	elseif (b <= 2.65e+69)
		tmp = t_1;
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -1.05e+83], N[(N[(b * (-N[(x / a), $MachinePrecision])), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 1.45e-94], t$95$1, If[LessEqual[b, 6.2e+68], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.65e+69], t$95$1, N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.05000000000000001e83

   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. Taylor expanded in y around 0 95.7%

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

   3. Taylor expanded in t around 0 91.4%

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

      1. sub-neg 91.4%

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

      2. mul-1-neg 91.4%

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

      3. distribute-neg-in 91.4%

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

      4. +-commutative 91.4%

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

      5. exp-neg 91.4%

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

      6. associate-*l/ 91.4%

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

      7. *-lft-identity 91.4%

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

      8. +-commutative 91.4%

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

      9. exp-sum 91.4%

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

      10. rem-exp-log 91.4%

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

      11. associate-/r* 84.9%

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

   5. Simplified 84.9%

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

   6. Taylor expanded in b around 0 48.3%

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

      1. +-commutative 48.3%

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

      2. mul-1-neg 48.3%

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

      3. unsub-neg 48.3%

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

      4. associate-/l* 40.2%

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

   8. Simplified 40.2%

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

   9. Taylor expanded in b around inf 48.3%

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

       1. mul-1-neg 48.3%

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

       2. associate-*r/ 40.2%

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

       3. distribute-lft-neg-out 40.2%

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

       4. *-commutative 40.2%

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

   11. Simplified 40.2%

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

   if -1.05000000000000001e83 < b < 1.44999999999999998e-94 or 6.1999999999999997e68 < b < 2.65e69

   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. Taylor expanded in t around 0 70.8%

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

      1. mul-1-neg 70.8%

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

   4. Simplified 70.8%

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

   5. Taylor expanded in b around 0 70.1%

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

      1. div-exp 70.1%

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

      2. *-commutative 70.1%

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

      3. exp-to-pow 70.1%

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

      4. rem-exp-log 71.2%

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

   7. Simplified 71.2%

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

   8. Taylor expanded in y around 0 37.9%

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

      1. *-commutative 37.9%

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

      2. associate-/r* 40.2%

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

   10. Simplified 40.2%

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

   if 1.44999999999999998e-94 < b < 6.1999999999999997e68

   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-*r/ 96.8%

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

      2. sub-neg 96.8%

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

      3. exp-sum 77.9%

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

      4. associate-/l* 77.9%

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

      5. associate-/r/ 77.9%

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

      6. exp-neg 77.9%

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

      7. associate-*r/ 77.9%

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

   3. Simplified 70.5%

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

   4. Taylor expanded in t around 0 62.9%

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

      1. associate-/r* 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in b around 0 64.4%

      \[\leadsto \color{blue}{\frac{{z}^{y} \cdot x}{a \cdot y}} \]
   8. Step-by-step derivation

      1. times-frac 77.5%

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

   9. Simplified 77.5%

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

   10. Taylor expanded in y around 0 48.6%

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

       1. *-commutative 48.6%

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

       2. clear-num 48.5%

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

       3. frac-times 48.6%

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

       4. metadata-eval 48.6%

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

   12. Applied egg-rr 48.6%

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

   if 2.65e69 < 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-*r/ 100.0%

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

      2. sub-neg 100.0%

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

      3. exp-sum 62.5%

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

      4. associate-/l* 62.5%

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

      5. associate-/r/ 62.5%

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

      6. exp-neg 62.5%

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

      7. associate-*r/ 62.5%

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

   3. Simplified 54.2%

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

   4. Taylor expanded in t around 0 71.0%

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

      1. associate-/r* 71.0%

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

   6. Simplified 71.0%

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

   7. Taylor expanded in y around 0 77.4%

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

   8. Taylor expanded in b around 0 46.5%

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

   9. Taylor expanded in b around inf 52.3%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+83}:\\ \;\;\;\;\frac{b \cdot \left(-\frac{x}{a}\right)}{y}\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-94}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+68}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq 2.65 \cdot 10^{+69}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]

Alternative 11: 39.9% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{a}}{y}\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{+71}:\\ \;\;\;\;\frac{-x \cdot b}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+67}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x a) y)))
   (if (<= b -1.25e+71)
     (/ (- (* x b)) (* y a))
     (if (<= b 1.06e-94)
       t_1
       (if (<= b 5e+67)
         (/ 1.0 (* a (/ y x)))
         (if (<= b 2.8e+69) t_1 (/ x (* a (* y b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) / y;
	double tmp;
	if (b <= -1.25e+71) {
		tmp = -(x * b) / (y * a);
	} else if (b <= 1.06e-94) {
		tmp = t_1;
	} else if (b <= 5e+67) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= 2.8e+69) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / a) / y
    if (b <= (-1.25d+71)) then
        tmp = -(x * b) / (y * a)
    else if (b <= 1.06d-94) then
        tmp = t_1
    else if (b <= 5d+67) then
        tmp = 1.0d0 / (a * (y / x))
    else if (b <= 2.8d+69) then
        tmp = t_1
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) / y;
	double tmp;
	if (b <= -1.25e+71) {
		tmp = -(x * b) / (y * a);
	} else if (b <= 1.06e-94) {
		tmp = t_1;
	} else if (b <= 5e+67) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= 2.8e+69) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / a) / y
	tmp = 0
	if b <= -1.25e+71:
		tmp = -(x * b) / (y * a)
	elif b <= 1.06e-94:
		tmp = t_1
	elif b <= 5e+67:
		tmp = 1.0 / (a * (y / x))
	elif b <= 2.8e+69:
		tmp = t_1
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / a) / y)
	tmp = 0.0
	if (b <= -1.25e+71)
		tmp = Float64(Float64(-Float64(x * b)) / Float64(y * a));
	elseif (b <= 1.06e-94)
		tmp = t_1;
	elseif (b <= 5e+67)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	elseif (b <= 2.8e+69)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / a) / y;
	tmp = 0.0;
	if (b <= -1.25e+71)
		tmp = -(x * b) / (y * a);
	elseif (b <= 1.06e-94)
		tmp = t_1;
	elseif (b <= 5e+67)
		tmp = 1.0 / (a * (y / x));
	elseif (b <= 2.8e+69)
		tmp = t_1;
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -1.25e+71], N[((-N[(x * b), $MachinePrecision]) / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.06e-94], t$95$1, If[LessEqual[b, 5e+67], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.8e+69], t$95$1, N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.24999999999999993e71

   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. Taylor expanded in y around 0 93.8%

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

   3. Taylor expanded in t around 0 89.7%

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

      1. sub-neg 89.7%

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

      2. mul-1-neg 89.7%

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

      3. distribute-neg-in 89.7%

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

      4. +-commutative 89.7%

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

      5. exp-neg 89.7%

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

      6. associate-*l/ 89.7%

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

      7. *-lft-identity 89.7%

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

      8. +-commutative 89.7%

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

      9. exp-sum 89.7%

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

      10. rem-exp-log 89.7%

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

      11. associate-/r* 83.5%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in b around 0 46.6%

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

      1. +-commutative 46.6%

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

      2. mul-1-neg 46.6%

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

      3. unsub-neg 46.6%

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

      4. associate-/l* 38.8%

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

   8. Simplified 38.8%

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

   9. Taylor expanded in b around inf 47.5%

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

   if -1.24999999999999993e71 < b < 1.06e-94 or 4.99999999999999976e67 < b < 2.79999999999999982e69

   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. Taylor expanded in t around 0 70.3%

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

      1. mul-1-neg 70.3%

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

   4. Simplified 70.3%

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

   5. Taylor expanded in b around 0 70.4%

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

      1. div-exp 70.4%

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

      2. *-commutative 70.4%

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

      3. exp-to-pow 70.4%

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

      4. rem-exp-log 71.5%

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

   7. Simplified 71.5%

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

   8. Taylor expanded in y around 0 36.9%

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

      1. *-commutative 36.9%

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

      2. associate-/r* 40.0%

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

   10. Simplified 40.0%

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

   if 1.06e-94 < b < 4.99999999999999976e67

   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-*r/ 96.8%

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

      2. sub-neg 96.8%

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

      3. exp-sum 77.9%

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

      4. associate-/l* 77.9%

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

      5. associate-/r/ 77.9%

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

      6. exp-neg 77.9%

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

      7. associate-*r/ 77.9%

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

   3. Simplified 70.5%

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

   4. Taylor expanded in t around 0 62.9%

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

      1. associate-/r* 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in b around 0 64.4%

      \[\leadsto \color{blue}{\frac{{z}^{y} \cdot x}{a \cdot y}} \]
   8. Step-by-step derivation

      1. times-frac 77.5%

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

   9. Simplified 77.5%

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

   10. Taylor expanded in y around 0 48.6%

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

       1. *-commutative 48.6%

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

       2. clear-num 48.5%

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

       3. frac-times 48.6%

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

       4. metadata-eval 48.6%

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

   12. Applied egg-rr 48.6%

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

   if 2.79999999999999982e69 < 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-*r/ 100.0%

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

      2. sub-neg 100.0%

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

      3. exp-sum 62.5%

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

      4. associate-/l* 62.5%

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

      5. associate-/r/ 62.5%

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

      6. exp-neg 62.5%

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

      7. associate-*r/ 62.5%

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

   3. Simplified 54.2%

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

   4. Taylor expanded in t around 0 71.0%

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

      1. associate-/r* 71.0%

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

   6. Simplified 71.0%

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

   7. Taylor expanded in y around 0 77.4%

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

   8. Taylor expanded in b around 0 46.5%

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

   9. Taylor expanded in b around inf 52.3%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+71}:\\ \;\;\;\;\frac{-x \cdot b}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{-94}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+67}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+69}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]

Alternative 12: 40.4% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{a}}{y}\\ \mathbf{if}\;b \leq -1.75 \cdot 10^{+82}:\\ \;\;\;\;\frac{\frac{-x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+67}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x a) y)))
   (if (<= b -1.75e+82)
     (/ (/ (- (* x b)) a) y)
     (if (<= b 7e-95)
       t_1
       (if (<= b 7.5e+67)
         (/ 1.0 (* a (/ y x)))
         (if (<= b 2.35e+69) t_1 (/ x (* a (* y b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) / y;
	double tmp;
	if (b <= -1.75e+82) {
		tmp = (-(x * b) / a) / y;
	} else if (b <= 7e-95) {
		tmp = t_1;
	} else if (b <= 7.5e+67) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= 2.35e+69) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / a) / y
    if (b <= (-1.75d+82)) then
        tmp = (-(x * b) / a) / y
    else if (b <= 7d-95) then
        tmp = t_1
    else if (b <= 7.5d+67) then
        tmp = 1.0d0 / (a * (y / x))
    else if (b <= 2.35d+69) then
        tmp = t_1
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) / y;
	double tmp;
	if (b <= -1.75e+82) {
		tmp = (-(x * b) / a) / y;
	} else if (b <= 7e-95) {
		tmp = t_1;
	} else if (b <= 7.5e+67) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= 2.35e+69) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / a) / y
	tmp = 0
	if b <= -1.75e+82:
		tmp = (-(x * b) / a) / y
	elif b <= 7e-95:
		tmp = t_1
	elif b <= 7.5e+67:
		tmp = 1.0 / (a * (y / x))
	elif b <= 2.35e+69:
		tmp = t_1
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / a) / y)
	tmp = 0.0
	if (b <= -1.75e+82)
		tmp = Float64(Float64(Float64(-Float64(x * b)) / a) / y);
	elseif (b <= 7e-95)
		tmp = t_1;
	elseif (b <= 7.5e+67)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	elseif (b <= 2.35e+69)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / a) / y;
	tmp = 0.0;
	if (b <= -1.75e+82)
		tmp = (-(x * b) / a) / y;
	elseif (b <= 7e-95)
		tmp = t_1;
	elseif (b <= 7.5e+67)
		tmp = 1.0 / (a * (y / x));
	elseif (b <= 2.35e+69)
		tmp = t_1;
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -1.75e+82], N[(N[((-N[(x * b), $MachinePrecision]) / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 7e-95], t$95$1, If[LessEqual[b, 7.5e+67], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.35e+69], t$95$1, N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.75e82

   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. Taylor expanded in y around 0 95.7%

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

   3. Taylor expanded in t around 0 91.4%

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

      1. sub-neg 91.4%

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

      2. mul-1-neg 91.4%

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

      3. distribute-neg-in 91.4%

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

      4. +-commutative 91.4%

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

      5. exp-neg 91.4%

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

      6. associate-*l/ 91.4%

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

      7. *-lft-identity 91.4%

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

      8. +-commutative 91.4%

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

      9. exp-sum 91.4%

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

      10. rem-exp-log 91.4%

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

      11. associate-/r* 84.9%

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

   5. Simplified 84.9%

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

   6. Taylor expanded in b around 0 48.3%

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

      1. +-commutative 48.3%

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

      2. mul-1-neg 48.3%

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

      3. unsub-neg 48.3%

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

      4. associate-/l* 40.2%

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

   8. Simplified 40.2%

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

   9. Taylor expanded in b around inf 48.3%

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

   if -1.75e82 < b < 6.9999999999999994e-95 or 7.5000000000000005e67 < b < 2.34999999999999998e69

   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. Taylor expanded in t around 0 70.8%

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

      1. mul-1-neg 70.8%

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

   4. Simplified 70.8%

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

   5. Taylor expanded in b around 0 70.1%

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

      1. div-exp 70.1%

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

      2. *-commutative 70.1%

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

      3. exp-to-pow 70.1%

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

      4. rem-exp-log 71.2%

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

   7. Simplified 71.2%

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

   8. Taylor expanded in y around 0 37.9%

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

      1. *-commutative 37.9%

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

      2. associate-/r* 40.2%

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

   10. Simplified 40.2%

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

   if 6.9999999999999994e-95 < b < 7.5000000000000005e67

   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-*r/ 96.8%

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

      2. sub-neg 96.8%

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

      3. exp-sum 77.9%

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

      4. associate-/l* 77.9%

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

      5. associate-/r/ 77.9%

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

      6. exp-neg 77.9%

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

      7. associate-*r/ 77.9%

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

   3. Simplified 70.5%

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

   4. Taylor expanded in t around 0 62.9%

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

      1. associate-/r* 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in b around 0 64.4%

      \[\leadsto \color{blue}{\frac{{z}^{y} \cdot x}{a \cdot y}} \]
   8. Step-by-step derivation

      1. times-frac 77.5%

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

   9. Simplified 77.5%

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

   10. Taylor expanded in y around 0 48.6%

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

       1. *-commutative 48.6%

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

       2. clear-num 48.5%

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

       3. frac-times 48.6%

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

       4. metadata-eval 48.6%

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

   12. Applied egg-rr 48.6%

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

   if 2.34999999999999998e69 < 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-*r/ 100.0%

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

      2. sub-neg 100.0%

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

      3. exp-sum 62.5%

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

      4. associate-/l* 62.5%

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

      5. associate-/r/ 62.5%

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

      6. exp-neg 62.5%

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

      7. associate-*r/ 62.5%

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

   3. Simplified 54.2%

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

   4. Taylor expanded in t around 0 71.0%

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

      1. associate-/r* 71.0%

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

   6. Simplified 71.0%

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

   7. Taylor expanded in y around 0 77.4%

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

   8. Taylor expanded in b around 0 46.5%

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

   9. Taylor expanded in b around inf 52.3%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+82}:\\ \;\;\;\;\frac{\frac{-x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-95}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+67}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{+69}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]

Alternative 13: 36.3% accurate, 23.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{a}}{y}\\ \mathbf{if}\;b \leq 7.4 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+68}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x a) y)))
   (if (<= b 7.4e-95)
     t_1
     (if (<= b 2e+68)
       (/ 1.0 (* a (/ y x)))
       (if (<= b 2.35e+69) t_1 (/ x (* a (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) / y;
	double tmp;
	if (b <= 7.4e-95) {
		tmp = t_1;
	} else if (b <= 2e+68) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= 2.35e+69) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / a) / y
    if (b <= 7.4d-95) then
        tmp = t_1
    else if (b <= 2d+68) then
        tmp = 1.0d0 / (a * (y / x))
    else if (b <= 2.35d+69) then
        tmp = t_1
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) / y;
	double tmp;
	if (b <= 7.4e-95) {
		tmp = t_1;
	} else if (b <= 2e+68) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= 2.35e+69) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / a) / y
	tmp = 0
	if b <= 7.4e-95:
		tmp = t_1
	elif b <= 2e+68:
		tmp = 1.0 / (a * (y / x))
	elif b <= 2.35e+69:
		tmp = t_1
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / a) / y)
	tmp = 0.0
	if (b <= 7.4e-95)
		tmp = t_1;
	elseif (b <= 2e+68)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	elseif (b <= 2.35e+69)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / a) / y;
	tmp = 0.0;
	if (b <= 7.4e-95)
		tmp = t_1;
	elseif (b <= 2e+68)
		tmp = 1.0 / (a * (y / x));
	elseif (b <= 2.35e+69)
		tmp = t_1;
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, 7.4e-95], t$95$1, If[LessEqual[b, 2e+68], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.35e+69], t$95$1, N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < 7.39999999999999989e-95 or 1.99999999999999991e68 < b < 2.34999999999999998e69

   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. Taylor expanded in t around 0 76.4%

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

      1. mul-1-neg 76.4%

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

   4. Simplified 76.4%

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

   5. Taylor expanded in b around 0 64.4%

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

      1. div-exp 64.5%

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

      2. *-commutative 64.5%

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

      3. exp-to-pow 64.5%

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

      4. rem-exp-log 65.3%

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

   7. Simplified 65.3%

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

   8. Taylor expanded in y around 0 34.7%

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

      1. *-commutative 34.7%

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

      2. associate-/r* 35.8%

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

   10. Simplified 35.8%

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

   if 7.39999999999999989e-95 < b < 1.99999999999999991e68

   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-*r/ 96.8%

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

      2. sub-neg 96.8%

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

      3. exp-sum 77.9%

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

      4. associate-/l* 77.9%

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

      5. associate-/r/ 77.9%

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

      6. exp-neg 77.9%

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

      7. associate-*r/ 77.9%

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

   3. Simplified 70.5%

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

   4. Taylor expanded in t around 0 62.9%

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

      1. associate-/r* 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in b around 0 64.4%

      \[\leadsto \color{blue}{\frac{{z}^{y} \cdot x}{a \cdot y}} \]
   8. Step-by-step derivation

      1. times-frac 77.5%

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

   9. Simplified 77.5%

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

   10. Taylor expanded in y around 0 48.6%

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

       1. *-commutative 48.6%

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

       2. clear-num 48.5%

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

       3. frac-times 48.6%

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

       4. metadata-eval 48.6%

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

   12. Applied egg-rr 48.6%

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

   if 2.34999999999999998e69 < 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-*r/ 100.0%

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

      2. sub-neg 100.0%

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

      3. exp-sum 62.5%

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

      4. associate-/l* 62.5%

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

      5. associate-/r/ 62.5%

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

      6. exp-neg 62.5%

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

      7. associate-*r/ 62.5%

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

   3. Simplified 54.2%

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

   4. Taylor expanded in t around 0 71.0%

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

      1. associate-/r* 71.0%

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

   6. Simplified 71.0%

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

   7. Taylor expanded in y around 0 77.4%

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

   8. Taylor expanded in b around 0 46.5%

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

   9. Taylor expanded in b around inf 52.3%

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

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 7.4 \cdot 10^{-95}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+68}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{+69}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]

Alternative 14: 40.5% accurate, 24.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 8 \cdot 10^{-95}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+69}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 8e-95)
   (/ (- (/ x a) (/ (* x b) a)) y)
   (if (<= b 5.6e+69) (/ 1.0 (* a (/ y x))) (/ x (* a (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 8e-95) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= 5.6e+69) {
		tmp = 1.0 / (a * (y / x));
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 8d-95) then
        tmp = ((x / a) - ((x * b) / a)) / y
    else if (b <= 5.6d+69) then
        tmp = 1.0d0 / (a * (y / x))
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 8e-95) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= 5.6e+69) {
		tmp = 1.0 / (a * (y / x));
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 8e-95:
		tmp = ((x / a) - ((x * b) / a)) / y
	elif b <= 5.6e+69:
		tmp = 1.0 / (a * (y / x))
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 8e-95)
		tmp = Float64(Float64(Float64(x / a) - Float64(Float64(x * b) / a)) / y);
	elseif (b <= 5.6e+69)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 8e-95)
		tmp = ((x / a) - ((x * b) / a)) / y;
	elseif (b <= 5.6e+69)
		tmp = 1.0 / (a * (y / x));
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 8e-95], N[(N[(N[(x / a), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 5.6e+69], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < 7.99999999999999992e-95

   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. Taylor expanded in y around 0 80.7%

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

   3. Taylor expanded in t around 0 53.8%

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

      1. sub-neg 53.8%

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

      2. mul-1-neg 53.8%

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

      3. distribute-neg-in 53.8%

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

      4. +-commutative 53.8%

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

      5. exp-neg 53.8%

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

      6. associate-*l/ 53.8%

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

      7. *-lft-identity 53.8%

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

      8. +-commutative 53.8%

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

      9. exp-sum 53.8%

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

      10. rem-exp-log 54.5%

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

      11. associate-/r* 52.7%

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

   5. Simplified 52.7%

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

   6. Taylor expanded in b around 0 41.1%

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

   if 7.99999999999999992e-95 < b < 5.59999999999999964e69

   1. Initial program 97.9%

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

      1. associate-*r/ 97.0%

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

      2. sub-neg 97.0%

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

      3. exp-sum 73.9%

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

      4. associate-/l* 73.9%

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

      5. associate-/r/ 73.9%

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

      6. exp-neg 73.9%

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

      7. associate-*r/ 73.9%

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

   3. Simplified 66.9%

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

   4. Taylor expanded in t around 0 59.7%

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

      1. associate-/r* 64.8%

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

   6. Simplified 64.8%

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

   7. Taylor expanded in b around 0 63.8%

      \[\leadsto \color{blue}{\frac{{z}^{y} \cdot x}{a \cdot y}} \]
   8. Step-by-step derivation

      1. times-frac 76.2%

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

   9. Simplified 76.2%

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

   10. Taylor expanded in y around 0 46.3%

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

       1. *-commutative 46.3%

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

       2. clear-num 46.3%

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

       3. frac-times 46.3%

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

       4. metadata-eval 46.3%

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

   12. Applied egg-rr 46.3%

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

   if 5.59999999999999964e69 < 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-*r/ 100.0%

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

      2. sub-neg 100.0%

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

      3. exp-sum 62.5%

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

      4. associate-/l* 62.5%

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

      5. associate-/r/ 62.5%

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

      6. exp-neg 62.5%

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

      7. associate-*r/ 62.5%

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

   3. Simplified 54.2%

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

   4. Taylor expanded in t around 0 71.0%

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

      1. associate-/r* 71.0%

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

   6. Simplified 71.0%

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

   7. Taylor expanded in y around 0 77.4%

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

   8. Taylor expanded in b around 0 46.5%

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

   9. Taylor expanded in b around inf 52.3%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 8 \cdot 10^{-95}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+69}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]

Alternative 15: 40.1% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.12 \cdot 10^{-123}:\\ \;\;\;\;\frac{x - x \cdot b}{y \cdot a}\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+69}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1.12e-123)
   (/ (- x (* x b)) (* y a))
   (if (<= b 5.5e+69) (/ 1.0 (* a (/ y x))) (/ x (* a (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.12e-123) {
		tmp = (x - (x * b)) / (y * a);
	} else if (b <= 5.5e+69) {
		tmp = 1.0 / (a * (y / x));
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 1.12d-123) then
        tmp = (x - (x * b)) / (y * a)
    else if (b <= 5.5d+69) then
        tmp = 1.0d0 / (a * (y / x))
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.12e-123) {
		tmp = (x - (x * b)) / (y * a);
	} else if (b <= 5.5e+69) {
		tmp = 1.0 / (a * (y / x));
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 1.12e-123:
		tmp = (x - (x * b)) / (y * a)
	elif b <= 5.5e+69:
		tmp = 1.0 / (a * (y / x))
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.12e-123)
		tmp = Float64(Float64(x - Float64(x * b)) / Float64(y * a));
	elseif (b <= 5.5e+69)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 1.12e-123)
		tmp = (x - (x * b)) / (y * a);
	elseif (b <= 5.5e+69)
		tmp = 1.0 / (a * (y / x));
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.12e-123], N[(N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.5e+69], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < 1.11999999999999999e-123

   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-*r/ 99.0%

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

      2. sub-neg 99.0%

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

      3. exp-sum 86.1%

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

      4. associate-/l* 86.1%

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

      5. associate-/r/ 86.1%

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

      6. exp-neg 86.1%

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

      7. associate-*r/ 86.1%

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

   3. Simplified 72.9%

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

   4. Taylor expanded in t around 0 65.6%

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

      1. associate-/r* 68.1%

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

   6. Simplified 68.1%

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

   7. Taylor expanded in y around 0 54.0%

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

   8. Taylor expanded in b around 0 26.8%

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

   9. Taylor expanded in b around 0 38.6%

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

       1. mul-1-neg 38.6%

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

       2. sub-neg 38.6%

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

       3. *-commutative 38.6%

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

       4. div-sub 40.5%

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

       5. *-commutative 40.5%

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

   11. Simplified 40.5%

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

   if 1.11999999999999999e-123 < b < 5.50000000000000002e69

   1. Initial program 97.9%

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

      1. associate-*r/ 95.3%

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

      2. sub-neg 95.3%

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

      3. exp-sum 75.3%

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

      4. associate-/l* 75.3%

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

      5. associate-/r/ 75.3%

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

      6. exp-neg 75.3%

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

      7. associate-*r/ 75.3%

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

   3. Simplified 64.7%

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

   4. Taylor expanded in t around 0 58.6%

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

      1. associate-/r* 63.0%

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

   6. Simplified 63.0%

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

   7. Taylor expanded in b around 0 62.1%

      \[\leadsto \color{blue}{\frac{{z}^{y} \cdot x}{a \cdot y}} \]
   8. Step-by-step derivation

      1. times-frac 74.8%

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

   9. Simplified 74.8%

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

   10. Taylor expanded in y around 0 46.8%

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

       1. *-commutative 46.8%

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

       2. clear-num 46.8%

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

       3. frac-times 46.8%

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

       4. metadata-eval 46.8%

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

   12. Applied egg-rr 46.8%

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

   if 5.50000000000000002e69 < 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-*r/ 100.0%

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

      2. sub-neg 100.0%

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

      3. exp-sum 62.5%

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

      4. associate-/l* 62.5%

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

      5. associate-/r/ 62.5%

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

      6. exp-neg 62.5%

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

      7. associate-*r/ 62.5%

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

   3. Simplified 54.2%

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

   4. Taylor expanded in t around 0 71.0%

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

      1. associate-/r* 71.0%

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

   6. Simplified 71.0%

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

   7. Taylor expanded in y around 0 77.4%

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

   8. Taylor expanded in b around 0 46.5%

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

   9. Taylor expanded in b around inf 52.3%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.12 \cdot 10^{-123}:\\ \;\;\;\;\frac{x - x \cdot b}{y \cdot a}\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+69}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]

Alternative 16: 33.2% accurate, 34.8× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1e+69) (/ (/ x a) y) (/ 1.0 (* a (/ y x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1e+69) {
		tmp = (x / a) / y;
	} else {
		tmp = 1.0 / (a * (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1d+69)) then
        tmp = (x / a) / y
    else
        tmp = 1.0d0 / (a * (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1e+69) {
		tmp = (x / a) / y;
	} else {
		tmp = 1.0 / (a * (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1e+69:
		tmp = (x / a) / y
	else:
		tmp = 1.0 / (a * (y / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1e+69)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1e+69)
		tmp = (x / a) / y;
	else
		tmp = 1.0 / (a * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1e+69], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.0000000000000001e69

   1. Initial program 99.4%

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

   2. Taylor expanded in t around 0 82.7%

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

      1. mul-1-neg 82.7%

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

   4. Simplified 82.7%

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

   5. Taylor expanded in b around 0 77.2%

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

      1. div-exp 77.2%

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

      2. *-commutative 77.2%

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

      3. exp-to-pow 77.2%

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

      4. rem-exp-log 77.8%

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

   7. Simplified 77.8%

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

   8. Taylor expanded in y around 0 35.9%

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

      1. *-commutative 35.9%

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

      2. associate-/r* 43.0%

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

   10. Simplified 43.0%

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

   if -1.0000000000000001e69 < x

   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-*r/ 98.3%

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

      2. sub-neg 98.3%

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

      3. exp-sum 81.6%

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

      4. associate-/l* 81.6%

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

      5. associate-/r/ 81.6%

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

      6. exp-neg 81.6%

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

      7. associate-*r/ 81.6%

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

   3. Simplified 67.5%

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

   4. Taylor expanded in t around 0 66.1%

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

      1. associate-/r* 69.1%

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

   6. Simplified 69.1%

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

   7. Taylor expanded in b around 0 57.5%

      \[\leadsto \color{blue}{\frac{{z}^{y} \cdot x}{a \cdot y}} \]
   8. Step-by-step derivation

      1. times-frac 55.5%

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

   9. Simplified 55.5%

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

   10. Taylor expanded in y around 0 33.3%

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

       1. *-commutative 33.3%

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

       2. clear-num 33.8%

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

       3. frac-times 34.1%

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

       4. metadata-eval 34.1%

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

   12. Applied egg-rr 34.1%

       \[\leadsto \color{blue}{\frac{1}{\frac{y}{x} \cdot a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.9%

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

Alternative 17: 32.1% accurate, 44.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 7.5 \cdot 10^{-95}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 7.5e-95) (/ (/ x a) y) (/ (/ x y) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 7.5e-95) {
		tmp = (x / a) / y;
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 7.5d-95) then
        tmp = (x / a) / y
    else
        tmp = (x / y) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 7.5e-95) {
		tmp = (x / a) / y;
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 7.5e-95:
		tmp = (x / a) / y
	else:
		tmp = (x / y) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 7.5e-95)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(Float64(x / y) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 7.5e-95)
		tmp = (x / a) / y;
	else
		tmp = (x / y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 7.5e-95], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 7.5000000000000003e-95

   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. Taylor expanded in t around 0 76.7%

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

      1. mul-1-neg 76.7%

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

   4. Simplified 76.7%

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

   5. Taylor expanded in b around 0 64.6%

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

      1. div-exp 64.6%

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

      2. *-commutative 64.6%

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

      3. exp-to-pow 64.6%

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

      4. rem-exp-log 65.4%

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

   7. Simplified 65.4%

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

   8. Taylor expanded in y around 0 35.1%

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

      1. *-commutative 35.1%

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

      2. associate-/r* 35.6%

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

   10. Simplified 35.6%

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

   if 7.5000000000000003e-95 < b

   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-*r/ 98.6%

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

      2. sub-neg 98.6%

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

      3. exp-sum 67.6%

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

      4. associate-/l* 67.6%

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

      5. associate-/r/ 67.6%

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

      6. exp-neg 67.6%

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

      7. associate-*r/ 67.6%

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

   3. Simplified 59.9%

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

   4. Taylor expanded in t around 0 65.9%

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

      1. associate-/r* 68.2%

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

   6. Simplified 68.2%

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

   7. Taylor expanded in b around 0 58.0%

      \[\leadsto \color{blue}{\frac{{z}^{y} \cdot x}{a \cdot y}} \]
   8. Step-by-step derivation

      1. times-frac 64.6%

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

   9. Simplified 64.6%

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

   10. Taylor expanded in y around 0 35.8%

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

       1. associate-*l/ 35.8%

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

       2. *-un-lft-identity 35.8%

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

   12. Applied egg-rr 35.8%

       \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 7.5 \cdot 10^{-95}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \]

Alternative 18: 32.4% 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 99.0%

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

2. Taylor expanded in t around 0 79.7%

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

   1. mul-1-neg 79.7%

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

4. Simplified 79.7%

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

5. Taylor expanded in b around 0 65.1%

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

   1. div-exp 65.2%

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

   2. *-commutative 65.2%

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

   3. exp-to-pow 65.2%

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

   4. rem-exp-log 65.8%

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

7. Simplified 65.8%

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

8. Taylor expanded in y around 0 32.8%

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

9. Final simplification 32.8%

   \[\leadsto \frac{x}{y \cdot a} \]

Alternative 19: 32.1% accurate, 63.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Taylor expanded in t around 0 79.7%

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

   1. mul-1-neg 79.7%

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

4. Simplified 79.7%

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

5. Taylor expanded in b around 0 65.1%

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

   1. div-exp 65.2%

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

   2. *-commutative 65.2%

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

   3. exp-to-pow 65.2%

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

   4. rem-exp-log 65.8%

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

7. Simplified 65.8%

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

8. Taylor expanded in y around 0 32.8%

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

   1. *-commutative 32.8%

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

   2. associate-/r* 33.3%

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

10. Simplified 33.3%

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

11. Final simplification 33.3%

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

Developer target: 71.8% 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 2023224 
(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))