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

Percentage Accurate: 98.5% → 98.5%

Time: 24.5s

Alternatives: 18

Speedup: 1.0×

• 48.0% 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 98.4%

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

3. Final simplification 98.4%

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

Alternative 2: 92.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -2 \cdot 10^{+37} \lor \neg \left(t + -1 \leq 2 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ t -1.0) -2e+37) (not (<= (+ t -1.0) 2e+38)))
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -2e+37) || !((t + -1.0) <= 2e+38)) {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	} else {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((t + (-1.0d0)) <= (-2d+37)) .or. (.not. ((t + (-1.0d0)) <= 2d+38))) then
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    else
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -2e+37) || !((t + -1.0) <= 2e+38)) {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	} else {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t + -1.0) <= -2e+37) or not ((t + -1.0) <= 2e+38):
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	else:
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(t + -1.0) <= -2e+37) || !(Float64(t + -1.0) <= 2e+38))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t + -1.0) <= -2e+37) || ~(((t + -1.0) <= 2e+38)))
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	else
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(t + -1.0), $MachinePrecision], -2e+37], N[Not[LessEqual[N[(t + -1.0), $MachinePrecision], 2e+38]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 t 1) < -1.99999999999999991e37 or 1.99999999999999995e38 < (-.f64 t 1)

   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. Add Preprocessing

   3. Taylor expanded in y around 0 95.1%

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

   if -1.99999999999999991e37 < (-.f64 t 1) < 1.99999999999999995e38

   1. Initial program 97.4%

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

   3. Taylor expanded in t around 0 96.8%

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

      1. +-commutative 96.8%

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

      2. mul-1-neg 96.8%

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

      3. unsub-neg 96.8%

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

   5. Simplified 96.8%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -2 \cdot 10^{+37} \lor \neg \left(t + -1 \leq 2 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{if}\;t \leq -7 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-274}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+38}:\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y \cdot e^{b}}}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (pow a (+ t -1.0))) y)))
   (if (<= t -7e+112)
     t_1
     (if (<= t 2.05e-274)
       (/ (/ x (* a (exp b))) y)
       (if (<= t 6e+38) (/ x (/ a (/ (pow z y) (* y (exp b))))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * pow(a, (t + -1.0))) / y;
	double tmp;
	if (t <= -7e+112) {
		tmp = t_1;
	} else if (t <= 2.05e-274) {
		tmp = (x / (a * exp(b))) / y;
	} else if (t <= 6e+38) {
		tmp = x / (a / (pow(z, y) / (y * exp(b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * (a ** (t + (-1.0d0)))) / y
    if (t <= (-7d+112)) then
        tmp = t_1
    else if (t <= 2.05d-274) then
        tmp = (x / (a * exp(b))) / y
    else if (t <= 6d+38) then
        tmp = x / (a / ((z ** y) / (y * exp(b))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * Math.pow(a, (t + -1.0))) / y;
	double tmp;
	if (t <= -7e+112) {
		tmp = t_1;
	} else if (t <= 2.05e-274) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else if (t <= 6e+38) {
		tmp = x / (a / (Math.pow(z, y) / (y * Math.exp(b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.pow(a, (t + -1.0))) / y
	tmp = 0
	if t <= -7e+112:
		tmp = t_1
	elif t <= 2.05e-274:
		tmp = (x / (a * math.exp(b))) / y
	elif t <= 6e+38:
		tmp = x / (a / (math.pow(z, y) / (y * math.exp(b))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y)
	tmp = 0.0
	if (t <= -7e+112)
		tmp = t_1;
	elseif (t <= 2.05e-274)
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	elseif (t <= 6e+38)
		tmp = Float64(x / Float64(a / Float64((z ^ y) / Float64(y * exp(b)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * (a ^ (t + -1.0))) / y;
	tmp = 0.0;
	if (t <= -7e+112)
		tmp = t_1;
	elseif (t <= 2.05e-274)
		tmp = (x / (a * exp(b))) / y;
	elseif (t <= 6e+38)
		tmp = x / (a / ((z ^ y) / (y * exp(b))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -7e+112], t$95$1, If[LessEqual[t, 2.05e-274], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 6e+38], N[(x / N[(a / N[(N[Power[z, y], $MachinePrecision] / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.99999999999999994e112 or 6.0000000000000002e38 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 94.5%

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

   4. Taylor expanded in b around 0 86.9%

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

      1. exp-to-pow 86.9%

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

      2. sub-neg 86.9%

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

      3. metadata-eval 86.9%

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

      4. +-commutative 86.9%

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

   6. Simplified 86.9%

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

   if -6.99999999999999994e112 < t < 2.04999999999999994e-274

   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. Add Preprocessing

   3. Taylor expanded in y around 0 86.4%

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

      1. div-exp 81.3%

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

      2. exp-to-pow 82.5%

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

      3. sub-neg 82.5%

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

      4. metadata-eval 82.5%

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

   5. Simplified 82.5%

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

   6. Taylor expanded in t around 0 84.7%

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

   if 2.04999999999999994e-274 < t < 6.0000000000000002e38

   1. Initial program 99.2%

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

      1. associate-/l* 98.3%

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

      2. associate--l+ 98.3%

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

      3. exp-sum 80.7%

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

      4. associate-/r* 80.7%

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

      5. *-commutative 80.7%

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

      6. exp-to-pow 80.7%

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

      7. exp-diff 79.2%

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

      8. *-commutative 79.2%

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

      9. exp-to-pow 79.4%

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

      10. sub-neg 79.4%

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

      11. metadata-eval 79.4%

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

   3. Simplified 79.4%

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

   5. Taylor expanded in t around 0 85.4%

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

      1. associate-/l* 85.4%

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

   7. Simplified 85.4%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+112}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-274}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+38}:\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y \cdot e^{b}}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+148} \lor \neg \left(y \leq 1.32 \cdot 10^{+123}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.4e+148) (not (<= y 1.32e+123)))
   (/ (/ (* 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 <= -4.4e+148) || !(y <= 1.32e+123)) {
		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 <= (-4.4d+148)) .or. (.not. (y <= 1.32d+123))) 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 <= -4.4e+148) || !(y <= 1.32e+123)) {
		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 <= -4.4e+148) or not (y <= 1.32e+123):
		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 <= -4.4e+148) || !(y <= 1.32e+123))
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4.4e+148) || ~((y <= 1.32e+123)))
		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, -4.4e+148], N[Not[LessEqual[y, 1.32e+123]], $MachinePrecision]], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.3999999999999998e148 or 1.32e123 < 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. Add Preprocessing

   3. Taylor expanded in b around 0 98.7%

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

      1. exp-sum 78.4%

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

      2. remove-double-neg 78.4%

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

      3. distribute-lft-neg-out 78.4%

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

      4. distribute-rgt-neg-out 78.4%

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

      5. neg-mul-1 78.4%

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

      6. log-rec 78.4%

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

      7. associate-*r* 78.4%

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

      8. associate-*r* 78.4%

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

      9. exp-to-pow 78.4%

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

      10. sub-neg 78.4%

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

      11. metadata-eval 78.4%

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

   5. Simplified 78.4%

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

   6. Taylor expanded in t around 0 93.3%

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

   if -4.3999999999999998e148 < y < 1.32e123

   1. Initial program 97.8%

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

   3. Taylor expanded in y around 0 92.4%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+148} \lor \neg \left(y \leq 1.32 \cdot 10^{+123}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+82} \lor \neg \left(y \leq 1.66 \cdot 10^{+40}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.2e+82) (not (<= y 1.66e+40)))
   (/ (/ (* 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 <= -3.2e+82) || !(y <= 1.66e+40)) {
		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 <= (-3.2d+82)) .or. (.not. (y <= 1.66d+40))) 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 <= -3.2e+82) || !(y <= 1.66e+40)) {
		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 <= -3.2e+82) or not (y <= 1.66e+40):
		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 <= -3.2e+82) || !(y <= 1.66e+40))
		tmp = Float64(Float64(Float64(x * (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 <= -3.2e+82) || ~((y <= 1.66e+40)))
		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, -3.2e+82], N[Not[LessEqual[y, 1.66e+40]], $MachinePrecision]], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $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 < -3.19999999999999975e82 or 1.6600000000000001e40 < 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. Add Preprocessing

   3. Taylor expanded in b around 0 94.5%

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

      1. exp-sum 73.9%

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

      2. remove-double-neg 73.9%

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

      3. distribute-lft-neg-out 73.9%

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

      4. distribute-rgt-neg-out 73.9%

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

      5. neg-mul-1 73.9%

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

      6. log-rec 73.9%

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

      7. associate-*r* 73.9%

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

      8. associate-*r* 73.9%

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

      9. exp-to-pow 73.9%

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

      10. sub-neg 73.9%

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

      11. metadata-eval 73.9%

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

   5. Simplified 73.9%

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

   6. Taylor expanded in t around 0 87.1%

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

   if -3.19999999999999975e82 < y < 1.6600000000000001e40

   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. Add Preprocessing

   3. Taylor expanded in y around 0 95.3%

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

      1. div-exp 86.6%

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

      2. exp-to-pow 87.5%

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

      3. sub-neg 87.5%

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

      4. metadata-eval 87.5%

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

   5. Simplified 87.5%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+82} \lor \neg \left(y \leq 1.66 \cdot 10^{+40}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{if}\;t \leq -7.4 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-214}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+39}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (pow a (+ t -1.0))) y)))
   (if (<= t -7.4e+112)
     t_1
     (if (<= t 4.6e-214)
       (/ (/ x (* a (exp b))) y)
       (if (<= t 1.05e+39) (/ (/ (* x (pow z y)) a) y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * pow(a, (t + -1.0))) / y;
	double tmp;
	if (t <= -7.4e+112) {
		tmp = t_1;
	} else if (t <= 4.6e-214) {
		tmp = (x / (a * exp(b))) / y;
	} else if (t <= 1.05e+39) {
		tmp = ((x * pow(z, y)) / a) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * (a ** (t + (-1.0d0)))) / y
    if (t <= (-7.4d+112)) then
        tmp = t_1
    else if (t <= 4.6d-214) then
        tmp = (x / (a * exp(b))) / y
    else if (t <= 1.05d+39) then
        tmp = ((x * (z ** y)) / 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(a, (t + -1.0))) / y;
	double tmp;
	if (t <= -7.4e+112) {
		tmp = t_1;
	} else if (t <= 4.6e-214) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else if (t <= 1.05e+39) {
		tmp = ((x * Math.pow(z, y)) / a) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.pow(a, (t + -1.0))) / y
	tmp = 0
	if t <= -7.4e+112:
		tmp = t_1
	elif t <= 4.6e-214:
		tmp = (x / (a * math.exp(b))) / y
	elif t <= 1.05e+39:
		tmp = ((x * math.pow(z, y)) / a) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y)
	tmp = 0.0
	if (t <= -7.4e+112)
		tmp = t_1;
	elseif (t <= 4.6e-214)
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	elseif (t <= 1.05e+39)
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * (a ^ (t + -1.0))) / y;
	tmp = 0.0;
	if (t <= -7.4e+112)
		tmp = t_1;
	elseif (t <= 4.6e-214)
		tmp = (x / (a * exp(b))) / y;
	elseif (t <= 1.05e+39)
		tmp = ((x * (z ^ y)) / 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[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -7.4e+112], t$95$1, If[LessEqual[t, 4.6e-214], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 1.05e+39], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.40000000000000008e112 or 1.0499999999999999e39 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 94.5%

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

   4. Taylor expanded in b around 0 86.9%

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

      1. exp-to-pow 86.9%

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

      2. sub-neg 86.9%

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

      3. metadata-eval 86.9%

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

      4. +-commutative 86.9%

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

   6. Simplified 86.9%

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

   if -7.40000000000000008e112 < t < 4.60000000000000022e-214

   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. Add Preprocessing

   3. Taylor expanded in y around 0 87.1%

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

      1. div-exp 82.7%

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

      2. exp-to-pow 83.7%

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

      3. sub-neg 83.7%

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

      4. metadata-eval 83.7%

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

   5. Simplified 83.7%

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

   6. Taylor expanded in t around 0 85.6%

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

   if 4.60000000000000022e-214 < t < 1.0499999999999999e39

   1. Initial program 99.7%

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

   3. Taylor expanded in b around 0 81.2%

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

      1. exp-sum 73.7%

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

      2. remove-double-neg 73.7%

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

      3. distribute-lft-neg-out 73.7%

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

      4. distribute-rgt-neg-out 73.7%

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

      5. neg-mul-1 73.7%

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

      6. log-rec 73.7%

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

      7. associate-*r* 73.7%

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

      8. associate-*r* 73.7%

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

      9. exp-to-pow 74.0%

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

      10. sub-neg 74.0%

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

      11. metadata-eval 74.0%

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

   5. Simplified 74.0%

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

   6. Taylor expanded in t around 0 81.5%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{+112}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-214}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+39}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+112} \lor \neg \left(t \leq 1.4 \cdot 10^{+39}\right):\\ \;\;\;\;{a}^{\left(t + -1\right)} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -7.2e+112) (not (<= t 1.4e+39)))
   (* (pow a (+ t -1.0)) (/ 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 ((t <= -7.2e+112) || !(t <= 1.4e+39)) {
		tmp = pow(a, (t + -1.0)) * (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 ((t <= (-7.2d+112)) .or. (.not. (t <= 1.4d+39))) then
        tmp = (a ** (t + (-1.0d0))) * (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 ((t <= -7.2e+112) || !(t <= 1.4e+39)) {
		tmp = Math.pow(a, (t + -1.0)) * (x / y);
	} else {
		tmp = (x / (a * Math.exp(b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -7.2e+112) or not (t <= 1.4e+39):
		tmp = math.pow(a, (t + -1.0)) * (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 ((t <= -7.2e+112) || !(t <= 1.4e+39))
		tmp = Float64((a ^ Float64(t + -1.0)) * 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 ((t <= -7.2e+112) || ~((t <= 1.4e+39)))
		tmp = (a ^ (t + -1.0)) * (x / y);
	else
		tmp = (x / (a * exp(b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -7.2e+112], N[Not[LessEqual[t, 1.4e+39]], $MachinePrecision]], N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.20000000000000001e112 or 1.40000000000000001e39 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 94.5%

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

   4. Taylor expanded in b around 0 86.9%

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

      1. *-commutative 86.9%

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

      2. exp-to-pow 86.9%

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

      3. sub-neg 86.9%

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

      4. metadata-eval 86.9%

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

      5. associate-*r/ 78.0%

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

      6. +-commutative 78.0%

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

   6. Simplified 78.0%

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

   if -7.20000000000000001e112 < t < 1.40000000000000001e39

   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. Add Preprocessing

   3. Taylor expanded in y around 0 81.2%

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

      1. div-exp 77.0%

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

      2. exp-to-pow 77.8%

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

      3. sub-neg 77.8%

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

      4. metadata-eval 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in t around 0 80.3%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+112} \lor \neg \left(t \leq 1.4 \cdot 10^{+39}\right):\\ \;\;\;\;{a}^{\left(t + -1\right)} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.5% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+112} \lor \neg \left(t \leq 1.5 \cdot 10^{+39}\right):\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -7.2e+112) (not (<= t 1.5e+39)))
   (/ (* x (pow a (+ t -1.0))) y)
   (/ (/ x (* a (exp b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -7.2e+112) || !(t <= 1.5e+39)) {
		tmp = (x * pow(a, (t + -1.0))) / y;
	} else {
		tmp = (x / (a * exp(b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-7.2d+112)) .or. (.not. (t <= 1.5d+39))) then
        tmp = (x * (a ** (t + (-1.0d0)))) / y
    else
        tmp = (x / (a * exp(b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -7.2e+112) || !(t <= 1.5e+39)) {
		tmp = (x * Math.pow(a, (t + -1.0))) / y;
	} else {
		tmp = (x / (a * Math.exp(b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -7.2e+112) or not (t <= 1.5e+39):
		tmp = (x * math.pow(a, (t + -1.0))) / y
	else:
		tmp = (x / (a * math.exp(b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -7.2e+112) || !(t <= 1.5e+39))
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y);
	else
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -7.2e+112) || ~((t <= 1.5e+39)))
		tmp = (x * (a ^ (t + -1.0))) / y;
	else
		tmp = (x / (a * exp(b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -7.2e+112], N[Not[LessEqual[t, 1.5e+39]], $MachinePrecision]], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $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 t < -7.20000000000000001e112 or 1.5e39 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 94.5%

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

   4. Taylor expanded in b around 0 86.9%

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

      1. exp-to-pow 86.9%

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

      2. sub-neg 86.9%

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

      3. metadata-eval 86.9%

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

      4. +-commutative 86.9%

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

   6. Simplified 86.9%

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

   if -7.20000000000000001e112 < t < 1.5e39

   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. Add Preprocessing

   3. Taylor expanded in y around 0 81.2%

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

      1. div-exp 77.0%

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

      2. exp-to-pow 77.8%

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

      3. sub-neg 77.8%

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

      4. metadata-eval 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in t around 0 80.3%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+112} \lor \neg \left(t \leq 1.5 \cdot 10^{+39}\right):\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.0% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 5 \cdot 10^{+20}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 5e+20) (/ (/ x (* a (exp b))) y) (/ x (* a (* y (exp b))))))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 5e+20)
		tmp = (x / (a * exp(b))) / y;
	else
		tmp = x / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 5e+20], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 5e20

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0 84.3%

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

      1. div-exp 78.0%

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

      2. exp-to-pow 78.6%

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

      3. sub-neg 78.6%

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

      4. metadata-eval 78.6%

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

   5. Simplified 78.6%

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

   6. Taylor expanded in t around 0 67.6%

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

   if 5e20 < a

   1. Initial program 97.4%

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

      1. associate-*l/ 90.0%

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

      2. *-commutative 90.0%

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

      3. +-commutative 90.0%

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

      4. associate--l+ 90.0%

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

      5. exp-sum 73.4%

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

      6. *-commutative 73.4%

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

      7. exp-to-pow 74.1%

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

      8. sub-neg 74.1%

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

      9. metadata-eval 74.1%

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

      10. exp-diff 64.6%

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

      11. *-commutative 64.6%

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

      12. exp-to-pow 64.6%

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

   3. Simplified 64.6%

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

   5. Taylor expanded in y around 0 69.4%

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

      1. times-frac 67.5%

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

      2. exp-to-pow 68.1%

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

      3. sub-neg 68.1%

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

      4. metadata-eval 68.1%

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

   7. Simplified 68.1%

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

   8. Taylor expanded in t around 0 75.2%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 5 \cdot 10^{+20}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.4% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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-*l/ 89.6%

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

   2. *-commutative 89.6%

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

   3. +-commutative 89.6%

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

   4. associate--l+ 89.6%

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

   5. exp-sum 74.4%

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

   6. *-commutative 74.4%

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

   7. exp-to-pow 75.0%

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

   8. sub-neg 75.0%

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

   9. metadata-eval 75.0%

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

   10. exp-diff 66.0%

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

   11. *-commutative 66.0%

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

   12. exp-to-pow 66.0%

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

3. Simplified 66.0%

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

5. Taylor expanded in y around 0 72.2%

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

   1. times-frac 69.4%

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

   2. exp-to-pow 70.0%

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

   3. sub-neg 70.0%

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

   4. metadata-eval 70.0%

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

7. Simplified 70.0%

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

8. Taylor expanded in t around 0 67.3%

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

9. Final simplification 67.3%

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

Alternative 11: 40.1% accurate, 17.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{-23}:\\ \;\;\;\;\frac{x}{y \cdot a} - \frac{x}{a} \cdot \frac{b}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7e-23)
   (- (/ x (* y a)) (* (/ x a) (/ b y)))
   (/ (/ x (+ a (* a b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7e-23) {
		tmp = (x / (y * a)) - ((x / a) * (b / y));
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-7d-23)) then
        tmp = (x / (y * a)) - ((x / a) * (b / y))
    else
        tmp = (x / (a + (a * b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7e-23) {
		tmp = (x / (y * a)) - ((x / a) * (b / y));
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7e-23:
		tmp = (x / (y * a)) - ((x / a) * (b / y))
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7e-23)
		tmp = Float64(Float64(x / Float64(y * a)) - Float64(Float64(x / a) * Float64(b / y)));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -7e-23)
		tmp = (x / (y * a)) - ((x / a) * (b / y));
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7e-23], N[(N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision] - N[(N[(x / a), $MachinePrecision] * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.99999999999999987e-23

   1. Initial program 98.6%

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

   3. Taylor expanded in y around 0 95.9%

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

   4. Taylor expanded in t around 0 87.7%

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

      1. *-commutative 87.7%

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

      2. exp-diff 87.7%

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

      3. mul-1-neg 87.7%

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

      4. log-rec 87.7%

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

      5. rem-exp-log 87.8%

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

      6. associate-/l/ 87.8%

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

      7. *-commutative 87.8%

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

   6. Simplified 87.8%

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

   7. Taylor expanded in b around 0 43.4%

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

      1. +-commutative 43.4%

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

      2. mul-1-neg 43.4%

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

      3. unsub-neg 43.4%

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

      4. *-commutative 43.4%

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

      5. times-frac 42.2%

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

   9. Simplified 42.2%

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

   if -6.99999999999999987e-23 < b

   1. Initial program 98.3%

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

   3. Taylor expanded in y around 0 82.0%

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

      1. div-exp 74.4%

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

      2. exp-to-pow 75.1%

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

      3. sub-neg 75.1%

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

      4. metadata-eval 75.1%

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

   5. Simplified 75.1%

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

   6. Taylor expanded in t around 0 61.5%

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

   7. Taylor expanded in b around 0 47.9%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{-23}:\\ \;\;\;\;\frac{x}{y \cdot a} - \frac{x}{a} \cdot \frac{b}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 40.4% accurate, 19.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 4.7 \cdot 10^{-26}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} - \frac{b}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 4.7e-26) (/ (* x (- (/ 1.0 a) (/ b a))) y) (/ (/ x (* a b)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 4.7e-26) {
		tmp = (x * ((1.0 / a) - (b / a))) / y;
	} else {
		tmp = (x / (a * b)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 4.7d-26) then
        tmp = (x * ((1.0d0 / a) - (b / a))) / y
    else
        tmp = (x / (a * b)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 4.7e-26) {
		tmp = (x * ((1.0 / a) - (b / a))) / y;
	} else {
		tmp = (x / (a * b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 4.7e-26:
		tmp = (x * ((1.0 / a) - (b / a))) / y
	else:
		tmp = (x / (a * b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 4.7e-26)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) - Float64(b / a))) / y);
	else
		tmp = Float64(Float64(x / Float64(a * b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 4.7e-26)
		tmp = (x * ((1.0 / a) - (b / a))) / y;
	else
		tmp = (x / (a * b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 4.7e-26], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 4.69999999999999989e-26

   1. Initial program 97.9%

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

   3. Taylor expanded in y around 0 85.5%

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

   4. Taylor expanded in t around 0 65.3%

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

      1. *-commutative 65.3%

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

      2. exp-diff 65.3%

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

      3. mul-1-neg 65.3%

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

      4. log-rec 65.3%

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

      5. rem-exp-log 66.1%

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

      6. associate-/l/ 66.1%

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

      7. *-commutative 66.1%

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

   6. Simplified 66.1%

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

   7. Taylor expanded in b around 0 47.3%

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

      1. +-commutative 47.3%

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

      2. mul-1-neg 47.3%

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

      3. unsub-neg 47.3%

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

   9. Simplified 47.3%

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

   if 4.69999999999999989e-26 < b

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 86.9%

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

      1. div-exp 68.7%

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

      2. exp-to-pow 68.7%

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

      3. sub-neg 68.7%

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

      4. metadata-eval 68.7%

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

   5. Simplified 68.7%

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

   6. Taylor expanded in t around 0 75.4%

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

   7. Taylor expanded in b around 0 43.0%

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

   8. Taylor expanded in b around inf 43.0%

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

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 4.7 \cdot 10^{-26}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} - \frac{b}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 40.6% accurate, 19.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-174}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1e-174)
   (/ (- (/ x a) (/ (* x b) a)) y)
   (/ (* x (/ 1.0 (+ a (* a b)))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1e-174) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else {
		tmp = (x * (1.0 / (a + (a * b)))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1d-174)) then
        tmp = ((x / a) - ((x * b) / a)) / y
    else
        tmp = (x * (1.0d0 / (a + (a * b)))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1e-174) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else {
		tmp = (x * (1.0 / (a + (a * b)))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1e-174:
		tmp = ((x / a) - ((x * b) / a)) / y
	else:
		tmp = (x * (1.0 / (a + (a * b)))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1e-174)
		tmp = Float64(Float64(Float64(x / a) - Float64(Float64(x * b) / a)) / y);
	else
		tmp = Float64(Float64(x * Float64(1.0 / Float64(a + Float64(a * b)))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1e-174)
		tmp = ((x / a) - ((x * b) / a)) / y;
	else
		tmp = (x * (1.0 / (a + (a * b)))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1e-174], N[(N[(N[(x / a), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[(1.0 / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1e-174

   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. Add Preprocessing

   3. Taylor expanded in y around 0 91.7%

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

   4. Taylor expanded in t around 0 75.2%

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

      1. *-commutative 75.2%

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

      2. exp-diff 75.2%

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

      3. mul-1-neg 75.2%

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

      4. log-rec 75.2%

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

      5. rem-exp-log 75.6%

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

      6. associate-/l/ 75.6%

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

      7. *-commutative 75.6%

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

   6. Simplified 75.6%

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

   7. Taylor expanded in b around 0 45.7%

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

   if -1e-174 < b

   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. Add Preprocessing

   3. Taylor expanded in y around 0 82.2%

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

   4. Taylor expanded in t around 0 63.9%

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

      1. *-commutative 63.9%

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

      2. exp-diff 63.9%

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

      3. mul-1-neg 63.9%

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

      4. log-rec 63.9%

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

      5. rem-exp-log 64.6%

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

      6. associate-/l/ 64.6%

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

      7. *-commutative 64.6%

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

   6. Simplified 64.6%

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

   7. Taylor expanded in b around 0 48.6%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-174}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a + a \cdot b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 34.4% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.08 \cdot 10^{+61}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 1.08e+61) (/ (/ x a) y) (/ x (* a (+ y (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1.08e+61) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 1.08d+61) then
        tmp = (x / a) / y
    else
        tmp = x / (a * (y + (y * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1.08e+61) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 1.08e+61:
		tmp = (x / a) / y
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 1.08e+61)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 1.08e+61)
		tmp = (x / a) / y;
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 1.08e+61], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.08e61

   1. Initial program 99.5%

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

   3. Taylor expanded in y around 0 84.6%

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

   4. Taylor expanded in t around 0 66.5%

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

      1. *-commutative 66.5%

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

      2. exp-diff 66.5%

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

      3. mul-1-neg 66.5%

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

      4. log-rec 66.5%

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

      5. rem-exp-log 67.0%

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

      6. associate-/l/ 67.0%

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

      7. *-commutative 67.0%

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

   6. Simplified 67.0%

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

   7. Taylor expanded in b around 0 40.1%

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

   if 1.08e61 < a

   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. Step-by-step derivation

      1. associate-*l/ 90.4%

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

      2. *-commutative 90.4%

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

      3. +-commutative 90.4%

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

      4. associate--l+ 90.4%

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

      5. exp-sum 72.6%

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

      6. *-commutative 72.6%

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

      7. exp-to-pow 73.3%

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

      8. sub-neg 73.3%

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

      9. metadata-eval 73.3%

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

      10. exp-diff 64.4%

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

      11. *-commutative 64.4%

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

      12. exp-to-pow 64.4%

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

   3. Simplified 64.4%

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

   5. Taylor expanded in y around 0 68.8%

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

      1. times-frac 67.5%

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

      2. exp-to-pow 68.2%

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

      3. sub-neg 68.2%

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

      4. metadata-eval 68.2%

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

   7. Simplified 68.2%

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

   8. Taylor expanded in t around 0 77.0%

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

   9. Taylor expanded in b around 0 47.1%

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

       1. distribute-lft-out 48.2%

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

       2. *-commutative 48.2%

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

   11. Simplified 48.2%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.08 \cdot 10^{+61}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 35.3% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.9 \cdot 10^{-24}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 2.9e-24) (/ (/ x a) y) (/ x (* a (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.9e-24) {
		tmp = (x / a) / y;
	} 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 <= 2.9d-24) then
        tmp = (x / a) / y
    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 <= 2.9e-24) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 2.9e-24:
		tmp = (x / a) / y
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 2.9e-24)
		tmp = Float64(Float64(x / a) / y);
	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 <= 2.9e-24)
		tmp = (x / a) / y;
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 2.9e-24], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 2.8999999999999999e-24

   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. Add Preprocessing

   3. Taylor expanded in y around 0 85.4%

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

   4. Taylor expanded in t around 0 65.3%

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

      1. *-commutative 65.3%

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

      2. exp-diff 65.3%

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

      3. mul-1-neg 65.3%

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

      4. log-rec 65.3%

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

      5. rem-exp-log 66.1%

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

      6. associate-/l/ 66.1%

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

      7. *-commutative 66.1%

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

   6. Simplified 66.1%

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

   7. Taylor expanded in b around 0 43.0%

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

   if 2.8999999999999999e-24 < 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. Add Preprocessing

   3. Taylor expanded in y around 0 87.0%

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

      1. div-exp 68.6%

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

      2. exp-to-pow 68.6%

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

      3. sub-neg 68.6%

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

      4. metadata-eval 68.6%

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

   5. Simplified 68.6%

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

   6. Taylor expanded in t around 0 75.5%

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

   7. Taylor expanded in b around 0 42.6%

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

   8. Taylor expanded in b around inf 41.2%

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

      1. *-commutative 41.2%

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

   10. Simplified 41.2%

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

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 2.9 \cdot 10^{-24}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 35.9% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 6 \cdot 10^{-26}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 6e-26) (/ (/ x a) y) (/ (/ x (* a b)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 6e-26) {
		tmp = (x / a) / y;
	} else {
		tmp = (x / (a * b)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 6d-26) then
        tmp = (x / a) / y
    else
        tmp = (x / (a * b)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 6e-26) {
		tmp = (x / a) / y;
	} else {
		tmp = (x / (a * b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 6e-26:
		tmp = (x / a) / y
	else:
		tmp = (x / (a * b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 6e-26)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(Float64(x / Float64(a * b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 6e-26)
		tmp = (x / a) / y;
	else
		tmp = (x / (a * b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 6e-26], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 6.00000000000000023e-26

   1. Initial program 97.9%

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

   3. Taylor expanded in y around 0 85.5%

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

   4. Taylor expanded in t around 0 65.3%

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

      1. *-commutative 65.3%

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

      2. exp-diff 65.3%

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

      3. mul-1-neg 65.3%

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

      4. log-rec 65.3%

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

      5. rem-exp-log 66.1%

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

      6. associate-/l/ 66.1%

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

      7. *-commutative 66.1%

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

   6. Simplified 66.1%

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

   7. Taylor expanded in b around 0 42.8%

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

   if 6.00000000000000023e-26 < b

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 86.9%

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

      1. div-exp 68.7%

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

      2. exp-to-pow 68.7%

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

      3. sub-neg 68.7%

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

      4. metadata-eval 68.7%

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

   5. Simplified 68.7%

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

   6. Taylor expanded in t around 0 75.4%

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

   7. Taylor expanded in b around 0 43.0%

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

   8. Taylor expanded in b around inf 43.0%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 6 \cdot 10^{-26}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 32.2% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 10^{+78}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 1e+78) (/ (/ x a) y) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1e+78) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 1d+78) then
        tmp = (x / a) / y
    else
        tmp = x / (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1e+78) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 1e+78:
		tmp = (x / a) / y
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 1e+78)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 1e+78)
		tmp = (x / a) / y;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 1e+78], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.00000000000000001e78

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0 85.3%

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

   4. Taylor expanded in t around 0 68.2%

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

      1. *-commutative 68.2%

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

      2. exp-diff 68.2%

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

      3. mul-1-neg 68.2%

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

      4. log-rec 68.2%

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

      5. rem-exp-log 68.8%

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

      6. associate-/l/ 68.8%

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

      7. *-commutative 68.8%

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

   6. Simplified 68.8%

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

   7. Taylor expanded in b around 0 40.1%

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

   if 1.00000000000000001e78 < a

   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. Add Preprocessing

   3. Taylor expanded in y around 0 86.7%

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

   4. Taylor expanded in t around 0 68.6%

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

      1. *-commutative 68.6%

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

      2. exp-diff 68.6%

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

      3. mul-1-neg 68.6%

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

      4. log-rec 68.6%

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

      5. rem-exp-log 69.1%

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

      6. associate-/l/ 69.1%

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

      7. *-commutative 69.1%

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

   6. Simplified 69.1%

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

   7. Taylor expanded in b around 0 41.3%

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

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 10^{+78}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 30.5% 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 98.4%

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

3. Taylor expanded in y around 0 85.9%

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

4. Taylor expanded in t around 0 68.3%

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

   1. *-commutative 68.3%

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

   2. exp-diff 68.3%

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

   3. mul-1-neg 68.3%

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

   4. log-rec 68.3%

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

   5. rem-exp-log 68.9%

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

   6. associate-/l/ 68.9%

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

   7. *-commutative 68.9%

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

6. Simplified 68.9%

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

7. Taylor expanded in b around 0 33.6%

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

8. Final simplification 33.6%

   \[\leadsto \frac{x}{y \cdot a} \]
9. Add Preprocessing

Developer target: 72.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t - 1\right)}\\ t_2 := \frac{x \cdot \frac{t\_1}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{if}\;t < -0.8845848504127471:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 852031.2288374073:\\ \;\;\;\;\frac{\frac{x}{y} \cdot t\_1}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (- t 1.0)))
        (t_2 (/ (* x (/ t_1 y)) (- (+ b 1.0) (* y (log z))))))
   (if (< t -0.8845848504127471)
     t_2
     (if (< t 852031.2288374073)
       (/ (* (/ x y) t_1) (exp (- b (* (log z) y))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a ** (t - 1.0d0)
    t_2 = (x * (t_1 / y)) / ((b + 1.0d0) - (y * log(z)))
    if (t < (-0.8845848504127471d0)) then
        tmp = t_2
    else if (t < 852031.2288374073d0) then
        tmp = ((x / y) * t_1) / exp((b - (log(z) * y)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * Math.log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / Math.exp((b - (Math.log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, (t - 1.0))
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * math.log(z)))
	tmp = 0
	if t < -0.8845848504127471:
		tmp = t_2
	elif t < 852031.2288374073:
		tmp = ((x / y) * t_1) / math.exp((b - (math.log(z) * y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = a ^ Float64(t - 1.0)
	t_2 = Float64(Float64(x * Float64(t_1 / y)) / Float64(Float64(b + 1.0) - Float64(y * log(z))))
	tmp = 0.0
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = Float64(Float64(Float64(x / y) * t_1) / exp(Float64(b - Float64(log(z) * y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a ^ (t - 1.0);
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	tmp = 0.0;
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] / N[(N[(b + 1.0), $MachinePrecision] - N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -0.8845848504127471], t$95$2, If[Less[t, 852031.2288374073], N[(N[(N[(x / y), $MachinePrecision] * t$95$1), $MachinePrecision] / N[Exp[N[(b - N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024036 
(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))