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

Percentage Accurate: 98.4% → 98.4%

Time: 24.4s

Alternatives: 24

Speedup: 1.0×

• 20.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.4% 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: 98.4% 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 97.9%

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

2. Final simplification 97.9%

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

Alternative 2: 93.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -5 \cdot 10^{+38} \lor \neg \left(t + -1 \leq 10000000\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ t -1.0) -5e+38) (not (<= (+ t -1.0) 10000000.0)))
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -5e+38) || !((t + -1.0) <= 10000000.0)) {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	} else {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((t + (-1.0d0)) <= (-5d+38)) .or. (.not. ((t + (-1.0d0)) <= 10000000.0d0))) then
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    else
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -5e+38) || !((t + -1.0) <= 10000000.0)) {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	} else {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t + -1.0) <= -5e+38) or not ((t + -1.0) <= 10000000.0):
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	else:
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(t + -1.0) <= -5e+38) || !(Float64(t + -1.0) <= 10000000.0))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t + -1.0) <= -5e+38) || ~(((t + -1.0) <= 10000000.0)))
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	else
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(t + -1.0), $MachinePrecision], -5e+38], N[Not[LessEqual[N[(t + -1.0), $MachinePrecision], 10000000.0]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 t 1) < -4.9999999999999997e38 or 1e7 < (-.f64 t 1)

   1. Initial program 99.2%

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

      1. associate-*l/ 88.1%

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

      2. associate--l+ 88.1%

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

      3. associate--l+ 88.1%

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

      4. fma-def 88.1%

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

      5. sub-neg 88.1%

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

      6. metadata-eval 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in y around 0 92.5%

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

   if -4.9999999999999997e38 < (-.f64 t 1) < 1e7

   1. Initial program 96.8%

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

   2. Taylor expanded in t around 0 96.8%

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

      1. *-commutative 96.8%

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

      2. mul-1-neg 96.8%

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

      3. unsub-neg 96.8%

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

   4. Simplified 96.8%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -5 \cdot 10^{+38} \lor \neg \left(t + -1 \leq 10000000\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \]

Alternative 3: 79.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{{a}^{\left(t + -1\right)}}{y} \cdot \frac{x}{e^{b}}\\ t_2 := \frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -2.85 \cdot 10^{+26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-296}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-62}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;y \leq 1020000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (pow a (+ t -1.0)) y) (/ x (exp b))))
        (t_2 (/ (/ (* x (pow z y)) a) y)))
   (if (<= y -2.85e+26)
     t_2
     (if (<= y -3e-296)
       t_1
       (if (<= y 5.3e-62)
         (/ (/ x (* a (exp b))) y)
         (if (<= y 1020000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (pow(a, (t + -1.0)) / y) * (x / exp(b));
	double t_2 = ((x * pow(z, y)) / a) / y;
	double tmp;
	if (y <= -2.85e+26) {
		tmp = t_2;
	} else if (y <= -3e-296) {
		tmp = t_1;
	} else if (y <= 5.3e-62) {
		tmp = (x / (a * exp(b))) / y;
	} else if (y <= 1020000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((a ** (t + (-1.0d0))) / y) * (x / exp(b))
    t_2 = ((x * (z ** y)) / a) / y
    if (y <= (-2.85d+26)) then
        tmp = t_2
    else if (y <= (-3d-296)) then
        tmp = t_1
    else if (y <= 5.3d-62) then
        tmp = (x / (a * exp(b))) / y
    else if (y <= 1020000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (Math.pow(a, (t + -1.0)) / y) * (x / Math.exp(b));
	double t_2 = ((x * Math.pow(z, y)) / a) / y;
	double tmp;
	if (y <= -2.85e+26) {
		tmp = t_2;
	} else if (y <= -3e-296) {
		tmp = t_1;
	} else if (y <= 5.3e-62) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else if (y <= 1020000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.pow(a, (t + -1.0)) / y) * (x / math.exp(b))
	t_2 = ((x * math.pow(z, y)) / a) / y
	tmp = 0
	if y <= -2.85e+26:
		tmp = t_2
	elif y <= -3e-296:
		tmp = t_1
	elif y <= 5.3e-62:
		tmp = (x / (a * math.exp(b))) / y
	elif y <= 1020000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64((a ^ Float64(t + -1.0)) / y) * Float64(x / exp(b)))
	t_2 = Float64(Float64(Float64(x * (z ^ y)) / a) / y)
	tmp = 0.0
	if (y <= -2.85e+26)
		tmp = t_2;
	elseif (y <= -3e-296)
		tmp = t_1;
	elseif (y <= 5.3e-62)
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	elseif (y <= 1020000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((a ^ (t + -1.0)) / y) * (x / exp(b));
	t_2 = ((x * (z ^ y)) / a) / y;
	tmp = 0.0;
	if (y <= -2.85e+26)
		tmp = t_2;
	elseif (y <= -3e-296)
		tmp = t_1;
	elseif (y <= 5.3e-62)
		tmp = (x / (a * exp(b))) / y;
	elseif (y <= 1020000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision] * N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -2.85e+26], t$95$2, If[LessEqual[y, -3e-296], t$95$1, If[LessEqual[y, 5.3e-62], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 1020000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.8500000000000002e26 or 1.02e6 < y

   1. Initial program 99.1%

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

   2. Taylor expanded in t around 0 90.2%

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

      1. *-commutative 90.2%

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

      2. mul-1-neg 90.2%

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

      3. unsub-neg 90.2%

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

   4. Simplified 90.2%

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

   5. Taylor expanded in b around 0 83.9%

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

      1. *-commutative 83.9%

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

      2. div-exp 83.9%

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

      3. *-commutative 83.9%

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

      4. exp-to-pow 83.9%

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

      5. rem-exp-log 83.9%

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

      6. associate-*r/ 83.9%

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

   7. Simplified 83.9%

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

   if -2.8500000000000002e26 < y < -2.9999999999999997e-296 or 5.2999999999999997e-62 < y < 1.02e6

   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/ 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. *-commutative 88.0%

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

      3. exp-diff 80.7%

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

      4. exp-sum 78.3%

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

      5. *-commutative 78.3%

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

      6. exp-to-pow 78.3%

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

      7. *-commutative 78.3%

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

      8. exp-to-pow 79.3%

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

   3. Simplified 79.3%

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

   4. Taylor expanded in y around 0 87.7%

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

      1. times-frac 89.0%

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

      2. sub-neg 89.0%

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

      3. metadata-eval 89.0%

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

   6. Simplified 89.0%

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

   if -2.9999999999999997e-296 < y < 5.2999999999999997e-62

   1. Initial program 94.8%

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

   2. Taylor expanded in y around 0 94.8%

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

      1. *-commutative 94.8%

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

      2. exp-diff 82.3%

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

      3. *-commutative 82.3%

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

      4. exp-to-pow 83.2%

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

      5. sub-neg 83.2%

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

      6. metadata-eval 83.2%

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

   4. Simplified 83.2%

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

   5. Taylor expanded in t around 0 88.1%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{+26}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-296}:\\ \;\;\;\;\frac{{a}^{\left(t + -1\right)}}{y} \cdot \frac{x}{e^{b}}\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-62}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;y \leq 1020000:\\ \;\;\;\;\frac{{a}^{\left(t + -1\right)}}{y} \cdot \frac{x}{e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \end{array} \]

Alternative 4: 88.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+177} \lor \neg \left(y \leq 8 \cdot 10^{+96}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.3e+177) (not (<= y 8e+96)))
   (/ (/ (* 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 <= -5.3e+177) || !(y <= 8e+96)) {
		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 <= (-5.3d+177)) .or. (.not. (y <= 8d+96))) 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 <= -5.3e+177) || !(y <= 8e+96)) {
		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 <= -5.3e+177) or not (y <= 8e+96):
		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 <= -5.3e+177) || !(y <= 8e+96))
		tmp = Float64(Float64(Float64(x * (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 <= -5.3e+177) || ~((y <= 8e+96)))
		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, -5.3e+177], N[Not[LessEqual[y, 8e+96]], $MachinePrecision]], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $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 < -5.2999999999999997e177 or 8.0000000000000004e96 < y

   1. Initial program 98.3%

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

   2. Taylor expanded in t around 0 96.7%

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

      1. *-commutative 96.7%

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

      2. mul-1-neg 96.7%

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

      3. unsub-neg 96.7%

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

   4. Simplified 96.7%

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

   5. Taylor expanded in b around 0 93.3%

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

      1. *-commutative 93.3%

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

      2. div-exp 93.3%

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

      3. *-commutative 93.3%

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

      4. exp-to-pow 93.3%

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

      5. rem-exp-log 93.3%

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

      6. associate-*r/ 93.3%

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

   7. Simplified 93.3%

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

   if -5.2999999999999997e177 < y < 8.0000000000000004e96

   1. Initial program 97.8%

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

      1. associate-*l/ 90.0%

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

      2. associate--l+ 90.0%

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

      3. associate--l+ 90.0%

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

      4. fma-def 90.0%

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

      5. sub-neg 90.0%

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

      6. metadata-eval 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in y around 0 91.3%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+177} \lor \neg \left(y \leq 8 \cdot 10^{+96}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]

Alternative 5: 81.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+31} \lor \neg \left(t \leq 4 \cdot 10^{+29}\right):\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{z}^{y}}{y} \cdot \frac{x}{a \cdot e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -7e+31) (not (<= t 4e+29)))
   (* x (/ (pow a (+ t -1.0)) y))
   (* (/ (pow z y) y) (/ x (* a (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -7e+31) || !(t <= 4e+29)) {
		tmp = x * (pow(a, (t + -1.0)) / y);
	} else {
		tmp = (pow(z, y) / y) * (x / (a * 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 <= (-7d+31)) .or. (.not. (t <= 4d+29))) then
        tmp = x * ((a ** (t + (-1.0d0))) / y)
    else
        tmp = ((z ** y) / y) * (x / (a * 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 <= -7e+31) || !(t <= 4e+29)) {
		tmp = x * (Math.pow(a, (t + -1.0)) / y);
	} else {
		tmp = (Math.pow(z, y) / y) * (x / (a * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -7e+31) or not (t <= 4e+29):
		tmp = x * (math.pow(a, (t + -1.0)) / y)
	else:
		tmp = (math.pow(z, y) / y) * (x / (a * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -7e+31) || !(t <= 4e+29))
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) / y));
	else
		tmp = Float64(Float64((z ^ y) / y) * Float64(x / Float64(a * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -7e+31) || ~((t <= 4e+29)))
		tmp = x * ((a ^ (t + -1.0)) / y);
	else
		tmp = ((z ^ y) / y) * (x / (a * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -7e+31], N[Not[LessEqual[t, 4e+29]], $MachinePrecision]], N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision] * N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7e31 or 3.99999999999999966e29 < t

   1. Initial program 99.1%

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

      1. associate-*l/ 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. *-commutative 88.0%

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

      3. exp-diff 70.1%

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

      4. exp-sum 53.0%

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

      5. *-commutative 53.0%

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

      6. exp-to-pow 53.0%

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

      7. *-commutative 53.0%

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

      8. exp-to-pow 53.0%

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

   3. Simplified 53.0%

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

   4. Taylor expanded in y around 0 71.9%

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

      1. times-frac 71.9%

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

      2. sub-neg 71.9%

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

      3. metadata-eval 71.9%

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

   6. Simplified 71.9%

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

   7. Taylor expanded in b around 0 84.0%

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

   if -7e31 < t < 3.99999999999999966e29

   1. Initial program 96.8%

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

      1. associate-*r/ 96.1%

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

      2. sub-neg 96.1%

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

      3. exp-sum 87.4%

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

      4. associate-/l* 87.4%

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

      5. associate-/r/ 86.0%

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

      6. exp-neg 86.0%

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

      7. associate-*r/ 86.0%

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

   3. Simplified 84.2%

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

   4. Taylor expanded in t around 0 84.9%

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

      1. times-frac 88.0%

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

   6. Simplified 88.0%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+31} \lor \neg \left(t \leq 4 \cdot 10^{+29}\right):\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{z}^{y}}{y} \cdot \frac{x}{a \cdot e^{b}}\\ \end{array} \]

Alternative 6: 75.7% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-294}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;y \leq 1040000:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ (* x (pow z y)) a) y)))
   (if (<= y -1.4e+26)
     t_1
     (if (<= y -2.35e-294)
       (* x (/ (pow a (+ t -1.0)) y))
       (if (<= y 1040000.0) (/ (/ 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 <= -1.4e+26) {
		tmp = t_1;
	} else if (y <= -2.35e-294) {
		tmp = x * (pow(a, (t + -1.0)) / y);
	} else if (y <= 1040000.0) {
		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 <= (-1.4d+26)) then
        tmp = t_1
    else if (y <= (-2.35d-294)) then
        tmp = x * ((a ** (t + (-1.0d0))) / y)
    else if (y <= 1040000.0d0) 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 <= -1.4e+26) {
		tmp = t_1;
	} else if (y <= -2.35e-294) {
		tmp = x * (Math.pow(a, (t + -1.0)) / y);
	} else if (y <= 1040000.0) {
		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 <= -1.4e+26:
		tmp = t_1
	elif y <= -2.35e-294:
		tmp = x * (math.pow(a, (t + -1.0)) / y)
	elif y <= 1040000.0:
		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(Float64(x * (z ^ y)) / a) / y)
	tmp = 0.0
	if (y <= -1.4e+26)
		tmp = t_1;
	elseif (y <= -2.35e-294)
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) / y));
	elseif (y <= 1040000.0)
		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 <= -1.4e+26)
		tmp = t_1;
	elseif (y <= -2.35e-294)
		tmp = x * ((a ^ (t + -1.0)) / y);
	elseif (y <= 1040000.0)
		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[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -1.4e+26], t$95$1, If[LessEqual[y, -2.35e-294], N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1040000.0], 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 < -1.4e26 or 1.04e6 < y

   1. Initial program 99.1%

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

   2. Taylor expanded in t around 0 90.2%

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

      1. *-commutative 90.2%

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

      2. mul-1-neg 90.2%

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

      3. unsub-neg 90.2%

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

   4. Simplified 90.2%

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

   5. Taylor expanded in b around 0 83.9%

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

      1. *-commutative 83.9%

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

      2. div-exp 83.9%

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

      3. *-commutative 83.9%

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

      4. exp-to-pow 83.9%

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

      5. rem-exp-log 83.9%

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

      6. associate-*r/ 83.9%

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

   7. Simplified 83.9%

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

   if -1.4e26 < y < -2.3500000000000001e-294

   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/ 87.5%

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

      2. *-commutative 87.5%

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

      3. exp-diff 80.2%

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

      4. exp-sum 77.2%

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

      5. *-commutative 77.2%

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

      6. exp-to-pow 77.2%

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

      7. *-commutative 77.2%

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

      8. exp-to-pow 78.0%

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

   3. Simplified 78.0%

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

   4. Taylor expanded in y around 0 85.2%

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

      1. times-frac 89.6%

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

      2. sub-neg 89.6%

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

      3. metadata-eval 89.6%

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

   6. Simplified 89.6%

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

   7. Taylor expanded in b around 0 78.4%

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

   if -2.3500000000000001e-294 < y < 1.04e6

   1. Initial program 95.4%

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

   2. Taylor expanded in y around 0 95.4%

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

      1. *-commutative 95.4%

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

      2. exp-diff 85.1%

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

      3. *-commutative 85.1%

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

      4. exp-to-pow 86.2%

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

      5. sub-neg 86.2%

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

      6. metadata-eval 86.2%

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

   4. Simplified 86.2%

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

   5. Taylor expanded in t around 0 84.0%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+26}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-294}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;y \leq 1040000:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \end{array} \]

Alternative 7: 74.7% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+25} \lor \neg \left(t \leq 4.2 \cdot 10^{+23}\right):\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.2e+25) (not (<= t 4.2e+23)))
   (* x (/ (pow a (+ t -1.0)) y))
   (/ (/ x (* a (exp b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.2e+25) || !(t <= 4.2e+23)) {
		tmp = x * (pow(a, (t + -1.0)) / y);
	} else {
		tmp = (x / (a * exp(b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2.2d+25)) .or. (.not. (t <= 4.2d+23))) then
        tmp = x * ((a ** (t + (-1.0d0))) / y)
    else
        tmp = (x / (a * exp(b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.2e+25) || !(t <= 4.2e+23)) {
		tmp = x * (Math.pow(a, (t + -1.0)) / y);
	} else {
		tmp = (x / (a * Math.exp(b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.2e+25) or not (t <= 4.2e+23):
		tmp = x * (math.pow(a, (t + -1.0)) / y)
	else:
		tmp = (x / (a * math.exp(b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.2e+25) || !(t <= 4.2e+23))
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) / y));
	else
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.2e+25) || ~((t <= 4.2e+23)))
		tmp = x * ((a ^ (t + -1.0)) / y);
	else
		tmp = (x / (a * exp(b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.2e+25], N[Not[LessEqual[t, 4.2e+23]], $MachinePrecision]], N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.2000000000000001e25 or 4.2000000000000003e23 < t

   1. Initial program 99.1%

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

      1. associate-*l/ 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. *-commutative 88.0%

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

      3. exp-diff 70.1%

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

      4. exp-sum 53.0%

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

      5. *-commutative 53.0%

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

      6. exp-to-pow 53.0%

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

      7. *-commutative 53.0%

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

      8. exp-to-pow 53.0%

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

   3. Simplified 53.0%

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

   4. Taylor expanded in y around 0 71.9%

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

      1. times-frac 71.9%

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

      2. sub-neg 71.9%

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

      3. metadata-eval 71.9%

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

   6. Simplified 71.9%

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

   7. Taylor expanded in b around 0 84.0%

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

   if -2.2000000000000001e25 < t < 4.2000000000000003e23

   1. Initial program 96.8%

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

   2. Taylor expanded in y around 0 75.1%

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

      1. *-commutative 75.1%

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

      2. exp-diff 73.6%

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

      3. *-commutative 73.6%

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

      4. exp-to-pow 74.8%

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

      5. sub-neg 74.8%

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

      6. metadata-eval 74.8%

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

   4. Simplified 74.8%

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

   5. Taylor expanded in t around 0 77.7%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+25} \lor \neg \left(t \leq 4.2 \cdot 10^{+23}\right):\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \end{array} \]

Alternative 8: 58.3% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot e^{b}}\\ \mathbf{if}\;b \leq -440:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-160}:\\ \;\;\;\;\frac{x \cdot \frac{1 - b}{y}}{a}\\ \mathbf{elif}\;b \leq 170000000:\\ \;\;\;\;\frac{1}{y} \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* y (exp b)))))
   (if (<= b -440.0)
     t_1
     (if (<= b 4e-160)
       (/ (* x (/ (- 1.0 b) y)) a)
       (if (<= b 170000000.0) (* (/ 1.0 y) (/ x a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * exp(b));
	double tmp;
	if (b <= -440.0) {
		tmp = t_1;
	} else if (b <= 4e-160) {
		tmp = (x * ((1.0 - b) / y)) / a;
	} else if (b <= 170000000.0) {
		tmp = (1.0 / y) * (x / a);
	} 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 / (y * exp(b))
    if (b <= (-440.0d0)) then
        tmp = t_1
    else if (b <= 4d-160) then
        tmp = (x * ((1.0d0 - b) / y)) / a
    else if (b <= 170000000.0d0) then
        tmp = (1.0d0 / y) * (x / a)
    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 / (y * Math.exp(b));
	double tmp;
	if (b <= -440.0) {
		tmp = t_1;
	} else if (b <= 4e-160) {
		tmp = (x * ((1.0 - b) / y)) / a;
	} else if (b <= 170000000.0) {
		tmp = (1.0 / y) * (x / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y * math.exp(b))
	tmp = 0
	if b <= -440.0:
		tmp = t_1
	elif b <= 4e-160:
		tmp = (x * ((1.0 - b) / y)) / a
	elif b <= 170000000.0:
		tmp = (1.0 / y) * (x / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y * exp(b)))
	tmp = 0.0
	if (b <= -440.0)
		tmp = t_1;
	elseif (b <= 4e-160)
		tmp = Float64(Float64(x * Float64(Float64(1.0 - b) / y)) / a);
	elseif (b <= 170000000.0)
		tmp = Float64(Float64(1.0 / y) * Float64(x / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y * exp(b));
	tmp = 0.0;
	if (b <= -440.0)
		tmp = t_1;
	elseif (b <= 4e-160)
		tmp = (x * ((1.0 - b) / y)) / a;
	elseif (b <= 170000000.0)
		tmp = (1.0 / y) * (x / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -440.0], t$95$1, If[LessEqual[b, 4e-160], N[(N[(x * N[(N[(1.0 - b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, 170000000.0], N[(N[(1.0 / y), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -440 or 1.7e8 < b

   1. Initial program 99.2%

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

      1. associate-*l/ 87.7%

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

      2. associate--l+ 87.7%

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

      3. associate--l+ 87.7%

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

      4. fma-def 87.7%

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

      5. sub-neg 87.7%

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

      6. metadata-eval 87.7%

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

   3. Simplified 87.7%

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

   4. Taylor expanded in b around inf 73.2%

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

      1. neg-mul-1 73.2%

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

   6. Simplified 73.2%

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

   7. Taylor expanded in x around 0 83.9%

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

      1. *-commutative 83.9%

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

      2. rem-exp-log 50.9%

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

      3. exp-sum 50.9%

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

      4. sub-neg 50.9%

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

      5. exp-diff 50.9%

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

      6. rem-exp-log 83.9%

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

      7. associate-/l/ 83.9%

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

   9. Simplified 83.9%

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

   if -440 < b < 4e-160

   1. Initial program 96.1%

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

   2. Taylor expanded in y around 0 71.6%

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

      1. *-commutative 71.6%

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

      2. exp-diff 71.6%

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

      3. *-commutative 71.6%

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

      4. exp-to-pow 72.9%

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

      5. sub-neg 72.9%

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

      6. metadata-eval 72.9%

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

   4. Simplified 72.9%

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

   5. Taylor expanded in t around 0 49.9%

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

   6. Taylor expanded in b around 0 49.5%

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

   7. Taylor expanded in b around 0 46.2%

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

      1. +-commutative 46.2%

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

      2. *-commutative 46.2%

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

      3. mul-1-neg 46.2%

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

      4. unsub-neg 46.2%

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

      5. *-commutative 46.2%

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

      6. *-commutative 46.2%

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

      7. div-sub 50.2%

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

      8. *-commutative 50.2%

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

      9. associate-/r* 53.4%

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

      10. div-sub 53.4%

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

      11. associate-*r/ 53.4%

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

      12. *-commutative 53.4%

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

      13. cancel-sign-sub-inv 53.4%

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

      14. *-lft-identity 53.4%

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

      15. associate-*l/ 53.4%

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

      16. mul-1-neg 53.4%

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

      17. distribute-rgt-in 53.4%

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

      18. mul-1-neg 53.4%

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

      19. sub-neg 53.4%

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

      20. div-sub 53.4%

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

   9. Simplified 53.4%

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

   if 4e-160 < b < 1.7e8

   1. Initial program 98.9%

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

   2. Taylor expanded in y around 0 76.2%

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

      1. *-commutative 76.2%

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

      2. exp-diff 72.9%

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

      3. *-commutative 72.9%

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

      4. exp-to-pow 73.9%

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

      5. sub-neg 73.9%

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

      6. metadata-eval 73.9%

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

   4. Simplified 73.9%

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

   5. Taylor expanded in t around 0 45.4%

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

   6. Taylor expanded in b around 0 39.2%

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

      1. *-un-lft-identity 39.2%

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

      2. times-frac 48.6%

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

   8. Applied egg-rr 48.6%

      \[\leadsto \color{blue}{\frac{1}{y} \cdot \frac{x}{a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -440:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-160}:\\ \;\;\;\;\frac{x \cdot \frac{1 - b}{y}}{a}\\ \mathbf{elif}\;b \leq 170000000:\\ \;\;\;\;\frac{1}{y} \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \end{array} \]

Alternative 9: 58.9% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.9%

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

   1. associate-*l/ 90.4%

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

   2. *-commutative 90.4%

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

   3. exp-diff 77.5%

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

   4. exp-sum 68.1%

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

   5. *-commutative 68.1%

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

   6. exp-to-pow 68.1%

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

   7. *-commutative 68.1%

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

   8. exp-to-pow 68.7%

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

3. Simplified 68.7%

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

4. Taylor expanded in y around 0 70.7%

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

   1. times-frac 71.1%

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

   2. sub-neg 71.1%

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

   3. metadata-eval 71.1%

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

6. Simplified 71.1%

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

7. Taylor expanded in t around 0 64.7%

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

8. Final simplification 64.7%

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

Alternative 10: 58.9% 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 97.9%

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

2. Taylor expanded in y around 0 83.0%

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

   1. *-commutative 83.0%

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

   2. exp-diff 72.8%

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

   3. *-commutative 72.8%

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

   4. exp-to-pow 73.5%

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

   5. sub-neg 73.5%

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

   6. metadata-eval 73.5%

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

4. Simplified 73.5%

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

5. Taylor expanded in t around 0 65.6%

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

6. Final simplification 65.6%

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

Alternative 11: 40.4% accurate, 16.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{x \cdot b}\\ \mathbf{if}\;b \leq -6.4 \cdot 10^{+104}:\\ \;\;\;\;\frac{x \cdot t_1 - y}{y \cdot t_1}\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-212}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-156}:\\ \;\;\;\;\frac{x \cdot \frac{1 - b}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ y (* x b))))
   (if (<= b -6.4e+104)
     (/ (- (* x t_1) y) (* y t_1))
     (if (<= b -2e-212)
       (/ (- (/ x a) (/ (* x b) a)) y)
       (if (<= b 1.5e-156)
         (/ (* x (/ (- 1.0 b) y)) a)
         (/ (/ x (+ a (* a b))) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y / (x * b);
	double tmp;
	if (b <= -6.4e+104) {
		tmp = ((x * t_1) - y) / (y * t_1);
	} else if (b <= -2e-212) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= 1.5e-156) {
		tmp = (x * ((1.0 - 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) :: t_1
    real(8) :: tmp
    t_1 = y / (x * b)
    if (b <= (-6.4d+104)) then
        tmp = ((x * t_1) - y) / (y * t_1)
    else if (b <= (-2d-212)) then
        tmp = ((x / a) - ((x * b) / a)) / y
    else if (b <= 1.5d-156) then
        tmp = (x * ((1.0d0 - 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 t_1 = y / (x * b);
	double tmp;
	if (b <= -6.4e+104) {
		tmp = ((x * t_1) - y) / (y * t_1);
	} else if (b <= -2e-212) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= 1.5e-156) {
		tmp = (x * ((1.0 - b) / y)) / a;
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y / (x * b)
	tmp = 0
	if b <= -6.4e+104:
		tmp = ((x * t_1) - y) / (y * t_1)
	elif b <= -2e-212:
		tmp = ((x / a) - ((x * b) / a)) / y
	elif b <= 1.5e-156:
		tmp = (x * ((1.0 - b) / y)) / a
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y / Float64(x * b))
	tmp = 0.0
	if (b <= -6.4e+104)
		tmp = Float64(Float64(Float64(x * t_1) - y) / Float64(y * t_1));
	elseif (b <= -2e-212)
		tmp = Float64(Float64(Float64(x / a) - Float64(Float64(x * b) / a)) / y);
	elseif (b <= 1.5e-156)
		tmp = Float64(Float64(x * Float64(Float64(1.0 - b) / 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)
	t_1 = y / (x * b);
	tmp = 0.0;
	if (b <= -6.4e+104)
		tmp = ((x * t_1) - y) / (y * t_1);
	elseif (b <= -2e-212)
		tmp = ((x / a) - ((x * b) / a)) / y;
	elseif (b <= 1.5e-156)
		tmp = (x * ((1.0 - b) / y)) / a;
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y / N[(x * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.4e+104], N[(N[(N[(x * t$95$1), $MachinePrecision] - y), $MachinePrecision] / N[(y * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2e-212], N[(N[(N[(x / a), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 1.5e-156], N[(N[(x * N[(N[(1.0 - b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.4e104

   1. Initial program 100.0%

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

      1. associate-*l/ 95.0%

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

      2. associate--l+ 95.0%

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

      3. associate--l+ 95.0%

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

      4. fma-def 95.0%

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

      5. sub-neg 95.0%

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

      6. metadata-eval 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in b around inf 90.1%

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

      1. neg-mul-1 90.1%

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

   6. Simplified 90.1%

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

   7. Taylor expanded in b around 0 47.8%

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

      1. +-commutative 47.8%

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

      2. mul-1-neg 47.8%

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

      3. unsub-neg 47.8%

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

   9. Simplified 47.8%

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

       1. clear-num 47.8%

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

       2. frac-sub 68.7%

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

       3. *-commutative 68.7%

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

       4. *-commutative 68.7%

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

   11. Applied egg-rr 68.7%

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

       1. *-rgt-identity 68.7%

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

   13. Simplified 68.7%

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

   if -6.4e104 < b < -1.99999999999999991e-212

   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 78.1%

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

      1. *-commutative 78.1%

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

      2. exp-diff 72.8%

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

      3. *-commutative 72.8%

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

      4. exp-to-pow 74.0%

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

      5. sub-neg 74.0%

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

      6. metadata-eval 74.0%

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

   4. Simplified 74.0%

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

   5. Taylor expanded in t around 0 59.0%

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

   6. Taylor expanded in b around 0 48.5%

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

   if -1.99999999999999991e-212 < b < 1.5e-156

   1. Initial program 94.0%

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

   2. Taylor expanded in y around 0 70.9%

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

      1. *-commutative 70.9%

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

      2. exp-diff 70.9%

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

      3. *-commutative 70.9%

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

      4. exp-to-pow 71.7%

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

      5. sub-neg 71.7%

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

      6. metadata-eval 71.7%

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

   4. Simplified 71.7%

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

   5. Taylor expanded in t around 0 47.3%

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

   6. Taylor expanded in b around 0 47.3%

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

   7. Taylor expanded in b around 0 46.3%

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

      1. +-commutative 46.3%

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

      2. *-commutative 46.3%

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

      3. mul-1-neg 46.3%

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

      4. unsub-neg 46.3%

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

      5. *-commutative 46.3%

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

      6. *-commutative 46.3%

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

      7. div-sub 54.3%

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

      8. *-commutative 54.3%

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

      9. associate-/r* 59.8%

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

      10. div-sub 59.8%

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

      11. associate-*r/ 59.8%

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

      12. *-commutative 59.8%

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

      13. cancel-sign-sub-inv 59.8%

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

      14. *-lft-identity 59.8%

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

      15. associate-*l/ 59.8%

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

      16. mul-1-neg 59.8%

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

      17. distribute-rgt-in 59.8%

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

      18. mul-1-neg 59.8%

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

      19. sub-neg 59.8%

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

      20. div-sub 59.8%

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

   9. Simplified 59.8%

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

   if 1.5e-156 < b

   1. Initial program 98.5%

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

   2. Taylor expanded in y around 0 86.5%

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

      1. *-commutative 86.5%

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

      2. exp-diff 69.6%

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

      3. *-commutative 69.6%

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

      4. exp-to-pow 70.0%

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

      5. sub-neg 70.0%

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

      6. metadata-eval 70.0%

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

   4. Simplified 70.0%

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

   5. Taylor expanded in t around 0 68.3%

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

   6. Taylor expanded in b around 0 48.9%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.4 \cdot 10^{+104}:\\ \;\;\;\;\frac{x \cdot \frac{y}{x \cdot b} - y}{y \cdot \frac{y}{x \cdot b}}\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-212}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-156}:\\ \;\;\;\;\frac{x \cdot \frac{1 - b}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]

Alternative 12: 37.2% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{1}{a} \cdot \frac{x}{y}\\ \mathbf{if}\;b \leq -8.5 \cdot 10^{+16}:\\ \;\;\;\;\frac{b}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+15}:\\ \;\;\;\;\frac{1}{y} \cdot \frac{x}{a}\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ 1.0 a) (/ x y))))
   (if (<= b -8.5e+16)
     (* (/ b y) (- x))
     (if (<= b 3.2e-157)
       t_1
       (if (<= b 1.35e+15)
         (* (/ 1.0 y) (/ x a))
         (if (<= b 7.5e+106) t_1 (/ x (+ y (* y b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 / a) * (x / y);
	double tmp;
	if (b <= -8.5e+16) {
		tmp = (b / y) * -x;
	} else if (b <= 3.2e-157) {
		tmp = t_1;
	} else if (b <= 1.35e+15) {
		tmp = (1.0 / y) * (x / a);
	} else if (b <= 7.5e+106) {
		tmp = t_1;
	} else {
		tmp = x / (y + (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (1.0d0 / a) * (x / y)
    if (b <= (-8.5d+16)) then
        tmp = (b / y) * -x
    else if (b <= 3.2d-157) then
        tmp = t_1
    else if (b <= 1.35d+15) then
        tmp = (1.0d0 / y) * (x / a)
    else if (b <= 7.5d+106) then
        tmp = t_1
    else
        tmp = x / (y + (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 / a) * (x / y);
	double tmp;
	if (b <= -8.5e+16) {
		tmp = (b / y) * -x;
	} else if (b <= 3.2e-157) {
		tmp = t_1;
	} else if (b <= 1.35e+15) {
		tmp = (1.0 / y) * (x / a);
	} else if (b <= 7.5e+106) {
		tmp = t_1;
	} else {
		tmp = x / (y + (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (1.0 / a) * (x / y)
	tmp = 0
	if b <= -8.5e+16:
		tmp = (b / y) * -x
	elif b <= 3.2e-157:
		tmp = t_1
	elif b <= 1.35e+15:
		tmp = (1.0 / y) * (x / a)
	elif b <= 7.5e+106:
		tmp = t_1
	else:
		tmp = x / (y + (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 / a) * Float64(x / y))
	tmp = 0.0
	if (b <= -8.5e+16)
		tmp = Float64(Float64(b / y) * Float64(-x));
	elseif (b <= 3.2e-157)
		tmp = t_1;
	elseif (b <= 1.35e+15)
		tmp = Float64(Float64(1.0 / y) * Float64(x / a));
	elseif (b <= 7.5e+106)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(y + Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (1.0 / a) * (x / y);
	tmp = 0.0;
	if (b <= -8.5e+16)
		tmp = (b / y) * -x;
	elseif (b <= 3.2e-157)
		tmp = t_1;
	elseif (b <= 1.35e+15)
		tmp = (1.0 / y) * (x / a);
	elseif (b <= 7.5e+106)
		tmp = t_1;
	else
		tmp = x / (y + (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.5e+16], N[(N[(b / y), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[b, 3.2e-157], t$95$1, If[LessEqual[b, 1.35e+15], N[(N[(1.0 / y), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.5e+106], t$95$1, N[(x / N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -8.5e16

   1. Initial program 100.0%

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

      1. associate-*l/ 93.2%

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

      2. associate--l+ 93.2%

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

      3. associate--l+ 93.2%

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

      4. fma-def 93.2%

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

      5. sub-neg 93.2%

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

      6. metadata-eval 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in b around inf 84.9%

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

      1. neg-mul-1 84.9%

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

   6. Simplified 84.9%

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

   7. Taylor expanded in b around 0 41.7%

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

      1. +-commutative 41.7%

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

      2. mul-1-neg 41.7%

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

      3. unsub-neg 41.7%

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

   9. Simplified 41.7%

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

   10. Taylor expanded in b around inf 41.7%

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

       1. mul-1-neg 41.7%

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

       2. associate-*l/ 48.0%

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

       3. distribute-rgt-neg-in 48.0%

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

   12. Simplified 48.0%

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

   if -8.5e16 < b < 3.20000000000000021e-157 or 1.35e15 < b < 7.50000000000000058e106

   1. Initial program 96.7%

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

   2. Taylor expanded in y around 0 75.4%

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

      1. *-commutative 75.4%

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

      2. exp-diff 69.7%

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

      3. *-commutative 69.7%

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

      4. exp-to-pow 70.8%

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

      5. sub-neg 70.8%

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

      6. metadata-eval 70.8%

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

   4. Simplified 70.8%

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

   5. Taylor expanded in t around 0 51.6%

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

   6. Taylor expanded in b around 0 46.8%

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

      1. *-un-lft-identity 46.8%

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

      2. *-commutative 46.8%

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

      3. times-frac 49.6%

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

   8. Applied egg-rr 49.6%

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

   if 3.20000000000000021e-157 < b < 1.35e15

   1. Initial program 99.0%

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

   2. Taylor expanded in y around 0 73.3%

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

      1. *-commutative 73.3%

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

      2. exp-diff 70.3%

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

      3. *-commutative 70.3%

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

      4. exp-to-pow 71.2%

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

      5. sub-neg 71.2%

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

      6. metadata-eval 71.2%

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

   4. Simplified 71.2%

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

   5. Taylor expanded in t around 0 46.0%

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

   6. Taylor expanded in b around 0 34.9%

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

      1. *-un-lft-identity 34.9%

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

      2. times-frac 46.0%

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

   8. Applied egg-rr 46.0%

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

   if 7.50000000000000058e106 < b

   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/ 82.1%

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

      2. associate--l+ 82.1%

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

      3. associate--l+ 82.1%

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

      4. fma-def 82.1%

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

      5. sub-neg 82.1%

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

      6. metadata-eval 82.1%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in b around inf 74.5%

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

      1. neg-mul-1 74.5%

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

   6. Simplified 74.5%

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

   7. Taylor expanded in x around 0 89.9%

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

      1. *-commutative 89.9%

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

      2. rem-exp-log 56.5%

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

      3. exp-sum 56.5%

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

      4. sub-neg 56.5%

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

      5. exp-diff 56.5%

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

      6. rem-exp-log 89.9%

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

      7. associate-/l/ 89.9%

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

   9. Simplified 89.9%

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

   10. Taylor expanded in b around 0 48.0%

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

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+16}:\\ \;\;\;\;\frac{b}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-157}:\\ \;\;\;\;\frac{1}{a} \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+15}:\\ \;\;\;\;\frac{1}{y} \cdot \frac{x}{a}\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+106}:\\ \;\;\;\;\frac{1}{a} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + y \cdot b}\\ \end{array} \]

Alternative 13: 37.9% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+118}:\\ \;\;\;\;\frac{b}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;b \leq -0.00018:\\ \;\;\;\;\frac{x \cdot \left(-b\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-158}:\\ \;\;\;\;\frac{1}{a} \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+106}:\\ \;\;\;\;\frac{1}{y} \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5e+118)
   (* (/ b y) (- x))
   (if (<= b -0.00018)
     (/ (* x (- b)) (* y a))
     (if (<= b 1.55e-158)
       (* (/ 1.0 a) (/ x y))
       (if (<= b 7.5e+106) (* (/ 1.0 y) (/ x a)) (/ x (+ y (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5e+118) {
		tmp = (b / y) * -x;
	} else if (b <= -0.00018) {
		tmp = (x * -b) / (y * a);
	} else if (b <= 1.55e-158) {
		tmp = (1.0 / a) * (x / y);
	} else if (b <= 7.5e+106) {
		tmp = (1.0 / y) * (x / a);
	} else {
		tmp = x / (y + (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-5d+118)) then
        tmp = (b / y) * -x
    else if (b <= (-0.00018d0)) then
        tmp = (x * -b) / (y * a)
    else if (b <= 1.55d-158) then
        tmp = (1.0d0 / a) * (x / y)
    else if (b <= 7.5d+106) then
        tmp = (1.0d0 / y) * (x / a)
    else
        tmp = x / (y + (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5e+118) {
		tmp = (b / y) * -x;
	} else if (b <= -0.00018) {
		tmp = (x * -b) / (y * a);
	} else if (b <= 1.55e-158) {
		tmp = (1.0 / a) * (x / y);
	} else if (b <= 7.5e+106) {
		tmp = (1.0 / y) * (x / a);
	} else {
		tmp = x / (y + (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5e+118:
		tmp = (b / y) * -x
	elif b <= -0.00018:
		tmp = (x * -b) / (y * a)
	elif b <= 1.55e-158:
		tmp = (1.0 / a) * (x / y)
	elif b <= 7.5e+106:
		tmp = (1.0 / y) * (x / a)
	else:
		tmp = x / (y + (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5e+118)
		tmp = Float64(Float64(b / y) * Float64(-x));
	elseif (b <= -0.00018)
		tmp = Float64(Float64(x * Float64(-b)) / Float64(y * a));
	elseif (b <= 1.55e-158)
		tmp = Float64(Float64(1.0 / a) * Float64(x / y));
	elseif (b <= 7.5e+106)
		tmp = Float64(Float64(1.0 / y) * Float64(x / a));
	else
		tmp = Float64(x / Float64(y + Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5e+118)
		tmp = (b / y) * -x;
	elseif (b <= -0.00018)
		tmp = (x * -b) / (y * a);
	elseif (b <= 1.55e-158)
		tmp = (1.0 / a) * (x / y);
	elseif (b <= 7.5e+106)
		tmp = (1.0 / y) * (x / a);
	else
		tmp = x / (y + (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5e+118], N[(N[(b / y), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[b, -0.00018], N[(N[(x * (-b)), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.55e-158], N[(N[(1.0 / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.5e+106], N[(N[(1.0 / y), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision], N[(x / N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.99999999999999972e118

   1. Initial program 100.0%

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

      1. associate-*l/ 94.9%

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

      2. associate--l+ 94.9%

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

      3. associate--l+ 94.9%

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

      4. fma-def 94.9%

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

      5. sub-neg 94.9%

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

      6. metadata-eval 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in b around inf 92.3%

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

      1. neg-mul-1 92.3%

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

   6. Simplified 92.3%

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

   7. Taylor expanded in b around 0 48.9%

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

      1. +-commutative 48.9%

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

      2. mul-1-neg 48.9%

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

      3. unsub-neg 48.9%

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

   9. Simplified 48.9%

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

   10. Taylor expanded in b around inf 48.9%

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

       1. mul-1-neg 48.9%

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

       2. associate-*l/ 60.9%

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

       3. distribute-rgt-neg-in 60.9%

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

   12. Simplified 60.9%

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

   if -4.99999999999999972e118 < b < -1.80000000000000011e-4

   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 y around 0 92.1%

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

      1. *-commutative 92.1%

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

      2. exp-diff 72.7%

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

      3. *-commutative 72.7%

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

      4. exp-to-pow 73.2%

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

      5. sub-neg 73.2%

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

      6. metadata-eval 73.2%

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

   4. Simplified 73.2%

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

   5. Taylor expanded in t around 0 69.8%

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

   6. Taylor expanded in b around 0 38.9%

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

   7. Taylor expanded in b around inf 41.9%

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

      1. associate-*r/ 41.9%

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

      2. mul-1-neg 41.9%

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

      3. *-commutative 41.9%

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

      4. distribute-rgt-neg-in 41.9%

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

      5. *-commutative 41.9%

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

   9. Simplified 41.9%

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

   if -1.80000000000000011e-4 < b < 1.55000000000000009e-158

   1. Initial program 96.1%

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

   2. Taylor expanded in y around 0 71.2%

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

      1. *-commutative 71.2%

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

      2. exp-diff 71.2%

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

      3. *-commutative 71.2%

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

      4. exp-to-pow 72.4%

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

      5. sub-neg 72.4%

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

      6. metadata-eval 72.4%

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

   4. Simplified 72.4%

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

   5. Taylor expanded in t around 0 49.9%

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

   6. Taylor expanded in b around 0 49.4%

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

      1. *-un-lft-identity 49.4%

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

      2. *-commutative 49.4%

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

      3. times-frac 53.8%

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

   8. Applied egg-rr 53.8%

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

   if 1.55000000000000009e-158 < b < 7.50000000000000058e106

   1. Initial program 99.3%

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

   2. Taylor expanded in y around 0 81.8%

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

      1. *-commutative 81.8%

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

      2. exp-diff 67.8%

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

      3. *-commutative 67.8%

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

      4. exp-to-pow 68.4%

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

      5. sub-neg 68.4%

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

      6. metadata-eval 68.4%

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

   4. Simplified 68.4%

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

   5. Taylor expanded in t around 0 51.5%

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

   6. Taylor expanded in b around 0 30.3%

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

      1. *-un-lft-identity 30.3%

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

      2. times-frac 39.8%

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

   8. Applied egg-rr 39.8%

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

   if 7.50000000000000058e106 < b

   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/ 82.1%

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

      2. associate--l+ 82.1%

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

      3. associate--l+ 82.1%

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

      4. fma-def 82.1%

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

      5. sub-neg 82.1%

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

      6. metadata-eval 82.1%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in b around inf 74.5%

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

      1. neg-mul-1 74.5%

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

   6. Simplified 74.5%

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

   7. Taylor expanded in x around 0 89.9%

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

      1. *-commutative 89.9%

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

      2. rem-exp-log 56.5%

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

      3. exp-sum 56.5%

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

      4. sub-neg 56.5%

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

      5. exp-diff 56.5%

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

      6. rem-exp-log 89.9%

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

      7. associate-/l/ 89.9%

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

   9. Simplified 89.9%

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

   10. Taylor expanded in b around 0 48.0%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+118}:\\ \;\;\;\;\frac{b}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;b \leq -0.00018:\\ \;\;\;\;\frac{x \cdot \left(-b\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-158}:\\ \;\;\;\;\frac{1}{a} \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+106}:\\ \;\;\;\;\frac{1}{y} \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + y \cdot b}\\ \end{array} \]

Alternative 14: 39.9% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.05 \cdot 10^{+209}:\\ \;\;\;\;\frac{b}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;b \leq -2.05 \cdot 10^{-278}:\\ \;\;\;\;\frac{\frac{x - x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-157}:\\ \;\;\;\;\frac{x \cdot \frac{1 - b}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.05e+209)
   (* (/ b y) (- x))
   (if (<= b -2.05e-278)
     (/ (/ (- x (* x b)) a) y)
     (if (<= b 7.2e-157)
       (/ (* x (/ (- 1.0 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 <= -2.05e+209) {
		tmp = (b / y) * -x;
	} else if (b <= -2.05e-278) {
		tmp = ((x - (x * b)) / a) / y;
	} else if (b <= 7.2e-157) {
		tmp = (x * ((1.0 - 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 <= (-2.05d+209)) then
        tmp = (b / y) * -x
    else if (b <= (-2.05d-278)) then
        tmp = ((x - (x * b)) / a) / y
    else if (b <= 7.2d-157) then
        tmp = (x * ((1.0d0 - 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 <= -2.05e+209) {
		tmp = (b / y) * -x;
	} else if (b <= -2.05e-278) {
		tmp = ((x - (x * b)) / a) / y;
	} else if (b <= 7.2e-157) {
		tmp = (x * ((1.0 - 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 <= -2.05e+209:
		tmp = (b / y) * -x
	elif b <= -2.05e-278:
		tmp = ((x - (x * b)) / a) / y
	elif b <= 7.2e-157:
		tmp = (x * ((1.0 - 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 <= -2.05e+209)
		tmp = Float64(Float64(b / y) * Float64(-x));
	elseif (b <= -2.05e-278)
		tmp = Float64(Float64(Float64(x - Float64(x * b)) / a) / y);
	elseif (b <= 7.2e-157)
		tmp = Float64(Float64(x * Float64(Float64(1.0 - b) / 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 <= -2.05e+209)
		tmp = (b / y) * -x;
	elseif (b <= -2.05e-278)
		tmp = ((x - (x * b)) / a) / y;
	elseif (b <= 7.2e-157)
		tmp = (x * ((1.0 - 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, -2.05e+209], N[(N[(b / y), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[b, -2.05e-278], N[(N[(N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 7.2e-157], N[(N[(x * N[(N[(1.0 - b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.05000000000000008e209

   1. Initial program 100.0%

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

      1. associate-*l/ 93.1%

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

      2. associate--l+ 93.1%

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

      3. associate--l+ 93.1%

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

      4. fma-def 93.1%

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

      5. sub-neg 93.1%

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

      6. metadata-eval 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in b around inf 89.7%

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

      1. neg-mul-1 89.7%

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

   6. Simplified 89.7%

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

   7. Taylor expanded in b around 0 54.1%

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

      1. +-commutative 54.1%

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

      2. mul-1-neg 54.1%

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

      3. unsub-neg 54.1%

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

   9. Simplified 54.1%

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

   10. Taylor expanded in b around inf 54.1%

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

       1. mul-1-neg 54.1%

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

       2. associate-*l/ 73.4%

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

       3. distribute-rgt-neg-in 73.4%

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

   12. Simplified 73.4%

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

   if -2.05000000000000008e209 < b < -2.05000000000000001e-278

   1. Initial program 98.9%

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

   2. Taylor expanded in y around 0 81.0%

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

      1. *-commutative 81.0%

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

      2. exp-diff 74.8%

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

      3. *-commutative 74.8%

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

      4. exp-to-pow 75.8%

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

      5. sub-neg 75.8%

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

      6. metadata-eval 75.8%

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

   4. Simplified 75.8%

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

   5. Taylor expanded in t around 0 62.3%

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

   6. Taylor expanded in b around 0 47.2%

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

   7. Taylor expanded in a around 0 47.2%

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

      1. +-commutative 47.2%

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

      2. mul-1-neg 47.2%

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

      3. sub-neg 47.2%

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

      4. *-commutative 47.2%

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

   9. Simplified 47.2%

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

   if -2.05000000000000001e-278 < b < 7.2e-157

   1. Initial program 92.5%

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

   2. Taylor expanded in y around 0 67.9%

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

      1. *-commutative 67.9%

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

      2. exp-diff 67.9%

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

      3. *-commutative 67.9%

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

      4. exp-to-pow 68.8%

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

      5. sub-neg 68.8%

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

      6. metadata-eval 68.8%

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

   4. Simplified 68.8%

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

   5. Taylor expanded in t around 0 44.9%

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

   6. Taylor expanded in b around 0 44.9%

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

   7. Taylor expanded in b around 0 41.4%

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

      1. +-commutative 41.4%

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

      2. *-commutative 41.4%

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

      3. mul-1-neg 41.4%

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

      4. unsub-neg 41.4%

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

      5. *-commutative 41.4%

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

      6. *-commutative 41.4%

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

      7. div-sub 51.5%

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

      8. *-commutative 51.5%

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

      9. associate-/r* 60.9%

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

      10. div-sub 60.9%

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

      11. associate-*r/ 60.9%

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

      12. *-commutative 60.9%

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

      13. cancel-sign-sub-inv 60.9%

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

      14. *-lft-identity 60.9%

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

      15. associate-*l/ 60.9%

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

      16. mul-1-neg 60.9%

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

      17. distribute-rgt-in 60.9%

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

      18. mul-1-neg 60.9%

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

      19. sub-neg 60.9%

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

      20. div-sub 60.9%

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

   9. Simplified 60.9%

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

   if 7.2e-157 < b

   1. Initial program 98.5%

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

   2. Taylor expanded in y around 0 86.5%

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

      1. *-commutative 86.5%

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

      2. exp-diff 69.6%

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

      3. *-commutative 69.6%

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

      4. exp-to-pow 70.0%

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

      5. sub-neg 70.0%

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

      6. metadata-eval 70.0%

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

   4. Simplified 70.0%

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

   5. Taylor expanded in t around 0 68.3%

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

   6. Taylor expanded in b around 0 48.9%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.05 \cdot 10^{+209}:\\ \;\;\;\;\frac{b}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;b \leq -2.05 \cdot 10^{-278}:\\ \;\;\;\;\frac{\frac{x - x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-157}:\\ \;\;\;\;\frac{x \cdot \frac{1 - b}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]

Alternative 15: 39.9% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+211}:\\ \;\;\;\;\frac{b}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-278}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-156}:\\ \;\;\;\;\frac{x \cdot \frac{1 - b}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.2e+211)
   (* (/ b y) (- x))
   (if (<= b -2.4e-278)
     (/ (- (/ x a) (/ (* x b) a)) y)
     (if (<= b 1.5e-156)
       (/ (* x (/ (- 1.0 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 <= -1.2e+211) {
		tmp = (b / y) * -x;
	} else if (b <= -2.4e-278) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= 1.5e-156) {
		tmp = (x * ((1.0 - 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 <= (-1.2d+211)) then
        tmp = (b / y) * -x
    else if (b <= (-2.4d-278)) then
        tmp = ((x / a) - ((x * b) / a)) / y
    else if (b <= 1.5d-156) then
        tmp = (x * ((1.0d0 - 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 <= -1.2e+211) {
		tmp = (b / y) * -x;
	} else if (b <= -2.4e-278) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= 1.5e-156) {
		tmp = (x * ((1.0 - 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 <= -1.2e+211:
		tmp = (b / y) * -x
	elif b <= -2.4e-278:
		tmp = ((x / a) - ((x * b) / a)) / y
	elif b <= 1.5e-156:
		tmp = (x * ((1.0 - 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 <= -1.2e+211)
		tmp = Float64(Float64(b / y) * Float64(-x));
	elseif (b <= -2.4e-278)
		tmp = Float64(Float64(Float64(x / a) - Float64(Float64(x * b) / a)) / y);
	elseif (b <= 1.5e-156)
		tmp = Float64(Float64(x * Float64(Float64(1.0 - b) / 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 <= -1.2e+211)
		tmp = (b / y) * -x;
	elseif (b <= -2.4e-278)
		tmp = ((x / a) - ((x * b) / a)) / y;
	elseif (b <= 1.5e-156)
		tmp = (x * ((1.0 - 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, -1.2e+211], N[(N[(b / y), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[b, -2.4e-278], N[(N[(N[(x / a), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 1.5e-156], N[(N[(x * N[(N[(1.0 - b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.20000000000000009e211

   1. Initial program 100.0%

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

      1. associate-*l/ 93.1%

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

      2. associate--l+ 93.1%

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

      3. associate--l+ 93.1%

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

      4. fma-def 93.1%

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

      5. sub-neg 93.1%

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

      6. metadata-eval 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in b around inf 89.7%

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

      1. neg-mul-1 89.7%

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

   6. Simplified 89.7%

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

   7. Taylor expanded in b around 0 54.1%

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

      1. +-commutative 54.1%

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

      2. mul-1-neg 54.1%

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

      3. unsub-neg 54.1%

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

   9. Simplified 54.1%

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

   10. Taylor expanded in b around inf 54.1%

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

       1. mul-1-neg 54.1%

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

       2. associate-*l/ 73.4%

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

       3. distribute-rgt-neg-in 73.4%

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

   12. Simplified 73.4%

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

   if -1.20000000000000009e211 < b < -2.4e-278

   1. Initial program 98.9%

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

   2. Taylor expanded in y around 0 81.0%

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

      1. *-commutative 81.0%

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

      2. exp-diff 74.8%

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

      3. *-commutative 74.8%

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

      4. exp-to-pow 75.8%

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

      5. sub-neg 75.8%

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

      6. metadata-eval 75.8%

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

   4. Simplified 75.8%

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

   5. Taylor expanded in t around 0 62.3%

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

   6. Taylor expanded in b around 0 47.2%

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

   if -2.4e-278 < b < 1.5e-156

   1. Initial program 92.5%

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

   2. Taylor expanded in y around 0 67.9%

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

      1. *-commutative 67.9%

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

      2. exp-diff 67.9%

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

      3. *-commutative 67.9%

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

      4. exp-to-pow 68.8%

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

      5. sub-neg 68.8%

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

      6. metadata-eval 68.8%

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

   4. Simplified 68.8%

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

   5. Taylor expanded in t around 0 44.9%

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

   6. Taylor expanded in b around 0 44.9%

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

   7. Taylor expanded in b around 0 41.4%

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

      1. +-commutative 41.4%

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

      2. *-commutative 41.4%

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

      3. mul-1-neg 41.4%

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

      4. unsub-neg 41.4%

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

      5. *-commutative 41.4%

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

      6. *-commutative 41.4%

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

      7. div-sub 51.5%

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

      8. *-commutative 51.5%

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

      9. associate-/r* 60.9%

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

      10. div-sub 60.9%

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

      11. associate-*r/ 60.9%

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

      12. *-commutative 60.9%

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

      13. cancel-sign-sub-inv 60.9%

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

      14. *-lft-identity 60.9%

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

      15. associate-*l/ 60.9%

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

      16. mul-1-neg 60.9%

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

      17. distribute-rgt-in 60.9%

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

      18. mul-1-neg 60.9%

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

      19. sub-neg 60.9%

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

      20. div-sub 60.9%

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

   9. Simplified 60.9%

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

   if 1.5e-156 < b

   1. Initial program 98.5%

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

   2. Taylor expanded in y around 0 86.5%

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

      1. *-commutative 86.5%

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

      2. exp-diff 69.6%

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

      3. *-commutative 69.6%

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

      4. exp-to-pow 70.0%

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

      5. sub-neg 70.0%

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

      6. metadata-eval 70.0%

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

   4. Simplified 70.0%

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

   5. Taylor expanded in t around 0 68.3%

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

   6. Taylor expanded in b around 0 48.9%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+211}:\\ \;\;\;\;\frac{b}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-278}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-156}:\\ \;\;\;\;\frac{x \cdot \frac{1 - b}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]

Alternative 16: 34.7% accurate, 23.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{+16}:\\ \;\;\;\;\frac{b}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-157}:\\ \;\;\;\;\frac{1}{a} \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+14}:\\ \;\;\;\;\frac{1}{y} \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.6e+16)
   (* (/ b y) (- x))
   (if (<= b 3.4e-157)
     (* (/ 1.0 a) (/ x y))
     (if (<= b 5e+14) (* (/ 1.0 y) (/ x a)) (/ 1.0 (* y (/ a x)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.6e+16) {
		tmp = (b / y) * -x;
	} else if (b <= 3.4e-157) {
		tmp = (1.0 / a) * (x / y);
	} else if (b <= 5e+14) {
		tmp = (1.0 / y) * (x / a);
	} else {
		tmp = 1.0 / (y * (a / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-6.6d+16)) then
        tmp = (b / y) * -x
    else if (b <= 3.4d-157) then
        tmp = (1.0d0 / a) * (x / y)
    else if (b <= 5d+14) then
        tmp = (1.0d0 / y) * (x / a)
    else
        tmp = 1.0d0 / (y * (a / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.6e+16) {
		tmp = (b / y) * -x;
	} else if (b <= 3.4e-157) {
		tmp = (1.0 / a) * (x / y);
	} else if (b <= 5e+14) {
		tmp = (1.0 / y) * (x / a);
	} else {
		tmp = 1.0 / (y * (a / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.6e+16:
		tmp = (b / y) * -x
	elif b <= 3.4e-157:
		tmp = (1.0 / a) * (x / y)
	elif b <= 5e+14:
		tmp = (1.0 / y) * (x / a)
	else:
		tmp = 1.0 / (y * (a / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.6e+16)
		tmp = Float64(Float64(b / y) * Float64(-x));
	elseif (b <= 3.4e-157)
		tmp = Float64(Float64(1.0 / a) * Float64(x / y));
	elseif (b <= 5e+14)
		tmp = Float64(Float64(1.0 / y) * Float64(x / a));
	else
		tmp = Float64(1.0 / Float64(y * Float64(a / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6.6e+16)
		tmp = (b / y) * -x;
	elseif (b <= 3.4e-157)
		tmp = (1.0 / a) * (x / y);
	elseif (b <= 5e+14)
		tmp = (1.0 / y) * (x / a);
	else
		tmp = 1.0 / (y * (a / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.6e+16], N[(N[(b / y), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[b, 3.4e-157], N[(N[(1.0 / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5e+14], N[(N[(1.0 / y), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.6e16

   1. Initial program 100.0%

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

      1. associate-*l/ 93.2%

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

      2. associate--l+ 93.2%

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

      3. associate--l+ 93.2%

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

      4. fma-def 93.2%

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

      5. sub-neg 93.2%

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

      6. metadata-eval 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in b around inf 84.9%

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

      1. neg-mul-1 84.9%

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

   6. Simplified 84.9%

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

   7. Taylor expanded in b around 0 41.7%

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

      1. +-commutative 41.7%

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

      2. mul-1-neg 41.7%

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

      3. unsub-neg 41.7%

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

   9. Simplified 41.7%

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

   10. Taylor expanded in b around inf 41.7%

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

       1. mul-1-neg 41.7%

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

       2. associate-*l/ 48.0%

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

       3. distribute-rgt-neg-in 48.0%

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

   12. Simplified 48.0%

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

   if -6.6e16 < b < 3.39999999999999977e-157

   1. Initial program 96.2%

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

   2. Taylor expanded in y around 0 71.8%

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

      1. *-commutative 71.8%

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

      2. exp-diff 70.8%

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

      3. *-commutative 70.8%

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

      4. exp-to-pow 72.1%

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

      5. sub-neg 72.1%

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

      6. metadata-eval 72.1%

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

   4. Simplified 72.1%

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

   5. Taylor expanded in t around 0 49.9%

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

   6. Taylor expanded in b around 0 50.7%

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

      1. *-un-lft-identity 50.7%

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

      2. *-commutative 50.7%

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

      3. times-frac 52.8%

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

   8. Applied egg-rr 52.8%

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

   if 3.39999999999999977e-157 < b < 5e14

   1. Initial program 99.0%

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

   2. Taylor expanded in y around 0 73.3%

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

      1. *-commutative 73.3%

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

      2. exp-diff 70.3%

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

      3. *-commutative 70.3%

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

      4. exp-to-pow 71.2%

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

      5. sub-neg 71.2%

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

      6. metadata-eval 71.2%

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

   4. Simplified 71.2%

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

   5. Taylor expanded in t around 0 46.0%

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

   6. Taylor expanded in b around 0 34.9%

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

      1. *-un-lft-identity 34.9%

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

      2. times-frac 46.0%

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

   8. Applied egg-rr 46.0%

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

   if 5e14 < b

   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 94.6%

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

      1. *-commutative 94.6%

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

      2. exp-diff 69.2%

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

      3. *-commutative 69.2%

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

      4. exp-to-pow 69.2%

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

      5. sub-neg 69.2%

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

      6. metadata-eval 69.2%

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

   4. Simplified 69.2%

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

   5. Taylor expanded in t around 0 82.1%

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

   6. Taylor expanded in b around 0 22.2%

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

      1. clear-num 22.5%

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

      2. inv-pow 22.5%

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

      3. *-commutative 22.5%

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

   8. Applied egg-rr 22.5%

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

      1. unpow-1 22.5%

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

      2. associate-*l/ 24.3%

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

      3. *-commutative 24.3%

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

   10. Simplified 24.3%

       \[\leadsto \color{blue}{\frac{1}{y \cdot \frac{a}{x}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{+16}:\\ \;\;\;\;\frac{b}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-157}:\\ \;\;\;\;\frac{1}{a} \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+14}:\\ \;\;\;\;\frac{1}{y} \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \end{array} \]

Alternative 17: 34.6% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+16}:\\ \;\;\;\;\frac{b}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-156}:\\ \;\;\;\;\frac{1}{a} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.2e+16)
   (* (/ b y) (- x))
   (if (<= b 1.4e-156) (* (/ 1.0 a) (/ x y)) (/ (/ x a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.2e+16) {
		tmp = (b / y) * -x;
	} else if (b <= 1.4e-156) {
		tmp = (1.0 / a) * (x / y);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-7.2d+16)) then
        tmp = (b / y) * -x
    else if (b <= 1.4d-156) then
        tmp = (1.0d0 / a) * (x / y)
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.2e+16) {
		tmp = (b / y) * -x;
	} else if (b <= 1.4e-156) {
		tmp = (1.0 / a) * (x / y);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7.2e+16:
		tmp = (b / y) * -x
	elif b <= 1.4e-156:
		tmp = (1.0 / a) * (x / y)
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7.2e+16)
		tmp = Float64(Float64(b / y) * Float64(-x));
	elseif (b <= 1.4e-156)
		tmp = Float64(Float64(1.0 / a) * Float64(x / y));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -7.2e+16)
		tmp = (b / y) * -x;
	elseif (b <= 1.4e-156)
		tmp = (1.0 / a) * (x / y);
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7.2e+16], N[(N[(b / y), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[b, 1.4e-156], N[(N[(1.0 / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.2e16

   1. Initial program 100.0%

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

      1. associate-*l/ 93.2%

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

      2. associate--l+ 93.2%

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

      3. associate--l+ 93.2%

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

      4. fma-def 93.2%

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

      5. sub-neg 93.2%

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

      6. metadata-eval 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in b around inf 84.9%

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

      1. neg-mul-1 84.9%

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

   6. Simplified 84.9%

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

   7. Taylor expanded in b around 0 41.7%

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

      1. +-commutative 41.7%

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

      2. mul-1-neg 41.7%

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

      3. unsub-neg 41.7%

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

   9. Simplified 41.7%

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

   10. Taylor expanded in b around inf 41.7%

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

       1. mul-1-neg 41.7%

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

       2. associate-*l/ 48.0%

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

       3. distribute-rgt-neg-in 48.0%

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

   12. Simplified 48.0%

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

   if -7.2e16 < b < 1.4000000000000001e-156

   1. Initial program 96.2%

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

   2. Taylor expanded in y around 0 71.8%

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

      1. *-commutative 71.8%

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

      2. exp-diff 70.8%

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

      3. *-commutative 70.8%

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

      4. exp-to-pow 72.1%

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

      5. sub-neg 72.1%

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

      6. metadata-eval 72.1%

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

   4. Simplified 72.1%

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

   5. Taylor expanded in t around 0 49.9%

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

   6. Taylor expanded in b around 0 50.7%

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

      1. *-un-lft-identity 50.7%

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

      2. *-commutative 50.7%

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

      3. times-frac 52.8%

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

   8. Applied egg-rr 52.8%

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

   if 1.4000000000000001e-156 < b

   1. Initial program 98.5%

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

   2. Taylor expanded in y around 0 86.5%

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

      1. *-commutative 86.5%

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

      2. exp-diff 69.6%

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

      3. *-commutative 69.6%

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

      4. exp-to-pow 70.0%

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

      5. sub-neg 70.0%

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

      6. metadata-eval 70.0%

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

   4. Simplified 70.0%

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

   5. Taylor expanded in t around 0 68.3%

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

   6. Taylor expanded in b around 0 27.1%

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

      1. associate-/l/ 31.7%

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

   8. Simplified 31.7%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+16}:\\ \;\;\;\;\frac{b}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-156}:\\ \;\;\;\;\frac{1}{a} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]

Alternative 18: 34.6% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+16}:\\ \;\;\;\;\frac{b}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{-160}:\\ \;\;\;\;\frac{1}{a} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y} \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -8.5e+16)
   (* (/ b y) (- x))
   (if (<= b 6.6e-160) (* (/ 1.0 a) (/ x y)) (* (/ 1.0 y) (/ x a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8.5e+16) {
		tmp = (b / y) * -x;
	} else if (b <= 6.6e-160) {
		tmp = (1.0 / a) * (x / y);
	} else {
		tmp = (1.0 / y) * (x / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-8.5d+16)) then
        tmp = (b / y) * -x
    else if (b <= 6.6d-160) then
        tmp = (1.0d0 / a) * (x / y)
    else
        tmp = (1.0d0 / y) * (x / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8.5e+16) {
		tmp = (b / y) * -x;
	} else if (b <= 6.6e-160) {
		tmp = (1.0 / a) * (x / y);
	} else {
		tmp = (1.0 / y) * (x / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -8.5e+16:
		tmp = (b / y) * -x
	elif b <= 6.6e-160:
		tmp = (1.0 / a) * (x / y)
	else:
		tmp = (1.0 / y) * (x / a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -8.5e+16)
		tmp = Float64(Float64(b / y) * Float64(-x));
	elseif (b <= 6.6e-160)
		tmp = Float64(Float64(1.0 / a) * Float64(x / y));
	else
		tmp = Float64(Float64(1.0 / y) * Float64(x / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -8.5e+16)
		tmp = (b / y) * -x;
	elseif (b <= 6.6e-160)
		tmp = (1.0 / a) * (x / y);
	else
		tmp = (1.0 / y) * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -8.5e+16], N[(N[(b / y), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[b, 6.6e-160], N[(N[(1.0 / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / y), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.5e16

   1. Initial program 100.0%

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

      1. associate-*l/ 93.2%

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

      2. associate--l+ 93.2%

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

      3. associate--l+ 93.2%

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

      4. fma-def 93.2%

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

      5. sub-neg 93.2%

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

      6. metadata-eval 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in b around inf 84.9%

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

      1. neg-mul-1 84.9%

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

   6. Simplified 84.9%

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

   7. Taylor expanded in b around 0 41.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y} + \frac{x}{y}} \]
   8. Step-by-step derivation

      1. +-commutative 41.7%

         \[\leadsto \color{blue}{\frac{x}{y} + -1 \cdot \frac{b \cdot x}{y}} \]

      2. mul-1-neg 41.7%

         \[\leadsto \frac{x}{y} + \color{blue}{\left(-\frac{b \cdot x}{y}\right)} \]

      3. unsub-neg 41.7%

         \[\leadsto \color{blue}{\frac{x}{y} - \frac{b \cdot x}{y}} \]

   9. Simplified 41.7%

      \[\leadsto \color{blue}{\frac{x}{y} - \frac{b \cdot x}{y}} \]

   10. Taylor expanded in b around inf 41.7%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y}} \]
   11. Step-by-step derivation

       1. mul-1-neg 41.7%

          \[\leadsto \color{blue}{-\frac{b \cdot x}{y}} \]

       2. associate-*l/ 48.0%

          \[\leadsto -\color{blue}{\frac{b}{y} \cdot x} \]

       3. distribute-rgt-neg-in 48.0%

          \[\leadsto \color{blue}{\frac{b}{y} \cdot \left(-x\right)} \]

   12. Simplified 48.0%

       \[\leadsto \color{blue}{\frac{b}{y} \cdot \left(-x\right)} \]

   if -8.5e16 < b < 6.6e-160

   1. Initial program 96.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in y around 0 71.8%

      \[\leadsto \frac{\color{blue}{e^{\left(t - 1\right) \cdot \log a - b} \cdot x}}{y} \]
   3. Step-by-step derivation

      1. *-commutative 71.8%

         \[\leadsto \frac{\color{blue}{x \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      2. exp-diff 70.8%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. *-commutative 70.8%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y} \]

      4. exp-to-pow 72.1%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      5. sub-neg 72.1%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      6. metadata-eval 72.1%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   4. Simplified 72.1%

      \[\leadsto \frac{\color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   5. Taylor expanded in t around 0 49.9%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   6. Taylor expanded in b around 0 50.7%

      \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
   7. Step-by-step derivation

      1. *-un-lft-identity 50.7%

         \[\leadsto \frac{\color{blue}{1 \cdot x}}{y \cdot a} \]

      2. *-commutative 50.7%

         \[\leadsto \frac{1 \cdot x}{\color{blue}{a \cdot y}} \]

      3. times-frac 52.8%

         \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y}} \]

   8. Applied egg-rr 52.8%

      \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y}} \]

   if 6.6e-160 < b

   1. Initial program 98.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in y around 0 86.5%

      \[\leadsto \frac{\color{blue}{e^{\left(t - 1\right) \cdot \log a - b} \cdot x}}{y} \]
   3. Step-by-step derivation

      1. *-commutative 86.5%

         \[\leadsto \frac{\color{blue}{x \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      2. exp-diff 69.6%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. *-commutative 69.6%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y} \]

      4. exp-to-pow 70.0%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      5. sub-neg 70.0%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      6. metadata-eval 70.0%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   4. Simplified 70.0%

      \[\leadsto \frac{\color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   5. Taylor expanded in t around 0 68.3%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   6. Taylor expanded in b around 0 27.1%

      \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
   7. Step-by-step derivation

      1. *-un-lft-identity 27.1%

         \[\leadsto \frac{\color{blue}{1 \cdot x}}{y \cdot a} \]

      2. times-frac 31.7%

         \[\leadsto \color{blue}{\frac{1}{y} \cdot \frac{x}{a}} \]

   8. Applied egg-rr 31.7%

      \[\leadsto \color{blue}{\frac{1}{y} \cdot \frac{x}{a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+16}:\\ \;\;\;\;\frac{b}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{-160}:\\ \;\;\;\;\frac{1}{a} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y} \cdot \frac{x}{a}\\ \end{array} \]

Alternative 19: 39.2% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.85 \cdot 10^{-158}:\\ \;\;\;\;\frac{x \cdot \frac{1 - b}{y}}{a}\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+106}:\\ \;\;\;\;\frac{1}{y} \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 2.85e-158)
   (/ (* x (/ (- 1.0 b) y)) a)
   (if (<= b 7.5e+106) (* (/ 1.0 y) (/ x a)) (/ x (+ y (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.85e-158) {
		tmp = (x * ((1.0 - b) / y)) / a;
	} else if (b <= 7.5e+106) {
		tmp = (1.0 / y) * (x / a);
	} else {
		tmp = x / (y + (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 2.85d-158) then
        tmp = (x * ((1.0d0 - b) / y)) / a
    else if (b <= 7.5d+106) then
        tmp = (1.0d0 / y) * (x / a)
    else
        tmp = x / (y + (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.85e-158) {
		tmp = (x * ((1.0 - b) / y)) / a;
	} else if (b <= 7.5e+106) {
		tmp = (1.0 / y) * (x / a);
	} else {
		tmp = x / (y + (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 2.85e-158:
		tmp = (x * ((1.0 - b) / y)) / a
	elif b <= 7.5e+106:
		tmp = (1.0 / y) * (x / a)
	else:
		tmp = x / (y + (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 2.85e-158)
		tmp = Float64(Float64(x * Float64(Float64(1.0 - b) / y)) / a);
	elseif (b <= 7.5e+106)
		tmp = Float64(Float64(1.0 / y) * Float64(x / a));
	else
		tmp = Float64(x / Float64(y + Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 2.85e-158)
		tmp = (x * ((1.0 - b) / y)) / a;
	elseif (b <= 7.5e+106)
		tmp = (1.0 / y) * (x / a);
	else
		tmp = x / (y + (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 2.85e-158], N[(N[(x * N[(N[(1.0 - b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, 7.5e+106], N[(N[(1.0 / y), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision], N[(x / N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < 2.84999999999999991e-158

   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 y around 0 81.1%

      \[\leadsto \frac{\color{blue}{e^{\left(t - 1\right) \cdot \log a - b} \cdot x}}{y} \]
   3. Step-by-step derivation

      1. *-commutative 81.1%

         \[\leadsto \frac{\color{blue}{x \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      2. exp-diff 74.5%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. *-commutative 74.5%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y} \]

      4. exp-to-pow 75.3%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      5. sub-neg 75.3%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      6. metadata-eval 75.3%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   4. Simplified 75.3%

      \[\leadsto \frac{\color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   5. Taylor expanded in t around 0 64.1%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   6. Taylor expanded in b around 0 47.8%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]

   7. Taylor expanded in b around 0 44.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y \cdot a} + \frac{x}{y \cdot a}} \]
   8. Step-by-step derivation

      1. +-commutative 44.7%

         \[\leadsto \color{blue}{\frac{x}{y \cdot a} + -1 \cdot \frac{b \cdot x}{y \cdot a}} \]

      2. *-commutative 44.7%

         \[\leadsto \frac{x}{\color{blue}{a \cdot y}} + -1 \cdot \frac{b \cdot x}{y \cdot a} \]

      3. mul-1-neg 44.7%

         \[\leadsto \frac{x}{a \cdot y} + \color{blue}{\left(-\frac{b \cdot x}{y \cdot a}\right)} \]

      4. unsub-neg 44.7%

         \[\leadsto \color{blue}{\frac{x}{a \cdot y} - \frac{b \cdot x}{y \cdot a}} \]

      5. *-commutative 44.7%

         \[\leadsto \frac{x}{a \cdot y} - \frac{\color{blue}{x \cdot b}}{y \cdot a} \]

      6. *-commutative 44.7%

         \[\leadsto \frac{x}{a \cdot y} - \frac{x \cdot b}{\color{blue}{a \cdot y}} \]

      7. div-sub 47.2%

         \[\leadsto \color{blue}{\frac{x - x \cdot b}{a \cdot y}} \]

      8. *-commutative 47.2%

         \[\leadsto \frac{x - x \cdot b}{\color{blue}{y \cdot a}} \]

      9. associate-/r* 50.4%

         \[\leadsto \color{blue}{\frac{\frac{x - x \cdot b}{y}}{a}} \]

      10. div-sub 50.4%

          \[\leadsto \frac{\color{blue}{\frac{x}{y} - \frac{x \cdot b}{y}}}{a} \]

      11. associate-*r/ 52.6%

          \[\leadsto \frac{\frac{x}{y} - \color{blue}{x \cdot \frac{b}{y}}}{a} \]

      12. *-commutative 52.6%

          \[\leadsto \frac{\frac{x}{y} - \color{blue}{\frac{b}{y} \cdot x}}{a} \]

      13. cancel-sign-sub-inv 52.6%

          \[\leadsto \frac{\color{blue}{\frac{x}{y} + \left(-\frac{b}{y}\right) \cdot x}}{a} \]

      14. *-lft-identity 52.6%

          \[\leadsto \frac{\frac{\color{blue}{1 \cdot x}}{y} + \left(-\frac{b}{y}\right) \cdot x}{a} \]

      15. associate-*l/ 52.6%

          \[\leadsto \frac{\color{blue}{\frac{1}{y} \cdot x} + \left(-\frac{b}{y}\right) \cdot x}{a} \]

      16. mul-1-neg 52.6%

          \[\leadsto \frac{\frac{1}{y} \cdot x + \color{blue}{\left(-1 \cdot \frac{b}{y}\right)} \cdot x}{a} \]

      17. distribute-rgt-in 52.6%

          \[\leadsto \frac{\color{blue}{x \cdot \left(\frac{1}{y} + -1 \cdot \frac{b}{y}\right)}}{a} \]

      18. mul-1-neg 52.6%

          \[\leadsto \frac{x \cdot \left(\frac{1}{y} + \color{blue}{\left(-\frac{b}{y}\right)}\right)}{a} \]

      19. sub-neg 52.6%

          \[\leadsto \frac{x \cdot \color{blue}{\left(\frac{1}{y} - \frac{b}{y}\right)}}{a} \]

      20. div-sub 52.6%

          \[\leadsto \frac{x \cdot \color{blue}{\frac{1 - b}{y}}}{a} \]

   9. Simplified 52.6%

      \[\leadsto \color{blue}{\frac{x \cdot \frac{1 - b}{y}}{a}} \]

   if 2.84999999999999991e-158 < b < 7.50000000000000058e106

   1. Initial program 99.3%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in y around 0 81.8%

      \[\leadsto \frac{\color{blue}{e^{\left(t - 1\right) \cdot \log a - b} \cdot x}}{y} \]
   3. Step-by-step derivation

      1. *-commutative 81.8%

         \[\leadsto \frac{\color{blue}{x \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      2. exp-diff 67.8%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. *-commutative 67.8%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y} \]

      4. exp-to-pow 68.4%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      5. sub-neg 68.4%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      6. metadata-eval 68.4%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   4. Simplified 68.4%

      \[\leadsto \frac{\color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   5. Taylor expanded in t around 0 51.5%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   6. Taylor expanded in b around 0 30.3%

      \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
   7. Step-by-step derivation

      1. *-un-lft-identity 30.3%

         \[\leadsto \frac{\color{blue}{1 \cdot x}}{y \cdot a} \]

      2. times-frac 39.8%

         \[\leadsto \color{blue}{\frac{1}{y} \cdot \frac{x}{a}} \]

   8. Applied egg-rr 39.8%

      \[\leadsto \color{blue}{\frac{1}{y} \cdot \frac{x}{a}} \]

   if 7.50000000000000058e106 < b

   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/ 82.1%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. associate--l+ 82.1%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \]

      3. associate--l+ 82.1%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      4. fma-def 82.1%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      5. sub-neg 82.1%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      6. metadata-eval 82.1%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 82.1%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in b around inf 74.5%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{-1 \cdot b}} \]
   5. Step-by-step derivation

      1. neg-mul-1 74.5%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{-b}} \]

   6. Simplified 74.5%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{-b}} \]

   7. Taylor expanded in x around 0 89.9%

      \[\leadsto \color{blue}{\frac{e^{-b} \cdot x}{y}} \]
   8. Step-by-step derivation

      1. *-commutative 89.9%

         \[\leadsto \frac{\color{blue}{x \cdot e^{-b}}}{y} \]

      2. rem-exp-log 56.5%

         \[\leadsto \frac{\color{blue}{e^{\log x}} \cdot e^{-b}}{y} \]

      3. exp-sum 56.5%

         \[\leadsto \frac{\color{blue}{e^{\log x + \left(-b\right)}}}{y} \]

      4. sub-neg 56.5%

         \[\leadsto \frac{e^{\color{blue}{\log x - b}}}{y} \]

      5. exp-diff 56.5%

         \[\leadsto \frac{\color{blue}{\frac{e^{\log x}}{e^{b}}}}{y} \]

      6. rem-exp-log 89.9%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b}}}{y} \]

      7. associate-/l/ 89.9%

         \[\leadsto \color{blue}{\frac{x}{y \cdot e^{b}}} \]

   9. Simplified 89.9%

      \[\leadsto \color{blue}{\frac{x}{y \cdot e^{b}}} \]

   10. Taylor expanded in b around 0 48.0%

       \[\leadsto \frac{x}{\color{blue}{y \cdot b + y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 2.85 \cdot 10^{-158}:\\ \;\;\;\;\frac{x \cdot \frac{1 - b}{y}}{a}\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+106}:\\ \;\;\;\;\frac{1}{y} \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + y \cdot b}\\ \end{array} \]

Alternative 20: 40.7% accurate, 28.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 4.8 \cdot 10^{-160}:\\ \;\;\;\;\frac{x \cdot \frac{1 - b}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 4.8e-160) (/ (* x (/ (- 1.0 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 <= 4.8e-160) {
		tmp = (x * ((1.0 - 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 <= 4.8d-160) then
        tmp = (x * ((1.0d0 - 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 <= 4.8e-160) {
		tmp = (x * ((1.0 - 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 <= 4.8e-160:
		tmp = (x * ((1.0 - 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 <= 4.8e-160)
		tmp = Float64(Float64(x * Float64(Float64(1.0 - b) / 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 <= 4.8e-160)
		tmp = (x * ((1.0 - 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, 4.8e-160], N[(N[(x * N[(N[(1.0 - b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 4.79999999999999982e-160

   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 y around 0 81.1%

      \[\leadsto \frac{\color{blue}{e^{\left(t - 1\right) \cdot \log a - b} \cdot x}}{y} \]
   3. Step-by-step derivation

      1. *-commutative 81.1%

         \[\leadsto \frac{\color{blue}{x \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      2. exp-diff 74.5%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. *-commutative 74.5%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y} \]

      4. exp-to-pow 75.3%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      5. sub-neg 75.3%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      6. metadata-eval 75.3%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   4. Simplified 75.3%

      \[\leadsto \frac{\color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   5. Taylor expanded in t around 0 64.1%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   6. Taylor expanded in b around 0 47.8%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]

   7. Taylor expanded in b around 0 44.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y \cdot a} + \frac{x}{y \cdot a}} \]
   8. Step-by-step derivation

      1. +-commutative 44.7%

         \[\leadsto \color{blue}{\frac{x}{y \cdot a} + -1 \cdot \frac{b \cdot x}{y \cdot a}} \]

      2. *-commutative 44.7%

         \[\leadsto \frac{x}{\color{blue}{a \cdot y}} + -1 \cdot \frac{b \cdot x}{y \cdot a} \]

      3. mul-1-neg 44.7%

         \[\leadsto \frac{x}{a \cdot y} + \color{blue}{\left(-\frac{b \cdot x}{y \cdot a}\right)} \]

      4. unsub-neg 44.7%

         \[\leadsto \color{blue}{\frac{x}{a \cdot y} - \frac{b \cdot x}{y \cdot a}} \]

      5. *-commutative 44.7%

         \[\leadsto \frac{x}{a \cdot y} - \frac{\color{blue}{x \cdot b}}{y \cdot a} \]

      6. *-commutative 44.7%

         \[\leadsto \frac{x}{a \cdot y} - \frac{x \cdot b}{\color{blue}{a \cdot y}} \]

      7. div-sub 47.2%

         \[\leadsto \color{blue}{\frac{x - x \cdot b}{a \cdot y}} \]

      8. *-commutative 47.2%

         \[\leadsto \frac{x - x \cdot b}{\color{blue}{y \cdot a}} \]

      9. associate-/r* 50.4%

         \[\leadsto \color{blue}{\frac{\frac{x - x \cdot b}{y}}{a}} \]

      10. div-sub 50.4%

          \[\leadsto \frac{\color{blue}{\frac{x}{y} - \frac{x \cdot b}{y}}}{a} \]

      11. associate-*r/ 52.6%

          \[\leadsto \frac{\frac{x}{y} - \color{blue}{x \cdot \frac{b}{y}}}{a} \]

      12. *-commutative 52.6%

          \[\leadsto \frac{\frac{x}{y} - \color{blue}{\frac{b}{y} \cdot x}}{a} \]

      13. cancel-sign-sub-inv 52.6%

          \[\leadsto \frac{\color{blue}{\frac{x}{y} + \left(-\frac{b}{y}\right) \cdot x}}{a} \]

      14. *-lft-identity 52.6%

          \[\leadsto \frac{\frac{\color{blue}{1 \cdot x}}{y} + \left(-\frac{b}{y}\right) \cdot x}{a} \]

      15. associate-*l/ 52.6%

          \[\leadsto \frac{\color{blue}{\frac{1}{y} \cdot x} + \left(-\frac{b}{y}\right) \cdot x}{a} \]

      16. mul-1-neg 52.6%

          \[\leadsto \frac{\frac{1}{y} \cdot x + \color{blue}{\left(-1 \cdot \frac{b}{y}\right)} \cdot x}{a} \]

      17. distribute-rgt-in 52.6%

          \[\leadsto \frac{\color{blue}{x \cdot \left(\frac{1}{y} + -1 \cdot \frac{b}{y}\right)}}{a} \]

      18. mul-1-neg 52.6%

          \[\leadsto \frac{x \cdot \left(\frac{1}{y} + \color{blue}{\left(-\frac{b}{y}\right)}\right)}{a} \]

      19. sub-neg 52.6%

          \[\leadsto \frac{x \cdot \color{blue}{\left(\frac{1}{y} - \frac{b}{y}\right)}}{a} \]

      20. div-sub 52.6%

          \[\leadsto \frac{x \cdot \color{blue}{\frac{1 - b}{y}}}{a} \]

   9. Simplified 52.6%

      \[\leadsto \color{blue}{\frac{x \cdot \frac{1 - b}{y}}{a}} \]

   if 4.79999999999999982e-160 < b

   1. Initial program 98.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in y around 0 86.5%

      \[\leadsto \frac{\color{blue}{e^{\left(t - 1\right) \cdot \log a - b} \cdot x}}{y} \]
   3. Step-by-step derivation

      1. *-commutative 86.5%

         \[\leadsto \frac{\color{blue}{x \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      2. exp-diff 69.6%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. *-commutative 69.6%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y} \]

      4. exp-to-pow 70.0%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      5. sub-neg 70.0%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      6. metadata-eval 70.0%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   4. Simplified 70.0%

      \[\leadsto \frac{\color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   5. Taylor expanded in t around 0 68.3%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   6. Taylor expanded in b around 0 48.9%

      \[\leadsto \frac{\frac{x}{\color{blue}{a \cdot b + a}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 4.8 \cdot 10^{-160}:\\ \;\;\;\;\frac{x \cdot \frac{1 - b}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]

Alternative 21: 34.9% accurate, 39.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+61}:\\ \;\;\;\;\frac{b}{y} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -8.2e+61) (* (/ b y) (- x)) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8.2e+61) {
		tmp = (b / y) * -x;
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-8.2d+61)) then
        tmp = (b / y) * -x
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8.2e+61) {
		tmp = (b / y) * -x;
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -8.2e+61:
		tmp = (b / y) * -x
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -8.2e+61)
		tmp = Float64(Float64(b / y) * Float64(-x));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -8.2e+61)
		tmp = (b / y) * -x;
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -8.2e+61], N[(N[(b / y), $MachinePrecision] * (-x)), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.19999999999999944e61

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.0%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. associate--l+ 94.0%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \]

      3. associate--l+ 94.0%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      4. fma-def 94.0%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      5. sub-neg 94.0%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      6. metadata-eval 94.0%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 94.0%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in b around inf 88.1%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{-1 \cdot b}} \]
   5. Step-by-step derivation

      1. neg-mul-1 88.1%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{-b}} \]

   6. Simplified 88.1%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{-b}} \]

   7. Taylor expanded in b around 0 44.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y} + \frac{x}{y}} \]
   8. Step-by-step derivation

      1. +-commutative 44.8%

         \[\leadsto \color{blue}{\frac{x}{y} + -1 \cdot \frac{b \cdot x}{y}} \]

      2. mul-1-neg 44.8%

         \[\leadsto \frac{x}{y} + \color{blue}{\left(-\frac{b \cdot x}{y}\right)} \]

      3. unsub-neg 44.8%

         \[\leadsto \color{blue}{\frac{x}{y} - \frac{b \cdot x}{y}} \]

   9. Simplified 44.8%

      \[\leadsto \color{blue}{\frac{x}{y} - \frac{b \cdot x}{y}} \]

   10. Taylor expanded in b around inf 44.8%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y}} \]
   11. Step-by-step derivation

       1. mul-1-neg 44.8%

          \[\leadsto \color{blue}{-\frac{b \cdot x}{y}} \]

       2. associate-*l/ 52.2%

          \[\leadsto -\color{blue}{\frac{b}{y} \cdot x} \]

       3. distribute-rgt-neg-in 52.2%

          \[\leadsto \color{blue}{\frac{b}{y} \cdot \left(-x\right)} \]

   12. Simplified 52.2%

       \[\leadsto \color{blue}{\frac{b}{y} \cdot \left(-x\right)} \]

   if -8.19999999999999944e61 < b

   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. Taylor expanded in y around 0 79.3%

      \[\leadsto \frac{\color{blue}{e^{\left(t - 1\right) \cdot \log a - b} \cdot x}}{y} \]
   3. Step-by-step derivation

      1. *-commutative 79.3%

         \[\leadsto \frac{\color{blue}{x \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      2. exp-diff 70.1%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. *-commutative 70.1%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y} \]

      4. exp-to-pow 70.9%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      5. sub-neg 70.9%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      6. metadata-eval 70.9%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   4. Simplified 70.9%

      \[\leadsto \frac{\color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   5. Taylor expanded in t around 0 58.6%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   6. Taylor expanded in b around 0 39.3%

      \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
   7. Step-by-step derivation

      1. associate-/l/ 40.4%

         \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y}} \]

   8. Simplified 40.4%

      \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+61}:\\ \;\;\;\;\frac{b}{y} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]

Alternative 22: 31.9% accurate, 44.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 3.8 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 3.8e+29) (/ x (* y a)) (/ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 3.8e+29) {
		tmp = x / (y * a);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= 3.8d+29) then
        tmp = x / (y * a)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 3.8e+29) {
		tmp = x / (y * a);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 3.8e+29:
		tmp = x / (y * a)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 3.8e+29)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 3.8e+29)
		tmp = x / (y * a);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 3.8e+29], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 3.79999999999999971e29

   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. Taylor expanded in y around 0 81.2%

      \[\leadsto \frac{\color{blue}{e^{\left(t - 1\right) \cdot \log a - b} \cdot x}}{y} \]
   3. Step-by-step derivation

      1. *-commutative 81.2%

         \[\leadsto \frac{\color{blue}{x \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      2. exp-diff 74.3%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. *-commutative 74.3%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y} \]

      4. exp-to-pow 75.1%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      5. sub-neg 75.1%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      6. metadata-eval 75.1%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   4. Simplified 75.1%

      \[\leadsto \frac{\color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   5. Taylor expanded in t around 0 70.3%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   6. Taylor expanded in b around 0 42.4%

      \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]

   if 3.79999999999999971e29 < t

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 90.2%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. associate--l+ 90.2%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \]

      3. associate--l+ 90.2%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      4. fma-def 90.2%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

      5. sub-neg 90.2%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

      6. metadata-eval 90.2%

         \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

   3. Simplified 90.2%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

   4. Taylor expanded in b around inf 46.3%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{-1 \cdot b}} \]
   5. Step-by-step derivation

      1. neg-mul-1 46.3%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{-b}} \]

   6. Simplified 46.3%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{-b}} \]

   7. Taylor expanded in b around 0 17.2%

      \[\leadsto \color{blue}{\frac{x}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3.8 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 23: 33.1% accurate, 44.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 5.5 \cdot 10^{-57}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 5.5e-57) (/ (/ 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 <= 5.5e-57) {
		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 <= 5.5d-57) 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 <= 5.5e-57) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 5.5e-57:
		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 <= 5.5e-57)
		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 <= 5.5e-57)
		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, 5.5e-57], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 5.50000000000000011e-57

   1. Initial program 99.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in y around 0 85.1%

      \[\leadsto \frac{\color{blue}{e^{\left(t - 1\right) \cdot \log a - b} \cdot x}}{y} \]
   3. Step-by-step derivation

      1. *-commutative 85.1%

         \[\leadsto \frac{\color{blue}{x \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      2. exp-diff 78.5%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. *-commutative 78.5%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y} \]

      4. exp-to-pow 79.3%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      5. sub-neg 79.3%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      6. metadata-eval 79.3%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   4. Simplified 79.3%

      \[\leadsto \frac{\color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   5. Taylor expanded in t around 0 68.0%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   6. Taylor expanded in b around 0 38.3%

      \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
   7. Step-by-step derivation

      1. associate-/l/ 46.5%

         \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y}} \]

   8. Simplified 46.5%

      \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y}} \]

   if 5.50000000000000011e-57 < a

   1. Initial program 97.3%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in y around 0 81.9%

      \[\leadsto \frac{\color{blue}{e^{\left(t - 1\right) \cdot \log a - b} \cdot x}}{y} \]
   3. Step-by-step derivation

      1. *-commutative 81.9%

         \[\leadsto \frac{\color{blue}{x \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      2. exp-diff 69.7%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. *-commutative 69.7%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y} \]

      4. exp-to-pow 70.2%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      5. sub-neg 70.2%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      6. metadata-eval 70.2%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   4. Simplified 70.2%

      \[\leadsto \frac{\color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   5. Taylor expanded in t around 0 64.2%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   6. Taylor expanded in b around 0 34.2%

      \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 5.5 \cdot 10^{-57}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]

Alternative 24: 15.8% accurate, 105.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / y;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / y;
}

Python

def code(x, y, z, t, a, b):
	return x / y

Julia

function code(x, y, z, t, a, b)
	return Float64(x / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / y), $MachinePrecision]

Derivation

1. Initial program 97.9%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. associate-*l/ 90.4%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

   2. associate--l+ 90.4%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \]

   3. associate--l+ 90.4%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

   4. fma-def 90.4%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b} \]

   5. sub-neg 90.4%

      \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b} \]

   6. metadata-eval 90.4%

      \[\leadsto \frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b} \]

3. Simplified 90.4%

   \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}} \]

4. Taylor expanded in b around inf 44.5%

   \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{-1 \cdot b}} \]
5. Step-by-step derivation

   1. neg-mul-1 44.5%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{-b}} \]

6. Simplified 44.5%

   \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{-b}} \]

7. Taylor expanded in b around 0 16.3%

   \[\leadsto \color{blue}{\frac{x}{y}} \]

8. Final simplification 16.3%

   \[\leadsto \frac{x}{y} \]

Developer target: 71.3% 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 2023199 
(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))