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

Percentage Accurate: 98.5% → 98.5%

Time: 25.9s

Alternatives: 23

Speedup: 1.0×

• 20.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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: 91.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+20}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+85}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -5e+20)
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)
   (if (<= y 6.2e+85)
     (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)
     (/ (* x (/ (pow z y) a)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5e+20) {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	} else if (y <= 6.2e+85) {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	} else {
		tmp = (x * (pow(z, y) / a)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-5d+20)) then
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y
    else if (y <= 6.2d+85) then
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    else
        tmp = (x * ((z ** y) / a)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5e+20) {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	} else if (y <= 6.2e+85) {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	} else {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -5e+20:
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	elif y <= 6.2e+85:
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	else:
		tmp = (x * (math.pow(z, y) / a)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -5e+20)
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	elseif (y <= 6.2e+85)
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -5e+20)
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	elseif (y <= 6.2e+85)
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	else
		tmp = (x * ((z ^ y) / a)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -5e+20], 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], If[LessEqual[y, 6.2e+85], 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[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5e20

   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 92.4%

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

      1. +-commutative 92.4%

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

      2. mul-1-neg 92.4%

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

      3. unsub-neg 92.4%

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

   4. Simplified 92.4%

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

   if -5e20 < y < 6.20000000000000023e85

   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 95.4%

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

   if 6.20000000000000023e85 < 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 93.7%

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

      1. +-commutative 93.7%

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

      2. mul-1-neg 93.7%

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

      3. unsub-neg 93.7%

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

   4. Simplified 93.7%

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

   5. Taylor expanded in b around 0 93.7%

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

      1. div-exp 93.7%

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

      2. *-commutative 93.7%

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

      3. exp-to-pow 93.7%

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

      4. rem-exp-log 93.7%

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

   7. Simplified 93.7%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+20}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+85}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \end{array} \]

Alternative 3: 88.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+167} \lor \neg \left(y \leq 2.2 \cdot 10^{+86}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5e+167) (not (<= y 2.2e+86)))
   (/ (* 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 <= -5e+167) || !(y <= 2.2e+86)) {
		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 <= (-5d+167)) .or. (.not. (y <= 2.2d+86))) 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 <= -5e+167) || !(y <= 2.2e+86)) {
		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 <= -5e+167) or not (y <= 2.2e+86):
		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 <= -5e+167) || !(y <= 2.2e+86))
		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 <= -5e+167) || ~((y <= 2.2e+86)))
		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, -5e+167], N[Not[LessEqual[y, 2.2e+86]], $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 < -4.9999999999999997e167 or 2.20000000000000003e86 < 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 93.8%

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

      1. +-commutative 93.8%

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

      2. mul-1-neg 93.8%

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

      3. unsub-neg 93.8%

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

   4. Simplified 93.8%

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

   5. Taylor expanded in b around 0 91.4%

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

      1. div-exp 91.4%

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

      2. *-commutative 91.4%

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

      3. exp-to-pow 91.4%

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

      4. rem-exp-log 91.4%

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

   7. Simplified 91.4%

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

   if -4.9999999999999997e167 < y < 2.20000000000000003e86

   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. Taylor expanded in y around 0 91.8%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+167} \lor \neg \left(y \leq 2.2 \cdot 10^{+86}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]

Alternative 4: 78.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+205} \lor \neg \left(t \leq 3500\right):\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5.4e+205) (not (<= t 3500.0)))
   (/ (* x (/ (pow a t) a)) y)
   (/ (* x (pow z y)) (* a (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5.4e+205) || !(t <= 3500.0)) {
		tmp = (x * (pow(a, t) / a)) / y;
	} else {
		tmp = (x * pow(z, y)) / (a * (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-5.4d+205)) .or. (.not. (t <= 3500.0d0))) then
        tmp = (x * ((a ** t) / a)) / y
    else
        tmp = (x * (z ** y)) / (a * (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5.4e+205) || !(t <= 3500.0)) {
		tmp = (x * (Math.pow(a, t) / a)) / y;
	} else {
		tmp = (x * Math.pow(z, y)) / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -5.4e+205) or not (t <= 3500.0):
		tmp = (x * (math.pow(a, t) / a)) / y
	else:
		tmp = (x * math.pow(z, y)) / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -5.4e+205) || !(t <= 3500.0))
		tmp = Float64(Float64(x * Float64((a ^ t) / a)) / y);
	else
		tmp = Float64(Float64(x * (z ^ y)) / Float64(a * Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -5.4e+205) || ~((t <= 3500.0)))
		tmp = (x * ((a ^ t) / a)) / y;
	else
		tmp = (x * (z ^ y)) / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -5.4e+205], N[Not[LessEqual[t, 3500.0]], $MachinePrecision]], N[(N[(x * N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.40000000000000025e205 or 3500 < 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 90.8%

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

   3. Taylor expanded in b around 0 82.8%

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

      1. exp-to-pow 82.8%

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

      2. sub-neg 82.8%

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

      3. metadata-eval 82.8%

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

      4. +-commutative 82.8%

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

   5. Simplified 82.8%

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

      1. +-commutative 82.8%

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

      2. unpow-prod-up 82.8%

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

      3. inv-pow 82.8%

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

   7. Applied egg-rr 82.8%

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

      1. associate-*r/ 82.8%

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

      2. *-rgt-identity 82.8%

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

   9. Simplified 82.8%

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

   if -5.40000000000000025e205 < t < 3500

   1. Initial program 98.5%

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

      1. associate-*l/ 89.3%

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

      2. associate--l+ 89.3%

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

      3. exp-sum 75.8%

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

      4. associate-*r* 75.8%

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

      5. *-commutative 75.8%

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

      6. exp-to-pow 75.8%

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

      7. exp-diff 67.6%

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

      8. *-commutative 67.6%

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

      9. exp-to-pow 68.0%

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

      10. sub-neg 68.0%

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

      11. metadata-eval 68.0%

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

   3. Simplified 68.0%

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

   4. Taylor expanded in t around 0 81.9%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+205} \lor \neg \left(t \leq 3500\right):\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 5: 75.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{{a}^{t}}{a}\\ t_2 := \frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -9 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-180}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{t_1}{e^{b}}\\ \mathbf{elif}\;y \leq -6.7 \cdot 10^{-289}:\\ \;\;\;\;\frac{x \cdot t_1}{y}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-8}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (pow a t) a)) (t_2 (/ (* x (/ (pow z y) a)) y)))
   (if (<= y -9e+22)
     t_2
     (if (<= y -5e-180)
       (* (/ x y) (/ t_1 (exp b)))
       (if (<= y -6.7e-289)
         (/ (* x t_1) y)
         (if (<= y 3.4e-8) (/ (/ x (* a (exp b))) y) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(a, t) / a;
	double t_2 = (x * (pow(z, y) / a)) / y;
	double tmp;
	if (y <= -9e+22) {
		tmp = t_2;
	} else if (y <= -5e-180) {
		tmp = (x / y) * (t_1 / exp(b));
	} else if (y <= -6.7e-289) {
		tmp = (x * t_1) / y;
	} else if (y <= 3.4e-8) {
		tmp = (x / (a * exp(b))) / 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) / a
    t_2 = (x * ((z ** y) / a)) / y
    if (y <= (-9d+22)) then
        tmp = t_2
    else if (y <= (-5d-180)) then
        tmp = (x / y) * (t_1 / exp(b))
    else if (y <= (-6.7d-289)) then
        tmp = (x * t_1) / y
    else if (y <= 3.4d-8) then
        tmp = (x / (a * exp(b))) / 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) / a;
	double t_2 = (x * (Math.pow(z, y) / a)) / y;
	double tmp;
	if (y <= -9e+22) {
		tmp = t_2;
	} else if (y <= -5e-180) {
		tmp = (x / y) * (t_1 / Math.exp(b));
	} else if (y <= -6.7e-289) {
		tmp = (x * t_1) / y;
	} else if (y <= 3.4e-8) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, t) / a
	t_2 = (x * (math.pow(z, y) / a)) / y
	tmp = 0
	if y <= -9e+22:
		tmp = t_2
	elif y <= -5e-180:
		tmp = (x / y) * (t_1 / math.exp(b))
	elif y <= -6.7e-289:
		tmp = (x * t_1) / y
	elif y <= 3.4e-8:
		tmp = (x / (a * math.exp(b))) / y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64((a ^ t) / a)
	t_2 = Float64(Float64(x * Float64((z ^ y) / a)) / y)
	tmp = 0.0
	if (y <= -9e+22)
		tmp = t_2;
	elseif (y <= -5e-180)
		tmp = Float64(Float64(x / y) * Float64(t_1 / exp(b)));
	elseif (y <= -6.7e-289)
		tmp = Float64(Float64(x * t_1) / y);
	elseif (y <= 3.4e-8)
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a ^ t) / a;
	t_2 = (x * ((z ^ y) / a)) / y;
	tmp = 0.0;
	if (y <= -9e+22)
		tmp = t_2;
	elseif (y <= -5e-180)
		tmp = (x / y) * (t_1 / exp(b));
	elseif (y <= -6.7e-289)
		tmp = (x * t_1) / y;
	elseif (y <= 3.4e-8)
		tmp = (x / (a * exp(b))) / y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -9e+22], t$95$2, If[LessEqual[y, -5e-180], N[(N[(x / y), $MachinePrecision] * N[(t$95$1 / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.7e-289], N[(N[(x * t$95$1), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 3.4e-8], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.9999999999999996e22 or 3.4e-8 < 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 88.8%

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

      1. +-commutative 88.8%

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

      2. mul-1-neg 88.8%

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

      3. unsub-neg 88.8%

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

   4. Simplified 88.8%

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

   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 82.1%

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

   7. Simplified 82.1%

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

   if -8.9999999999999996e22 < y < -5.0000000000000001e-180

   1. Initial program 99.0%

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

      1. associate-*l/ 96.4%

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

      2. associate--l+ 96.4%

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

      3. exp-sum 85.9%

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

      4. associate-*r* 85.9%

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

      5. *-commutative 85.9%

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

      6. exp-to-pow 85.9%

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

      7. exp-diff 75.4%

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

      8. *-commutative 75.4%

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

      9. exp-to-pow 76.0%

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

      10. sub-neg 76.0%

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

      11. metadata-eval 76.0%

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

   3. Simplified 76.0%

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

   4. Taylor expanded in y around 0 85.2%

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

      1. times-frac 85.2%

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

      2. exp-to-pow 85.5%

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

      3. sub-neg 85.5%

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

      4. metadata-eval 85.5%

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

   6. Simplified 85.5%

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

      1. unpow-prod-up 85.7%

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

      2. *-un-lft-identity 85.7%

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

      3. times-frac 85.7%

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

      4. unpow-1 85.7%

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

   8. Applied egg-rr 85.7%

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

      1. /-rgt-identity 85.7%

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

      2. associate-*r/ 85.7%

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

      3. associate-*r/ 85.7%

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

      4. *-rgt-identity 85.7%

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

   10. Simplified 85.7%

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

   if -5.0000000000000001e-180 < y < -6.70000000000000015e-289

   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 y around 0 99.4%

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

   3. Taylor expanded in b around 0 90.9%

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

      1. exp-to-pow 91.4%

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

      2. sub-neg 91.4%

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

      3. metadata-eval 91.4%

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

      4. +-commutative 91.4%

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

   5. Simplified 91.4%

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

      1. +-commutative 91.4%

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

      2. unpow-prod-up 91.4%

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

      3. inv-pow 91.4%

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

   7. Applied egg-rr 91.4%

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

      1. associate-*r/ 91.4%

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

      2. *-rgt-identity 91.4%

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

   9. Simplified 91.4%

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

   if -6.70000000000000015e-289 < y < 3.4e-8

   1. Initial program 96.6%

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

   2. Taylor expanded in t around 0 80.6%

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

      1. +-commutative 80.6%

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

      2. mul-1-neg 80.6%

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

      3. unsub-neg 80.6%

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

   4. Simplified 80.6%

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

   5. Taylor expanded in y around 0 80.6%

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

      1. exp-neg 80.6%

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

      2. associate-*r/ 80.6%

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

      3. *-rgt-identity 80.6%

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

      4. +-commutative 80.6%

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

      5. exp-sum 80.6%

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

      6. rem-exp-log 81.0%

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

   7. Simplified 81.0%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+22}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-180}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{\frac{{a}^{t}}{a}}{e^{b}}\\ \mathbf{elif}\;y \leq -6.7 \cdot 10^{-289}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-8}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \end{array} \]

Alternative 6: 72.6% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{if}\;b \leq -1.9 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-273}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y}\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+102}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x (* a (exp b))) y)))
   (if (<= b -1.9e+29)
     t_1
     (if (<= b -7.5e-273)
       (* (/ x a) (/ (pow z y) y))
       (if (<= b 3.2e+102) (/ (* x (/ (pow a t) a)) y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / (a * exp(b))) / y;
	double tmp;
	if (b <= -1.9e+29) {
		tmp = t_1;
	} else if (b <= -7.5e-273) {
		tmp = (x / a) * (pow(z, y) / y);
	} else if (b <= 3.2e+102) {
		tmp = (x * (pow(a, t) / a)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / (a * exp(b))) / y
    if (b <= (-1.9d+29)) then
        tmp = t_1
    else if (b <= (-7.5d-273)) then
        tmp = (x / a) * ((z ** y) / y)
    else if (b <= 3.2d+102) then
        tmp = (x * ((a ** t) / a)) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / (a * Math.exp(b))) / y;
	double tmp;
	if (b <= -1.9e+29) {
		tmp = t_1;
	} else if (b <= -7.5e-273) {
		tmp = (x / a) * (Math.pow(z, y) / y);
	} else if (b <= 3.2e+102) {
		tmp = (x * (Math.pow(a, t) / a)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / (a * math.exp(b))) / y
	tmp = 0
	if b <= -1.9e+29:
		tmp = t_1
	elif b <= -7.5e-273:
		tmp = (x / a) * (math.pow(z, y) / y)
	elif b <= 3.2e+102:
		tmp = (x * (math.pow(a, t) / a)) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / Float64(a * exp(b))) / y)
	tmp = 0.0
	if (b <= -1.9e+29)
		tmp = t_1;
	elseif (b <= -7.5e-273)
		tmp = Float64(Float64(x / a) * Float64((z ^ y) / y));
	elseif (b <= 3.2e+102)
		tmp = Float64(Float64(x * Float64((a ^ t) / a)) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / (a * exp(b))) / y;
	tmp = 0.0;
	if (b <= -1.9e+29)
		tmp = t_1;
	elseif (b <= -7.5e-273)
		tmp = (x / a) * ((z ^ y) / y);
	elseif (b <= 3.2e+102)
		tmp = (x * ((a ^ t) / a)) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -1.9e+29], t$95$1, If[LessEqual[b, -7.5e-273], N[(N[(x / a), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.2e+102], N[(N[(x * N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.89999999999999985e29 or 3.1999999999999999e102 < 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. Taylor expanded in t around 0 91.1%

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

      1. +-commutative 91.1%

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

      2. mul-1-neg 91.1%

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

      3. unsub-neg 91.1%

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

   4. Simplified 91.1%

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

   5. Taylor expanded in y around 0 85.7%

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

      1. exp-neg 85.7%

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

      2. associate-*r/ 85.7%

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

      3. *-rgt-identity 85.7%

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

      4. +-commutative 85.7%

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

      5. exp-sum 85.7%

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

      6. rem-exp-log 85.7%

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

   7. Simplified 85.7%

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

   if -1.89999999999999985e29 < b < -7.5000000000000007e-273

   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. Taylor expanded in t around 0 79.3%

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

      1. +-commutative 79.3%

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

      2. mul-1-neg 79.3%

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

      3. unsub-neg 79.3%

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

   4. Simplified 79.3%

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

   5. Taylor expanded in b around 0 76.1%

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

      1. div-exp 76.1%

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

      2. *-commutative 76.1%

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

      3. exp-to-pow 76.1%

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

      4. rem-exp-log 76.6%

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

      5. associate-*r/ 76.6%

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

      6. associate-/r* 68.3%

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

      7. times-frac 71.6%

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

   7. Simplified 71.6%

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

   if -7.5000000000000007e-273 < b < 3.1999999999999999e102

   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 y around 0 74.9%

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

   3. Taylor expanded in b around 0 70.9%

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

      1. exp-to-pow 71.2%

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

      2. sub-neg 71.2%

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

      3. metadata-eval 71.2%

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

      4. +-commutative 71.2%

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

   5. Simplified 71.2%

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

      1. +-commutative 71.2%

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

      2. unpow-prod-up 71.3%

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

      3. inv-pow 71.3%

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

   7. Applied egg-rr 71.3%

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

      1. associate-*r/ 71.3%

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

      2. *-rgt-identity 71.3%

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

   9. Simplified 71.3%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+29}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-273}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y}\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+102}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \end{array} \]

Alternative 7: 74.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -8 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{-289}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-8}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (/ (pow z y) a)) y)))
   (if (<= y -8e+22)
     t_1
     (if (<= y -6.4e-289)
       (/ (* x (/ (pow a t) a)) y)
       (if (<= y 3.4e-8) (/ (/ x (* a (exp b))) y) t_1)))))

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 tmp;
	if (y <= -8e+22) {
		tmp = t_1;
	} else if (y <= -6.4e-289) {
		tmp = (x * (pow(a, t) / a)) / y;
	} else if (y <= 3.4e-8) {
		tmp = (x / (a * exp(b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * ((z ** y) / a)) / y
    if (y <= (-8d+22)) then
        tmp = t_1
    else if (y <= (-6.4d-289)) then
        tmp = (x * ((a ** t) / a)) / y
    else if (y <= 3.4d-8) then
        tmp = (x / (a * exp(b))) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * (Math.pow(z, y) / a)) / y;
	double tmp;
	if (y <= -8e+22) {
		tmp = t_1;
	} else if (y <= -6.4e-289) {
		tmp = (x * (Math.pow(a, t) / a)) / y;
	} else if (y <= 3.4e-8) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * (math.pow(z, y) / a)) / y
	tmp = 0
	if y <= -8e+22:
		tmp = t_1
	elif y <= -6.4e-289:
		tmp = (x * (math.pow(a, t) / a)) / y
	elif y <= 3.4e-8:
		tmp = (x / (a * math.exp(b))) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64((z ^ y) / a)) / y)
	tmp = 0.0
	if (y <= -8e+22)
		tmp = t_1;
	elseif (y <= -6.4e-289)
		tmp = Float64(Float64(x * Float64((a ^ t) / a)) / y);
	elseif (y <= 3.4e-8)
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * ((z ^ y) / a)) / y;
	tmp = 0.0;
	if (y <= -8e+22)
		tmp = t_1;
	elseif (y <= -6.4e-289)
		tmp = (x * ((a ^ t) / a)) / y;
	elseif (y <= 3.4e-8)
		tmp = (x / (a * exp(b))) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -8e+22], t$95$1, If[LessEqual[y, -6.4e-289], N[(N[(x * N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 3.4e-8], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8e22 or 3.4e-8 < 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 88.8%

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

      1. +-commutative 88.8%

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

      2. mul-1-neg 88.8%

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

      3. unsub-neg 88.8%

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

   4. Simplified 88.8%

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

   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 82.1%

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

   7. Simplified 82.1%

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

   if -8e22 < y < -6.4000000000000004e-289

   1. Initial program 99.2%

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

   2. Taylor expanded in y around 0 98.7%

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

   3. Taylor expanded in b around 0 76.3%

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

      1. exp-to-pow 76.7%

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

      2. sub-neg 76.7%

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

      3. metadata-eval 76.7%

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

      4. +-commutative 76.7%

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

   5. Simplified 76.7%

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

      1. +-commutative 76.7%

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

      2. unpow-prod-up 76.8%

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

      3. inv-pow 76.8%

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

   7. Applied egg-rr 76.8%

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

      1. associate-*r/ 76.8%

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

      2. *-rgt-identity 76.8%

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

   9. Simplified 76.8%

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

   if -6.4000000000000004e-289 < y < 3.4e-8

   1. Initial program 96.6%

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

   2. Taylor expanded in t around 0 80.6%

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

      1. +-commutative 80.6%

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

      2. mul-1-neg 80.6%

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

      3. unsub-neg 80.6%

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

   4. Simplified 80.6%

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

   5. Taylor expanded in y around 0 80.6%

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

      1. exp-neg 80.6%

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

      2. associate-*r/ 80.6%

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

      3. *-rgt-identity 80.6%

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

      4. +-commutative 80.6%

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

      5. exp-sum 80.6%

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

      6. rem-exp-log 81.0%

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

   7. Simplified 81.0%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+22}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{-289}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-8}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \end{array} \]

Alternative 8: 72.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+36} \lor \neg \left(b \leq 6.6 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -6e+36) (not (<= b 6.6e-10)))
   (/ (/ x (* a (exp b))) y)
   (* (/ x a) (/ (pow z y) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6e+36) || !(b <= 6.6e-10)) {
		tmp = (x / (a * exp(b))) / y;
	} else {
		tmp = (x / a) * (pow(z, y) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-6d+36)) .or. (.not. (b <= 6.6d-10))) then
        tmp = (x / (a * exp(b))) / y
    else
        tmp = (x / a) * ((z ** y) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6e+36) || !(b <= 6.6e-10)) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else {
		tmp = (x / a) * (Math.pow(z, y) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -6e+36) or not (b <= 6.6e-10):
		tmp = (x / (a * math.exp(b))) / y
	else:
		tmp = (x / a) * (math.pow(z, y) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -6e+36) || !(b <= 6.6e-10))
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	else
		tmp = Float64(Float64(x / a) * Float64((z ^ y) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -6e+36) || ~((b <= 6.6e-10)))
		tmp = (x / (a * exp(b))) / y;
	else
		tmp = (x / a) * ((z ^ y) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -6e+36], N[Not[LessEqual[b, 6.6e-10]], $MachinePrecision]], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / a), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6e36 or 6.6e-10 < 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. Taylor expanded in t around 0 87.6%

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

      1. +-commutative 87.6%

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

      2. mul-1-neg 87.6%

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

      3. unsub-neg 87.6%

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

   4. Simplified 87.6%

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

   5. Taylor expanded in y around 0 82.1%

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

      1. exp-neg 82.1%

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

      2. associate-*r/ 82.1%

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

      3. *-rgt-identity 82.1%

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

      4. +-commutative 82.1%

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

      5. exp-sum 82.1%

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

      6. rem-exp-log 82.2%

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

   7. Simplified 82.2%

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

   if -6e36 < b < 6.6e-10

   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. Taylor expanded in t around 0 73.4%

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

      1. +-commutative 73.4%

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

      2. mul-1-neg 73.4%

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

      3. unsub-neg 73.4%

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

   4. Simplified 73.4%

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

   5. Taylor expanded in b around 0 71.9%

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

      1. div-exp 71.9%

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

      2. *-commutative 71.9%

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

      3. exp-to-pow 71.9%

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

      4. rem-exp-log 72.3%

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

      5. associate-*r/ 72.3%

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

      6. associate-/r* 66.8%

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

      7. times-frac 66.1%

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

   7. Simplified 66.1%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+36} \lor \neg \left(b \leq 6.6 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y}\\ \end{array} \]

Alternative 9: 53.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.5 \cdot 10^{+174}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-b}{a \cdot \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 4.5e+174) (/ (/ x (exp b)) (* y a)) (/ (- b) (* a (/ y x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 4.5e+174) {
		tmp = (x / exp(b)) / (y * a);
	} else {
		tmp = -b / (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 (y <= 4.5d+174) then
        tmp = (x / exp(b)) / (y * a)
    else
        tmp = -b / (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 (y <= 4.5e+174) {
		tmp = (x / Math.exp(b)) / (y * a);
	} else {
		tmp = -b / (a * (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 4.5e+174:
		tmp = (x / math.exp(b)) / (y * a)
	else:
		tmp = -b / (a * (y / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 4.5e+174)
		tmp = Float64(Float64(x / exp(b)) / Float64(y * a));
	else
		tmp = Float64(Float64(-b) / Float64(a * Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 4.5e+174)
		tmp = (x / exp(b)) / (y * a);
	else
		tmp = -b / (a * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 4.5e+174], N[(N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], N[((-b) / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.50000000000000042e174

   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. Step-by-step derivation

      1. associate-*l/ 88.0%

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

      2. associate--l+ 88.0%

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

      3. exp-sum 72.8%

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

      4. associate-*r* 72.8%

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

      5. *-commutative 72.8%

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

      6. exp-to-pow 72.8%

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

      7. exp-diff 60.0%

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

      8. *-commutative 60.0%

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

      9. exp-to-pow 60.3%

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

      10. sub-neg 60.3%

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

      11. metadata-eval 60.3%

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

   3. Simplified 60.3%

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

   4. Taylor expanded in t around 0 66.4%

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

      1. times-frac 61.5%

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

   6. Simplified 61.5%

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

   7. Taylor expanded in y around 0 60.6%

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

      1. associate-*r* 54.8%

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

      2. *-commutative 54.8%

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

      3. associate-/r* 54.8%

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

      4. *-commutative 54.8%

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

   9. Simplified 54.8%

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

   if 4.50000000000000042e174 < 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 93.6%

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

      1. +-commutative 93.6%

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

      2. mul-1-neg 93.6%

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

      3. unsub-neg 93.6%

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

   4. Simplified 93.6%

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

   5. Taylor expanded in y around 0 48.1%

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

      1. exp-neg 48.1%

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

      2. associate-*r/ 48.1%

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

      3. *-rgt-identity 48.1%

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

      4. +-commutative 48.1%

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

      5. exp-sum 48.1%

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

      6. rem-exp-log 48.1%

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

   7. Simplified 48.1%

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

   8. Taylor expanded in b around 0 36.5%

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

      1. +-commutative 36.5%

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

      2. mul-1-neg 36.5%

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

      3. unsub-neg 36.5%

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

      4. *-commutative 36.5%

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

      5. *-commutative 36.5%

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

      6. times-frac 36.4%

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

   10. Simplified 36.4%

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

   11. Taylor expanded in b around inf 47.2%

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

       1. mul-1-neg 47.2%

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

       2. *-commutative 47.2%

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

       3. associate-/l* 50.3%

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

       4. associate-*l/ 53.3%

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

       5. *-commutative 53.3%

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

   13. Simplified 53.3%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.5 \cdot 10^{+174}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-b}{a \cdot \frac{y}{x}}\\ \end{array} \]

Alternative 10: 58.8% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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 80.4%

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

   1. +-commutative 80.4%

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

   2. mul-1-neg 80.4%

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

   3. unsub-neg 80.4%

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

4. Simplified 80.4%

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

5. Taylor expanded in y around 0 58.5%

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

   1. exp-neg 58.5%

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

   2. associate-*r/ 58.5%

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

   3. *-rgt-identity 58.5%

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

   4. +-commutative 58.5%

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

   5. exp-sum 58.5%

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

   6. rem-exp-log 58.7%

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

7. Simplified 58.7%

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

8. Final simplification 58.7%

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

Alternative 11: 41.9% accurate, 16.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 4.5 \cdot 10^{-68}:\\ \;\;\;\;\frac{a \cdot \frac{x}{a} - y \cdot \left(x \cdot \frac{b}{y}\right)}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 4.5e-68)
   (/ (- (* a (/ x a)) (* y (* x (/ b y)))) (* y a))
   (/ (/ x (+ a (* a b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 4.5e-68) {
		tmp = ((a * (x / a)) - (y * (x * (b / y)))) / (y * a);
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 4.5d-68) then
        tmp = ((a * (x / a)) - (y * (x * (b / y)))) / (y * a)
    else
        tmp = (x / (a + (a * b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 4.5e-68) {
		tmp = ((a * (x / a)) - (y * (x * (b / y)))) / (y * a);
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 4.5e-68:
		tmp = ((a * (x / a)) - (y * (x * (b / y)))) / (y * a)
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 4.5e-68)
		tmp = Float64(Float64(Float64(a * Float64(x / a)) - Float64(y * Float64(x * Float64(b / y)))) / Float64(y * a));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 4.5e-68)
		tmp = ((a * (x / a)) - (y * (x * (b / y)))) / (y * a);
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 4.5e-68], N[(N[(N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision] - N[(y * N[(x * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 4.49999999999999999e-68

   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. Taylor expanded in t around 0 77.7%

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

      1. +-commutative 77.7%

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

      2. mul-1-neg 77.7%

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

      3. unsub-neg 77.7%

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

   4. Simplified 77.7%

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

   5. Taylor expanded in y around 0 51.3%

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

      1. exp-neg 51.3%

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

      2. associate-*r/ 51.3%

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

      3. *-rgt-identity 51.3%

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

      4. +-commutative 51.3%

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

      5. exp-sum 51.3%

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

      6. rem-exp-log 51.6%

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

   7. Simplified 51.6%

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

   8. Taylor expanded in b around 0 39.9%

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

      1. +-commutative 39.9%

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

      2. mul-1-neg 39.9%

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

      3. unsub-neg 39.9%

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

      4. *-commutative 39.9%

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

      5. *-commutative 39.9%

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

      6. times-frac 38.3%

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

   10. Simplified 38.3%

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

       1. associate-/r* 38.1%

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

       2. un-div-inv 38.1%

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

       3. associate-*r/ 39.3%

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

       4. frac-sub 43.7%

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

       5. un-div-inv 43.7%

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

   12. Applied egg-rr 43.7%

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

       1. *-commutative 43.7%

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

       2. associate-*l/ 43.8%

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

       3. associate-*r/ 44.9%

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

       4. *-commutative 44.9%

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

   14. Simplified 44.9%

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

   if 4.49999999999999999e-68 < b

   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 t around 0 85.9%

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

      1. +-commutative 85.9%

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

      2. mul-1-neg 85.9%

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

      3. unsub-neg 85.9%

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

   4. Simplified 85.9%

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

   5. Taylor expanded in y around 0 73.2%

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

      1. exp-neg 73.2%

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

      2. associate-*r/ 73.2%

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

      3. *-rgt-identity 73.2%

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

      4. +-commutative 73.2%

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

      5. exp-sum 73.2%

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

      6. rem-exp-log 73.3%

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

   7. Simplified 73.3%

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

   8. Taylor expanded in b around 0 36.2%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 4.5 \cdot 10^{-68}:\\ \;\;\;\;\frac{a \cdot \frac{x}{a} - y \cdot \left(x \cdot \frac{b}{y}\right)}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]

Alternative 12: 39.3% accurate, 18.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+15}:\\ \;\;\;\;\frac{x \cdot \left(-b\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-281}:\\ \;\;\;\;\frac{\frac{1}{\frac{a}{x}}}{y}\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{-253}:\\ \;\;\;\;\frac{\frac{-b}{a}}{\frac{y}{x}}\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-10}:\\ \;\;\;\;\left(1 - b\right) \cdot \frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.3e+15)
   (/ (* x (- b)) (* y a))
   (if (<= b 1.8e-281)
     (/ (/ 1.0 (/ a x)) y)
     (if (<= b 5.3e-253)
       (/ (/ (- b) a) (/ y x))
       (if (<= b 2.2e-10) (* (- 1.0 b) (/ x (* y a))) (/ (/ x (* a b)) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.3e+15) {
		tmp = (x * -b) / (y * a);
	} else if (b <= 1.8e-281) {
		tmp = (1.0 / (a / x)) / y;
	} else if (b <= 5.3e-253) {
		tmp = (-b / a) / (y / x);
	} else if (b <= 2.2e-10) {
		tmp = (1.0 - b) * (x / (y * a));
	} else {
		tmp = (x / (a * b)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.3d+15)) then
        tmp = (x * -b) / (y * a)
    else if (b <= 1.8d-281) then
        tmp = (1.0d0 / (a / x)) / y
    else if (b <= 5.3d-253) then
        tmp = (-b / a) / (y / x)
    else if (b <= 2.2d-10) then
        tmp = (1.0d0 - b) * (x / (y * a))
    else
        tmp = (x / (a * b)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.3e+15) {
		tmp = (x * -b) / (y * a);
	} else if (b <= 1.8e-281) {
		tmp = (1.0 / (a / x)) / y;
	} else if (b <= 5.3e-253) {
		tmp = (-b / a) / (y / x);
	} else if (b <= 2.2e-10) {
		tmp = (1.0 - b) * (x / (y * a));
	} else {
		tmp = (x / (a * b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.3e+15:
		tmp = (x * -b) / (y * a)
	elif b <= 1.8e-281:
		tmp = (1.0 / (a / x)) / y
	elif b <= 5.3e-253:
		tmp = (-b / a) / (y / x)
	elif b <= 2.2e-10:
		tmp = (1.0 - b) * (x / (y * a))
	else:
		tmp = (x / (a * b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.3e+15)
		tmp = Float64(Float64(x * Float64(-b)) / Float64(y * a));
	elseif (b <= 1.8e-281)
		tmp = Float64(Float64(1.0 / Float64(a / x)) / y);
	elseif (b <= 5.3e-253)
		tmp = Float64(Float64(Float64(-b) / a) / Float64(y / x));
	elseif (b <= 2.2e-10)
		tmp = Float64(Float64(1.0 - b) * Float64(x / Float64(y * a)));
	else
		tmp = Float64(Float64(x / Float64(a * b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.3e+15)
		tmp = (x * -b) / (y * a);
	elseif (b <= 1.8e-281)
		tmp = (1.0 / (a / x)) / y;
	elseif (b <= 5.3e-253)
		tmp = (-b / a) / (y / x);
	elseif (b <= 2.2e-10)
		tmp = (1.0 - b) * (x / (y * a));
	else
		tmp = (x / (a * b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.3e+15], N[(N[(x * (-b)), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.8e-281], N[(N[(1.0 / N[(a / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 5.3e-253], N[(N[((-b) / a), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.2e-10], N[(N[(1.0 - b), $MachinePrecision] * N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -3.3e15

   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 88.7%

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

      1. +-commutative 88.7%

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

      2. mul-1-neg 88.7%

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

      3. unsub-neg 88.7%

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

   4. Simplified 88.7%

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

   5. Taylor expanded in y around 0 79.0%

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

      1. exp-neg 79.0%

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

      2. associate-*r/ 79.0%

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

      3. *-rgt-identity 79.0%

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

      4. +-commutative 79.0%

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

      5. exp-sum 79.0%

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

      6. rem-exp-log 79.0%

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

   7. Simplified 79.0%

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

   8. Taylor expanded in b around 0 50.6%

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

      1. +-commutative 50.6%

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

      2. mul-1-neg 50.6%

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

      3. unsub-neg 50.6%

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

      4. *-commutative 50.6%

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

      5. *-commutative 50.6%

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

      6. times-frac 44.4%

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

   10. Simplified 44.4%

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

   11. Taylor expanded in b around inf 50.6%

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

   if -3.3e15 < b < 1.80000000000000003e-281

   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. Taylor expanded in t around 0 73.1%

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

      1. +-commutative 73.1%

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

      2. mul-1-neg 73.1%

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

      3. unsub-neg 73.1%

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

   4. Simplified 73.1%

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

   5. Taylor expanded in b around 0 71.8%

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

      1. div-exp 71.8%

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

      2. *-commutative 71.8%

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

      3. exp-to-pow 71.8%

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

      4. rem-exp-log 72.2%

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

   7. Simplified 72.2%

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

   8. Taylor expanded in y around 0 36.5%

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

      1. un-div-inv 36.6%

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

      2. clear-num 36.6%

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

   10. Applied egg-rr 36.6%

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

   if 1.80000000000000003e-281 < b < 5.3000000000000002e-253

   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 75.6%

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

      1. +-commutative 75.6%

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

      2. mul-1-neg 75.6%

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

      3. unsub-neg 75.6%

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

   4. Simplified 75.6%

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

   5. Taylor expanded in y around 0 15.9%

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

      1. exp-neg 15.9%

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

      2. associate-*r/ 15.9%

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

      3. *-rgt-identity 15.9%

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

      4. +-commutative 15.9%

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

      5. exp-sum 15.9%

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

      6. rem-exp-log 15.9%

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

   7. Simplified 15.9%

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

   8. Taylor expanded in b around 0 15.8%

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

      1. +-commutative 15.8%

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

      2. mul-1-neg 15.8%

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

      3. unsub-neg 15.8%

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

      4. *-commutative 15.8%

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

      5. *-commutative 15.8%

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

      6. times-frac 15.8%

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

   10. Simplified 15.8%

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

   11. Taylor expanded in b around inf 63.8%

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

       1. *-commutative 63.8%

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

       2. associate-/l* 52.6%

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

       3. associate-*l/ 52.6%

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

       4. associate-/l/ 63.8%

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

       5. associate-*r/ 63.8%

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

       6. neg-mul-1 63.8%

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

       7. distribute-neg-frac 63.8%

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

   13. Simplified 63.8%

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

   if 5.3000000000000002e-253 < b < 2.1999999999999999e-10

   1. Initial program 97.5%

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

   2. Taylor expanded in t around 0 71.7%

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

      1. +-commutative 71.7%

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

      2. mul-1-neg 71.7%

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

      3. unsub-neg 71.7%

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

   4. Simplified 71.7%

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

   5. Taylor expanded in y around 0 34.8%

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

      1. exp-neg 34.9%

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

      2. associate-*r/ 34.8%

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

      3. *-rgt-identity 34.8%

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

      4. +-commutative 34.8%

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

      5. exp-sum 34.8%

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

      6. rem-exp-log 35.4%

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

   7. Simplified 35.4%

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

   8. Taylor expanded in b around 0 35.4%

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

   9. Taylor expanded in b around 0 37.3%

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

       1. +-commutative 37.3%

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

       2. *-commutative 37.3%

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

       3. mul-1-neg 37.3%

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

       4. *-commutative 37.3%

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

       5. times-frac 35.2%

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

       6. *-commutative 35.2%

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

       7. sub-neg 35.2%

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

       8. *-commutative 35.2%

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

       9. times-frac 37.3%

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

       10. *-commutative 37.3%

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

       11. *-rgt-identity 37.3%

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

       12. associate-/r* 35.4%

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

       13. associate-*l/ 35.4%

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

       14. associate-/l* 35.4%

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

       15. associate-/r/ 33.1%

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

       16. associate-/r* 35.0%

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

       17. distribute-lft-out-- 41.7%

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

       18. *-commutative 41.7%

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

   11. Simplified 41.7%

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

   if 2.1999999999999999e-10 < b

   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 t around 0 87.1%

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

      1. +-commutative 87.1%

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

      2. mul-1-neg 87.1%

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

      3. unsub-neg 87.1%

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

   4. Simplified 87.1%

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

   5. Taylor expanded in y around 0 82.8%

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

      1. exp-neg 82.8%

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

      2. associate-*r/ 82.8%

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

      3. *-rgt-identity 82.8%

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

      4. +-commutative 82.8%

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

      5. exp-sum 82.8%

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

      6. rem-exp-log 82.9%

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

   7. Simplified 82.9%

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

   8. Taylor expanded in b around 0 37.7%

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

   9. Taylor expanded in b around inf 36.7%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot b}}}{y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+15}:\\ \;\;\;\;\frac{x \cdot \left(-b\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-281}:\\ \;\;\;\;\frac{\frac{1}{\frac{a}{x}}}{y}\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{-253}:\\ \;\;\;\;\frac{\frac{-b}{a}}{\frac{y}{x}}\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-10}:\\ \;\;\;\;\left(1 - b\right) \cdot \frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \end{array} \]

Alternative 13: 39.3% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+14}:\\ \;\;\;\;\frac{x \cdot \left(-b\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.03 \cdot 10^{-280}:\\ \;\;\;\;\frac{\frac{1}{\frac{a}{x}}}{y}\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{-253}:\\ \;\;\;\;\frac{\frac{-b}{a}}{\frac{y}{x}}\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5e+14)
   (/ (* x (- b)) (* y a))
   (if (<= b 1.03e-280)
     (/ (/ 1.0 (/ a x)) y)
     (if (<= b 5.3e-253)
       (/ (/ (- b) a) (/ y x))
       (if (<= b 5.5e-10) (/ x (* y a)) (/ (/ x (* a b)) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5e+14) {
		tmp = (x * -b) / (y * a);
	} else if (b <= 1.03e-280) {
		tmp = (1.0 / (a / x)) / y;
	} else if (b <= 5.3e-253) {
		tmp = (-b / a) / (y / x);
	} else if (b <= 5.5e-10) {
		tmp = x / (y * a);
	} else {
		tmp = (x / (a * b)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-5d+14)) then
        tmp = (x * -b) / (y * a)
    else if (b <= 1.03d-280) then
        tmp = (1.0d0 / (a / x)) / y
    else if (b <= 5.3d-253) then
        tmp = (-b / a) / (y / x)
    else if (b <= 5.5d-10) then
        tmp = x / (y * a)
    else
        tmp = (x / (a * b)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5e+14) {
		tmp = (x * -b) / (y * a);
	} else if (b <= 1.03e-280) {
		tmp = (1.0 / (a / x)) / y;
	} else if (b <= 5.3e-253) {
		tmp = (-b / a) / (y / x);
	} else if (b <= 5.5e-10) {
		tmp = x / (y * a);
	} else {
		tmp = (x / (a * b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5e+14:
		tmp = (x * -b) / (y * a)
	elif b <= 1.03e-280:
		tmp = (1.0 / (a / x)) / y
	elif b <= 5.3e-253:
		tmp = (-b / a) / (y / x)
	elif b <= 5.5e-10:
		tmp = x / (y * a)
	else:
		tmp = (x / (a * b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5e+14)
		tmp = Float64(Float64(x * Float64(-b)) / Float64(y * a));
	elseif (b <= 1.03e-280)
		tmp = Float64(Float64(1.0 / Float64(a / x)) / y);
	elseif (b <= 5.3e-253)
		tmp = Float64(Float64(Float64(-b) / a) / Float64(y / x));
	elseif (b <= 5.5e-10)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(Float64(x / Float64(a * b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5e+14)
		tmp = (x * -b) / (y * a);
	elseif (b <= 1.03e-280)
		tmp = (1.0 / (a / x)) / y;
	elseif (b <= 5.3e-253)
		tmp = (-b / a) / (y / x);
	elseif (b <= 5.5e-10)
		tmp = x / (y * a);
	else
		tmp = (x / (a * b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5e+14], N[(N[(x * (-b)), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.03e-280], N[(N[(1.0 / N[(a / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 5.3e-253], N[(N[((-b) / a), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.5e-10], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -5e14

   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 88.7%

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

      1. +-commutative 88.7%

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

      2. mul-1-neg 88.7%

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

      3. unsub-neg 88.7%

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

   4. Simplified 88.7%

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

   5. Taylor expanded in y around 0 79.0%

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

      1. exp-neg 79.0%

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

      2. associate-*r/ 79.0%

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

      3. *-rgt-identity 79.0%

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

      4. +-commutative 79.0%

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

      5. exp-sum 79.0%

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

      6. rem-exp-log 79.0%

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

   7. Simplified 79.0%

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

   8. Taylor expanded in b around 0 50.6%

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

      1. +-commutative 50.6%

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

      2. mul-1-neg 50.6%

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

      3. unsub-neg 50.6%

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

      4. *-commutative 50.6%

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

      5. *-commutative 50.6%

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

      6. times-frac 44.4%

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

   10. Simplified 44.4%

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

   11. Taylor expanded in b around inf 50.6%

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

   if -5e14 < b < 1.03000000000000003e-280

   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. Taylor expanded in t around 0 73.1%

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

      1. +-commutative 73.1%

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

      2. mul-1-neg 73.1%

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

      3. unsub-neg 73.1%

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

   4. Simplified 73.1%

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

   5. Taylor expanded in b around 0 71.8%

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

      1. div-exp 71.8%

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

      2. *-commutative 71.8%

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

      3. exp-to-pow 71.8%

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

      4. rem-exp-log 72.2%

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

   7. Simplified 72.2%

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

   8. Taylor expanded in y around 0 36.5%

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

      1. un-div-inv 36.6%

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

      2. clear-num 36.6%

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

   10. Applied egg-rr 36.6%

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

   if 1.03000000000000003e-280 < b < 5.3000000000000002e-253

   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 75.6%

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

      1. +-commutative 75.6%

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

      2. mul-1-neg 75.6%

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

      3. unsub-neg 75.6%

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

   4. Simplified 75.6%

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

   5. Taylor expanded in y around 0 15.9%

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

      1. exp-neg 15.9%

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

      2. associate-*r/ 15.9%

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

      3. *-rgt-identity 15.9%

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

      4. +-commutative 15.9%

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

      5. exp-sum 15.9%

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

      6. rem-exp-log 15.9%

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

   7. Simplified 15.9%

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

   8. Taylor expanded in b around 0 15.8%

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

      1. +-commutative 15.8%

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

      2. mul-1-neg 15.8%

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

      3. unsub-neg 15.8%

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

      4. *-commutative 15.8%

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

      5. *-commutative 15.8%

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

      6. times-frac 15.8%

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

   10. Simplified 15.8%

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

   11. Taylor expanded in b around inf 63.8%

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

       1. *-commutative 63.8%

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

       2. associate-/l* 52.6%

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

       3. associate-*l/ 52.6%

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

       4. associate-/l/ 63.8%

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

       5. associate-*r/ 63.8%

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

       6. neg-mul-1 63.8%

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

       7. distribute-neg-frac 63.8%

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

   13. Simplified 63.8%

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

   if 5.3000000000000002e-253 < b < 5.4999999999999996e-10

   1. Initial program 97.5%

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

      1. associate-*l/ 92.5%

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

      2. associate--l+ 92.5%

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

      3. exp-sum 79.4%

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

      4. associate-*r* 79.4%

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

      5. *-commutative 79.4%

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

      6. exp-to-pow 79.4%

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

      7. exp-diff 79.4%

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

      8. *-commutative 79.4%

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

      9. exp-to-pow 80.2%

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

      10. sub-neg 80.2%

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

      11. metadata-eval 80.2%

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

   3. Simplified 80.2%

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

   4. Taylor expanded in t around 0 67.5%

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

      1. times-frac 63.5%

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

   6. Simplified 63.5%

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

   7. Taylor expanded in y around 0 41.7%

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

      1. associate-*r* 41.7%

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

      2. *-commutative 41.7%

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

      3. associate-/r* 41.7%

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

      4. *-commutative 41.7%

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

   9. Simplified 41.7%

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

   10. Taylor expanded in b around 0 41.7%

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

   if 5.4999999999999996e-10 < b

   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 t around 0 87.1%

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

      1. +-commutative 87.1%

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

      2. mul-1-neg 87.1%

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

      3. unsub-neg 87.1%

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

   4. Simplified 87.1%

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

   5. Taylor expanded in y around 0 82.8%

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

      1. exp-neg 82.8%

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

      2. associate-*r/ 82.8%

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

      3. *-rgt-identity 82.8%

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

      4. +-commutative 82.8%

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

      5. exp-sum 82.8%

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

      6. rem-exp-log 82.9%

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

   7. Simplified 82.9%

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

   8. Taylor expanded in b around 0 37.7%

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

   9. Taylor expanded in b around inf 36.7%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot b}}}{y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+14}:\\ \;\;\;\;\frac{x \cdot \left(-b\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.03 \cdot 10^{-280}:\\ \;\;\;\;\frac{\frac{1}{\frac{a}{x}}}{y}\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{-253}:\\ \;\;\;\;\frac{\frac{-b}{a}}{\frac{y}{x}}\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \end{array} \]

Alternative 14: 39.5% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{-122}:\\ \;\;\;\;\frac{\frac{x}{a} - x \cdot \frac{b}{a}}{y}\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{-41}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq 3.2:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+252}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.2e-122)
   (/ (- (/ x a) (* x (/ b a))) y)
   (if (<= b 1.06e-41)
     (/ 1.0 (* a (/ y x)))
     (if (<= b 3.2)
       (/ (/ x (+ a (* a b))) y)
       (if (<= b 5.2e+252) (/ x (* a (* y b))) (/ (/ x (* a b)) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.2e-122) {
		tmp = ((x / a) - (x * (b / a))) / y;
	} else if (b <= 1.06e-41) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= 3.2) {
		tmp = (x / (a + (a * b))) / y;
	} else if (b <= 5.2e+252) {
		tmp = x / (a * (y * b));
	} else {
		tmp = (x / (a * b)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-7.2d-122)) then
        tmp = ((x / a) - (x * (b / a))) / y
    else if (b <= 1.06d-41) then
        tmp = 1.0d0 / (a * (y / x))
    else if (b <= 3.2d0) then
        tmp = (x / (a + (a * b))) / y
    else if (b <= 5.2d+252) then
        tmp = x / (a * (y * b))
    else
        tmp = (x / (a * b)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.2e-122) {
		tmp = ((x / a) - (x * (b / a))) / y;
	} else if (b <= 1.06e-41) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= 3.2) {
		tmp = (x / (a + (a * b))) / y;
	} else if (b <= 5.2e+252) {
		tmp = x / (a * (y * b));
	} else {
		tmp = (x / (a * b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7.2e-122:
		tmp = ((x / a) - (x * (b / a))) / y
	elif b <= 1.06e-41:
		tmp = 1.0 / (a * (y / x))
	elif b <= 3.2:
		tmp = (x / (a + (a * b))) / y
	elif b <= 5.2e+252:
		tmp = x / (a * (y * b))
	else:
		tmp = (x / (a * b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7.2e-122)
		tmp = Float64(Float64(Float64(x / a) - Float64(x * Float64(b / a))) / y);
	elseif (b <= 1.06e-41)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	elseif (b <= 3.2)
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	elseif (b <= 5.2e+252)
		tmp = Float64(x / Float64(a * Float64(y * b)));
	else
		tmp = Float64(Float64(x / Float64(a * b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -7.2e-122)
		tmp = ((x / a) - (x * (b / a))) / y;
	elseif (b <= 1.06e-41)
		tmp = 1.0 / (a * (y / x));
	elseif (b <= 3.2)
		tmp = (x / (a + (a * b))) / y;
	elseif (b <= 5.2e+252)
		tmp = x / (a * (y * b));
	else
		tmp = (x / (a * b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7.2e-122], N[(N[(N[(x / a), $MachinePrecision] - N[(x * N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 1.06e-41], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.2], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 5.2e+252], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -7.19999999999999989e-122

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 84.7%

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

      1. +-commutative 84.7%

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

      2. mul-1-neg 84.7%

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

      3. unsub-neg 84.7%

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

   4. Simplified 84.7%

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

   5. Taylor expanded in y around 0 68.6%

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

      1. exp-neg 68.6%

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

      2. associate-*r/ 68.6%

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

      3. *-rgt-identity 68.6%

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

      4. +-commutative 68.6%

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

      5. exp-sum 68.6%

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

      6. rem-exp-log 68.8%

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

   7. Simplified 68.8%

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

   8. Taylor expanded in b around 0 19.0%

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

   9. Taylor expanded in b around 0 48.8%

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

       1. +-commutative 48.8%

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

       2. mul-1-neg 48.8%

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

       3. sub-neg 48.8%

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

       4. *-commutative 48.8%

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

       5. associate-*r/ 48.8%

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

   11. Simplified 48.8%

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

   if -7.19999999999999989e-122 < b < 1.06e-41

   1. Initial program 97.4%

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

      1. associate-*l/ 87.6%

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

      2. associate--l+ 87.6%

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

      3. exp-sum 72.7%

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

      4. associate-*r* 72.7%

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

      5. *-commutative 72.7%

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

      6. exp-to-pow 72.7%

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

      7. exp-diff 72.7%

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

      8. *-commutative 72.7%

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

      9. exp-to-pow 73.3%

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

      10. sub-neg 73.3%

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

      11. metadata-eval 73.3%

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

   3. Simplified 73.3%

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

   4. Taylor expanded in t around 0 66.3%

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

      1. times-frac 64.3%

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

   6. Simplified 64.3%

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

   7. Taylor expanded in y around 0 35.7%

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

      1. associate-*r* 35.7%

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

      2. *-commutative 35.7%

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

      3. associate-/r* 35.7%

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

      4. *-commutative 35.7%

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

   9. Simplified 35.7%

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

   10. Taylor expanded in b around 0 35.7%

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

       1. clear-num 36.1%

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

       2. inv-pow 36.1%

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

   12. Applied egg-rr 36.1%

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

       1. unpow-1 36.1%

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

       2. associate-*l/ 37.2%

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

       3. *-commutative 37.2%

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

   14. Simplified 37.2%

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

   if 1.06e-41 < b < 3.2000000000000002

   1. Initial program 99.5%

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

   2. Taylor expanded in t around 0 74.9%

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

      1. +-commutative 74.9%

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

      2. mul-1-neg 74.9%

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

      3. unsub-neg 74.9%

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

   4. Simplified 74.9%

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

   5. Taylor expanded in y around 0 43.5%

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

      1. exp-neg 43.5%

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

      2. associate-*r/ 43.6%

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

      3. *-rgt-identity 43.6%

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

      4. +-commutative 43.6%

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

      5. exp-sum 43.5%

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

      6. rem-exp-log 43.9%

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

   7. Simplified 43.9%

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

   8. Taylor expanded in b around 0 42.3%

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

   if 3.2000000000000002 < b < 5.20000000000000035e252

   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 85.4%

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

      1. +-commutative 85.4%

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

      2. mul-1-neg 85.4%

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

      3. unsub-neg 85.4%

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

   4. Simplified 85.4%

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

   5. Taylor expanded in y around 0 79.9%

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

      1. exp-neg 79.9%

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

      2. associate-*r/ 79.9%

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

      3. *-rgt-identity 79.9%

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

      4. +-commutative 79.9%

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

      5. exp-sum 79.9%

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

      6. rem-exp-log 79.9%

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

   7. Simplified 79.9%

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

   8. Taylor expanded in b around 0 33.4%

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

   9. Taylor expanded in b around inf 37.0%

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

       1. *-commutative 37.0%

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

   11. Simplified 37.0%

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

   if 5.20000000000000035e252 < 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. Taylor expanded in t around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 100.0%

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

      1. exp-neg 100.0%

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

      2. associate-*r/ 100.0%

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

      3. *-rgt-identity 100.0%

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

      4. +-commutative 100.0%

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

      5. exp-sum 100.0%

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

      6. rem-exp-log 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in b around 0 51.3%

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

   9. Taylor expanded in b around inf 51.3%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot b}}}{y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{-122}:\\ \;\;\;\;\frac{\frac{x}{a} - x \cdot \frac{b}{a}}{y}\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{-41}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq 3.2:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+252}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \end{array} \]

Alternative 15: 39.1% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+14}:\\ \;\;\;\;\frac{x \cdot \left(-b\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.03 \cdot 10^{-280}:\\ \;\;\;\;\frac{\frac{1}{\frac{a}{x}}}{y}\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{-253}:\\ \;\;\;\;\frac{\frac{-b}{a}}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.5e+14)
   (/ (* x (- b)) (* y a))
   (if (<= b 1.03e-280)
     (/ (/ 1.0 (/ a x)) y)
     (if (<= b 5.3e-253) (/ (/ (- b) a) (/ y x)) (/ x (* y (+ a (* a b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.5e+14) {
		tmp = (x * -b) / (y * a);
	} else if (b <= 1.03e-280) {
		tmp = (1.0 / (a / x)) / y;
	} else if (b <= 5.3e-253) {
		tmp = (-b / a) / (y / x);
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-6.5d+14)) then
        tmp = (x * -b) / (y * a)
    else if (b <= 1.03d-280) then
        tmp = (1.0d0 / (a / x)) / y
    else if (b <= 5.3d-253) then
        tmp = (-b / a) / (y / x)
    else
        tmp = x / (y * (a + (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.5e+14) {
		tmp = (x * -b) / (y * a);
	} else if (b <= 1.03e-280) {
		tmp = (1.0 / (a / x)) / y;
	} else if (b <= 5.3e-253) {
		tmp = (-b / a) / (y / x);
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.5e+14:
		tmp = (x * -b) / (y * a)
	elif b <= 1.03e-280:
		tmp = (1.0 / (a / x)) / y
	elif b <= 5.3e-253:
		tmp = (-b / a) / (y / x)
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.5e+14)
		tmp = Float64(Float64(x * Float64(-b)) / Float64(y * a));
	elseif (b <= 1.03e-280)
		tmp = Float64(Float64(1.0 / Float64(a / x)) / y);
	elseif (b <= 5.3e-253)
		tmp = Float64(Float64(Float64(-b) / a) / Float64(y / x));
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6.5e+14)
		tmp = (x * -b) / (y * a);
	elseif (b <= 1.03e-280)
		tmp = (1.0 / (a / x)) / y;
	elseif (b <= 5.3e-253)
		tmp = (-b / a) / (y / x);
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.5e+14], N[(N[(x * (-b)), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.03e-280], N[(N[(1.0 / N[(a / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 5.3e-253], N[(N[((-b) / a), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.5e14

   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 88.7%

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

      1. +-commutative 88.7%

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

      2. mul-1-neg 88.7%

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

      3. unsub-neg 88.7%

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

   4. Simplified 88.7%

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

   5. Taylor expanded in y around 0 79.0%

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

      1. exp-neg 79.0%

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

      2. associate-*r/ 79.0%

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

      3. *-rgt-identity 79.0%

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

      4. +-commutative 79.0%

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

      5. exp-sum 79.0%

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

      6. rem-exp-log 79.0%

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

   7. Simplified 79.0%

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

   8. Taylor expanded in b around 0 50.6%

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

      1. +-commutative 50.6%

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

      2. mul-1-neg 50.6%

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

      3. unsub-neg 50.6%

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

      4. *-commutative 50.6%

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

      5. *-commutative 50.6%

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

      6. times-frac 44.4%

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

   10. Simplified 44.4%

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

   11. Taylor expanded in b around inf 50.6%

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

   if -6.5e14 < b < 1.03000000000000003e-280

   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. Taylor expanded in t around 0 73.1%

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

      1. +-commutative 73.1%

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

      2. mul-1-neg 73.1%

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

      3. unsub-neg 73.1%

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

   4. Simplified 73.1%

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

   5. Taylor expanded in b around 0 71.8%

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

      1. div-exp 71.8%

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

      2. *-commutative 71.8%

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

      3. exp-to-pow 71.8%

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

      4. rem-exp-log 72.2%

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

   7. Simplified 72.2%

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

   8. Taylor expanded in y around 0 36.5%

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

      1. un-div-inv 36.6%

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

      2. clear-num 36.6%

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

   10. Applied egg-rr 36.6%

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

   if 1.03000000000000003e-280 < b < 5.3000000000000002e-253

   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 75.6%

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

      1. +-commutative 75.6%

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

      2. mul-1-neg 75.6%

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

      3. unsub-neg 75.6%

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

   4. Simplified 75.6%

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

   5. Taylor expanded in y around 0 15.9%

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

      1. exp-neg 15.9%

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

      2. associate-*r/ 15.9%

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

      3. *-rgt-identity 15.9%

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

      4. +-commutative 15.9%

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

      5. exp-sum 15.9%

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

      6. rem-exp-log 15.9%

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

   7. Simplified 15.9%

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

   8. Taylor expanded in b around 0 15.8%

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

      1. +-commutative 15.8%

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

      2. mul-1-neg 15.8%

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

      3. unsub-neg 15.8%

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

      4. *-commutative 15.8%

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

      5. *-commutative 15.8%

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

      6. times-frac 15.8%

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

   10. Simplified 15.8%

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

   11. Taylor expanded in b around inf 63.8%

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

       1. *-commutative 63.8%

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

       2. associate-/l* 52.6%

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

       3. associate-*l/ 52.6%

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

       4. associate-/l/ 63.8%

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

       5. associate-*r/ 63.8%

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

       6. neg-mul-1 63.8%

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

       7. distribute-neg-frac 63.8%

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

   13. Simplified 63.8%

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

   if 5.3000000000000002e-253 < b

   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 80.9%

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

      1. +-commutative 80.9%

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

      2. mul-1-neg 80.9%

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

      3. unsub-neg 80.9%

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

   4. Simplified 80.9%

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

   5. Taylor expanded in y around 0 63.6%

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

      1. exp-neg 63.6%

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

      2. associate-*r/ 63.6%

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

      3. *-rgt-identity 63.6%

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

      4. +-commutative 63.6%

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

      5. exp-sum 63.6%

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

      6. rem-exp-log 63.9%

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

   7. Simplified 63.9%

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

   8. Taylor expanded in b around 0 36.8%

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

   9. Taylor expanded in x around 0 37.7%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+14}:\\ \;\;\;\;\frac{x \cdot \left(-b\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.03 \cdot 10^{-280}:\\ \;\;\;\;\frac{\frac{1}{\frac{a}{x}}}{y}\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{-253}:\\ \;\;\;\;\frac{\frac{-b}{a}}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 16: 38.1% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.06 \cdot 10^{-15}:\\ \;\;\;\;\frac{-b}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.06e-15)
   (/ (- b) (* a (/ y x)))
   (if (<= b 8e-67) (* (/ x y) (/ 1.0 a)) (/ (/ x (* a b)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.06e-15) {
		tmp = -b / (a * (y / x));
	} else if (b <= 8e-67) {
		tmp = (x / y) * (1.0 / a);
	} else {
		tmp = (x / (a * b)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.06d-15)) then
        tmp = -b / (a * (y / x))
    else if (b <= 8d-67) then
        tmp = (x / y) * (1.0d0 / a)
    else
        tmp = (x / (a * b)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.06e-15) {
		tmp = -b / (a * (y / x));
	} else if (b <= 8e-67) {
		tmp = (x / y) * (1.0 / a);
	} else {
		tmp = (x / (a * b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.06e-15:
		tmp = -b / (a * (y / x))
	elif b <= 8e-67:
		tmp = (x / y) * (1.0 / a)
	else:
		tmp = (x / (a * b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.06e-15)
		tmp = Float64(Float64(-b) / Float64(a * Float64(y / x)));
	elseif (b <= 8e-67)
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	else
		tmp = Float64(Float64(x / Float64(a * b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.06e-15)
		tmp = -b / (a * (y / x));
	elseif (b <= 8e-67)
		tmp = (x / y) * (1.0 / a);
	else
		tmp = (x / (a * b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.06e-15], N[((-b) / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8e-67], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.06000000000000007e-15

   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 87.9%

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

      1. +-commutative 87.9%

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

      2. mul-1-neg 87.9%

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

      3. unsub-neg 87.9%

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

   4. Simplified 87.9%

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

   5. Taylor expanded in y around 0 77.3%

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

      1. exp-neg 77.3%

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

      2. associate-*r/ 77.3%

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

      3. *-rgt-identity 77.3%

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

      4. +-commutative 77.3%

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

      5. exp-sum 77.3%

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

      6. rem-exp-log 77.3%

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

   7. Simplified 77.3%

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

   8. Taylor expanded in b around 0 47.6%

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

      1. +-commutative 47.6%

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

      2. mul-1-neg 47.6%

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

      3. unsub-neg 47.6%

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

      4. *-commutative 47.6%

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

      5. *-commutative 47.6%

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

      6. times-frac 41.9%

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

   10. Simplified 41.9%

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

   11. Taylor expanded in b around inf 47.6%

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

       1. mul-1-neg 47.6%

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

       2. *-commutative 47.6%

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

       3. associate-/l* 42.0%

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

       4. associate-*l/ 40.6%

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

       5. *-commutative 40.6%

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

   13. Simplified 40.6%

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

   if -1.06000000000000007e-15 < b < 7.99999999999999954e-67

   1. Initial program 97.6%

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

      1. associate-*l/ 90.6%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. associate--l+ 90.6%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \]

      3. exp-sum 78.5%

         \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}\right)} \]

      4. associate-*r* 78.5%

         \[\leadsto \color{blue}{\left(\frac{x}{y} \cdot e^{y \cdot \log z}\right) \cdot e^{\left(t - 1\right) \cdot \log a - b}} \]

      5. *-commutative 78.5%

         \[\leadsto \left(\frac{x}{y} \cdot e^{\color{blue}{\log z \cdot y}}\right) \cdot e^{\left(t - 1\right) \cdot \log a - b} \]

      6. exp-to-pow 78.5%

         \[\leadsto \left(\frac{x}{y} \cdot \color{blue}{{z}^{y}}\right) \cdot e^{\left(t - 1\right) \cdot \log a - b} \]

      7. exp-diff 78.5%

         \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}} \]

      8. *-commutative 78.5%

         \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}} \]

      9. exp-to-pow 79.1%

         \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}} \]

      10. sub-neg 79.1%

          \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}} \]

      11. metadata-eval 79.1%

          \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}} \]

   3. Simplified 79.1%

      \[\leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}} \]

   4. Taylor expanded in t around 0 66.4%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   5. Step-by-step derivation

      1. times-frac 65.6%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   6. Simplified 65.6%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Taylor expanded in y around 0 37.0%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   8. Step-by-step derivation

      1. associate-*r* 37.0%

         \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

      2. *-commutative 37.0%

         \[\leadsto \frac{x}{\color{blue}{e^{b} \cdot \left(a \cdot y\right)}} \]

      3. associate-/r* 37.0%

         \[\leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{a \cdot y}} \]

      4. *-commutative 37.0%

         \[\leadsto \frac{\frac{x}{e^{b}}}{\color{blue}{y \cdot a}} \]

   9. Simplified 37.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{y \cdot a}} \]

   10. Taylor expanded in b around 0 37.0%

       \[\leadsto \frac{\color{blue}{x}}{y \cdot a} \]
   11. Step-by-step derivation

       1. associate-/r* 38.9%

          \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]

       2. div-inv 38.8%

          \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{a}} \]

   12. Applied egg-rr 38.8%

       \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{a}} \]

   if 7.99999999999999954e-67 < b

   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 t around 0 85.9%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   3. Step-by-step derivation

      1. +-commutative 85.9%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 85.9%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 85.9%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   4. Simplified 85.9%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   5. Taylor expanded in y around 0 73.2%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-\left(b + \log a\right)}}{y}} \]
   6. Step-by-step derivation

      1. exp-neg 73.2%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 73.2%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 73.2%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 73.2%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 73.2%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{\log a} \cdot e^{b}}}}{y} \]

      6. rem-exp-log 73.3%

         \[\leadsto \frac{\frac{x}{\color{blue}{a} \cdot e^{b}}}{y} \]

   7. Simplified 73.3%

      \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]

   8. Taylor expanded in b around 0 36.2%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + a \cdot b}}}{y} \]

   9. Taylor expanded in b around inf 35.3%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot b}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.06 \cdot 10^{-15}:\\ \;\;\;\;\frac{-b}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \end{array} \]

Alternative 17: 39.7% accurate, 28.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 8.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{x - x \cdot b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 8.5e-11) (/ (- x (* x b)) (* y a)) (/ (/ x (* a b)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 8.5e-11) {
		tmp = (x - (x * b)) / (y * a);
	} else {
		tmp = (x / (a * b)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 8.5d-11) then
        tmp = (x - (x * b)) / (y * a)
    else
        tmp = (x / (a * b)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 8.5e-11) {
		tmp = (x - (x * b)) / (y * a);
	} else {
		tmp = (x / (a * b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 8.5e-11:
		tmp = (x - (x * b)) / (y * a)
	else:
		tmp = (x / (a * b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 8.5e-11)
		tmp = Float64(Float64(x - Float64(x * b)) / Float64(y * a));
	else
		tmp = Float64(Float64(x / Float64(a * b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 8.5e-11)
		tmp = (x - (x * b)) / (y * a);
	else
		tmp = (x / (a * b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 8.5e-11], N[(N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 8.50000000000000037e-11

   1. Initial program 98.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.3%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. associate--l+ 89.3%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \]

      3. exp-sum 73.8%

         \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}\right)} \]

      4. associate-*r* 73.8%

         \[\leadsto \color{blue}{\left(\frac{x}{y} \cdot e^{y \cdot \log z}\right) \cdot e^{\left(t - 1\right) \cdot \log a - b}} \]

      5. *-commutative 73.8%

         \[\leadsto \left(\frac{x}{y} \cdot e^{\color{blue}{\log z \cdot y}}\right) \cdot e^{\left(t - 1\right) \cdot \log a - b} \]

      6. exp-to-pow 73.8%

         \[\leadsto \left(\frac{x}{y} \cdot \color{blue}{{z}^{y}}\right) \cdot e^{\left(t - 1\right) \cdot \log a - b} \]

      7. exp-diff 68.4%

         \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}} \]

      8. *-commutative 68.4%

         \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}} \]

      9. exp-to-pow 68.8%

         \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}} \]

      10. sub-neg 68.8%

          \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}} \]

      11. metadata-eval 68.8%

          \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}} \]

   3. Simplified 68.8%

      \[\leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}} \]

   4. Taylor expanded in t around 0 65.4%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   5. Step-by-step derivation

      1. times-frac 64.3%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   6. Simplified 64.3%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Taylor expanded in y around 0 50.4%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   8. Step-by-step derivation

      1. associate-*r* 47.7%

         \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

      2. *-commutative 47.7%

         \[\leadsto \frac{x}{\color{blue}{e^{b} \cdot \left(a \cdot y\right)}} \]

      3. associate-/r* 47.7%

         \[\leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{a \cdot y}} \]

      4. *-commutative 47.7%

         \[\leadsto \frac{\frac{x}{e^{b}}}{\color{blue}{y \cdot a}} \]

   9. Simplified 47.7%

      \[\leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{y \cdot a}} \]

   10. Taylor expanded in b around 0 40.1%

       \[\leadsto \frac{\color{blue}{x + -1 \cdot \left(b \cdot x\right)}}{y \cdot a} \]
   11. Step-by-step derivation

       1. mul-1-neg 40.1%

          \[\leadsto \frac{x + \color{blue}{\left(-b \cdot x\right)}}{y \cdot a} \]

       2. unsub-neg 40.1%

          \[\leadsto \frac{\color{blue}{x - b \cdot x}}{y \cdot a} \]

       3. *-commutative 40.1%

          \[\leadsto \frac{x - \color{blue}{x \cdot b}}{y \cdot a} \]

   12. Simplified 40.1%

       \[\leadsto \frac{\color{blue}{x - x \cdot b}}{y \cdot a} \]

   if 8.50000000000000037e-11 < b

   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 t around 0 87.1%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   3. Step-by-step derivation

      1. +-commutative 87.1%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 87.1%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 87.1%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   4. Simplified 87.1%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   5. Taylor expanded in y around 0 82.8%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-\left(b + \log a\right)}}{y}} \]
   6. Step-by-step derivation

      1. exp-neg 82.8%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 82.8%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 82.8%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 82.8%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 82.8%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{\log a} \cdot e^{b}}}}{y} \]

      6. rem-exp-log 82.9%

         \[\leadsto \frac{\frac{x}{\color{blue}{a} \cdot e^{b}}}{y} \]

   7. Simplified 82.9%

      \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]

   8. Taylor expanded in b around 0 37.7%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + a \cdot b}}}{y} \]

   9. Taylor expanded in b around inf 36.7%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot b}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 8.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{x - x \cdot b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \end{array} \]

Alternative 18: 39.7% accurate, 28.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.8 \cdot 10^{-27}:\\ \;\;\;\;\frac{x - x \cdot b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 2.8e-27) (/ (- x (* x b)) (* y a)) (/ (/ x (+ a (* a b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.8e-27) {
		tmp = (x - (x * b)) / (y * a);
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 2.8d-27) then
        tmp = (x - (x * b)) / (y * a)
    else
        tmp = (x / (a + (a * b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.8e-27) {
		tmp = (x - (x * b)) / (y * a);
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 2.8e-27:
		tmp = (x - (x * b)) / (y * a)
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 2.8e-27)
		tmp = Float64(Float64(x - Float64(x * b)) / Float64(y * a));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 2.8e-27)
		tmp = (x - (x * b)) / (y * a);
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 2.8e-27], N[(N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 2.8e-27

   1. Initial program 98.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.5%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. associate--l+ 89.5%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \]

      3. exp-sum 73.5%

         \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}\right)} \]

      4. associate-*r* 73.5%

         \[\leadsto \color{blue}{\left(\frac{x}{y} \cdot e^{y \cdot \log z}\right) \cdot e^{\left(t - 1\right) \cdot \log a - b}} \]

      5. *-commutative 73.5%

         \[\leadsto \left(\frac{x}{y} \cdot e^{\color{blue}{\log z \cdot y}}\right) \cdot e^{\left(t - 1\right) \cdot \log a - b} \]

      6. exp-to-pow 73.5%

         \[\leadsto \left(\frac{x}{y} \cdot \color{blue}{{z}^{y}}\right) \cdot e^{\left(t - 1\right) \cdot \log a - b} \]

      7. exp-diff 67.9%

         \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}} \]

      8. *-commutative 67.9%

         \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}} \]

      9. exp-to-pow 68.3%

         \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}} \]

      10. sub-neg 68.3%

          \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}} \]

      11. metadata-eval 68.3%

          \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}} \]

   3. Simplified 68.3%

      \[\leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}} \]

   4. Taylor expanded in t around 0 64.7%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   5. Step-by-step derivation

      1. times-frac 64.2%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   6. Simplified 64.2%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Taylor expanded in y around 0 50.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   8. Step-by-step derivation

      1. associate-*r* 48.1%

         \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

      2. *-commutative 48.1%

         \[\leadsto \frac{x}{\color{blue}{e^{b} \cdot \left(a \cdot y\right)}} \]

      3. associate-/r* 48.1%

         \[\leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{a \cdot y}} \]

      4. *-commutative 48.1%

         \[\leadsto \frac{\frac{x}{e^{b}}}{\color{blue}{y \cdot a}} \]

   9. Simplified 48.1%

      \[\leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{y \cdot a}} \]

   10. Taylor expanded in b around 0 40.2%

       \[\leadsto \frac{\color{blue}{x + -1 \cdot \left(b \cdot x\right)}}{y \cdot a} \]
   11. Step-by-step derivation

       1. mul-1-neg 40.2%

          \[\leadsto \frac{x + \color{blue}{\left(-b \cdot x\right)}}{y \cdot a} \]

       2. unsub-neg 40.2%

          \[\leadsto \frac{\color{blue}{x - b \cdot x}}{y \cdot a} \]

       3. *-commutative 40.2%

          \[\leadsto \frac{x - \color{blue}{x \cdot b}}{y \cdot a} \]

   12. Simplified 40.2%

       \[\leadsto \frac{\color{blue}{x - x \cdot b}}{y \cdot a} \]

   if 2.8e-27 < b

   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 t around 0 86.8%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   3. Step-by-step derivation

      1. +-commutative 86.8%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 86.8%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 86.8%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   4. Simplified 86.8%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   5. Taylor expanded in y around 0 79.1%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-\left(b + \log a\right)}}{y}} \]
   6. Step-by-step derivation

      1. exp-neg 79.1%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 79.1%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 79.1%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 79.1%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 79.1%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{\log a} \cdot e^{b}}}}{y} \]

      6. rem-exp-log 79.2%

         \[\leadsto \frac{\frac{x}{\color{blue}{a} \cdot e^{b}}}{y} \]

   7. Simplified 79.2%

      \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]

   8. Taylor expanded in b around 0 37.6%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + a \cdot b}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 2.8 \cdot 10^{-27}:\\ \;\;\;\;\frac{x - x \cdot b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]

Alternative 19: 31.3% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.8 \cdot 10^{-65}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 1.8e-65) (* (/ x y) (/ 1.0 a)) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 1.8e-65) {
		tmp = (x / y) * (1.0 / a);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= 1.8d-65) then
        tmp = (x / y) * (1.0d0 / a)
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 1.8e-65) {
		tmp = (x / y) * (1.0 / a);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 1.8e-65:
		tmp = (x / y) * (1.0 / a)
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 1.8e-65)
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 1.8e-65)
		tmp = (x / y) * (1.0 / a);
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 1.8e-65], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.7999999999999999e-65

   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. Step-by-step derivation

      1. associate-*l/ 87.2%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. associate--l+ 87.2%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \]

      3. exp-sum 73.6%

         \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}\right)} \]

      4. associate-*r* 73.6%

         \[\leadsto \color{blue}{\left(\frac{x}{y} \cdot e^{y \cdot \log z}\right) \cdot e^{\left(t - 1\right) \cdot \log a - b}} \]

      5. *-commutative 73.6%

         \[\leadsto \left(\frac{x}{y} \cdot e^{\color{blue}{\log z \cdot y}}\right) \cdot e^{\left(t - 1\right) \cdot \log a - b} \]

      6. exp-to-pow 73.6%

         \[\leadsto \left(\frac{x}{y} \cdot \color{blue}{{z}^{y}}\right) \cdot e^{\left(t - 1\right) \cdot \log a - b} \]

      7. exp-diff 63.0%

         \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}} \]

      8. *-commutative 63.0%

         \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}} \]

      9. exp-to-pow 63.3%

         \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}} \]

      10. sub-neg 63.3%

          \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}} \]

      11. metadata-eval 63.3%

          \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}} \]

   3. Simplified 63.3%

      \[\leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}} \]

   4. Taylor expanded in t around 0 71.5%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   5. Step-by-step derivation

      1. times-frac 66.8%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   6. Simplified 66.8%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Taylor expanded in y around 0 59.0%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   8. Step-by-step derivation

      1. associate-*r* 51.9%

         \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

      2. *-commutative 51.9%

         \[\leadsto \frac{x}{\color{blue}{e^{b} \cdot \left(a \cdot y\right)}} \]

      3. associate-/r* 51.9%

         \[\leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{a \cdot y}} \]

      4. *-commutative 51.9%

         \[\leadsto \frac{\frac{x}{e^{b}}}{\color{blue}{y \cdot a}} \]

   9. Simplified 51.9%

      \[\leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{y \cdot a}} \]

   10. Taylor expanded in b around 0 29.6%

       \[\leadsto \frac{\color{blue}{x}}{y \cdot a} \]
   11. Step-by-step derivation

       1. associate-/r* 31.9%

          \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]

       2. div-inv 31.9%

          \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{a}} \]

   12. Applied egg-rr 31.9%

       \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{a}} \]

   if 1.7999999999999999e-65 < x

   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 79.5%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   3. Step-by-step derivation

      1. +-commutative 79.5%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 79.5%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 79.5%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   4. Simplified 79.5%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   5. Taylor expanded in y around 0 57.9%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-\left(b + \log a\right)}}{y}} \]
   6. Step-by-step derivation

      1. exp-neg 57.9%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 57.9%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 57.9%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 57.9%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 57.9%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{\log a} \cdot e^{b}}}}{y} \]

      6. rem-exp-log 58.2%

         \[\leadsto \frac{\frac{x}{\color{blue}{a} \cdot e^{b}}}{y} \]

   7. Simplified 58.2%

      \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]

   8. Taylor expanded in b around 0 27.0%

      \[\leadsto \frac{\frac{x}{\color{blue}{a}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.8 \cdot 10^{-65}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]

Alternative 20: 35.2% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 7.2 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 7.2e-36) (* (/ x y) (/ 1.0 a)) (/ x (* a (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 7.2e-36) {
		tmp = (x / y) * (1.0 / a);
	} 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 <= 7.2d-36) then
        tmp = (x / y) * (1.0d0 / a)
    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 <= 7.2e-36) {
		tmp = (x / y) * (1.0 / a);
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 7.2e-36:
		tmp = (x / y) * (1.0 / a)
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 7.2e-36)
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	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 <= 7.2e-36)
		tmp = (x / y) * (1.0 / a);
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 7.2e-36], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 7.20000000000000064e-36

   1. Initial program 98.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.4%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. associate--l+ 89.4%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \]

      3. exp-sum 73.7%

         \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}\right)} \]

      4. associate-*r* 73.7%

         \[\leadsto \color{blue}{\left(\frac{x}{y} \cdot e^{y \cdot \log z}\right) \cdot e^{\left(t - 1\right) \cdot \log a - b}} \]

      5. *-commutative 73.7%

         \[\leadsto \left(\frac{x}{y} \cdot e^{\color{blue}{\log z \cdot y}}\right) \cdot e^{\left(t - 1\right) \cdot \log a - b} \]

      6. exp-to-pow 73.7%

         \[\leadsto \left(\frac{x}{y} \cdot \color{blue}{{z}^{y}}\right) \cdot e^{\left(t - 1\right) \cdot \log a - b} \]

      7. exp-diff 68.1%

         \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}} \]

      8. *-commutative 68.1%

         \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}} \]

      9. exp-to-pow 68.5%

         \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}} \]

      10. sub-neg 68.5%

          \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}} \]

      11. metadata-eval 68.5%

          \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}} \]

   3. Simplified 68.5%

      \[\leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}} \]

   4. Taylor expanded in t around 0 64.9%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   5. Step-by-step derivation

      1. times-frac 64.4%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   6. Simplified 64.4%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Taylor expanded in y around 0 50.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   8. Step-by-step derivation

      1. associate-*r* 48.0%

         \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

      2. *-commutative 48.0%

         \[\leadsto \frac{x}{\color{blue}{e^{b} \cdot \left(a \cdot y\right)}} \]

      3. associate-/r* 48.0%

         \[\leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{a \cdot y}} \]

      4. *-commutative 48.0%

         \[\leadsto \frac{\frac{x}{e^{b}}}{\color{blue}{y \cdot a}} \]

   9. Simplified 48.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{y \cdot a}} \]

   10. Taylor expanded in b around 0 33.2%

       \[\leadsto \frac{\color{blue}{x}}{y \cdot a} \]
   11. Step-by-step derivation

       1. associate-/r* 34.3%

          \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]

       2. div-inv 34.2%

          \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{a}} \]

   12. Applied egg-rr 34.2%

       \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{a}} \]

   if 7.20000000000000064e-36 < b

   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 t around 0 85.9%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   3. Step-by-step derivation

      1. +-commutative 85.9%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 85.9%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 85.9%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   4. Simplified 85.9%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   5. Taylor expanded in y around 0 77.1%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-\left(b + \log a\right)}}{y}} \]
   6. Step-by-step derivation

      1. exp-neg 77.1%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 77.1%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 77.1%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 77.1%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 77.1%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{\log a} \cdot e^{b}}}}{y} \]

      6. rem-exp-log 77.2%

         \[\leadsto \frac{\frac{x}{\color{blue}{a} \cdot e^{b}}}{y} \]

   7. Simplified 77.2%

      \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]

   8. Taylor expanded in b around 0 36.7%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + a \cdot b}}}{y} \]

   9. Taylor expanded in b around inf 33.2%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. *-commutative 33.2%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y \cdot b\right)}} \]

   11. Simplified 33.2%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot b\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 7.2 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]

Alternative 21: 35.5% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.9 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1.9e-67) (* (/ x y) (/ 1.0 a)) (/ (/ x (* a b)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.9e-67) {
		tmp = (x / y) * (1.0 / a);
	} else {
		tmp = (x / (a * b)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 1.9d-67) then
        tmp = (x / y) * (1.0d0 / a)
    else
        tmp = (x / (a * b)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.9e-67) {
		tmp = (x / y) * (1.0 / a);
	} else {
		tmp = (x / (a * b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 1.9e-67:
		tmp = (x / y) * (1.0 / a)
	else:
		tmp = (x / (a * b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.9e-67)
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	else
		tmp = Float64(Float64(x / Float64(a * b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 1.9e-67)
		tmp = (x / y) * (1.0 / a);
	else
		tmp = (x / (a * b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.9e-67], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.89999999999999994e-67

   1. Initial program 98.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 90.1%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. associate--l+ 90.1%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \]

      3. exp-sum 73.8%

         \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}\right)} \]

      4. associate-*r* 73.8%

         \[\leadsto \color{blue}{\left(\frac{x}{y} \cdot e^{y \cdot \log z}\right) \cdot e^{\left(t - 1\right) \cdot \log a - b}} \]

      5. *-commutative 73.8%

         \[\leadsto \left(\frac{x}{y} \cdot e^{\color{blue}{\log z \cdot y}}\right) \cdot e^{\left(t - 1\right) \cdot \log a - b} \]

      6. exp-to-pow 73.8%

         \[\leadsto \left(\frac{x}{y} \cdot \color{blue}{{z}^{y}}\right) \cdot e^{\left(t - 1\right) \cdot \log a - b} \]

      7. exp-diff 68.0%

         \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}} \]

      8. *-commutative 68.0%

         \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}} \]

      9. exp-to-pow 68.4%

         \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}} \]

      10. sub-neg 68.4%

          \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}} \]

      11. metadata-eval 68.4%

          \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}} \]

   3. Simplified 68.4%

      \[\leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}} \]

   4. Taylor expanded in t around 0 65.2%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   5. Step-by-step derivation

      1. times-frac 63.5%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   6. Simplified 63.5%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Taylor expanded in y around 0 52.2%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   8. Step-by-step derivation

      1. associate-*r* 49.3%

         \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

      2. *-commutative 49.3%

         \[\leadsto \frac{x}{\color{blue}{e^{b} \cdot \left(a \cdot y\right)}} \]

      3. associate-/r* 49.3%

         \[\leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{a \cdot y}} \]

      4. *-commutative 49.3%

         \[\leadsto \frac{\frac{x}{e^{b}}}{\color{blue}{y \cdot a}} \]

   9. Simplified 49.3%

      \[\leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{y \cdot a}} \]

   10. Taylor expanded in b around 0 33.8%

       \[\leadsto \frac{\color{blue}{x}}{y \cdot a} \]
   11. Step-by-step derivation

       1. associate-/r* 35.0%

          \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]

       2. div-inv 35.0%

          \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{a}} \]

   12. Applied egg-rr 35.0%

       \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{a}} \]

   if 1.89999999999999994e-67 < b

   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 t around 0 85.9%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   3. Step-by-step derivation

      1. +-commutative 85.9%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 85.9%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 85.9%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   4. Simplified 85.9%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   5. Taylor expanded in y around 0 73.2%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-\left(b + \log a\right)}}{y}} \]
   6. Step-by-step derivation

      1. exp-neg 73.2%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 73.2%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 73.2%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 73.2%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 73.2%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{\log a} \cdot e^{b}}}}{y} \]

      6. rem-exp-log 73.3%

         \[\leadsto \frac{\frac{x}{\color{blue}{a} \cdot e^{b}}}{y} \]

   7. Simplified 73.3%

      \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]

   8. Taylor expanded in b around 0 36.2%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + a \cdot b}}}{y} \]

   9. Taylor expanded in b around inf 35.3%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot b}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.9 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \end{array} \]

Alternative 22: 32.4% accurate, 44.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 5 \cdot 10^{+15}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 5e+15) (/ (/ x a) y) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 5e+15) {
		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 (a <= 5d+15) 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 (a <= 5e+15) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 5e+15:
		tmp = (x / a) / y
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 5e+15)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 5e+15)
		tmp = (x / a) / y;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 5e+15], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 5e15

   1. Initial program 99.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 82.6%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   3. Step-by-step derivation

      1. +-commutative 82.6%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 82.6%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 82.6%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   4. Simplified 82.6%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   5. Taylor expanded in y around 0 60.5%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-\left(b + \log a\right)}}{y}} \]
   6. Step-by-step derivation

      1. exp-neg 60.5%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 60.5%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 60.5%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 60.5%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 60.5%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{\log a} \cdot e^{b}}}}{y} \]

      6. rem-exp-log 60.6%

         \[\leadsto \frac{\frac{x}{\color{blue}{a} \cdot e^{b}}}{y} \]

   7. Simplified 60.6%

      \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]

   8. Taylor expanded in b around 0 28.2%

      \[\leadsto \frac{\frac{x}{\color{blue}{a}}}{y} \]

   if 5e15 < a

   1. Initial program 98.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.7%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. associate--l+ 89.7%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \]

      3. exp-sum 75.0%

         \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}\right)} \]

      4. associate-*r* 75.0%

         \[\leadsto \color{blue}{\left(\frac{x}{y} \cdot e^{y \cdot \log z}\right) \cdot e^{\left(t - 1\right) \cdot \log a - b}} \]

      5. *-commutative 75.0%

         \[\leadsto \left(\frac{x}{y} \cdot e^{\color{blue}{\log z \cdot y}}\right) \cdot e^{\left(t - 1\right) \cdot \log a - b} \]

      6. exp-to-pow 75.0%

         \[\leadsto \left(\frac{x}{y} \cdot \color{blue}{{z}^{y}}\right) \cdot e^{\left(t - 1\right) \cdot \log a - b} \]

      7. exp-diff 63.6%

         \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}} \]

      8. *-commutative 63.6%

         \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}} \]

      9. exp-to-pow 64.1%

         \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}} \]

      10. sub-neg 64.1%

          \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}} \]

      11. metadata-eval 64.1%

          \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}} \]

   3. Simplified 64.1%

      \[\leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}} \]

   4. Taylor expanded in t around 0 61.3%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   5. Step-by-step derivation

      1. times-frac 63.7%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   6. Simplified 63.7%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Taylor expanded in y around 0 59.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   8. Step-by-step derivation

      1. associate-*r* 54.9%

         \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

      2. *-commutative 54.9%

         \[\leadsto \frac{x}{\color{blue}{e^{b} \cdot \left(a \cdot y\right)}} \]

      3. associate-/r* 54.9%

         \[\leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{a \cdot y}} \]

      4. *-commutative 54.9%

         \[\leadsto \frac{\frac{x}{e^{b}}}{\color{blue}{y \cdot a}} \]

   9. Simplified 54.9%

      \[\leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{y \cdot a}} \]

   10. Taylor expanded in b around 0 34.7%

       \[\leadsto \frac{\color{blue}{x}}{y \cdot a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 5 \cdot 10^{+15}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]

Alternative 23: 31.0% 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. Step-by-step derivation

   1. associate-*l/ 88.2%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

   2. associate--l+ 88.2%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \]

   3. exp-sum 71.8%

      \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}\right)} \]

   4. associate-*r* 71.8%

      \[\leadsto \color{blue}{\left(\frac{x}{y} \cdot e^{y \cdot \log z}\right) \cdot e^{\left(t - 1\right) \cdot \log a - b}} \]

   5. *-commutative 71.8%

      \[\leadsto \left(\frac{x}{y} \cdot e^{\color{blue}{\log z \cdot y}}\right) \cdot e^{\left(t - 1\right) \cdot \log a - b} \]

   6. exp-to-pow 71.8%

      \[\leadsto \left(\frac{x}{y} \cdot \color{blue}{{z}^{y}}\right) \cdot e^{\left(t - 1\right) \cdot \log a - b} \]

   7. exp-diff 60.1%

      \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}} \]

   8. *-commutative 60.1%

      \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}} \]

   9. exp-to-pow 60.4%

      \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}} \]

   10. sub-neg 60.4%

       \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}} \]

   11. metadata-eval 60.4%

       \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}} \]

3. Simplified 60.4%

   \[\leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}} \]

4. Taylor expanded in t around 0 67.3%

   \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
5. Step-by-step derivation

   1. times-frac 63.4%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

6. Simplified 63.4%

   \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

7. Taylor expanded in y around 0 58.8%

   \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
8. Step-by-step derivation

   1. associate-*r* 52.9%

      \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

   2. *-commutative 52.9%

      \[\leadsto \frac{x}{\color{blue}{e^{b} \cdot \left(a \cdot y\right)}} \]

   3. associate-/r* 52.9%

      \[\leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{a \cdot y}} \]

   4. *-commutative 52.9%

      \[\leadsto \frac{\frac{x}{e^{b}}}{\color{blue}{y \cdot a}} \]

9. Simplified 52.9%

   \[\leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{y \cdot a}} \]

10. Taylor expanded in b around 0 29.1%

    \[\leadsto \frac{\color{blue}{x}}{y \cdot a} \]

11. Final simplification 29.1%

    \[\leadsto \frac{x}{y \cdot a} \]

Developer target: 72.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t - 1\right)}\\ t_2 := \frac{x \cdot \frac{t_1}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{if}\;t < -0.8845848504127471:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < 852031.2288374073:\\ \;\;\;\;\frac{\frac{x}{y} \cdot t_1}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (- t 1.0)))
        (t_2 (/ (* x (/ t_1 y)) (- (+ b 1.0) (* y (log z))))))
   (if (< t -0.8845848504127471)
     t_2
     (if (< t 852031.2288374073)
       (/ (* (/ x y) t_1) (exp (- b (* (log z) y))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a ** (t - 1.0d0)
    t_2 = (x * (t_1 / y)) / ((b + 1.0d0) - (y * log(z)))
    if (t < (-0.8845848504127471d0)) then
        tmp = t_2
    else if (t < 852031.2288374073d0) then
        tmp = ((x / y) * t_1) / exp((b - (log(z) * y)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * Math.log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / Math.exp((b - (Math.log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, (t - 1.0))
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * math.log(z)))
	tmp = 0
	if t < -0.8845848504127471:
		tmp = t_2
	elif t < 852031.2288374073:
		tmp = ((x / y) * t_1) / math.exp((b - (math.log(z) * y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = a ^ Float64(t - 1.0)
	t_2 = Float64(Float64(x * Float64(t_1 / y)) / Float64(Float64(b + 1.0) - Float64(y * log(z))))
	tmp = 0.0
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = Float64(Float64(Float64(x / y) * t_1) / exp(Float64(b - Float64(log(z) * y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a ^ (t - 1.0);
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	tmp = 0.0;
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] / N[(N[(b + 1.0), $MachinePrecision] - N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -0.8845848504127471], t$95$2, If[Less[t, 852031.2288374073], N[(N[(N[(x / y), $MachinePrecision] * t$95$1), $MachinePrecision] / N[Exp[N[(b - N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023322 
(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))