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

Percentage Accurate: 98.5% → 98.5%

Time: 26.8s

Alternatives: 25

Speedup: 1.0×

• 21.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

2. Final simplification 98.0%

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

Alternative 2: 92.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+59} \lor \neg \left(y \leq 1.35 \cdot 10^{+26}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.4e+59) (not (<= y 1.35e+26)))
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.4e+59) || !(y <= 1.35e+26)) {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	} else {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-3.4d+59)) .or. (.not. (y <= 1.35d+26))) then
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y
    else
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.4e+59) || !(y <= 1.35e+26)) {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	} else {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.4e+59) or not (y <= 1.35e+26):
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	else:
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.4e+59) || !(y <= 1.35e+26))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.4e+59) || ~((y <= 1.35e+26)))
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	else
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.4e+59], N[Not[LessEqual[y, 1.35e+26]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.40000000000000006e59 or 1.35e26 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 94.9%

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

      1. mul-1-neg 94.9%

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

   4. Simplified 94.9%

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

   if -3.40000000000000006e59 < y < 1.35e26

   1. Initial program 96.4%

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

   2. Taylor expanded in y around 0 95.7%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+59} \lor \neg \left(y \leq 1.35 \cdot 10^{+26}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]

Alternative 3: 79.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{\frac{\frac{{a}^{t}}{a}}{y}}{e^{b}}\\ t_2 := \frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-289}:\\ \;\;\;\;x \cdot \frac{1}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (/ (/ (pow a t) a) y) (exp b))))
        (t_2 (/ (* x (/ (pow z y) a)) y)))
   (if (<= y -3.5e+59)
     t_2
     (if (<= y -2.9e-181)
       t_1
       (if (<= y -3.3e-289)
         (* x (/ 1.0 (* a (* y (exp b)))))
         (if (<= y 6.2e+36) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (((pow(a, t) / a) / y) / exp(b));
	double t_2 = (x * (pow(z, y) / a)) / y;
	double tmp;
	if (y <= -3.5e+59) {
		tmp = t_2;
	} else if (y <= -2.9e-181) {
		tmp = t_1;
	} else if (y <= -3.3e-289) {
		tmp = x * (1.0 / (a * (y * exp(b))));
	} else if (y <= 6.2e+36) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((((a ** t) / a) / y) / exp(b))
    t_2 = (x * ((z ** y) / a)) / y
    if (y <= (-3.5d+59)) then
        tmp = t_2
    else if (y <= (-2.9d-181)) then
        tmp = t_1
    else if (y <= (-3.3d-289)) then
        tmp = x * (1.0d0 / (a * (y * exp(b))))
    else if (y <= 6.2d+36) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (((Math.pow(a, t) / a) / y) / Math.exp(b));
	double t_2 = (x * (Math.pow(z, y) / a)) / y;
	double tmp;
	if (y <= -3.5e+59) {
		tmp = t_2;
	} else if (y <= -2.9e-181) {
		tmp = t_1;
	} else if (y <= -3.3e-289) {
		tmp = x * (1.0 / (a * (y * Math.exp(b))));
	} else if (y <= 6.2e+36) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (((math.pow(a, t) / a) / y) / math.exp(b))
	t_2 = (x * (math.pow(z, y) / a)) / y
	tmp = 0
	if y <= -3.5e+59:
		tmp = t_2
	elif y <= -2.9e-181:
		tmp = t_1
	elif y <= -3.3e-289:
		tmp = x * (1.0 / (a * (y * math.exp(b))))
	elif y <= 6.2e+36:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(Float64(Float64((a ^ t) / a) / y) / exp(b)))
	t_2 = Float64(Float64(x * Float64((z ^ y) / a)) / y)
	tmp = 0.0
	if (y <= -3.5e+59)
		tmp = t_2;
	elseif (y <= -2.9e-181)
		tmp = t_1;
	elseif (y <= -3.3e-289)
		tmp = Float64(x * Float64(1.0 / Float64(a * Float64(y * exp(b)))));
	elseif (y <= 6.2e+36)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * ((((a ^ t) / a) / y) / exp(b));
	t_2 = (x * ((z ^ y) / a)) / y;
	tmp = 0.0;
	if (y <= -3.5e+59)
		tmp = t_2;
	elseif (y <= -2.9e-181)
		tmp = t_1;
	elseif (y <= -3.3e-289)
		tmp = x * (1.0 / (a * (y * exp(b))));
	elseif (y <= 6.2e+36)
		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[(x * N[(N[(N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -3.5e+59], t$95$2, If[LessEqual[y, -2.9e-181], t$95$1, If[LessEqual[y, -3.3e-289], N[(x * N[(1.0 / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e+36], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.5e59 or 6.1999999999999999e36 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 94.7%

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

      1. mul-1-neg 94.7%

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

   4. Simplified 94.7%

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

   5. Taylor expanded in b around 0 84.0%

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

      1. exp-diff 84.0%

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

      2. *-commutative 84.0%

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

      3. exp-to-pow 84.0%

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

      4. rem-exp-log 84.0%

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

   7. Simplified 84.0%

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

   if -3.5e59 < y < -2.8999999999999998e-181 or -3.29999999999999997e-289 < y < 6.1999999999999999e36

   1. Initial program 96.0%

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

      1. associate-*r/ 98.0%

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

      2. sub-neg 98.0%

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

      3. exp-sum 85.5%

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

      4. associate-/l* 85.5%

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

      5. associate-/r/ 83.9%

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

      6. exp-neg 83.9%

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

      7. associate-*r/ 83.9%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in y around 0 86.6%

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

   if -2.8999999999999998e-181 < y < -3.29999999999999997e-289

   1. Initial program 98.4%

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

      1. associate-*r/ 98.4%

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

      2. sub-neg 98.4%

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

      3. exp-sum 82.5%

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

      4. associate-/l* 82.5%

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

      5. associate-/r/ 70.5%

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

      6. exp-neg 70.5%

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

      7. associate-*r/ 70.5%

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

   3. Simplified 71.9%

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

   4. Taylor expanded in y around 0 71.9%

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

   5. Taylor expanded in t around 0 96.1%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+59}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-181}:\\ \;\;\;\;x \cdot \frac{\frac{\frac{{a}^{t}}{a}}{y}}{e^{b}}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-289}:\\ \;\;\;\;x \cdot \frac{1}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \frac{\frac{\frac{{a}^{t}}{a}}{y}}{e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \end{array} \]

Alternative 4: 88.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{+61} \lor \neg \left(y \leq 8.5 \cdot 10^{+136}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8.4e+61) (not (<= y 8.5e+136)))
   (/ (* 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 <= -8.4e+61) || !(y <= 8.5e+136)) {
		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 <= (-8.4d+61)) .or. (.not. (y <= 8.5d+136))) 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 <= -8.4e+61) || !(y <= 8.5e+136)) {
		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 <= -8.4e+61) or not (y <= 8.5e+136):
		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 <= -8.4e+61) || !(y <= 8.5e+136))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -8.4e+61) || ~((y <= 8.5e+136)))
		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, -8.4e+61], N[Not[LessEqual[y, 8.5e+136]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.4000000000000004e61 or 8.49999999999999966e136 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 95.7%

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

      1. mul-1-neg 95.7%

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

   4. Simplified 95.7%

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

   5. Taylor expanded in b around 0 88.2%

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

      1. exp-diff 88.2%

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

      2. *-commutative 88.2%

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

      3. exp-to-pow 88.2%

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

      4. rem-exp-log 88.2%

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

   7. Simplified 88.2%

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

   if -8.4000000000000004e61 < y < 8.49999999999999966e136

   1. Initial program 96.9%

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

   2. Taylor expanded in y around 0 93.9%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{+61} \lor \neg \left(y \leq 8.5 \cdot 10^{+136}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]

Alternative 5: 82.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+59} \lor \neg \left(y \leq 6.5 \cdot 10^{+35}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.8e+59) (not (<= y 6.5e+35)))
   (/ (* x (/ (pow z y) a)) y)
   (/ (* x (/ (pow a (+ t -1.0)) (exp b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.8e+59) || !(y <= 6.5e+35)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = (x * (pow(a, (t + -1.0)) / exp(b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-3.8d+59)) .or. (.not. (y <= 6.5d+35))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = (x * ((a ** (t + (-1.0d0))) / exp(b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.8e+59) || !(y <= 6.5e+35)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = (x * (Math.pow(a, (t + -1.0)) / Math.exp(b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.8e+59) or not (y <= 6.5e+35):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = (x * (math.pow(a, (t + -1.0)) / math.exp(b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.8e+59) || !(y <= 6.5e+35))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(Float64(x * Float64((a ^ Float64(t + -1.0)) / exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.8e+59) || ~((y <= 6.5e+35)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = (x * ((a ^ (t + -1.0)) / exp(b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.8e+59], N[Not[LessEqual[y, 6.5e+35]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.8000000000000001e59 or 6.5000000000000003e35 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 94.7%

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

      1. mul-1-neg 94.7%

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

   4. Simplified 94.7%

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

   5. Taylor expanded in b around 0 84.0%

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

      1. exp-diff 84.0%

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

      2. *-commutative 84.0%

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

      3. exp-to-pow 84.0%

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

      4. rem-exp-log 84.0%

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

   7. Simplified 84.0%

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

   if -3.8000000000000001e59 < y < 6.5000000000000003e35

   1. Initial program 96.5%

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

   2. Taylor expanded in y around 0 95.8%

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

      1. exp-diff 84.8%

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

      2. *-commutative 84.8%

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

      3. exp-to-pow 85.6%

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

      4. sub-neg 85.6%

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

      5. metadata-eval 85.6%

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

   4. Simplified 85.6%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+59} \lor \neg \left(y \leq 6.5 \cdot 10^{+35}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \]

Alternative 6: 74.3% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{1}{a \cdot \left(y \cdot e^{b}\right)}\\ t_2 := \frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-249}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-146}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ 1.0 (* a (* y (exp b))))))
        (t_2 (/ (* x (/ (pow z y) a)) y)))
   (if (<= y -3.4e+59)
     t_2
     (if (<= y 3.9e-249)
       t_1
       (if (<= y 2.6e-146)
         (/ (* x (pow a (+ t -1.0))) y)
         (if (<= y 1.4e+49) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (1.0 / (a * (y * exp(b))));
	double t_2 = (x * (pow(z, y) / a)) / y;
	double tmp;
	if (y <= -3.4e+59) {
		tmp = t_2;
	} else if (y <= 3.9e-249) {
		tmp = t_1;
	} else if (y <= 2.6e-146) {
		tmp = (x * pow(a, (t + -1.0))) / y;
	} else if (y <= 1.4e+49) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 / (a * (y * exp(b))))
    t_2 = (x * ((z ** y) / a)) / y
    if (y <= (-3.4d+59)) then
        tmp = t_2
    else if (y <= 3.9d-249) then
        tmp = t_1
    else if (y <= 2.6d-146) then
        tmp = (x * (a ** (t + (-1.0d0)))) / y
    else if (y <= 1.4d+49) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (1.0 / (a * (y * Math.exp(b))));
	double t_2 = (x * (Math.pow(z, y) / a)) / y;
	double tmp;
	if (y <= -3.4e+59) {
		tmp = t_2;
	} else if (y <= 3.9e-249) {
		tmp = t_1;
	} else if (y <= 2.6e-146) {
		tmp = (x * Math.pow(a, (t + -1.0))) / y;
	} else if (y <= 1.4e+49) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (1.0 / (a * (y * math.exp(b))))
	t_2 = (x * (math.pow(z, y) / a)) / y
	tmp = 0
	if y <= -3.4e+59:
		tmp = t_2
	elif y <= 3.9e-249:
		tmp = t_1
	elif y <= 2.6e-146:
		tmp = (x * math.pow(a, (t + -1.0))) / y
	elif y <= 1.4e+49:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(1.0 / Float64(a * Float64(y * exp(b)))))
	t_2 = Float64(Float64(x * Float64((z ^ y) / a)) / y)
	tmp = 0.0
	if (y <= -3.4e+59)
		tmp = t_2;
	elseif (y <= 3.9e-249)
		tmp = t_1;
	elseif (y <= 2.6e-146)
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y);
	elseif (y <= 1.4e+49)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (1.0 / (a * (y * exp(b))));
	t_2 = (x * ((z ^ y) / a)) / y;
	tmp = 0.0;
	if (y <= -3.4e+59)
		tmp = t_2;
	elseif (y <= 3.9e-249)
		tmp = t_1;
	elseif (y <= 2.6e-146)
		tmp = (x * (a ^ (t + -1.0))) / y;
	elseif (y <= 1.4e+49)
		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[(x * N[(1.0 / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -3.4e+59], t$95$2, If[LessEqual[y, 3.9e-249], t$95$1, If[LessEqual[y, 2.6e-146], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 1.4e+49], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.40000000000000006e59 or 1.3999999999999999e49 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 94.6%

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

      1. mul-1-neg 94.6%

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

   4. Simplified 94.6%

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

   5. Taylor expanded in b around 0 84.6%

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

      1. exp-diff 84.6%

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

      2. *-commutative 84.6%

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

      3. exp-to-pow 84.6%

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

      4. rem-exp-log 84.6%

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

   7. Simplified 84.6%

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

   if -3.40000000000000006e59 < y < 3.8999999999999999e-249 or 2.59999999999999987e-146 < y < 1.3999999999999999e49

   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/ 98.6%

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

      2. sub-neg 98.6%

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

      3. exp-sum 82.9%

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

      4. associate-/l* 82.9%

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

      5. associate-/r/ 79.0%

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

      6. exp-neg 79.0%

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

      7. associate-*r/ 79.0%

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

   3. Simplified 76.3%

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

   4. Taylor expanded in y around 0 81.8%

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

   5. Taylor expanded in t around 0 82.6%

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

   if 3.8999999999999999e-249 < y < 2.59999999999999987e-146

   1. Initial program 94.6%

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

   2. Taylor expanded in y around 0 94.6%

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

   3. Taylor expanded in b around 0 80.6%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+59}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-249}:\\ \;\;\;\;x \cdot \frac{1}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-146}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{1}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \end{array} \]

Alternative 7: 74.3% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-249}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-148}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;y \leq 10^{+49}:\\ \;\;\;\;\frac{\frac{\frac{x}{e^{b}}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (/ (pow z y) a)) y)))
   (if (<= y -3.2e+59)
     t_1
     (if (<= y 4.8e-249)
       (/ (/ x (* a (exp b))) y)
       (if (<= y 7.5e-148)
         (/ (* x (pow a (+ t -1.0))) y)
         (if (<= y 1e+49) (/ (/ (/ x (exp b)) a) 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 <= -3.2e+59) {
		tmp = t_1;
	} else if (y <= 4.8e-249) {
		tmp = (x / (a * exp(b))) / y;
	} else if (y <= 7.5e-148) {
		tmp = (x * pow(a, (t + -1.0))) / y;
	} else if (y <= 1e+49) {
		tmp = ((x / exp(b)) / a) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * ((z ** y) / a)) / y
    if (y <= (-3.2d+59)) then
        tmp = t_1
    else if (y <= 4.8d-249) then
        tmp = (x / (a * exp(b))) / y
    else if (y <= 7.5d-148) then
        tmp = (x * (a ** (t + (-1.0d0)))) / y
    else if (y <= 1d+49) then
        tmp = ((x / exp(b)) / a) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * (Math.pow(z, y) / a)) / y;
	double tmp;
	if (y <= -3.2e+59) {
		tmp = t_1;
	} else if (y <= 4.8e-249) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else if (y <= 7.5e-148) {
		tmp = (x * Math.pow(a, (t + -1.0))) / y;
	} else if (y <= 1e+49) {
		tmp = ((x / Math.exp(b)) / a) / 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 <= -3.2e+59:
		tmp = t_1
	elif y <= 4.8e-249:
		tmp = (x / (a * math.exp(b))) / y
	elif y <= 7.5e-148:
		tmp = (x * math.pow(a, (t + -1.0))) / y
	elif y <= 1e+49:
		tmp = ((x / math.exp(b)) / a) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64((z ^ y) / a)) / y)
	tmp = 0.0
	if (y <= -3.2e+59)
		tmp = t_1;
	elseif (y <= 4.8e-249)
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	elseif (y <= 7.5e-148)
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y);
	elseif (y <= 1e+49)
		tmp = Float64(Float64(Float64(x / exp(b)) / a) / 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 <= -3.2e+59)
		tmp = t_1;
	elseif (y <= 4.8e-249)
		tmp = (x / (a * exp(b))) / y;
	elseif (y <= 7.5e-148)
		tmp = (x * (a ^ (t + -1.0))) / y;
	elseif (y <= 1e+49)
		tmp = ((x / exp(b)) / a) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -3.2e+59], t$95$1, If[LessEqual[y, 4.8e-249], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 7.5e-148], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 1e+49], N[(N[(N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.19999999999999982e59 or 9.99999999999999946e48 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 94.6%

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

      1. mul-1-neg 94.6%

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

   4. Simplified 94.6%

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

   5. Taylor expanded in b around 0 84.6%

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

      1. exp-diff 84.6%

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

      2. *-commutative 84.6%

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

      3. exp-to-pow 84.6%

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

      4. rem-exp-log 84.6%

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

   7. Simplified 84.6%

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

   if -3.19999999999999982e59 < y < 4.80000000000000026e-249

   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 78.5%

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

      1. mul-1-neg 78.5%

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

   4. Simplified 78.5%

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

   5. Taylor expanded in y around 0 77.4%

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

      1. exp-neg 77.4%

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

      2. associate-*l/ 77.5%

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

      3. *-lft-identity 77.5%

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

      4. exp-sum 77.5%

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

      5. rem-exp-log 78.5%

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

      6. *-commutative 78.5%

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

      7. *-commutative 78.5%

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

      8. associate-/r* 78.4%

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

   7. Simplified 78.4%

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

   8. Taylor expanded in x around 0 78.5%

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

   if 4.80000000000000026e-249 < y < 7.5000000000000005e-148

   1. Initial program 94.6%

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

   2. Taylor expanded in y around 0 94.6%

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

   3. Taylor expanded in b around 0 80.6%

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

   if 7.5000000000000005e-148 < y < 9.99999999999999946e48

   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 89.2%

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

      1. mul-1-neg 89.2%

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

   4. Simplified 89.2%

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

   5. Taylor expanded in y around 0 84.5%

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

      1. exp-neg 84.5%

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

      2. associate-*l/ 84.5%

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

      3. *-lft-identity 84.5%

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

      4. exp-sum 84.6%

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

      5. rem-exp-log 85.2%

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

      6. *-commutative 85.2%

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

      7. *-commutative 85.2%

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

      8. associate-/r* 85.2%

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

   7. Simplified 85.2%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+59}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-249}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-148}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;y \leq 10^{+49}:\\ \;\;\;\;\frac{\frac{\frac{x}{e^{b}}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \end{array} \]

Alternative 8: 74.3% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+59} \lor \neg \left(y \leq 1.35 \cdot 10^{+49}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.2e+59) (not (<= y 1.35e+49)))
   (/ (* x (/ (pow z y) a)) y)
   (/ (/ x (* a (exp b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.2e+59) || !(y <= 1.35e+49)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = (x / (a * exp(b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-3.2d+59)) .or. (.not. (y <= 1.35d+49))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = (x / (a * exp(b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.2e+59) || !(y <= 1.35e+49)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = (x / (a * Math.exp(b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.2e+59) or not (y <= 1.35e+49):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = (x / (a * math.exp(b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.2e+59) || !(y <= 1.35e+49))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.2e+59) || ~((y <= 1.35e+49)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = (x / (a * exp(b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.2e+59], N[Not[LessEqual[y, 1.35e+49]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.19999999999999982e59 or 1.35000000000000005e49 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 94.6%

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

      1. mul-1-neg 94.6%

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

   4. Simplified 94.6%

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

   5. Taylor expanded in b around 0 84.6%

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

      1. exp-diff 84.6%

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

      2. *-commutative 84.6%

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

      3. exp-to-pow 84.6%

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

      4. rem-exp-log 84.6%

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

   7. Simplified 84.6%

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

   if -3.19999999999999982e59 < y < 1.35000000000000005e49

   1. Initial program 96.5%

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

   2. Taylor expanded in t around 0 77.1%

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

      1. mul-1-neg 77.1%

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

   4. Simplified 77.1%

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

   5. Taylor expanded in y around 0 75.1%

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

      1. exp-neg 75.1%

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

      2. associate-*l/ 75.1%

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

      3. *-lft-identity 75.1%

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

      4. exp-sum 75.1%

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

      5. rem-exp-log 76.0%

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

      6. *-commutative 76.0%

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

      7. *-commutative 76.0%

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

      8. associate-/r* 76.0%

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

   7. Simplified 76.0%

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

   8. Taylor expanded in x around 0 76.0%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+59} \lor \neg \left(y \leq 1.35 \cdot 10^{+49}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \end{array} \]

Alternative 9: 72.9% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.0029:\\ \;\;\;\;\frac{\frac{\frac{x}{e^{b}}}{a}}{y}\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+31}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.0029)
   (/ (/ (/ x (exp b)) a) y)
   (if (<= b 3e+31) (* (/ (pow z y) a) (/ x y)) (/ (/ x (* a (exp b))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.0029) {
		tmp = ((x / exp(b)) / a) / y;
	} else if (b <= 3e+31) {
		tmp = (pow(z, y) / a) * (x / y);
	} else {
		tmp = (x / (a * exp(b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-0.0029d0)) then
        tmp = ((x / exp(b)) / a) / y
    else if (b <= 3d+31) then
        tmp = ((z ** y) / a) * (x / y)
    else
        tmp = (x / (a * exp(b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.0029) {
		tmp = ((x / Math.exp(b)) / a) / y;
	} else if (b <= 3e+31) {
		tmp = (Math.pow(z, y) / a) * (x / y);
	} else {
		tmp = (x / (a * Math.exp(b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -0.0029:
		tmp = ((x / math.exp(b)) / a) / y
	elif b <= 3e+31:
		tmp = (math.pow(z, y) / a) * (x / y)
	else:
		tmp = (x / (a * math.exp(b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.0029)
		tmp = Float64(Float64(Float64(x / exp(b)) / a) / y);
	elseif (b <= 3e+31)
		tmp = Float64(Float64((z ^ y) / a) * Float64(x / y));
	else
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -0.0029)
		tmp = ((x / exp(b)) / a) / y;
	elseif (b <= 3e+31)
		tmp = ((z ^ y) / a) * (x / y);
	else
		tmp = (x / (a * exp(b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.0029], N[(N[(N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 3e+31], N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -0.0029

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 96.7%

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

      1. mul-1-neg 96.7%

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

   4. Simplified 96.7%

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

   5. Taylor expanded in y around 0 89.6%

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

      1. exp-neg 89.6%

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

      2. associate-*l/ 89.6%

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

      3. *-lft-identity 89.6%

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

      4. exp-sum 89.6%

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

      5. rem-exp-log 89.6%

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

      6. *-commutative 89.6%

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

      7. *-commutative 89.6%

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

      8. associate-/r* 89.7%

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

   7. Simplified 89.7%

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

   if -0.0029 < b < 2.99999999999999989e31

   1. Initial program 95.9%

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

   2. Taylor expanded in t around 0 70.0%

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

      1. mul-1-neg 70.0%

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

   4. Simplified 70.0%

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

   5. Taylor expanded in b around 0 68.7%

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

      1. exp-diff 68.7%

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

      2. *-commutative 68.7%

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

      3. exp-to-pow 68.7%

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

      4. rem-exp-log 69.7%

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

      5. associate-*r/ 63.5%

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

   7. Simplified 63.5%

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

   if 2.99999999999999989e31 < b

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 98.5%

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

      1. mul-1-neg 98.5%

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

   4. Simplified 98.5%

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

   5. Taylor expanded in y around 0 80.6%

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

      1. exp-neg 80.6%

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

      2. associate-*l/ 80.6%

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

      3. *-lft-identity 80.6%

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

      4. exp-sum 80.6%

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

      5. rem-exp-log 80.6%

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

      6. *-commutative 80.6%

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

      7. *-commutative 80.6%

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

      8. associate-/r* 80.6%

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

   7. Simplified 80.6%

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

   8. Taylor expanded in x around 0 80.6%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.0029:\\ \;\;\;\;\frac{\frac{\frac{x}{e^{b}}}{a}}{y}\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+31}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \end{array} \]

Alternative 10: 54.6% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

2. Taylor expanded in t around 0 84.5%

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

   1. mul-1-neg 84.5%

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

4. Simplified 84.5%

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

5. Taylor expanded in y around 0 59.5%

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

   1. exp-neg 59.5%

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

   2. associate-*l/ 59.5%

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

   3. *-lft-identity 59.5%

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

   4. exp-sum 59.5%

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

   5. rem-exp-log 60.0%

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

   6. *-commutative 60.0%

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

   7. associate-/r* 61.0%

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

   8. *-commutative 61.0%

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

   9. associate-*r* 55.5%

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

   10. *-commutative 55.5%

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

7. Simplified 55.5%

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

8. Final simplification 55.5%

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

Alternative 11: 59.5% 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 98.0%

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

2. Taylor expanded in t around 0 84.5%

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

   1. mul-1-neg 84.5%

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

4. Simplified 84.5%

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

5. Taylor expanded in y around 0 59.5%

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

   1. exp-neg 59.5%

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

   2. associate-*l/ 59.5%

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

   3. *-lft-identity 59.5%

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

   4. exp-sum 59.5%

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

   5. rem-exp-log 60.0%

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

   6. *-commutative 60.0%

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

   7. *-commutative 60.0%

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

   8. associate-/r* 60.0%

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

7. Simplified 60.0%

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

8. Taylor expanded in x around 0 60.0%

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

9. Final simplification 60.0%

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

Alternative 12: 42.2% accurate, 11.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{y}}{a}\\ \mathbf{if}\;b \leq -1.2 \cdot 10^{-110}:\\ \;\;\;\;t_1 - \left(\frac{b}{y} \cdot \frac{x}{a} + \left(b \cdot b\right) \cdot \left(t_1 \cdot -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x y) a)))
   (if (<= b -1.2e-110)
     (- t_1 (+ (* (/ b y) (/ x a)) (* (* b b) (* t_1 -0.5))))
     (* x (/ 1.0 (* y (+ a (* a b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / y) / a;
	double tmp;
	if (b <= -1.2e-110) {
		tmp = t_1 - (((b / y) * (x / a)) + ((b * b) * (t_1 * -0.5)));
	} else {
		tmp = x * (1.0 / (y * (a + (a * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) / a
    if (b <= (-1.2d-110)) then
        tmp = t_1 - (((b / y) * (x / a)) + ((b * b) * (t_1 * (-0.5d0))))
    else
        tmp = x * (1.0d0 / (y * (a + (a * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / y) / a;
	double tmp;
	if (b <= -1.2e-110) {
		tmp = t_1 - (((b / y) * (x / a)) + ((b * b) * (t_1 * -0.5)));
	} else {
		tmp = x * (1.0 / (y * (a + (a * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / y) / a
	tmp = 0
	if b <= -1.2e-110:
		tmp = t_1 - (((b / y) * (x / a)) + ((b * b) * (t_1 * -0.5)))
	else:
		tmp = x * (1.0 / (y * (a + (a * b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / y) / a)
	tmp = 0.0
	if (b <= -1.2e-110)
		tmp = Float64(t_1 - Float64(Float64(Float64(b / y) * Float64(x / a)) + Float64(Float64(b * b) * Float64(t_1 * -0.5))));
	else
		tmp = Float64(x * Float64(1.0 / Float64(y * Float64(a + Float64(a * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / y) / a;
	tmp = 0.0;
	if (b <= -1.2e-110)
		tmp = t_1 - (((b / y) * (x / a)) + ((b * b) * (t_1 * -0.5)));
	else
		tmp = x * (1.0 / (y * (a + (a * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[b, -1.2e-110], N[(t$95$1 - N[(N[(N[(b / y), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision] + N[(N[(b * b), $MachinePrecision] * N[(t$95$1 * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.20000000000000003e-110

   1. Initial program 99.6%

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

   2. Taylor expanded in t around 0 93.2%

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

      1. mul-1-neg 93.2%

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

   4. Simplified 93.2%

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

   5. Taylor expanded in y around 0 71.5%

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

      1. exp-neg 71.5%

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

      2. associate-*l/ 71.5%

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

      3. *-lft-identity 71.5%

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

      4. exp-sum 71.5%

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

      5. rem-exp-log 71.8%

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

      6. *-commutative 71.8%

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

      7. associate-/r* 70.7%

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

      8. *-commutative 70.7%

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

      9. associate-*r* 63.3%

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

      10. *-commutative 63.3%

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

   7. Simplified 63.3%

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

   8. Taylor expanded in b around 0 34.0%

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

      1. associate-/l/ 34.0%

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

      2. distribute-lft-out 34.0%

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

      3. times-frac 33.0%

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

      4. *-commutative 33.0%

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

      5. unpow2 33.0%

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

      6. distribute-rgt-out 47.9%

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

      7. *-commutative 47.9%

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

      8. metadata-eval 47.9%

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

      9. *-commutative 47.9%

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

      10. associate-/r* 52.2%

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

   10. Simplified 52.2%

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

   if -1.20000000000000003e-110 < b

   1. Initial program 97.1%

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

   2. Taylor expanded in t around 0 79.5%

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

      1. mul-1-neg 79.5%

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

   4. Simplified 79.5%

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

   5. Taylor expanded in y around 0 52.5%

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

      1. exp-neg 52.5%

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

      2. associate-*l/ 52.5%

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

      3. *-lft-identity 52.5%

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

      4. exp-sum 52.5%

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

      5. rem-exp-log 53.1%

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

      6. *-commutative 53.1%

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

      7. associate-/r* 55.3%

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

      8. *-commutative 55.3%

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

      9. associate-*r* 51.0%

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

      10. *-commutative 51.0%

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

   7. Simplified 51.0%

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

   8. Taylor expanded in b around 0 36.0%

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

      1. div-inv 36.5%

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

      2. distribute-lft-out 36.5%

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

      3. *-commutative 36.5%

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

   10. Applied egg-rr 36.5%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{-110}:\\ \;\;\;\;\frac{\frac{x}{y}}{a} - \left(\frac{b}{y} \cdot \frac{x}{a} + \left(b \cdot b\right) \cdot \left(\frac{\frac{x}{y}}{a} \cdot -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 13: 43.5% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-12}:\\ \;\;\;\;\left(\frac{x}{y \cdot a} - x \cdot \frac{b}{y \cdot a}\right) + \frac{x}{a} \cdot \frac{b \cdot b}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5e-12)
   (+ (- (/ x (* y a)) (* x (/ b (* y a)))) (* (/ x a) (/ (* b b) y)))
   (* x (/ 1.0 (* y (+ a (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5e-12) {
		tmp = ((x / (y * a)) - (x * (b / (y * a)))) + ((x / a) * ((b * b) / y));
	} else {
		tmp = x * (1.0 / (y * (a + (a * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-5d-12)) then
        tmp = ((x / (y * a)) - (x * (b / (y * a)))) + ((x / a) * ((b * b) / y))
    else
        tmp = x * (1.0d0 / (y * (a + (a * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5e-12) {
		tmp = ((x / (y * a)) - (x * (b / (y * a)))) + ((x / a) * ((b * b) / y));
	} else {
		tmp = x * (1.0 / (y * (a + (a * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5e-12:
		tmp = ((x / (y * a)) - (x * (b / (y * a)))) + ((x / a) * ((b * b) / y))
	else:
		tmp = x * (1.0 / (y * (a + (a * b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5e-12)
		tmp = Float64(Float64(Float64(x / Float64(y * a)) - Float64(x * Float64(b / Float64(y * a)))) + Float64(Float64(x / a) * Float64(Float64(b * b) / y)));
	else
		tmp = Float64(x * Float64(1.0 / Float64(y * Float64(a + Float64(a * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5e-12)
		tmp = ((x / (y * a)) - (x * (b / (y * a)))) + ((x / a) * ((b * b) / y));
	else
		tmp = x * (1.0 / (y * (a + (a * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5e-12], N[(N[(N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision] - N[(x * N[(b / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x / a), $MachinePrecision] * N[(N[(b * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.9999999999999997e-12

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 96.7%

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

      1. mul-1-neg 96.7%

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

   4. Simplified 96.7%

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

   5. Taylor expanded in y around 0 89.6%

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

      1. exp-neg 89.6%

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

      2. associate-*l/ 89.6%

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

      3. *-lft-identity 89.6%

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

      4. exp-sum 89.6%

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

      5. rem-exp-log 89.6%

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

      6. *-commutative 89.6%

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

      7. associate-/r* 89.6%

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

      8. *-commutative 89.6%

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

      9. associate-*r* 79.4%

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

      10. *-commutative 79.4%

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

   7. Simplified 79.4%

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

   8. Taylor expanded in b around 0 4.5%

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

   9. Taylor expanded in b around 0 61.2%

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

       1. +-commutative 61.2%

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

       2. associate-/r* 62.5%

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

       3. times-frac 58.2%

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

       4. neg-mul-1 58.2%

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

       5. sub-neg 58.2%

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

       6. *-commutative 58.2%

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

       7. times-frac 62.5%

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

       8. associate-*r/ 62.5%

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

       9. associate-/l/ 61.2%

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

       10. *-commutative 61.2%

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

       11. *-commutative 61.2%

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

       12. times-frac 64.1%

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

       13. unpow2 64.1%

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

   11. Simplified 64.1%

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

   if -4.9999999999999997e-12 < b

   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 t around 0 80.0%

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

      1. mul-1-neg 80.0%

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

   4. Simplified 80.0%

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

   5. Taylor expanded in y around 0 48.4%

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

      1. exp-neg 48.4%

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

      2. associate-*l/ 48.4%

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

      3. *-lft-identity 48.4%

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

      4. exp-sum 48.4%

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

      5. rem-exp-log 49.0%

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

      6. *-commutative 49.0%

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

      7. associate-/r* 50.4%

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

      8. *-commutative 50.4%

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

      9. associate-*r* 46.6%

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

      10. *-commutative 46.6%

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

   7. Simplified 46.6%

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

   8. Taylor expanded in b around 0 33.1%

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

      1. div-inv 33.6%

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

      2. distribute-lft-out 34.1%

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

      3. *-commutative 34.1%

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

   10. Applied egg-rr 34.1%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-12}:\\ \;\;\;\;\left(\frac{x}{y \cdot a} - x \cdot \frac{b}{y \cdot a}\right) + \frac{x}{a} \cdot \frac{b \cdot b}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 14: 42.3% accurate, 13.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{-77}:\\ \;\;\;\;\frac{\frac{x}{a}}{y} \cdot \left(1 - b\right) + \left(b \cdot b\right) \cdot \left(x \cdot \frac{0.5}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.5e-77)
   (+ (* (/ (/ x a) y) (- 1.0 b)) (* (* b b) (* x (/ 0.5 (* y a)))))
   (* x (/ 1.0 (* y (+ a (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.5e-77) {
		tmp = (((x / a) / y) * (1.0 - b)) + ((b * b) * (x * (0.5 / (y * a))));
	} else {
		tmp = x * (1.0 / (y * (a + (a * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.5d-77)) then
        tmp = (((x / a) / y) * (1.0d0 - b)) + ((b * b) * (x * (0.5d0 / (y * a))))
    else
        tmp = x * (1.0d0 / (y * (a + (a * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.5e-77) {
		tmp = (((x / a) / y) * (1.0 - b)) + ((b * b) * (x * (0.5 / (y * a))));
	} else {
		tmp = x * (1.0 / (y * (a + (a * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.5e-77:
		tmp = (((x / a) / y) * (1.0 - b)) + ((b * b) * (x * (0.5 / (y * a))))
	else:
		tmp = x * (1.0 / (y * (a + (a * b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.5e-77)
		tmp = Float64(Float64(Float64(Float64(x / a) / y) * Float64(1.0 - b)) + Float64(Float64(b * b) * Float64(x * Float64(0.5 / Float64(y * a)))));
	else
		tmp = Float64(x * Float64(1.0 / Float64(y * Float64(a + Float64(a * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.5e-77)
		tmp = (((x / a) / y) * (1.0 - b)) + ((b * b) * (x * (0.5 / (y * a))));
	else
		tmp = x * (1.0 / (y * (a + (a * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.5e-77], N[(N[(N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision] * N[(1.0 - b), $MachinePrecision]), $MachinePrecision] + N[(N[(b * b), $MachinePrecision] * N[(x * N[(0.5 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.50000000000000013e-77

   1. Initial program 99.6%

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

   2. Taylor expanded in t around 0 94.9%

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

      1. mul-1-neg 94.9%

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

   4. Simplified 94.9%

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

   5. Taylor expanded in y around 0 76.9%

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

      1. exp-neg 76.9%

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

      2. associate-*l/ 76.9%

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

      3. *-lft-identity 76.9%

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

      4. exp-sum 76.9%

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

      5. rem-exp-log 77.1%

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

      6. *-commutative 77.1%

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

      7. *-commutative 77.1%

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

      8. associate-/r* 77.1%

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

   7. Simplified 77.1%

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

   8. Taylor expanded in b around 0 35.9%

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

      1. associate-+r+ 35.9%

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

      2. associate-/r* 38.0%

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

      3. times-frac 33.6%

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

      4. neg-mul-1 33.6%

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

      5. sub-neg 33.6%

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

      6. *-lft-identity 33.6%

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

      7. associate-*l/ 35.9%

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

      8. associate-*r/ 37.0%

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

      9. distribute-rgt-out-- 37.0%

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

      10. mul-1-neg 37.0%

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

      11. *-commutative 37.0%

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

      12. distribute-rgt-out 53.3%

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

      13. associate-/r* 55.7%

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

      14. distribute-rgt-out 37.0%

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

   10. Simplified 53.3%

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

   if -3.50000000000000013e-77 < b

   1. Initial program 97.2%

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

   2. Taylor expanded in t around 0 79.3%

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

      1. mul-1-neg 79.3%

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

   4. Simplified 79.3%

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

   5. Taylor expanded in y around 0 50.7%

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

      1. exp-neg 50.7%

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

      2. associate-*l/ 50.7%

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

      3. *-lft-identity 50.7%

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

      4. exp-sum 50.7%

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

      5. rem-exp-log 51.3%

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

      6. *-commutative 51.3%

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

      7. associate-/r* 53.4%

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

      8. *-commutative 53.4%

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

      9. associate-*r* 49.2%

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

      10. *-commutative 49.2%

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

   7. Simplified 49.2%

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

   8. Taylor expanded in b around 0 34.9%

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

      1. div-inv 35.5%

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

      2. distribute-lft-out 35.5%

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

      3. *-commutative 35.5%

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

   10. Applied egg-rr 35.5%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{-77}:\\ \;\;\;\;\frac{\frac{x}{a}}{y} \cdot \left(1 - b\right) + \left(b \cdot b\right) \cdot \left(x \cdot \frac{0.5}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 15: 39.3% accurate, 14.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+202}:\\ \;\;\;\;\frac{\frac{x}{y} - x \cdot \frac{b}{y}}{a}\\ \mathbf{elif}\;b \leq -1.85 \cdot 10^{-148}:\\ \;\;\;\;\frac{a \cdot \left(\frac{x \cdot y}{y} - x \cdot b\right)}{a \cdot \left(y \cdot a\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4.5e+202)
   (/ (- (/ x y) (* x (/ b y))) a)
   (if (<= b -1.85e-148)
     (/ (* a (- (/ (* x y) y) (* x b))) (* a (* y a)))
     (* x (/ 1.0 (* y (+ a (* a b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.5e+202) {
		tmp = ((x / y) - (x * (b / y))) / a;
	} else if (b <= -1.85e-148) {
		tmp = (a * (((x * y) / y) - (x * b))) / (a * (y * a));
	} else {
		tmp = x * (1.0 / (y * (a + (a * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-4.5d+202)) then
        tmp = ((x / y) - (x * (b / y))) / a
    else if (b <= (-1.85d-148)) then
        tmp = (a * (((x * y) / y) - (x * b))) / (a * (y * a))
    else
        tmp = x * (1.0d0 / (y * (a + (a * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.5e+202) {
		tmp = ((x / y) - (x * (b / y))) / a;
	} else if (b <= -1.85e-148) {
		tmp = (a * (((x * y) / y) - (x * b))) / (a * (y * a));
	} else {
		tmp = x * (1.0 / (y * (a + (a * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4.5e+202:
		tmp = ((x / y) - (x * (b / y))) / a
	elif b <= -1.85e-148:
		tmp = (a * (((x * y) / y) - (x * b))) / (a * (y * a))
	else:
		tmp = x * (1.0 / (y * (a + (a * b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4.5e+202)
		tmp = Float64(Float64(Float64(x / y) - Float64(x * Float64(b / y))) / a);
	elseif (b <= -1.85e-148)
		tmp = Float64(Float64(a * Float64(Float64(Float64(x * y) / y) - Float64(x * b))) / Float64(a * Float64(y * a)));
	else
		tmp = Float64(x * Float64(1.0 / Float64(y * Float64(a + Float64(a * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -4.5e+202)
		tmp = ((x / y) - (x * (b / y))) / a;
	elseif (b <= -1.85e-148)
		tmp = (a * (((x * y) / y) - (x * b))) / (a * (y * a));
	else
		tmp = x * (1.0 / (y * (a + (a * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4.5e+202], N[(N[(N[(x / y), $MachinePrecision] - N[(x * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, -1.85e-148], N[(N[(a * N[(N[(N[(x * y), $MachinePrecision] / y), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.49999999999999978e202

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 95.7%

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

      1. mul-1-neg 95.7%

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

   4. Simplified 95.7%

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

   5. Taylor expanded in y around 0 95.7%

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

      1. exp-neg 95.7%

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

      2. associate-*l/ 95.7%

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

      3. *-lft-identity 95.7%

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

      4. exp-sum 95.7%

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

      5. rem-exp-log 95.7%

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

      6. *-commutative 95.7%

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

      7. associate-/r* 95.7%

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

      8. *-commutative 95.7%

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

      9. associate-*r* 87.0%

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

      10. *-commutative 87.0%

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

   7. Simplified 87.0%

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

   8. Taylor expanded in b around 0 66.8%

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

   9. Taylor expanded in a around 0 78.8%

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

       1. +-commutative 78.8%

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

       2. mul-1-neg 78.8%

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

       3. unsub-neg 78.8%

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

       4. *-commutative 78.8%

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

       5. associate-*r/ 87.2%

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

   11. Simplified 87.2%

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

   if -4.49999999999999978e202 < b < -1.85000000000000017e-148

   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 t around 0 90.4%

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

      1. mul-1-neg 90.4%

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

   4. Simplified 90.4%

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

   5. Taylor expanded in y around 0 63.0%

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

      1. exp-neg 63.0%

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

      2. associate-*l/ 63.0%

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

      3. *-lft-identity 63.0%

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

      4. exp-sum 63.0%

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

      5. rem-exp-log 63.5%

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

      6. *-commutative 63.5%

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

      7. associate-/r* 62.3%

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

      8. *-commutative 62.3%

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

      9. associate-*r* 55.8%

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

      10. *-commutative 55.8%

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

   7. Simplified 55.8%

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

   8. Taylor expanded in b around 0 33.5%

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

      1. *-commutative 33.5%

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

      2. associate-/r* 32.3%

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

      3. associate-*r/ 32.3%

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

      4. frac-add 31.2%

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

      5. *-commutative 31.2%

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

      6. *-commutative 31.2%

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

      7. *-commutative 31.2%

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

   10. Applied egg-rr 31.2%

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

       1. *-commutative 31.2%

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

       2. associate-*l* 37.8%

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

       3. distribute-lft-out 37.8%

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

       4. associate-*r/ 40.2%

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

       5. mul-1-neg 40.2%

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

       6. *-commutative 40.2%

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

       7. distribute-rgt-neg-in 40.2%

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

       8. *-commutative 40.2%

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

   12. Simplified 40.2%

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

   if -1.85000000000000017e-148 < b

   1. Initial program 97.0%

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

   2. Taylor expanded in t around 0 79.9%

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

      1. mul-1-neg 79.9%

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

   4. Simplified 79.9%

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

   5. Taylor expanded in y around 0 52.3%

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

      1. exp-neg 52.3%

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

      2. associate-*l/ 52.3%

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

      3. *-lft-identity 52.3%

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

      4. exp-sum 52.3%

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

      5. rem-exp-log 52.9%

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

      6. *-commutative 52.9%

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

      7. associate-/r* 55.2%

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

      8. *-commutative 55.2%

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

      9. associate-*r* 50.6%

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

      10. *-commutative 50.6%

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

   7. Simplified 50.6%

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

   8. Taylor expanded in b around 0 35.0%

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

      1. div-inv 35.6%

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

      2. distribute-lft-out 35.6%

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

      3. *-commutative 35.6%

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

   10. Applied egg-rr 35.6%

       \[\leadsto \color{blue}{x \cdot \frac{1}{y \cdot \left(a + b \cdot a\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+202}:\\ \;\;\;\;\frac{\frac{x}{y} - x \cdot \frac{b}{y}}{a}\\ \mathbf{elif}\;b \leq -1.85 \cdot 10^{-148}:\\ \;\;\;\;\frac{a \cdot \left(\frac{x \cdot y}{y} - x \cdot b\right)}{a \cdot \left(y \cdot a\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 16: 39.5% accurate, 18.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{+202}:\\ \;\;\;\;\frac{\frac{x}{y} - x \cdot \frac{b}{y}}{a}\\ \mathbf{elif}\;b \leq -3.9 \cdot 10^{-235}:\\ \;\;\;\;\frac{\frac{x}{a} - x \cdot \frac{b}{a}}{y}\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+73}:\\ \;\;\;\;\frac{1}{\frac{a}{\frac{x}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y} \cdot \frac{x}{a + a \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.2e+202)
   (/ (- (/ x y) (* x (/ b y))) a)
   (if (<= b -3.9e-235)
     (/ (- (/ x a) (* x (/ b a))) y)
     (if (<= b 2.6e+73)
       (/ 1.0 (/ a (/ x y)))
       (* (/ 1.0 y) (/ x (+ a (* a b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.2e+202) {
		tmp = ((x / y) - (x * (b / y))) / a;
	} else if (b <= -3.9e-235) {
		tmp = ((x / a) - (x * (b / a))) / y;
	} else if (b <= 2.6e+73) {
		tmp = 1.0 / (a / (x / y));
	} else {
		tmp = (1.0 / y) * (x / (a + (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-6.2d+202)) then
        tmp = ((x / y) - (x * (b / y))) / a
    else if (b <= (-3.9d-235)) then
        tmp = ((x / a) - (x * (b / a))) / y
    else if (b <= 2.6d+73) then
        tmp = 1.0d0 / (a / (x / y))
    else
        tmp = (1.0d0 / y) * (x / (a + (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.2e+202) {
		tmp = ((x / y) - (x * (b / y))) / a;
	} else if (b <= -3.9e-235) {
		tmp = ((x / a) - (x * (b / a))) / y;
	} else if (b <= 2.6e+73) {
		tmp = 1.0 / (a / (x / y));
	} else {
		tmp = (1.0 / y) * (x / (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.2e+202:
		tmp = ((x / y) - (x * (b / y))) / a
	elif b <= -3.9e-235:
		tmp = ((x / a) - (x * (b / a))) / y
	elif b <= 2.6e+73:
		tmp = 1.0 / (a / (x / y))
	else:
		tmp = (1.0 / y) * (x / (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.2e+202)
		tmp = Float64(Float64(Float64(x / y) - Float64(x * Float64(b / y))) / a);
	elseif (b <= -3.9e-235)
		tmp = Float64(Float64(Float64(x / a) - Float64(x * Float64(b / a))) / y);
	elseif (b <= 2.6e+73)
		tmp = Float64(1.0 / Float64(a / Float64(x / y)));
	else
		tmp = Float64(Float64(1.0 / y) * Float64(x / Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6.2e+202)
		tmp = ((x / y) - (x * (b / y))) / a;
	elseif (b <= -3.9e-235)
		tmp = ((x / a) - (x * (b / a))) / y;
	elseif (b <= 2.6e+73)
		tmp = 1.0 / (a / (x / y));
	else
		tmp = (1.0 / y) * (x / (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.2e+202], N[(N[(N[(x / y), $MachinePrecision] - N[(x * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, -3.9e-235], N[(N[(N[(x / a), $MachinePrecision] - N[(x * N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 2.6e+73], N[(1.0 / N[(a / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / y), $MachinePrecision] * N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.19999999999999983e202

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 95.7%

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

      1. mul-1-neg 95.7%

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

   4. Simplified 95.7%

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

   5. Taylor expanded in y around 0 95.7%

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

      1. exp-neg 95.7%

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

      2. associate-*l/ 95.7%

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

      3. *-lft-identity 95.7%

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

      4. exp-sum 95.7%

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

      5. rem-exp-log 95.7%

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

      6. *-commutative 95.7%

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

      7. associate-/r* 95.7%

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

      8. *-commutative 95.7%

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

      9. associate-*r* 87.0%

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

      10. *-commutative 87.0%

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

   7. Simplified 87.0%

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

   8. Taylor expanded in b around 0 66.8%

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

   9. Taylor expanded in a around 0 78.8%

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

       1. +-commutative 78.8%

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

       2. mul-1-neg 78.8%

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

       3. unsub-neg 78.8%

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

       4. *-commutative 78.8%

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

       5. associate-*r/ 87.2%

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

   11. Simplified 87.2%

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

   if -6.19999999999999983e202 < b < -3.8999999999999997e-235

   1. Initial program 99.2%

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

   2. Taylor expanded in t around 0 87.0%

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

      1. mul-1-neg 87.0%

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

   4. Simplified 87.0%

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

   5. Taylor expanded in y around 0 57.9%

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

      1. exp-neg 57.9%

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

      2. associate-*l/ 57.9%

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

      3. *-lft-identity 57.9%

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

      4. exp-sum 57.9%

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

      5. rem-exp-log 58.4%

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

      6. *-commutative 58.4%

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

      7. *-commutative 58.4%

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

      8. associate-/r* 58.4%

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

   7. Simplified 58.4%

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

   8. Taylor expanded in b around 0 35.7%

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

      1. +-commutative 35.7%

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

      2. mul-1-neg 35.7%

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

      3. unsub-neg 35.7%

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

      4. *-commutative 35.7%

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

      5. associate-*r/ 36.7%

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

   10. Simplified 36.7%

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

   if -3.8999999999999997e-235 < b < 2.6000000000000001e73

   1. Initial program 94.9%

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

   2. Taylor expanded in t around 0 70.2%

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

      1. mul-1-neg 70.2%

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

   4. Simplified 70.2%

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

   5. Taylor expanded in y around 0 37.9%

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

      1. exp-neg 37.9%

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

      2. associate-*l/ 37.9%

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

      3. *-lft-identity 37.9%

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

      4. exp-sum 37.9%

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

      5. rem-exp-log 38.8%

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

      6. *-commutative 38.8%

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

      7. associate-/r* 41.8%

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

      8. *-commutative 41.8%

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

      9. associate-*r* 40.6%

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

      10. *-commutative 40.6%

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

   7. Simplified 40.6%

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

   8. Taylor expanded in b around 0 32.1%

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

      1. clear-num 32.0%

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

      2. inv-pow 32.0%

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

      3. *-commutative 32.0%

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

   10. Applied egg-rr 32.0%

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

       1. unpow-1 32.0%

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

       2. associate-/l* 35.3%

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

   12. Simplified 35.3%

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

   if 2.6000000000000001e73 < b

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 98.2%

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

      1. mul-1-neg 98.2%

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

   4. Simplified 98.2%

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

   5. Taylor expanded in y around 0 80.7%

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

      1. exp-neg 80.7%

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

      2. associate-*l/ 80.7%

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

      3. *-lft-identity 80.7%

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

      4. exp-sum 80.7%

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

      5. rem-exp-log 80.7%

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

      6. *-commutative 80.7%

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

      7. associate-/r* 80.7%

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

      8. *-commutative 80.7%

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

      9. associate-*r* 69.9%

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

      10. *-commutative 69.9%

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

   7. Simplified 69.9%

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

   8. Taylor expanded in b around 0 39.5%

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

      1. *-un-lft-identity 39.5%

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

      2. distribute-lft-out 39.5%

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

      3. times-frac 41.2%

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

      4. *-commutative 41.2%

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

   10. Applied egg-rr 41.2%

       \[\leadsto \color{blue}{\frac{1}{y} \cdot \frac{x}{a + b \cdot a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{+202}:\\ \;\;\;\;\frac{\frac{x}{y} - x \cdot \frac{b}{y}}{a}\\ \mathbf{elif}\;b \leq -3.9 \cdot 10^{-235}:\\ \;\;\;\;\frac{\frac{x}{a} - x \cdot \frac{b}{a}}{y}\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+73}:\\ \;\;\;\;\frac{1}{\frac{a}{\frac{x}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y} \cdot \frac{x}{a + a \cdot b}\\ \end{array} \]

Alternative 17: 39.8% accurate, 24.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{-78}:\\ \;\;\;\;\frac{\frac{x - x \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -8.2e-78)
   (/ (/ (- x (* x b)) a) y)
   (* x (/ 1.0 (* y (+ a (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8.2e-78) {
		tmp = ((x - (x * b)) / a) / y;
	} else {
		tmp = x * (1.0 / (y * (a + (a * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-8.2d-78)) then
        tmp = ((x - (x * b)) / a) / y
    else
        tmp = x * (1.0d0 / (y * (a + (a * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8.2e-78) {
		tmp = ((x - (x * b)) / a) / y;
	} else {
		tmp = x * (1.0 / (y * (a + (a * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -8.2e-78:
		tmp = ((x - (x * b)) / a) / y
	else:
		tmp = x * (1.0 / (y * (a + (a * b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -8.2e-78)
		tmp = Float64(Float64(Float64(x - Float64(x * b)) / a) / y);
	else
		tmp = Float64(x * Float64(1.0 / Float64(y * Float64(a + Float64(a * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -8.2e-78)
		tmp = ((x - (x * b)) / a) / y;
	else
		tmp = x * (1.0 / (y * (a + (a * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -8.2e-78], N[(N[(N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(1.0 / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.1999999999999996e-78

   1. Initial program 99.6%

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

   2. Taylor expanded in t around 0 94.9%

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

      1. mul-1-neg 94.9%

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

   4. Simplified 94.9%

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

   5. Taylor expanded in y around 0 76.9%

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

      1. exp-neg 76.9%

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

      2. associate-*l/ 76.9%

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

      3. *-lft-identity 76.9%

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

      4. exp-sum 76.9%

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

      5. rem-exp-log 77.1%

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

      6. *-commutative 77.1%

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

      7. *-commutative 77.1%

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

      8. associate-/r* 77.1%

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

   7. Simplified 77.1%

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

   8. Taylor expanded in b around 0 46.8%

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

      1. +-commutative 46.8%

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

      2. mul-1-neg 46.8%

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

      3. *-commutative 46.8%

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

      4. unsub-neg 46.8%

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

   10. Simplified 46.8%

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

   if -8.1999999999999996e-78 < b

   1. Initial program 97.2%

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

   2. Taylor expanded in t around 0 79.3%

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

      1. mul-1-neg 79.3%

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

   4. Simplified 79.3%

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

   5. Taylor expanded in y around 0 50.7%

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

      1. exp-neg 50.7%

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

      2. associate-*l/ 50.7%

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

      3. *-lft-identity 50.7%

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

      4. exp-sum 50.7%

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

      5. rem-exp-log 51.3%

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

      6. *-commutative 51.3%

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

      7. associate-/r* 53.4%

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

      8. *-commutative 53.4%

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

      9. associate-*r* 49.2%

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

      10. *-commutative 49.2%

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

   7. Simplified 49.2%

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

   8. Taylor expanded in b around 0 34.9%

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

      1. div-inv 35.5%

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

      2. distribute-lft-out 35.5%

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

      3. *-commutative 35.5%

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

   10. Applied egg-rr 35.5%

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

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{-78}:\\ \;\;\;\;\frac{\frac{x - x \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 18: 39.5% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{-20}:\\ \;\;\;\;x \cdot \frac{-b}{y \cdot a}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.15e-20)
   (* x (/ (- b) (* y a)))
   (if (<= b 4e+29) (* x (/ 1.0 (* y a))) (/ x (* y (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.15e-20) {
		tmp = x * (-b / (y * a));
	} else if (b <= 4e+29) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.15d-20)) then
        tmp = x * (-b / (y * a))
    else if (b <= 4d+29) then
        tmp = x * (1.0d0 / (y * a))
    else
        tmp = x / (y * (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.15e-20) {
		tmp = x * (-b / (y * a));
	} else if (b <= 4e+29) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.15e-20:
		tmp = x * (-b / (y * a))
	elif b <= 4e+29:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.15e-20)
		tmp = Float64(x * Float64(Float64(-b) / Float64(y * a)));
	elseif (b <= 4e+29)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	else
		tmp = Float64(x / Float64(y * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.15e-20)
		tmp = x * (-b / (y * a));
	elseif (b <= 4e+29)
		tmp = x * (1.0 / (y * a));
	else
		tmp = x / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.15e-20], N[(x * N[((-b) / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4e+29], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.15e-20

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 96.7%

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

      1. mul-1-neg 96.7%

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

   4. Simplified 96.7%

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

   5. Taylor expanded in y around 0 88.6%

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

      1. exp-neg 88.6%

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

      2. associate-*l/ 88.6%

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

      3. *-lft-identity 88.6%

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

      4. exp-sum 88.6%

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

      5. rem-exp-log 88.7%

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

      6. *-commutative 88.7%

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

      7. associate-/r* 88.7%

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

      8. *-commutative 88.7%

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

      9. associate-*r* 78.6%

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

      10. *-commutative 78.6%

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

   7. Simplified 78.6%

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

   8. Taylor expanded in b around 0 47.1%

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

   9. Taylor expanded in b around inf 47.7%

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

       1. times-frac 46.4%

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

       2. neg-mul-1 46.4%

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

       3. *-commutative 46.4%

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

       4. times-frac 47.7%

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

       5. associate-*r/ 49.2%

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

       6. distribute-rgt-neg-in 49.2%

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

       7. distribute-frac-neg 49.2%

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

       8. *-commutative 49.2%

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

   11. Simplified 49.2%

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

   if -1.15e-20 < b < 3.99999999999999966e29

   1. Initial program 95.9%

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

   2. Taylor expanded in t around 0 69.7%

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

      1. mul-1-neg 69.7%

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

   4. Simplified 69.7%

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

   5. Taylor expanded in y around 0 30.9%

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

      1. exp-neg 30.9%

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

      2. associate-*l/ 30.9%

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

      3. *-lft-identity 30.9%

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

      4. exp-sum 30.9%

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

      5. rem-exp-log 31.9%

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

      6. *-commutative 31.9%

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

      7. associate-/r* 34.0%

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

      8. *-commutative 34.0%

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

      9. associate-*r* 34.0%

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

      10. *-commutative 34.0%

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

   7. Simplified 34.0%

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

   8. Taylor expanded in b around 0 32.6%

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

      1. *-commutative 32.6%

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

      2. div-inv 33.4%

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

   10. Applied egg-rr 33.4%

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

   if 3.99999999999999966e29 < b

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 98.5%

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

      1. mul-1-neg 98.5%

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

   4. Simplified 98.5%

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

   5. Taylor expanded in y around 0 80.6%

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

      1. exp-neg 80.6%

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

      2. associate-*l/ 80.6%

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

      3. *-lft-identity 80.6%

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

      4. exp-sum 80.6%

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

      5. rem-exp-log 80.6%

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

      6. *-commutative 80.6%

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

      7. associate-/r* 80.6%

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

      8. *-commutative 80.6%

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

      9. associate-*r* 70.0%

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

      10. *-commutative 70.0%

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

   7. Simplified 70.0%

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

   8. Taylor expanded in b around 0 35.4%

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

   9. Taylor expanded in b around inf 32.4%

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

       1. *-commutative 32.4%

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

       2. associate-*r* 35.4%

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

       3. *-commutative 35.4%

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

   11. Simplified 35.4%

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

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{-20}:\\ \;\;\;\;x \cdot \frac{-b}{y \cdot a}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]

Alternative 19: 39.6% accurate, 28.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{-20}:\\ \;\;\;\;x \cdot \frac{-b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.6e-20) (* x (/ (- b) (* y a))) (/ x (* y (+ a (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.6e-20) {
		tmp = x * (-b / (y * a));
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.6d-20)) then
        tmp = x * (-b / (y * a))
    else
        tmp = x / (y * (a + (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.6e-20) {
		tmp = x * (-b / (y * a));
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.6e-20:
		tmp = x * (-b / (y * a))
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.6e-20)
		tmp = Float64(x * Float64(Float64(-b) / Float64(y * a)));
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.6e-20)
		tmp = x * (-b / (y * a));
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.6e-20], N[(x * N[((-b) / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.59999999999999985e-20

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 96.7%

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

      1. mul-1-neg 96.7%

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

   4. Simplified 96.7%

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

   5. Taylor expanded in y around 0 88.6%

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

      1. exp-neg 88.6%

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

      2. associate-*l/ 88.6%

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

      3. *-lft-identity 88.6%

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

      4. exp-sum 88.6%

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

      5. rem-exp-log 88.7%

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

      6. *-commutative 88.7%

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

      7. associate-/r* 88.7%

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

      8. *-commutative 88.7%

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

      9. associate-*r* 78.6%

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

      10. *-commutative 78.6%

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

   7. Simplified 78.6%

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

   8. Taylor expanded in b around 0 47.1%

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

   9. Taylor expanded in b around inf 47.7%

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

       1. times-frac 46.4%

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

       2. neg-mul-1 46.4%

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

       3. *-commutative 46.4%

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

       4. times-frac 47.7%

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

       5. associate-*r/ 49.2%

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

       6. distribute-rgt-neg-in 49.2%

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

       7. distribute-frac-neg 49.2%

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

       8. *-commutative 49.2%

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

   11. Simplified 49.2%

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

   if -1.59999999999999985e-20 < b

   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 t around 0 79.9%

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

      1. mul-1-neg 79.9%

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

   4. Simplified 79.9%

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

   5. Taylor expanded in y around 0 48.5%

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

      1. exp-neg 48.5%

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

      2. associate-*l/ 48.5%

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

      3. *-lft-identity 48.5%

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

      4. exp-sum 48.5%

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

      5. rem-exp-log 49.2%

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

      6. *-commutative 49.2%

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

      7. associate-/r* 50.5%

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

      8. *-commutative 50.5%

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

      9. associate-*r* 46.8%

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

      10. *-commutative 46.8%

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

   7. Simplified 46.8%

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

   8. Taylor expanded in b around 0 33.1%

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

      1. distribute-lft-out 33.7%

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

   10. Simplified 33.7%

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

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{-20}:\\ \;\;\;\;x \cdot \frac{-b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 20: 39.8% accurate, 28.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{-77}:\\ \;\;\;\;\frac{\frac{x - x \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3e-77) (/ (/ (- x (* x b)) a) y) (/ x (* y (+ a (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3e-77) {
		tmp = ((x - (x * b)) / a) / y;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3d-77)) then
        tmp = ((x - (x * b)) / a) / y
    else
        tmp = x / (y * (a + (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3e-77) {
		tmp = ((x - (x * b)) / a) / y;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3e-77:
		tmp = ((x - (x * b)) / a) / y
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3e-77)
		tmp = Float64(Float64(Float64(x - Float64(x * b)) / a) / y);
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3e-77)
		tmp = ((x - (x * b)) / a) / y;
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3e-77], N[(N[(N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.00000000000000016e-77

   1. Initial program 99.6%

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

   2. Taylor expanded in t around 0 94.9%

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

      1. mul-1-neg 94.9%

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

   4. Simplified 94.9%

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

   5. Taylor expanded in y around 0 76.9%

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

      1. exp-neg 76.9%

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

      2. associate-*l/ 76.9%

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

      3. *-lft-identity 76.9%

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

      4. exp-sum 76.9%

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

      5. rem-exp-log 77.1%

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

      6. *-commutative 77.1%

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

      7. *-commutative 77.1%

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

      8. associate-/r* 77.1%

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

   7. Simplified 77.1%

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

   8. Taylor expanded in b around 0 46.8%

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

      1. +-commutative 46.8%

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

      2. mul-1-neg 46.8%

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

      3. *-commutative 46.8%

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

      4. unsub-neg 46.8%

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

   10. Simplified 46.8%

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

   if -3.00000000000000016e-77 < b

   1. Initial program 97.2%

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

   2. Taylor expanded in t around 0 79.3%

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

      1. mul-1-neg 79.3%

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

   4. Simplified 79.3%

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

   5. Taylor expanded in y around 0 50.7%

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

      1. exp-neg 50.7%

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

      2. associate-*l/ 50.7%

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

      3. *-lft-identity 50.7%

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

      4. exp-sum 50.7%

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

      5. rem-exp-log 51.3%

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

      6. *-commutative 51.3%

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

      7. associate-/r* 53.4%

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

      8. *-commutative 53.4%

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

      9. associate-*r* 49.2%

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

      10. *-commutative 49.2%

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

   7. Simplified 49.2%

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

   8. Taylor expanded in b around 0 34.9%

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

      1. distribute-lft-out 34.9%

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

   10. Simplified 34.9%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{-77}:\\ \;\;\;\;\frac{\frac{x - x \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 21: 31.7% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.6 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 2.6e+69) (* (/ x y) (/ 1.0 a)) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 2.6e+69) {
		tmp = (x / y) * (1.0 / a);
	} 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 (x <= 2.6d+69) then
        tmp = (x / y) * (1.0d0 / a)
    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 (x <= 2.6e+69) {
		tmp = (x / y) * (1.0 / a);
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 2.6e+69:
		tmp = (x / y) * (1.0 / a)
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 2.6e+69)
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	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 (x <= 2.6e+69)
		tmp = (x / y) * (1.0 / a);
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 2.6e+69], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.6000000000000002e69

   1. Initial program 97.7%

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

   2. Taylor expanded in t around 0 83.9%

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

      1. mul-1-neg 83.9%

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

   4. Simplified 83.9%

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

   5. Taylor expanded in y around 0 60.2%

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

      1. exp-neg 60.3%

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

      2. associate-*l/ 60.3%

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

      3. *-lft-identity 60.3%

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

      4. exp-sum 60.3%

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

      5. rem-exp-log 60.7%

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

      6. *-commutative 60.7%

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

      7. associate-/r* 61.4%

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

      8. *-commutative 61.4%

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

      9. associate-*r* 57.0%

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

      10. *-commutative 57.0%

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

   7. Simplified 57.0%

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

   8. Taylor expanded in b around 0 24.5%

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

      1. *-un-lft-identity 24.5%

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

      2. *-commutative 24.5%

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

      3. times-frac 28.3%

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

   10. Applied egg-rr 28.3%

       \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y}} \]

   if 2.6000000000000002e69 < x

   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 86.7%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{-1 \cdot \log a}\right) - b}}{y} \]
   3. Step-by-step derivation

      1. mul-1-neg 86.7%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   4. Simplified 86.7%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   5. Taylor expanded in y around 0 56.6%

      \[\leadsto \color{blue}{\frac{e^{-\left(b + \log a\right)} \cdot x}{y}} \]
   6. Step-by-step derivation

      1. exp-neg 56.6%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b + \log a}}} \cdot x}{y} \]

      2. associate-*l/ 56.6%

         \[\leadsto \frac{\color{blue}{\frac{1 \cdot x}{e^{b + \log a}}}}{y} \]

      3. *-lft-identity 56.6%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. exp-sum 56.6%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{b} \cdot e^{\log a}}}}{y} \]

      5. rem-exp-log 57.4%

         \[\leadsto \frac{\frac{x}{e^{b} \cdot \color{blue}{a}}}{y} \]

      6. *-commutative 57.4%

         \[\leadsto \frac{\frac{x}{\color{blue}{a \cdot e^{b}}}}{y} \]

      7. associate-/r* 59.2%

         \[\leadsto \color{blue}{\frac{x}{\left(a \cdot e^{b}\right) \cdot y}} \]

      8. *-commutative 59.2%

         \[\leadsto \frac{x}{\color{blue}{y \cdot \left(a \cdot e^{b}\right)}} \]

      9. associate-*r* 50.1%

         \[\leadsto \frac{x}{\color{blue}{\left(y \cdot a\right) \cdot e^{b}}} \]

      10. *-commutative 50.1%

          \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right)} \cdot e^{b}} \]

   7. Simplified 50.1%

      \[\leadsto \color{blue}{\frac{x}{\left(a \cdot y\right) \cdot e^{b}}} \]

   8. Taylor expanded in b around 0 29.1%

      \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 28.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.6 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]

Alternative 22: 35.2% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 8.2 \cdot 10^{+102}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 8.2e+102) (* x (/ 1.0 (* y a))) (/ x (* a (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 8.2e+102) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 8.2d+102) then
        tmp = x * (1.0d0 / (y * a))
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 8.2e+102) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 8.2e+102:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 8.2e+102)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 8.2e+102)
		tmp = x * (1.0 / (y * a));
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 8.2e+102], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 8.1999999999999999e102

   1. Initial program 97.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 81.1%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{-1 \cdot \log a}\right) - b}}{y} \]
   3. Step-by-step derivation

      1. mul-1-neg 81.1%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   4. Simplified 81.1%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   5. Taylor expanded in y around 0 53.5%

      \[\leadsto \color{blue}{\frac{e^{-\left(b + \log a\right)} \cdot x}{y}} \]
   6. Step-by-step derivation

      1. exp-neg 53.5%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b + \log a}}} \cdot x}{y} \]

      2. associate-*l/ 53.5%

         \[\leadsto \frac{\color{blue}{\frac{1 \cdot x}{e^{b + \log a}}}}{y} \]

      3. *-lft-identity 53.5%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. exp-sum 53.5%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{b} \cdot e^{\log a}}}}{y} \]

      5. rem-exp-log 54.1%

         \[\leadsto \frac{\frac{x}{e^{b} \cdot \color{blue}{a}}}{y} \]

      6. *-commutative 54.1%

         \[\leadsto \frac{\frac{x}{\color{blue}{a \cdot e^{b}}}}{y} \]

      7. associate-/r* 55.4%

         \[\leadsto \color{blue}{\frac{x}{\left(a \cdot e^{b}\right) \cdot y}} \]

      8. *-commutative 55.4%

         \[\leadsto \frac{x}{\color{blue}{y \cdot \left(a \cdot e^{b}\right)}} \]

      9. associate-*r* 51.4%

         \[\leadsto \frac{x}{\color{blue}{\left(y \cdot a\right) \cdot e^{b}}} \]

      10. *-commutative 51.4%

          \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right)} \cdot e^{b}} \]

   7. Simplified 51.4%

      \[\leadsto \color{blue}{\frac{x}{\left(a \cdot y\right) \cdot e^{b}}} \]

   8. Taylor expanded in b around 0 29.3%

      \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
   9. Step-by-step derivation

      1. *-commutative 29.3%

         \[\leadsto \frac{x}{\color{blue}{a \cdot y}} \]

      2. div-inv 29.8%

         \[\leadsto \color{blue}{x \cdot \frac{1}{a \cdot y}} \]

   10. Applied egg-rr 29.8%

       \[\leadsto \color{blue}{x \cdot \frac{1}{a \cdot y}} \]

   if 8.1999999999999999e102 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 98.1%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{-1 \cdot \log a}\right) - b}}{y} \]
   3. Step-by-step derivation

      1. mul-1-neg 98.1%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   4. Simplified 98.1%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   5. Taylor expanded in y around 0 83.0%

      \[\leadsto \color{blue}{\frac{e^{-\left(b + \log a\right)} \cdot x}{y}} \]
   6. Step-by-step derivation

      1. exp-neg 83.0%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b + \log a}}} \cdot x}{y} \]

      2. associate-*l/ 83.0%

         \[\leadsto \frac{\color{blue}{\frac{1 \cdot x}{e^{b + \log a}}}}{y} \]

      3. *-lft-identity 83.0%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. exp-sum 83.0%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{b} \cdot e^{\log a}}}}{y} \]

      5. rem-exp-log 83.0%

         \[\leadsto \frac{\frac{x}{e^{b} \cdot \color{blue}{a}}}{y} \]

      6. *-commutative 83.0%

         \[\leadsto \frac{\frac{x}{\color{blue}{a \cdot e^{b}}}}{y} \]

      7. associate-/r* 83.0%

         \[\leadsto \color{blue}{\frac{x}{\left(a \cdot e^{b}\right) \cdot y}} \]

      8. *-commutative 83.0%

         \[\leadsto \frac{x}{\color{blue}{y \cdot \left(a \cdot e^{b}\right)}} \]

      9. associate-*r* 71.4%

         \[\leadsto \frac{x}{\color{blue}{\left(y \cdot a\right) \cdot e^{b}}} \]

      10. *-commutative 71.4%

          \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right)} \cdot e^{b}} \]

   7. Simplified 71.4%

      \[\leadsto \color{blue}{\frac{x}{\left(a \cdot y\right) \cdot e^{b}}} \]

   8. Taylor expanded in b around 0 40.4%

      \[\leadsto \frac{x}{\color{blue}{y \cdot a + y \cdot \left(a \cdot b\right)}} \]

   9. Taylor expanded in b around inf 38.5%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot b\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 8.2 \cdot 10^{+102}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]

Alternative 23: 35.5% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 4 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 4e+29) (* x (/ 1.0 (* y a))) (/ x (* y (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 4e+29) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 4d+29) then
        tmp = x * (1.0d0 / (y * a))
    else
        tmp = x / (y * (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 4e+29) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 4e+29:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 4e+29)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	else
		tmp = Float64(x / Float64(y * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 4e+29)
		tmp = x * (1.0 / (y * a));
	else
		tmp = x / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 4e+29], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 3.99999999999999966e29

   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 t around 0 79.7%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{-1 \cdot \log a}\right) - b}}{y} \]
   3. Step-by-step derivation

      1. mul-1-neg 79.7%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   4. Simplified 79.7%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   5. Taylor expanded in y around 0 52.1%

      \[\leadsto \color{blue}{\frac{e^{-\left(b + \log a\right)} \cdot x}{y}} \]
   6. Step-by-step derivation

      1. exp-neg 52.1%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b + \log a}}} \cdot x}{y} \]

      2. associate-*l/ 52.1%

         \[\leadsto \frac{\color{blue}{\frac{1 \cdot x}{e^{b + \log a}}}}{y} \]

      3. *-lft-identity 52.1%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. exp-sum 52.1%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{b} \cdot e^{\log a}}}}{y} \]

      5. rem-exp-log 52.8%

         \[\leadsto \frac{\frac{x}{e^{b} \cdot \color{blue}{a}}}{y} \]

      6. *-commutative 52.8%

         \[\leadsto \frac{\frac{x}{\color{blue}{a \cdot e^{b}}}}{y} \]

      7. associate-/r* 54.1%

         \[\leadsto \color{blue}{\frac{x}{\left(a \cdot e^{b}\right) \cdot y}} \]

      8. *-commutative 54.1%

         \[\leadsto \frac{x}{\color{blue}{y \cdot \left(a \cdot e^{b}\right)}} \]

      9. associate-*r* 50.4%

         \[\leadsto \frac{x}{\color{blue}{\left(y \cdot a\right) \cdot e^{b}}} \]

      10. *-commutative 50.4%

          \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right)} \cdot e^{b}} \]

   7. Simplified 50.4%

      \[\leadsto \color{blue}{\frac{x}{\left(a \cdot y\right) \cdot e^{b}}} \]

   8. Taylor expanded in b around 0 30.8%

      \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
   9. Step-by-step derivation

      1. *-commutative 30.8%

         \[\leadsto \frac{x}{\color{blue}{a \cdot y}} \]

      2. div-inv 31.3%

         \[\leadsto \color{blue}{x \cdot \frac{1}{a \cdot y}} \]

   10. Applied egg-rr 31.3%

       \[\leadsto \color{blue}{x \cdot \frac{1}{a \cdot y}} \]

   if 3.99999999999999966e29 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 98.5%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{-1 \cdot \log a}\right) - b}}{y} \]
   3. Step-by-step derivation

      1. mul-1-neg 98.5%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   4. Simplified 98.5%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   5. Taylor expanded in y around 0 80.6%

      \[\leadsto \color{blue}{\frac{e^{-\left(b + \log a\right)} \cdot x}{y}} \]
   6. Step-by-step derivation

      1. exp-neg 80.6%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b + \log a}}} \cdot x}{y} \]

      2. associate-*l/ 80.6%

         \[\leadsto \frac{\color{blue}{\frac{1 \cdot x}{e^{b + \log a}}}}{y} \]

      3. *-lft-identity 80.6%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. exp-sum 80.6%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{b} \cdot e^{\log a}}}}{y} \]

      5. rem-exp-log 80.6%

         \[\leadsto \frac{\frac{x}{e^{b} \cdot \color{blue}{a}}}{y} \]

      6. *-commutative 80.6%

         \[\leadsto \frac{\frac{x}{\color{blue}{a \cdot e^{b}}}}{y} \]

      7. associate-/r* 80.6%

         \[\leadsto \color{blue}{\frac{x}{\left(a \cdot e^{b}\right) \cdot y}} \]

      8. *-commutative 80.6%

         \[\leadsto \frac{x}{\color{blue}{y \cdot \left(a \cdot e^{b}\right)}} \]

      9. associate-*r* 70.0%

         \[\leadsto \frac{x}{\color{blue}{\left(y \cdot a\right) \cdot e^{b}}} \]

      10. *-commutative 70.0%

          \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right)} \cdot e^{b}} \]

   7. Simplified 70.0%

      \[\leadsto \color{blue}{\frac{x}{\left(a \cdot y\right) \cdot e^{b}}} \]

   8. Taylor expanded in b around 0 35.4%

      \[\leadsto \frac{x}{\color{blue}{y \cdot a + y \cdot \left(a \cdot b\right)}} \]

   9. Taylor expanded in b around inf 32.4%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot b\right)}} \]
   10. Step-by-step derivation

       1. *-commutative 32.4%

          \[\leadsto \frac{x}{\color{blue}{\left(y \cdot b\right) \cdot a}} \]

       2. associate-*r* 35.4%

          \[\leadsto \frac{x}{\color{blue}{y \cdot \left(b \cdot a\right)}} \]

       3. *-commutative 35.4%

          \[\leadsto \frac{x}{y \cdot \color{blue}{\left(a \cdot b\right)}} \]

   11. Simplified 35.4%

       \[\leadsto \color{blue}{\frac{x}{y \cdot \left(a \cdot b\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 4 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]

Alternative 24: 31.7% accurate, 44.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 10^{+69}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 1e+69) (/ (/ x y) a) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 1e+69) {
		tmp = (x / y) / a;
	} 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 (x <= 1d+69) then
        tmp = (x / y) / a
    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 (x <= 1e+69) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 1e+69:
		tmp = (x / y) / a
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 1e+69)
		tmp = Float64(Float64(x / y) / a);
	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 (x <= 1e+69)
		tmp = (x / y) / a;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 1e+69], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.0000000000000001e69

   1. Initial program 97.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 83.9%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{-1 \cdot \log a}\right) - b}}{y} \]
   3. Step-by-step derivation

      1. mul-1-neg 83.9%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   4. Simplified 83.9%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   5. Taylor expanded in y around 0 60.2%

      \[\leadsto \color{blue}{\frac{e^{-\left(b + \log a\right)} \cdot x}{y}} \]
   6. Step-by-step derivation

      1. exp-neg 60.3%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b + \log a}}} \cdot x}{y} \]

      2. associate-*l/ 60.3%

         \[\leadsto \frac{\color{blue}{\frac{1 \cdot x}{e^{b + \log a}}}}{y} \]

      3. *-lft-identity 60.3%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. exp-sum 60.3%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{b} \cdot e^{\log a}}}}{y} \]

      5. rem-exp-log 60.7%

         \[\leadsto \frac{\frac{x}{e^{b} \cdot \color{blue}{a}}}{y} \]

      6. *-commutative 60.7%

         \[\leadsto \frac{\frac{x}{\color{blue}{a \cdot e^{b}}}}{y} \]

      7. associate-/r* 61.4%

         \[\leadsto \color{blue}{\frac{x}{\left(a \cdot e^{b}\right) \cdot y}} \]

      8. *-commutative 61.4%

         \[\leadsto \frac{x}{\color{blue}{y \cdot \left(a \cdot e^{b}\right)}} \]

      9. associate-*r* 57.0%

         \[\leadsto \frac{x}{\color{blue}{\left(y \cdot a\right) \cdot e^{b}}} \]

      10. *-commutative 57.0%

          \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right)} \cdot e^{b}} \]

   7. Simplified 57.0%

      \[\leadsto \color{blue}{\frac{x}{\left(a \cdot y\right) \cdot e^{b}}} \]

   8. Taylor expanded in b around 0 24.5%

      \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
   9. Step-by-step derivation

      1. associate-/r* 28.3%

         \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]

   10. Simplified 28.3%

       \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]

   if 1.0000000000000001e69 < x

   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 86.7%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{-1 \cdot \log a}\right) - b}}{y} \]
   3. Step-by-step derivation

      1. mul-1-neg 86.7%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   4. Simplified 86.7%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   5. Taylor expanded in y around 0 56.6%

      \[\leadsto \color{blue}{\frac{e^{-\left(b + \log a\right)} \cdot x}{y}} \]
   6. Step-by-step derivation

      1. exp-neg 56.6%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b + \log a}}} \cdot x}{y} \]

      2. associate-*l/ 56.6%

         \[\leadsto \frac{\color{blue}{\frac{1 \cdot x}{e^{b + \log a}}}}{y} \]

      3. *-lft-identity 56.6%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. exp-sum 56.6%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{b} \cdot e^{\log a}}}}{y} \]

      5. rem-exp-log 57.4%

         \[\leadsto \frac{\frac{x}{e^{b} \cdot \color{blue}{a}}}{y} \]

      6. *-commutative 57.4%

         \[\leadsto \frac{\frac{x}{\color{blue}{a \cdot e^{b}}}}{y} \]

      7. associate-/r* 59.2%

         \[\leadsto \color{blue}{\frac{x}{\left(a \cdot e^{b}\right) \cdot y}} \]

      8. *-commutative 59.2%

         \[\leadsto \frac{x}{\color{blue}{y \cdot \left(a \cdot e^{b}\right)}} \]

      9. associate-*r* 50.1%

         \[\leadsto \frac{x}{\color{blue}{\left(y \cdot a\right) \cdot e^{b}}} \]

      10. *-commutative 50.1%

          \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right)} \cdot e^{b}} \]

   7. Simplified 50.1%

      \[\leadsto \color{blue}{\frac{x}{\left(a \cdot y\right) \cdot e^{b}}} \]

   8. Taylor expanded in b around 0 29.1%

      \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 28.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 10^{+69}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]

Alternative 25: 30.9% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot a} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x (* y a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / (y * a)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Python

def code(x, y, z, t, a, b):
	return x / (y * a)

Julia

function code(x, y, z, t, a, b)
	return Float64(x / Float64(y * a))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / (y * a);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.0%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

2. Taylor expanded in t around 0 84.5%

   \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{-1 \cdot \log a}\right) - b}}{y} \]
3. Step-by-step derivation

   1. mul-1-neg 84.5%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

4. Simplified 84.5%

   \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

5. Taylor expanded in y around 0 59.5%

   \[\leadsto \color{blue}{\frac{e^{-\left(b + \log a\right)} \cdot x}{y}} \]
6. Step-by-step derivation

   1. exp-neg 59.5%

      \[\leadsto \frac{\color{blue}{\frac{1}{e^{b + \log a}}} \cdot x}{y} \]

   2. associate-*l/ 59.5%

      \[\leadsto \frac{\color{blue}{\frac{1 \cdot x}{e^{b + \log a}}}}{y} \]

   3. *-lft-identity 59.5%

      \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

   4. exp-sum 59.5%

      \[\leadsto \frac{\frac{x}{\color{blue}{e^{b} \cdot e^{\log a}}}}{y} \]

   5. rem-exp-log 60.0%

      \[\leadsto \frac{\frac{x}{e^{b} \cdot \color{blue}{a}}}{y} \]

   6. *-commutative 60.0%

      \[\leadsto \frac{\frac{x}{\color{blue}{a \cdot e^{b}}}}{y} \]

   7. associate-/r* 61.0%

      \[\leadsto \color{blue}{\frac{x}{\left(a \cdot e^{b}\right) \cdot y}} \]

   8. *-commutative 61.0%

      \[\leadsto \frac{x}{\color{blue}{y \cdot \left(a \cdot e^{b}\right)}} \]

   9. associate-*r* 55.5%

      \[\leadsto \frac{x}{\color{blue}{\left(y \cdot a\right) \cdot e^{b}}} \]

   10. *-commutative 55.5%

       \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right)} \cdot e^{b}} \]

7. Simplified 55.5%

   \[\leadsto \color{blue}{\frac{x}{\left(a \cdot y\right) \cdot e^{b}}} \]

8. Taylor expanded in b around 0 25.5%

   \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]

9. Final simplification 25.5%

   \[\leadsto \frac{x}{y \cdot a} \]

Developer target: 72.0% 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 2023171 
(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))