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

Percentage Accurate: 98.4% → 98.4%

Time: 24.1s

Alternatives: 27

Speedup: 1.0×

• 47.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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. Final simplification 98.3%

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

Alternative 2: 92.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+125} \lor \neg \left(t \leq 3.6 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.2e+125) (not (<= t 3.6e-6)))
   (/ (* 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 <= -3.2e+125) || !(t <= 3.6e-6)) {
		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 <= (-3.2d+125)) .or. (.not. (t <= 3.6d-6))) 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 <= -3.2e+125) || !(t <= 3.6e-6)) {
		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 <= -3.2e+125) or not (t <= 3.6e-6):
		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 ((t <= -3.2e+125) || !(t <= 3.6e-6))
		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 <= -3.2e+125) || ~((t <= 3.6e-6)))
		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[t, -3.2e+125], N[Not[LessEqual[t, 3.6e-6]], $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 t < -3.19999999999999983e125 or 3.59999999999999984e-6 < 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 95.1%

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

   if -3.19999999999999983e125 < t < 3.59999999999999984e-6

   1. Initial program 97.2%

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

   3. Taylor expanded in t around 0 95.4%

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

      1. +-commutative 95.4%

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

      2. mul-1-neg 95.4%

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

      3. unsub-neg 95.4%

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

   5. Simplified 95.4%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+125} \lor \neg \left(t \leq 3.6 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}\\ t_2 := \frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -470000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-281}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-204}:\\ \;\;\;\;\frac{1}{\frac{y \cdot e^{b}}{\frac{x}{a}}}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (/ (pow a (+ t -1.0)) y) (exp b))))
        (t_2 (/ (/ (* x (pow z y)) a) y)))
   (if (<= y -470000000000.0)
     t_2
     (if (<= y 1.25e-281)
       t_1
       (if (<= y 5.5e-204)
         (/ 1.0 (/ (* y (exp b)) (/ x a)))
         (if (<= y 3.6e+68) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * ((pow(a, (t + -1.0)) / y) / exp(b));
	double t_2 = ((x * pow(z, y)) / a) / y;
	double tmp;
	if (y <= -470000000000.0) {
		tmp = t_2;
	} else if (y <= 1.25e-281) {
		tmp = t_1;
	} else if (y <= 5.5e-204) {
		tmp = 1.0 / ((y * exp(b)) / (x / a));
	} else if (y <= 3.6e+68) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (((a ** (t + (-1.0d0))) / y) / exp(b))
    t_2 = ((x * (z ** y)) / a) / y
    if (y <= (-470000000000.0d0)) then
        tmp = t_2
    else if (y <= 1.25d-281) then
        tmp = t_1
    else if (y <= 5.5d-204) then
        tmp = 1.0d0 / ((y * exp(b)) / (x / a))
    else if (y <= 3.6d+68) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * ((Math.pow(a, (t + -1.0)) / y) / Math.exp(b));
	double t_2 = ((x * Math.pow(z, y)) / a) / y;
	double tmp;
	if (y <= -470000000000.0) {
		tmp = t_2;
	} else if (y <= 1.25e-281) {
		tmp = t_1;
	} else if (y <= 5.5e-204) {
		tmp = 1.0 / ((y * Math.exp(b)) / (x / a));
	} else if (y <= 3.6e+68) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * ((math.pow(a, (t + -1.0)) / y) / math.exp(b))
	t_2 = ((x * math.pow(z, y)) / a) / y
	tmp = 0
	if y <= -470000000000.0:
		tmp = t_2
	elif y <= 1.25e-281:
		tmp = t_1
	elif y <= 5.5e-204:
		tmp = 1.0 / ((y * math.exp(b)) / (x / a))
	elif y <= 3.6e+68:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(Float64((a ^ Float64(t + -1.0)) / y) / exp(b)))
	t_2 = Float64(Float64(Float64(x * (z ^ y)) / a) / y)
	tmp = 0.0
	if (y <= -470000000000.0)
		tmp = t_2;
	elseif (y <= 1.25e-281)
		tmp = t_1;
	elseif (y <= 5.5e-204)
		tmp = Float64(1.0 / Float64(Float64(y * exp(b)) / Float64(x / a)));
	elseif (y <= 3.6e+68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (((a ^ (t + -1.0)) / y) / exp(b));
	t_2 = ((x * (z ^ y)) / a) / y;
	tmp = 0.0;
	if (y <= -470000000000.0)
		tmp = t_2;
	elseif (y <= 1.25e-281)
		tmp = t_1;
	elseif (y <= 5.5e-204)
		tmp = 1.0 / ((y * exp(b)) / (x / a));
	elseif (y <= 3.6e+68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -470000000000.0], t$95$2, If[LessEqual[y, 1.25e-281], t$95$1, If[LessEqual[y, 5.5e-204], N[(1.0 / N[(N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision] / N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+68], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.7e11 or 3.5999999999999999e68 < 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 95.0%

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

      1. exp-sum 73.0%

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

      2. *-commutative 73.0%

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

      3. exp-to-pow 73.0%

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

      4. exp-to-pow 73.0%

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

   5. Simplified 73.0%

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

   6. Taylor expanded in t around 0 81.6%

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

   if -4.7e11 < y < 1.2499999999999999e-281 or 5.4999999999999999e-204 < y < 3.5999999999999999e68

   1. Initial program 96.8%

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

      1. associate-/l* 98.9%

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

      2. exp-diff 82.8%

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

      3. associate-/l/ 82.8%

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

      4. exp-sum 81.1%

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

      5. associate-/l* 81.1%

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

      6. *-commutative 81.1%

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

      7. exp-to-pow 81.1%

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

      8. *-commutative 81.1%

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

      9. exp-to-pow 82.1%

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

      10. sub-neg 82.1%

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

      11. metadata-eval 82.1%

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

   3. Simplified 82.1%

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

   5. Taylor expanded in y around 0 83.9%

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

      1. associate-/r* 82.3%

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

      2. exp-to-pow 83.2%

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

      3. sub-neg 83.2%

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

      4. metadata-eval 83.2%

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

      5. metadata-eval 83.2%

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

      6. sub-neg 83.2%

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

   7. Simplified 83.2%

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

   if 1.2499999999999999e-281 < y < 5.4999999999999999e-204

   1. Initial program 97.6%

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

      1. associate-/l* 86.1%

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

      2. exp-diff 64.6%

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

      3. associate-/l/ 64.6%

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

      4. exp-sum 64.6%

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

      5. associate-/l* 64.6%

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

      6. *-commutative 64.6%

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

      7. exp-to-pow 64.6%

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

      8. *-commutative 64.6%

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

      9. exp-to-pow 65.4%

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

      10. sub-neg 65.4%

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

      11. metadata-eval 65.4%

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

   3. Simplified 65.4%

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

   5. Taylor expanded in y around 0 64.6%

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

      1. associate-/r* 50.3%

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

      2. exp-to-pow 51.2%

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

      3. sub-neg 51.2%

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

      4. metadata-eval 51.2%

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

      5. metadata-eval 51.2%

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

      6. sub-neg 51.2%

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

   7. Simplified 51.2%

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

   8. Taylor expanded in t around 0 73.0%

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

      1. associate-/r* 85.9%

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

      2. clear-num 86.2%

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

   10. Applied egg-rr 86.2%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -470000000000:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-281}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-204}:\\ \;\;\;\;\frac{1}{\frac{y \cdot e^{b}}{\frac{x}{a}}}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+42} \lor \neg \left(t \leq 1.15 \cdot 10^{-22}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x \cdot \frac{{z}^{y}}{a \cdot e^{b}}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.5e+42) (not (<= t 1.15e-22)))
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)
   (/ 1.0 (/ y (* x (/ (pow z y) (* a (exp b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.5e+42) || !(t <= 1.15e-22)) {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	} else {
		tmp = 1.0 / (y / (x * (pow(z, y) / (a * exp(b)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-3.5d+42)) .or. (.not. (t <= 1.15d-22))) then
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    else
        tmp = 1.0d0 / (y / (x * ((z ** y) / (a * exp(b)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.5e+42) || !(t <= 1.15e-22)) {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	} else {
		tmp = 1.0 / (y / (x * (Math.pow(z, y) / (a * Math.exp(b)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3.5e+42) or not (t <= 1.15e-22):
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	else:
		tmp = 1.0 / (y / (x * (math.pow(z, y) / (a * math.exp(b)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3.5e+42) || !(t <= 1.15e-22))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	else
		tmp = Float64(1.0 / Float64(y / Float64(x * Float64((z ^ y) / Float64(a * exp(b))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -3.5e+42) || ~((t <= 1.15e-22)))
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	else
		tmp = 1.0 / (y / (x * ((z ^ y) / (a * exp(b)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3.5e+42], N[Not[LessEqual[t, 1.15e-22]], $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[(1.0 / N[(y / N[(x * N[(N[Power[z, y], $MachinePrecision] / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.50000000000000023e42 or 1.1499999999999999e-22 < 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 93.1%

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

   if -3.50000000000000023e42 < t < 1.1499999999999999e-22

   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 t around 0 96.3%

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

      1. +-commutative 96.3%

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

      2. mul-1-neg 96.3%

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

      3. unsub-neg 96.3%

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

   5. Simplified 96.3%

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

      1. clear-num 96.3%

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

      2. *-commutative 96.3%

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

      3. associate--l- 96.3%

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

      4. exp-diff 88.5%

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

      5. *-commutative 88.5%

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

      6. pow-to-exp 88.5%

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

      7. prod-exp 88.5%

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

      8. add-exp-log 89.5%

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

   7. Applied egg-rr 89.5%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+42} \lor \neg \left(t \leq 1.15 \cdot 10^{-22}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x \cdot \frac{{z}^{y}}{a \cdot e^{b}}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+42} \lor \neg \left(t \leq 1.15 \cdot 10^{-22}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left({z}^{y} \cdot \frac{\frac{1}{a}}{y \cdot e^{b}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5e+42) (not (<= t 1.15e-22)))
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)
   (* x (* (pow z y) (/ (/ 1.0 a) (* y (exp b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5e+42) || !(t <= 1.15e-22)) {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	} else {
		tmp = x * (pow(z, y) * ((1.0 / a) / (y * exp(b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-5d+42)) .or. (.not. (t <= 1.15d-22))) then
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    else
        tmp = x * ((z ** y) * ((1.0d0 / a) / (y * exp(b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5e+42) || !(t <= 1.15e-22)) {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	} else {
		tmp = x * (Math.pow(z, y) * ((1.0 / a) / (y * Math.exp(b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -5e+42) or not (t <= 1.15e-22):
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	else:
		tmp = x * (math.pow(z, y) * ((1.0 / a) / (y * math.exp(b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -5e+42) || !(t <= 1.15e-22))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	else
		tmp = Float64(x * Float64((z ^ y) * Float64(Float64(1.0 / a) / Float64(y * exp(b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -5e+42) || ~((t <= 1.15e-22)))
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	else
		tmp = x * ((z ^ y) * ((1.0 / a) / (y * exp(b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -5e+42], N[Not[LessEqual[t, 1.15e-22]], $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[(x * N[(N[Power[z, y], $MachinePrecision] * N[(N[(1.0 / a), $MachinePrecision] / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.00000000000000007e42 or 1.1499999999999999e-22 < 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 93.1%

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

   if -5.00000000000000007e42 < t < 1.1499999999999999e-22

   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. Step-by-step derivation

      1. associate-/l* 97.7%

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

      2. exp-diff 89.2%

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

      3. associate-/l/ 89.2%

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

      4. exp-sum 87.1%

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

      5. associate-/l* 83.5%

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

      6. *-commutative 83.5%

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

      7. exp-to-pow 83.5%

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

      8. *-commutative 83.5%

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

      9. exp-to-pow 84.5%

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

      10. sub-neg 84.5%

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

      11. metadata-eval 84.5%

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

   3. Simplified 84.5%

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

   5. Taylor expanded in t around 0 87.3%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+42} \lor \neg \left(t \leq 1.15 \cdot 10^{-22}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left({z}^{y} \cdot \frac{\frac{1}{a}}{y \cdot e^{b}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{+34} \lor \neg \left(t \leq 3.6 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5.1e+34) (not (<= t 3.6e-23)))
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)
   (/ (* x (pow z y)) (* a (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5.1e+34) || !(t <= 3.6e-23)) {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	} else {
		tmp = (x * pow(z, y)) / (a * (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-5.1d+34)) .or. (.not. (t <= 3.6d-23))) then
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    else
        tmp = (x * (z ** y)) / (a * (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5.1e+34) || !(t <= 3.6e-23)) {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	} else {
		tmp = (x * Math.pow(z, y)) / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -5.1e+34) or not (t <= 3.6e-23):
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	else:
		tmp = (x * math.pow(z, y)) / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -5.1e+34) || !(t <= 3.6e-23))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * (z ^ y)) / Float64(a * Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -5.1e+34) || ~((t <= 3.6e-23)))
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	else
		tmp = (x * (z ^ y)) / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -5.1e+34], N[Not[LessEqual[t, 3.6e-23]], $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[Power[z, y], $MachinePrecision]), $MachinePrecision] / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.10000000000000036e34 or 3.5999999999999998e-23 < 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 92.3%

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

   if -5.10000000000000036e34 < t < 3.5999999999999998e-23

   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. Step-by-step derivation

      1. associate-/l* 97.7%

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

      2. exp-diff 89.1%

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

      3. associate-/l/ 89.1%

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

      4. exp-sum 87.7%

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

      5. associate-/l* 84.1%

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

      6. *-commutative 84.1%

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

      7. exp-to-pow 84.1%

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

      8. *-commutative 84.1%

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

      9. exp-to-pow 85.1%

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

      10. sub-neg 85.1%

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

      11. metadata-eval 85.1%

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

   3. Simplified 85.1%

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

   5. Taylor expanded in t around 0 87.3%

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

      1. *-commutative 87.3%

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

   7. Simplified 87.3%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{+34} \lor \neg \left(t \leq 3.6 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+39} \lor \neg \left(t \leq 110\right):\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.85e+39) (not (<= t 110.0)))
   (* x (/ (pow a (+ t -1.0)) y))
   (/ (* x (pow z y)) (* a (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.85e+39) || !(t <= 110.0)) {
		tmp = x * (pow(a, (t + -1.0)) / y);
	} else {
		tmp = (x * pow(z, y)) / (a * (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.85d+39)) .or. (.not. (t <= 110.0d0))) then
        tmp = x * ((a ** (t + (-1.0d0))) / y)
    else
        tmp = (x * (z ** y)) / (a * (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.85e+39) || !(t <= 110.0)) {
		tmp = x * (Math.pow(a, (t + -1.0)) / y);
	} else {
		tmp = (x * Math.pow(z, y)) / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.85e+39) or not (t <= 110.0):
		tmp = x * (math.pow(a, (t + -1.0)) / y)
	else:
		tmp = (x * math.pow(z, y)) / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.85e+39) || !(t <= 110.0))
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) / y));
	else
		tmp = Float64(Float64(x * (z ^ y)) / Float64(a * Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.85e+39) || ~((t <= 110.0)))
		tmp = x * ((a ^ (t + -1.0)) / y);
	else
		tmp = (x * (z ^ y)) / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.85e+39], N[Not[LessEqual[t, 110.0]], $MachinePrecision]], N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.85000000000000006e39 or 110 < t

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. exp-diff 72.7%

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

      3. associate-/l/ 72.7%

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

      4. exp-sum 54.5%

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

      5. associate-/l* 54.5%

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

      6. *-commutative 54.5%

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

      7. exp-to-pow 54.5%

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

      8. *-commutative 54.5%

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

      9. exp-to-pow 54.5%

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

      10. sub-neg 54.5%

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

      11. metadata-eval 54.5%

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

   3. Simplified 54.5%

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

   5. Taylor expanded in y around 0 67.4%

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

      1. associate-/r* 67.4%

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

      2. exp-to-pow 67.4%

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

      3. sub-neg 67.4%

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

      4. metadata-eval 67.4%

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

      5. metadata-eval 67.4%

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

      6. sub-neg 67.4%

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

   7. Simplified 67.4%

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

   8. Taylor expanded in b around 0 82.1%

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

   10. Simplified 82.1%

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

   if -1.85000000000000006e39 < t < 110

   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* 97.7%

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

      2. exp-diff 87.5%

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

      3. associate-/l/ 87.5%

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

      4. exp-sum 86.0%

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

      5. associate-/l* 82.6%

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

      6. *-commutative 82.6%

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

      7. exp-to-pow 82.6%

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

      8. *-commutative 82.6%

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

      9. exp-to-pow 83.6%

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

      10. sub-neg 83.6%

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

      11. metadata-eval 83.6%

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

   3. Simplified 83.6%

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

   5. Taylor expanded in t around 0 85.7%

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

      1. *-commutative 85.7%

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

   7. Simplified 85.7%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+39} \lor \neg \left(t \leq 110\right):\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+92} \lor \neg \left(y \leq 7.2 \cdot 10^{+32}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.5e+92) (not (<= y 7.2e+32)))
   (/ (/ (* 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 <= -4.5e+92) || !(y <= 7.2e+32)) {
		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 <= (-4.5d+92)) .or. (.not. (y <= 7.2d+32))) 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 <= -4.5e+92) || !(y <= 7.2e+32)) {
		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 <= -4.5e+92) or not (y <= 7.2e+32):
		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 <= -4.5e+92) || !(y <= 7.2e+32))
		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 <= -4.5e+92) || ~((y <= 7.2e+32)))
		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, -4.5e+92], N[Not[LessEqual[y, 7.2e+32]], $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 < -4.4999999999999999e92 or 7.1999999999999994e32 < 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 94.6%

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

      1. exp-sum 73.5%

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

      2. *-commutative 73.5%

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

      3. exp-to-pow 73.5%

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

      4. exp-to-pow 73.5%

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

   5. Simplified 73.5%

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

   6. Taylor expanded in t around 0 82.8%

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

   if -4.4999999999999999e92 < y < 7.1999999999999994e32

   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. Add Preprocessing

   3. Taylor expanded in y around 0 93.4%

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

      1. div-exp 80.5%

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

      2. exp-to-pow 81.3%

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

   5. Simplified 81.3%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+92} \lor \neg \left(y \leq 7.2 \cdot 10^{+32}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{if}\;b \leq -4 \cdot 10^{-35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.85 \cdot 10^{-270}:\\ \;\;\;\;\frac{x}{a \cdot \frac{y \cdot y - \left(y \cdot b\right) \cdot \left(y \cdot b\right)}{y - y \cdot b}}\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-175}:\\ \;\;\;\;\frac{x}{a \cdot \left(b \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;b \leq 5.1 \cdot 10^{-166}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* a (* y (exp b))))))
   (if (<= b -4e-35)
     t_1
     (if (<= b -1.85e-270)
       (/ x (* a (/ (- (* y y) (* (* y b) (* y b))) (- y (* y b)))))
       (if (<= b 1.8e-175)
         (/ x (* a (* b (+ y (/ y b)))))
         (if (<= b 5.1e-166) (/ x (* a (* y b))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * (y * exp(b)));
	double tmp;
	if (b <= -4e-35) {
		tmp = t_1;
	} else if (b <= -1.85e-270) {
		tmp = x / (a * (((y * y) - ((y * b) * (y * b))) / (y - (y * b))));
	} else if (b <= 1.8e-175) {
		tmp = x / (a * (b * (y + (y / b))));
	} else if (b <= 5.1e-166) {
		tmp = x / (a * (y * 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 * (y * exp(b)))
    if (b <= (-4d-35)) then
        tmp = t_1
    else if (b <= (-1.85d-270)) then
        tmp = x / (a * (((y * y) - ((y * b) * (y * b))) / (y - (y * b))))
    else if (b <= 1.8d-175) then
        tmp = x / (a * (b * (y + (y / b))))
    else if (b <= 5.1d-166) then
        tmp = x / (a * (y * 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 / (a * (y * Math.exp(b)));
	double tmp;
	if (b <= -4e-35) {
		tmp = t_1;
	} else if (b <= -1.85e-270) {
		tmp = x / (a * (((y * y) - ((y * b) * (y * b))) / (y - (y * b))));
	} else if (b <= 1.8e-175) {
		tmp = x / (a * (b * (y + (y / b))));
	} else if (b <= 5.1e-166) {
		tmp = x / (a * (y * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a * (y * math.exp(b)))
	tmp = 0
	if b <= -4e-35:
		tmp = t_1
	elif b <= -1.85e-270:
		tmp = x / (a * (((y * y) - ((y * b) * (y * b))) / (y - (y * b))))
	elif b <= 1.8e-175:
		tmp = x / (a * (b * (y + (y / b))))
	elif b <= 5.1e-166:
		tmp = x / (a * (y * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a * Float64(y * exp(b))))
	tmp = 0.0
	if (b <= -4e-35)
		tmp = t_1;
	elseif (b <= -1.85e-270)
		tmp = Float64(x / Float64(a * Float64(Float64(Float64(y * y) - Float64(Float64(y * b) * Float64(y * b))) / Float64(y - Float64(y * b)))));
	elseif (b <= 1.8e-175)
		tmp = Float64(x / Float64(a * Float64(b * Float64(y + Float64(y / b)))));
	elseif (b <= 5.1e-166)
		tmp = Float64(x / Float64(a * Float64(y * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a * (y * exp(b)));
	tmp = 0.0;
	if (b <= -4e-35)
		tmp = t_1;
	elseif (b <= -1.85e-270)
		tmp = x / (a * (((y * y) - ((y * b) * (y * b))) / (y - (y * b))));
	elseif (b <= 1.8e-175)
		tmp = x / (a * (b * (y + (y / b))));
	elseif (b <= 5.1e-166)
		tmp = x / (a * (y * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4e-35], t$95$1, If[LessEqual[b, -1.85e-270], N[(x / N[(a * N[(N[(N[(y * y), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.8e-175], N[(x / N[(a * N[(b * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.1e-166], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.00000000000000003e-35 or 5.1000000000000002e-166 < b

   1. Initial program 99.2%

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

      1. associate-/l* 99.2%

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

      2. exp-diff 72.8%

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

      3. associate-/l/ 72.8%

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

      4. exp-sum 65.2%

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

      5. associate-/l* 63.4%

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

      6. *-commutative 63.4%

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

      7. exp-to-pow 63.4%

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

      8. *-commutative 63.4%

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

      9. exp-to-pow 63.7%

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

      10. sub-neg 63.7%

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

      11. metadata-eval 63.7%

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

   3. Simplified 63.7%

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

   5. Taylor expanded in y around 0 65.8%

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

      1. associate-/r* 62.3%

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

      2. exp-to-pow 62.5%

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

      3. sub-neg 62.5%

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

      4. metadata-eval 62.5%

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

      5. metadata-eval 62.5%

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

      6. sub-neg 62.5%

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

   7. Simplified 62.5%

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

   8. Taylor expanded in t around 0 68.7%

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

   if -4.00000000000000003e-35 < b < -1.8500000000000001e-270

   1. Initial program 96.2%

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

      1. associate-/l* 96.5%

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

      2. exp-diff 96.5%

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

      3. associate-/l/ 96.5%

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

      4. exp-sum 82.9%

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

      5. associate-/l* 82.9%

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

      6. *-commutative 82.9%

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

      7. exp-to-pow 82.9%

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

      8. *-commutative 82.9%

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

      9. exp-to-pow 84.1%

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

      10. sub-neg 84.1%

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

      11. metadata-eval 84.1%

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

   3. Simplified 84.1%

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

   5. Taylor expanded in y around 0 70.2%

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

      1. associate-/r* 70.2%

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

      2. exp-to-pow 71.3%

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

      3. sub-neg 71.3%

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

      4. metadata-eval 71.3%

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

      5. metadata-eval 71.3%

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

      6. sub-neg 71.3%

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

   7. Simplified 71.3%

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

   8. Taylor expanded in t around 0 36.3%

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

   9. Taylor expanded in b around 0 34.1%

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

       1. distribute-lft-out 36.3%

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

   11. Simplified 36.3%

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

       1. flip-+ 55.8%

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

       2. *-commutative 55.8%

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

       3. *-commutative 55.8%

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

       4. *-commutative 55.8%

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

   13. Applied egg-rr 55.8%

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

   if -1.8500000000000001e-270 < b < 1.8e-175

   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. Step-by-step derivation

      1. associate-/l* 99.1%

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

      2. exp-diff 99.1%

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

      3. associate-/l/ 99.1%

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

      4. exp-sum 91.2%

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

      5. associate-/l* 86.0%

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

      6. *-commutative 86.0%

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

      7. exp-to-pow 86.0%

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

      8. *-commutative 86.0%

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

      9. exp-to-pow 86.8%

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

      10. sub-neg 86.8%

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

      11. metadata-eval 86.8%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in y around 0 63.3%

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

      1. associate-/r* 63.3%

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

      2. exp-to-pow 64.1%

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

      3. sub-neg 64.1%

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

      4. metadata-eval 64.1%

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

      5. metadata-eval 64.1%

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

      6. sub-neg 64.1%

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

   7. Simplified 64.1%

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

   8. Taylor expanded in t around 0 38.5%

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

   9. Taylor expanded in b around 0 38.5%

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

       1. distribute-lft-out 38.5%

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

   11. Simplified 38.5%

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

   12. Taylor expanded in b around inf 53.5%

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

   if 1.8e-175 < b < 5.1000000000000002e-166

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. exp-diff 100.0%

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

      3. associate-/l/ 100.0%

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

      4. exp-sum 100.0%

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

      5. associate-/l* 100.0%

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

      6. *-commutative 100.0%

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

      7. exp-to-pow 100.0%

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

      8. *-commutative 100.0%

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

      9. exp-to-pow 100.0%

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

      10. sub-neg 100.0%

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

      11. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 39.8%

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

      1. associate-/r* 39.8%

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

      2. exp-to-pow 39.8%

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

      3. sub-neg 39.8%

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

      4. metadata-eval 39.8%

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

      5. metadata-eval 39.8%

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

      6. sub-neg 39.8%

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

   7. Simplified 39.8%

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

   8. Taylor expanded in t around 0 8.3%

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

   9. Taylor expanded in b around 0 8.3%

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

       1. distribute-lft-out 8.3%

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

   11. Simplified 8.3%

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

   12. Taylor expanded in b around inf 100.0%

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

       1. *-commutative 100.0%

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

   14. Simplified 100.0%

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

Alternative 10: 73.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{if}\;t \leq -1.02 \cdot 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-6}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (pow a (+ t -1.0)) y))))
   (if (<= t -1.02e+118)
     t_1
     (if (<= t 1.7e-6)
       (/ (/ (* x (pow z y)) a) y)
       (if (<= t 8.5e+44) (/ x (* a (* 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 <= -1.02e+118) {
		tmp = t_1;
	} else if (t <= 1.7e-6) {
		tmp = ((x * pow(z, y)) / a) / y;
	} else if (t <= 8.5e+44) {
		tmp = x / (a * (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 <= (-1.02d+118)) then
        tmp = t_1
    else if (t <= 1.7d-6) then
        tmp = ((x * (z ** y)) / a) / y
    else if (t <= 8.5d+44) then
        tmp = x / (a * (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 <= -1.02e+118) {
		tmp = t_1;
	} else if (t <= 1.7e-6) {
		tmp = ((x * Math.pow(z, y)) / a) / y;
	} else if (t <= 8.5e+44) {
		tmp = x / (a * (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 <= -1.02e+118:
		tmp = t_1
	elif t <= 1.7e-6:
		tmp = ((x * math.pow(z, y)) / a) / y
	elif t <= 8.5e+44:
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64((a ^ Float64(t + -1.0)) / y))
	tmp = 0.0
	if (t <= -1.02e+118)
		tmp = t_1;
	elseif (t <= 1.7e-6)
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	elseif (t <= 8.5e+44)
		tmp = Float64(x / Float64(a * 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 <= -1.02e+118)
		tmp = t_1;
	elseif (t <= 1.7e-6)
		tmp = ((x * (z ^ y)) / a) / y;
	elseif (t <= 8.5e+44)
		tmp = x / (a * (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[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.02e+118], t$95$1, If[LessEqual[t, 1.7e-6], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 8.5e+44], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.0199999999999999e118 or 8.5e44 < t

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. exp-diff 76.4%

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

      3. associate-/l/ 76.4%

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

      4. exp-sum 56.2%

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

      5. associate-/l* 56.2%

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

      6. *-commutative 56.2%

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

      7. exp-to-pow 56.2%

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

      8. *-commutative 56.2%

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

      9. exp-to-pow 56.2%

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

      10. sub-neg 56.2%

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

      11. metadata-eval 56.2%

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

   3. Simplified 56.2%

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

   5. Taylor expanded in y around 0 70.9%

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

      1. associate-/r* 70.9%

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

      2. exp-to-pow 70.9%

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

      3. sub-neg 70.9%

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

      4. metadata-eval 70.9%

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

      5. metadata-eval 70.9%

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

      6. sub-neg 70.9%

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

   7. Simplified 70.9%

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

   8. Taylor expanded in b around 0 88.9%

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

   10. Simplified 88.9%

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

   if -1.0199999999999999e118 < t < 1.70000000000000003e-6

   1. Initial program 97.2%

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

   3. Taylor expanded in b around 0 76.4%

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

      1. exp-sum 73.2%

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

      2. *-commutative 73.2%

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

      3. exp-to-pow 73.2%

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

      4. exp-to-pow 73.9%

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

   5. Simplified 73.9%

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

   6. Taylor expanded in t around 0 75.4%

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

   if 1.70000000000000003e-6 < t < 8.5e44

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. exp-diff 58.3%

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

      3. associate-/l/ 58.3%

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

      4. exp-sum 50.0%

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

      5. associate-/l* 50.0%

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

      6. *-commutative 50.0%

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

      7. exp-to-pow 50.0%

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

      8. *-commutative 50.0%

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

      9. exp-to-pow 50.0%

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

      10. sub-neg 50.0%

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

      11. metadata-eval 50.0%

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

   3. Simplified 50.0%

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

   5. Taylor expanded in y around 0 66.7%

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

      1. associate-/r* 66.7%

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

      2. exp-to-pow 66.7%

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

      3. sub-neg 66.7%

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

      4. metadata-eval 66.7%

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

      5. metadata-eval 66.7%

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

      6. sub-neg 66.7%

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

   7. Simplified 66.7%

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

   8. Taylor expanded in t around 0 83.7%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-6}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.0% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+35} \lor \neg \left(b \leq 2.2 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.2e+35) (not (<= b 2.2e-45)))
   (/ x (* a (* y (exp b))))
   (* (/ x a) (/ (pow z y) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.2e+35) || !(b <= 2.2e-45)) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = (x / a) * (pow(z, y) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.2d+35)) .or. (.not. (b <= 2.2d-45))) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = (x / a) * ((z ** y) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.2e+35) || !(b <= 2.2e-45)) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = (x / a) * (Math.pow(z, y) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.2e+35) or not (b <= 2.2e-45):
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = (x / a) * (math.pow(z, y) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.2e+35) || !(b <= 2.2e-45))
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(Float64(x / a) * Float64((z ^ y) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.2e+35) || ~((b <= 2.2e-45)))
		tmp = x / (a * (y * exp(b)));
	else
		tmp = (x / a) * ((z ^ y) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.2e+35], N[Not[LessEqual[b, 2.2e-45]], $MachinePrecision]], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.20000000000000007e35 or 2.19999999999999993e-45 < b

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

      2. exp-diff 65.8%

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

      3. associate-/l/ 65.8%

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

      4. exp-sum 61.0%

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

      5. associate-/l* 61.0%

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

      6. *-commutative 61.0%

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

      7. exp-to-pow 61.0%

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

      8. *-commutative 61.0%

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

      9. exp-to-pow 61.1%

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

      10. sub-neg 61.1%

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

      11. metadata-eval 61.1%

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

   3. Simplified 61.1%

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

   5. Taylor expanded in y around 0 70.6%

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

      1. associate-/r* 65.9%

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

      2. exp-to-pow 66.0%

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

      3. sub-neg 66.0%

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

      4. metadata-eval 66.0%

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

      5. metadata-eval 66.0%

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

      6. sub-neg 66.0%

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

   7. Simplified 66.0%

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

   8. Taylor expanded in t around 0 80.5%

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

   if -1.20000000000000007e35 < b < 2.19999999999999993e-45

   1. Initial program 96.8%

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

   3. Taylor expanded in b around 0 96.1%

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

      1. exp-sum 83.7%

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

      2. *-commutative 83.7%

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

      3. exp-to-pow 83.7%

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

      4. exp-to-pow 84.6%

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

   5. Simplified 84.6%

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

   6. Taylor expanded in t around 0 75.3%

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

      1. associate-/l/ 69.9%

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

      2. *-commutative 69.9%

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

      3. times-frac 71.4%

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

   8. Applied egg-rr 71.4%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+35} \lor \neg \left(b \leq 2.2 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 75.0% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+46} \lor \neg \left(t \leq 1.05 \cdot 10^{+44}\right):\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.1e+46) (not (<= t 1.05e+44)))
   (* x (/ (pow a (+ t -1.0)) y))
   (/ x (* a (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.1e+46) || !(t <= 1.05e+44)) {
		tmp = x * (pow(a, (t + -1.0)) / 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 ((t <= (-1.1d+46)) .or. (.not. (t <= 1.05d+44))) then
        tmp = x * ((a ** (t + (-1.0d0))) / 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 ((t <= -1.1e+46) || !(t <= 1.05e+44)) {
		tmp = x * (Math.pow(a, (t + -1.0)) / y);
	} else {
		tmp = x / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.1e+46) or not (t <= 1.05e+44):
		tmp = x * (math.pow(a, (t + -1.0)) / y)
	else:
		tmp = x / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.1e+46) || !(t <= 1.05e+44))
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) / 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 ((t <= -1.1e+46) || ~((t <= 1.05e+44)))
		tmp = x * ((a ^ (t + -1.0)) / y);
	else
		tmp = x / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.1e+46], N[Not[LessEqual[t, 1.05e+44]], $MachinePrecision]], N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.1e46 or 1.04999999999999993e44 < t

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. exp-diff 74.0%

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

      3. associate-/l/ 74.0%

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

      4. exp-sum 56.0%

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

      5. associate-/l* 56.0%

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

      6. *-commutative 56.0%

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

      7. exp-to-pow 56.0%

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

      8. *-commutative 56.0%

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

      9. exp-to-pow 56.0%

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

      10. sub-neg 56.0%

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

      11. metadata-eval 56.0%

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

   3. Simplified 56.0%

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

   5. Taylor expanded in y around 0 69.1%

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

      1. associate-/r* 69.1%

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

      2. exp-to-pow 69.1%

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

      3. sub-neg 69.1%

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

      4. metadata-eval 69.1%

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

      5. metadata-eval 69.1%

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

      6. sub-neg 69.1%

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

   7. Simplified 69.1%

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

   8. Taylor expanded in b around 0 85.2%

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

   10. Simplified 85.2%

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

   if -1.1e46 < t < 1.04999999999999993e44

   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. Step-by-step derivation

      1. associate-/l* 97.9%

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

      2. exp-diff 85.7%

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

      3. associate-/l/ 85.7%

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

      4. exp-sum 83.1%

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

      5. associate-/l* 79.9%

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

      6. *-commutative 79.9%

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

      7. exp-to-pow 79.9%

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

      8. *-commutative 79.9%

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

      9. exp-to-pow 80.8%

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

      10. sub-neg 80.8%

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

      11. metadata-eval 80.8%

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

   3. Simplified 80.8%

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

   5. Taylor expanded in y around 0 63.8%

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

      1. associate-/r* 60.0%

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

      2. exp-to-pow 60.7%

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

      3. sub-neg 60.7%

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

      4. metadata-eval 60.7%

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

      5. metadata-eval 60.7%

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

      6. sub-neg 60.7%

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

   7. Simplified 60.7%

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

   8. Taylor expanded in t around 0 67.8%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+46} \lor \neg \left(t \leq 1.05 \cdot 10^{+44}\right):\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.2% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot a}\\ t_2 := a \cdot \left(y \cdot b\right)\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{+50}:\\ \;\;\;\;t\_1 + b \cdot \left(b \cdot \left(t\_1 - \frac{x \cdot b}{y \cdot a}\right) - t\_1\right)\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-276}:\\ \;\;\;\;\frac{x}{a \cdot \frac{y \cdot y - \left(y \cdot b\right) \cdot \left(y \cdot b\right)}{y - y \cdot b}}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-173}:\\ \;\;\;\;\frac{x}{a \cdot \left(b \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-166}:\\ \;\;\;\;\frac{x}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a + b \cdot \left(y \cdot a + b \cdot \left(0.16666666666666666 \cdot t\_2 + \left(y \cdot a\right) \cdot 0.5\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* y a))) (t_2 (* a (* y b))))
   (if (<= b -1.25e+50)
     (+ t_1 (* b (- (* b (- t_1 (/ (* x b) (* y a)))) t_1)))
     (if (<= b -3.8e-276)
       (/ x (* a (/ (- (* y y) (* (* y b) (* y b))) (- y (* y b)))))
       (if (<= b 4e-173)
         (/ x (* a (* b (+ y (/ y b)))))
         (if (<= b 6e-166)
           (/ x t_2)
           (/
            x
            (+
             (* y a)
             (*
              b
              (+
               (* y a)
               (* b (+ (* 0.16666666666666666 t_2) (* (* y a) 0.5)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * a);
	double t_2 = a * (y * b);
	double tmp;
	if (b <= -1.25e+50) {
		tmp = t_1 + (b * ((b * (t_1 - ((x * b) / (y * a)))) - t_1));
	} else if (b <= -3.8e-276) {
		tmp = x / (a * (((y * y) - ((y * b) * (y * b))) / (y - (y * b))));
	} else if (b <= 4e-173) {
		tmp = x / (a * (b * (y + (y / b))));
	} else if (b <= 6e-166) {
		tmp = x / t_2;
	} else {
		tmp = x / ((y * a) + (b * ((y * a) + (b * ((0.16666666666666666 * t_2) + ((y * a) * 0.5))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (y * a)
    t_2 = a * (y * b)
    if (b <= (-1.25d+50)) then
        tmp = t_1 + (b * ((b * (t_1 - ((x * b) / (y * a)))) - t_1))
    else if (b <= (-3.8d-276)) then
        tmp = x / (a * (((y * y) - ((y * b) * (y * b))) / (y - (y * b))))
    else if (b <= 4d-173) then
        tmp = x / (a * (b * (y + (y / b))))
    else if (b <= 6d-166) then
        tmp = x / t_2
    else
        tmp = x / ((y * a) + (b * ((y * a) + (b * ((0.16666666666666666d0 * t_2) + ((y * a) * 0.5d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * a);
	double t_2 = a * (y * b);
	double tmp;
	if (b <= -1.25e+50) {
		tmp = t_1 + (b * ((b * (t_1 - ((x * b) / (y * a)))) - t_1));
	} else if (b <= -3.8e-276) {
		tmp = x / (a * (((y * y) - ((y * b) * (y * b))) / (y - (y * b))));
	} else if (b <= 4e-173) {
		tmp = x / (a * (b * (y + (y / b))));
	} else if (b <= 6e-166) {
		tmp = x / t_2;
	} else {
		tmp = x / ((y * a) + (b * ((y * a) + (b * ((0.16666666666666666 * t_2) + ((y * a) * 0.5))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y * a)
	t_2 = a * (y * b)
	tmp = 0
	if b <= -1.25e+50:
		tmp = t_1 + (b * ((b * (t_1 - ((x * b) / (y * a)))) - t_1))
	elif b <= -3.8e-276:
		tmp = x / (a * (((y * y) - ((y * b) * (y * b))) / (y - (y * b))))
	elif b <= 4e-173:
		tmp = x / (a * (b * (y + (y / b))))
	elif b <= 6e-166:
		tmp = x / t_2
	else:
		tmp = x / ((y * a) + (b * ((y * a) + (b * ((0.16666666666666666 * t_2) + ((y * a) * 0.5))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y * a))
	t_2 = Float64(a * Float64(y * b))
	tmp = 0.0
	if (b <= -1.25e+50)
		tmp = Float64(t_1 + Float64(b * Float64(Float64(b * Float64(t_1 - Float64(Float64(x * b) / Float64(y * a)))) - t_1)));
	elseif (b <= -3.8e-276)
		tmp = Float64(x / Float64(a * Float64(Float64(Float64(y * y) - Float64(Float64(y * b) * Float64(y * b))) / Float64(y - Float64(y * b)))));
	elseif (b <= 4e-173)
		tmp = Float64(x / Float64(a * Float64(b * Float64(y + Float64(y / b)))));
	elseif (b <= 6e-166)
		tmp = Float64(x / t_2);
	else
		tmp = Float64(x / Float64(Float64(y * a) + Float64(b * Float64(Float64(y * a) + Float64(b * Float64(Float64(0.16666666666666666 * t_2) + Float64(Float64(y * a) * 0.5)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y * a);
	t_2 = a * (y * b);
	tmp = 0.0;
	if (b <= -1.25e+50)
		tmp = t_1 + (b * ((b * (t_1 - ((x * b) / (y * a)))) - t_1));
	elseif (b <= -3.8e-276)
		tmp = x / (a * (((y * y) - ((y * b) * (y * b))) / (y - (y * b))));
	elseif (b <= 4e-173)
		tmp = x / (a * (b * (y + (y / b))));
	elseif (b <= 6e-166)
		tmp = x / t_2;
	else
		tmp = x / ((y * a) + (b * ((y * a) + (b * ((0.16666666666666666 * t_2) + ((y * a) * 0.5))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.25e+50], N[(t$95$1 + N[(b * N[(N[(b * N[(t$95$1 - N[(N[(x * b), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.8e-276], N[(x / N[(a * N[(N[(N[(y * y), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4e-173], N[(x / N[(a * N[(b * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6e-166], N[(x / t$95$2), $MachinePrecision], N[(x / N[(N[(y * a), $MachinePrecision] + N[(b * N[(N[(y * a), $MachinePrecision] + N[(b * N[(N[(0.16666666666666666 * t$95$2), $MachinePrecision] + N[(N[(y * a), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.25e50

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. exp-diff 64.0%

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

      3. associate-/l/ 64.0%

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

      4. exp-sum 64.0%

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

      5. associate-/l* 64.0%

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

      6. *-commutative 64.0%

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

      7. exp-to-pow 64.0%

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

      8. *-commutative 64.0%

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

      9. exp-to-pow 64.0%

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

      10. sub-neg 64.0%

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

      11. metadata-eval 64.0%

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

   3. Simplified 64.0%

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

   5. Taylor expanded in y around 0 72.1%

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

      1. associate-/r* 68.1%

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

      2. exp-to-pow 68.1%

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

      3. sub-neg 68.1%

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

      4. metadata-eval 68.1%

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

      5. metadata-eval 68.1%

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

      6. sub-neg 68.1%

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

   7. Simplified 68.1%

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

   8. Taylor expanded in t around 0 86.2%

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

   9. Taylor expanded in b around 0 8.9%

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

       1. distribute-lft-out 9.1%

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

   11. Simplified 9.1%

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

   12. Taylor expanded in b around 0 59.3%

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

   if -1.25e50 < b < -3.8e-276

   1. Initial program 95.5%

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

      1. associate-/l* 97.2%

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

      2. exp-diff 93.8%

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

      3. associate-/l/ 93.8%

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

      4. exp-sum 82.0%

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

      5. associate-/l* 82.0%

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

      6. *-commutative 82.0%

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

      7. exp-to-pow 82.0%

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

      8. *-commutative 82.0%

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

      9. exp-to-pow 83.0%

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

      10. sub-neg 83.0%

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

      11. metadata-eval 83.0%

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

   3. Simplified 83.0%

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

   5. Taylor expanded in y around 0 70.9%

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

      1. associate-/r* 70.9%

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

      2. exp-to-pow 71.9%

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

      3. sub-neg 71.9%

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

      4. metadata-eval 71.9%

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

      5. metadata-eval 71.9%

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

      6. sub-neg 71.9%

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

   7. Simplified 71.9%

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

   8. Taylor expanded in t around 0 40.9%

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

   9. Taylor expanded in b around 0 30.9%

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

       1. distribute-lft-out 32.6%

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

   11. Simplified 32.6%

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

       1. flip-+ 50.3%

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

       2. *-commutative 50.3%

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

       3. *-commutative 50.3%

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

       4. *-commutative 50.3%

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

   13. Applied egg-rr 50.3%

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

   if -3.8e-276 < b < 4.0000000000000002e-173

   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. Step-by-step derivation

      1. associate-/l* 99.1%

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

      2. exp-diff 99.1%

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

      3. associate-/l/ 99.1%

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

      4. exp-sum 91.2%

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

      5. associate-/l* 86.0%

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

      6. *-commutative 86.0%

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

      7. exp-to-pow 86.0%

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

      8. *-commutative 86.0%

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

      9. exp-to-pow 86.8%

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

      10. sub-neg 86.8%

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

      11. metadata-eval 86.8%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in y around 0 63.3%

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

      1. associate-/r* 63.3%

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

      2. exp-to-pow 64.1%

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

      3. sub-neg 64.1%

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

      4. metadata-eval 64.1%

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

      5. metadata-eval 64.1%

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

      6. sub-neg 64.1%

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

   7. Simplified 64.1%

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

   8. Taylor expanded in t around 0 38.5%

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

   9. Taylor expanded in b around 0 38.5%

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

       1. distribute-lft-out 38.5%

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

   11. Simplified 38.5%

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

   12. Taylor expanded in b around inf 53.5%

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

   if 4.0000000000000002e-173 < b < 6.0000000000000005e-166

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. exp-diff 100.0%

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

      3. associate-/l/ 100.0%

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

      4. exp-sum 100.0%

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

      5. associate-/l* 100.0%

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

      6. *-commutative 100.0%

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

      7. exp-to-pow 100.0%

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

      8. *-commutative 100.0%

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

      9. exp-to-pow 100.0%

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

      10. sub-neg 100.0%

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

      11. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 39.8%

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

      1. associate-/r* 39.8%

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

      2. exp-to-pow 39.8%

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

      3. sub-neg 39.8%

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

      4. metadata-eval 39.8%

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

      5. metadata-eval 39.8%

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

      6. sub-neg 39.8%

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

   7. Simplified 39.8%

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

   8. Taylor expanded in t around 0 8.3%

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

   9. Taylor expanded in b around 0 8.3%

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

       1. distribute-lft-out 8.3%

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

   11. Simplified 8.3%

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

   12. Taylor expanded in b around inf 100.0%

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

       1. *-commutative 100.0%

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

   14. Simplified 100.0%

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

   if 6.0000000000000005e-166 < b

   1. Initial program 99.6%

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

      1. associate-/l* 98.8%

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

      2. exp-diff 75.2%

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

      3. associate-/l/ 75.2%

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

      4. exp-sum 63.8%

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

      5. associate-/l* 60.9%

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

      6. *-commutative 60.9%

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

      7. exp-to-pow 60.9%

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

      8. *-commutative 60.9%

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

      9. exp-to-pow 61.3%

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

      10. sub-neg 61.3%

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

      11. metadata-eval 61.3%

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

   3. Simplified 61.3%

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

   5. Taylor expanded in y around 0 61.8%

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

      1. associate-/r* 58.0%

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

      2. exp-to-pow 58.3%

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

      3. sub-neg 58.3%

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

      4. metadata-eval 58.3%

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

      5. metadata-eval 58.3%

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

      6. sub-neg 58.3%

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

   7. Simplified 58.3%

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

   8. Taylor expanded in t around 0 62.5%

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

      1. associate-*r* 54.9%

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

      2. *-commutative 54.9%

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

   10. Simplified 54.9%

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

   11. Taylor expanded in b around 0 46.2%

       \[\leadsto \frac{x}{\color{blue}{a \cdot y + b \cdot \left(a \cdot y + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot \left(b \cdot y\right)\right) + 0.5 \cdot \left(a \cdot y\right)\right)\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+50}:\\ \;\;\;\;\frac{x}{y \cdot a} + b \cdot \left(b \cdot \left(\frac{x}{y \cdot a} - \frac{x \cdot b}{y \cdot a}\right) - \frac{x}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-276}:\\ \;\;\;\;\frac{x}{a \cdot \frac{y \cdot y - \left(y \cdot b\right) \cdot \left(y \cdot b\right)}{y - y \cdot b}}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-173}:\\ \;\;\;\;\frac{x}{a \cdot \left(b \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-166}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a + b \cdot \left(y \cdot a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot \left(y \cdot b\right)\right) + \left(y \cdot a\right) \cdot 0.5\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 45.9% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y \cdot b\right)\\ \mathbf{if}\;b \leq -1.42 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(\frac{1}{y \cdot a} - \frac{b}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-275}:\\ \;\;\;\;\frac{x}{a \cdot \frac{y \cdot y - \left(y \cdot b\right) \cdot \left(y \cdot b\right)}{y - y \cdot b}}\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-174}:\\ \;\;\;\;\frac{x}{a \cdot \left(b \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-166}:\\ \;\;\;\;\frac{x}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a + b \cdot \left(y \cdot a + b \cdot \left(0.16666666666666666 \cdot t\_1 + \left(y \cdot a\right) \cdot 0.5\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* y b))))
   (if (<= b -1.42e+48)
     (* x (- (/ 1.0 (* y a)) (/ b (* y a))))
     (if (<= b -2.4e-275)
       (/ x (* a (/ (- (* y y) (* (* y b) (* y b))) (- y (* y b)))))
       (if (<= b 2.8e-174)
         (/ x (* a (* b (+ y (/ y b)))))
         (if (<= b 6.5e-166)
           (/ x t_1)
           (/
            x
            (+
             (* y a)
             (*
              b
              (+
               (* y a)
               (* b (+ (* 0.16666666666666666 t_1) (* (* y a) 0.5)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y * b);
	double tmp;
	if (b <= -1.42e+48) {
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)));
	} else if (b <= -2.4e-275) {
		tmp = x / (a * (((y * y) - ((y * b) * (y * b))) / (y - (y * b))));
	} else if (b <= 2.8e-174) {
		tmp = x / (a * (b * (y + (y / b))));
	} else if (b <= 6.5e-166) {
		tmp = x / t_1;
	} else {
		tmp = x / ((y * a) + (b * ((y * a) + (b * ((0.16666666666666666 * t_1) + ((y * a) * 0.5))))));
	}
	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 = a * (y * b)
    if (b <= (-1.42d+48)) then
        tmp = x * ((1.0d0 / (y * a)) - (b / (y * a)))
    else if (b <= (-2.4d-275)) then
        tmp = x / (a * (((y * y) - ((y * b) * (y * b))) / (y - (y * b))))
    else if (b <= 2.8d-174) then
        tmp = x / (a * (b * (y + (y / b))))
    else if (b <= 6.5d-166) then
        tmp = x / t_1
    else
        tmp = x / ((y * a) + (b * ((y * a) + (b * ((0.16666666666666666d0 * t_1) + ((y * a) * 0.5d0))))))
    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 = a * (y * b);
	double tmp;
	if (b <= -1.42e+48) {
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)));
	} else if (b <= -2.4e-275) {
		tmp = x / (a * (((y * y) - ((y * b) * (y * b))) / (y - (y * b))));
	} else if (b <= 2.8e-174) {
		tmp = x / (a * (b * (y + (y / b))));
	} else if (b <= 6.5e-166) {
		tmp = x / t_1;
	} else {
		tmp = x / ((y * a) + (b * ((y * a) + (b * ((0.16666666666666666 * t_1) + ((y * a) * 0.5))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (y * b)
	tmp = 0
	if b <= -1.42e+48:
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)))
	elif b <= -2.4e-275:
		tmp = x / (a * (((y * y) - ((y * b) * (y * b))) / (y - (y * b))))
	elif b <= 2.8e-174:
		tmp = x / (a * (b * (y + (y / b))))
	elif b <= 6.5e-166:
		tmp = x / t_1
	else:
		tmp = x / ((y * a) + (b * ((y * a) + (b * ((0.16666666666666666 * t_1) + ((y * a) * 0.5))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y * b))
	tmp = 0.0
	if (b <= -1.42e+48)
		tmp = Float64(x * Float64(Float64(1.0 / Float64(y * a)) - Float64(b / Float64(y * a))));
	elseif (b <= -2.4e-275)
		tmp = Float64(x / Float64(a * Float64(Float64(Float64(y * y) - Float64(Float64(y * b) * Float64(y * b))) / Float64(y - Float64(y * b)))));
	elseif (b <= 2.8e-174)
		tmp = Float64(x / Float64(a * Float64(b * Float64(y + Float64(y / b)))));
	elseif (b <= 6.5e-166)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(x / Float64(Float64(y * a) + Float64(b * Float64(Float64(y * a) + Float64(b * Float64(Float64(0.16666666666666666 * t_1) + Float64(Float64(y * a) * 0.5)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (y * b);
	tmp = 0.0;
	if (b <= -1.42e+48)
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)));
	elseif (b <= -2.4e-275)
		tmp = x / (a * (((y * y) - ((y * b) * (y * b))) / (y - (y * b))));
	elseif (b <= 2.8e-174)
		tmp = x / (a * (b * (y + (y / b))));
	elseif (b <= 6.5e-166)
		tmp = x / t_1;
	else
		tmp = x / ((y * a) + (b * ((y * a) + (b * ((0.16666666666666666 * t_1) + ((y * a) * 0.5))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.42e+48], N[(x * N[(N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision] - N[(b / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.4e-275], N[(x / N[(a * N[(N[(N[(y * y), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.8e-174], N[(x / N[(a * N[(b * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.5e-166], N[(x / t$95$1), $MachinePrecision], N[(x / N[(N[(y * a), $MachinePrecision] + N[(b * N[(N[(y * a), $MachinePrecision] + N[(b * N[(N[(0.16666666666666666 * t$95$1), $MachinePrecision] + N[(N[(y * a), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.42e48

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. exp-diff 64.0%

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

      3. associate-/l/ 64.0%

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

      4. exp-sum 64.0%

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

      5. associate-/l* 64.0%

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

      6. *-commutative 64.0%

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

      7. exp-to-pow 64.0%

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

      8. *-commutative 64.0%

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

      9. exp-to-pow 64.0%

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

      10. sub-neg 64.0%

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

      11. metadata-eval 64.0%

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

   3. Simplified 64.0%

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

   5. Taylor expanded in y around 0 72.1%

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

      1. associate-/r* 68.1%

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

      2. exp-to-pow 68.1%

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

      3. sub-neg 68.1%

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

      4. metadata-eval 68.1%

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

      5. metadata-eval 68.1%

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

      6. sub-neg 68.1%

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

   7. Simplified 68.1%

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

   8. Taylor expanded in t around 0 86.2%

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

   9. Taylor expanded in b around 0 38.0%

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

   10. Taylor expanded in x around 0 51.3%

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

   if -1.42e48 < b < -2.39999999999999991e-275

   1. Initial program 95.5%

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

      1. associate-/l* 97.2%

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

      2. exp-diff 93.8%

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

      3. associate-/l/ 93.8%

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

      4. exp-sum 82.0%

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

      5. associate-/l* 82.0%

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

      6. *-commutative 82.0%

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

      7. exp-to-pow 82.0%

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

      8. *-commutative 82.0%

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

      9. exp-to-pow 83.0%

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

      10. sub-neg 83.0%

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

      11. metadata-eval 83.0%

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

   3. Simplified 83.0%

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

   5. Taylor expanded in y around 0 70.9%

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

      1. associate-/r* 70.9%

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

      2. exp-to-pow 71.9%

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

      3. sub-neg 71.9%

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

      4. metadata-eval 71.9%

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

      5. metadata-eval 71.9%

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

      6. sub-neg 71.9%

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

   7. Simplified 71.9%

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

   8. Taylor expanded in t around 0 40.9%

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

   9. Taylor expanded in b around 0 30.9%

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

       1. distribute-lft-out 32.6%

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

   11. Simplified 32.6%

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

       1. flip-+ 50.3%

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

       2. *-commutative 50.3%

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

       3. *-commutative 50.3%

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

       4. *-commutative 50.3%

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

   13. Applied egg-rr 50.3%

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

   if -2.39999999999999991e-275 < b < 2.79999999999999999e-174

   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. Step-by-step derivation

      1. associate-/l* 99.1%

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

      2. exp-diff 99.1%

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

      3. associate-/l/ 99.1%

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

      4. exp-sum 91.2%

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

      5. associate-/l* 86.0%

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

      6. *-commutative 86.0%

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

      7. exp-to-pow 86.0%

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

      8. *-commutative 86.0%

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

      9. exp-to-pow 86.8%

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

      10. sub-neg 86.8%

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

      11. metadata-eval 86.8%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in y around 0 63.3%

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

      1. associate-/r* 63.3%

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

      2. exp-to-pow 64.1%

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

      3. sub-neg 64.1%

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

      4. metadata-eval 64.1%

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

      5. metadata-eval 64.1%

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

      6. sub-neg 64.1%

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

   7. Simplified 64.1%

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

   8. Taylor expanded in t around 0 38.5%

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

   9. Taylor expanded in b around 0 38.5%

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

       1. distribute-lft-out 38.5%

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

   11. Simplified 38.5%

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

   12. Taylor expanded in b around inf 53.5%

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

   if 2.79999999999999999e-174 < b < 6.50000000000000019e-166

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. exp-diff 100.0%

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

      3. associate-/l/ 100.0%

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

      4. exp-sum 100.0%

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

      5. associate-/l* 100.0%

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

      6. *-commutative 100.0%

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

      7. exp-to-pow 100.0%

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

      8. *-commutative 100.0%

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

      9. exp-to-pow 100.0%

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

      10. sub-neg 100.0%

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

      11. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 39.8%

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

      1. associate-/r* 39.8%

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

      2. exp-to-pow 39.8%

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

      3. sub-neg 39.8%

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

      4. metadata-eval 39.8%

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

      5. metadata-eval 39.8%

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

      6. sub-neg 39.8%

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

   7. Simplified 39.8%

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

   8. Taylor expanded in t around 0 8.3%

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

   9. Taylor expanded in b around 0 8.3%

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

       1. distribute-lft-out 8.3%

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

   11. Simplified 8.3%

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

   12. Taylor expanded in b around inf 100.0%

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

       1. *-commutative 100.0%

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

   14. Simplified 100.0%

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

   if 6.50000000000000019e-166 < b

   1. Initial program 99.6%

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

      1. associate-/l* 98.8%

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

      2. exp-diff 75.2%

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

      3. associate-/l/ 75.2%

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

      4. exp-sum 63.8%

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

      5. associate-/l* 60.9%

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

      6. *-commutative 60.9%

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

      7. exp-to-pow 60.9%

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

      8. *-commutative 60.9%

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

      9. exp-to-pow 61.3%

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

      10. sub-neg 61.3%

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

      11. metadata-eval 61.3%

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

   3. Simplified 61.3%

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

   5. Taylor expanded in y around 0 61.8%

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

      1. associate-/r* 58.0%

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

      2. exp-to-pow 58.3%

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

      3. sub-neg 58.3%

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

      4. metadata-eval 58.3%

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

      5. metadata-eval 58.3%

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

      6. sub-neg 58.3%

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

   7. Simplified 58.3%

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

   8. Taylor expanded in t around 0 62.5%

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

      1. associate-*r* 54.9%

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

      2. *-commutative 54.9%

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

   10. Simplified 54.9%

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

   11. Taylor expanded in b around 0 46.2%

       \[\leadsto \frac{x}{\color{blue}{a \cdot y + b \cdot \left(a \cdot y + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot \left(b \cdot y\right)\right) + 0.5 \cdot \left(a \cdot y\right)\right)\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.42 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(\frac{1}{y \cdot a} - \frac{b}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-275}:\\ \;\;\;\;\frac{x}{a \cdot \frac{y \cdot y - \left(y \cdot b\right) \cdot \left(y \cdot b\right)}{y - y \cdot b}}\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-174}:\\ \;\;\;\;\frac{x}{a \cdot \left(b \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-166}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a + b \cdot \left(y \cdot a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot \left(y \cdot b\right)\right) + \left(y \cdot a\right) \cdot 0.5\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 43.4% accurate, 8.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y \cdot b\right)\\ \mathbf{if}\;b \leq -1.35 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(\frac{1}{y \cdot a} - \frac{b}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-274}:\\ \;\;\;\;\frac{x}{a \cdot \frac{y \cdot y - \left(y \cdot b\right) \cdot \left(y \cdot b\right)}{y - y \cdot b}}\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-173}:\\ \;\;\;\;\frac{x}{a \cdot \left(b \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{-166}:\\ \;\;\;\;\frac{x}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a + b \cdot \left(y \cdot a + t\_1 \cdot 0.5\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* y b))))
   (if (<= b -1.35e+48)
     (* x (- (/ 1.0 (* y a)) (/ b (* y a))))
     (if (<= b -1.05e-274)
       (/ x (* a (/ (- (* y y) (* (* y b) (* y b))) (- y (* y b)))))
       (if (<= b 4.5e-173)
         (/ x (* a (* b (+ y (/ y b)))))
         (if (<= b 5.4e-166)
           (/ x t_1)
           (/ x (+ (* y a) (* b (+ (* y a) (* t_1 0.5)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y * b);
	double tmp;
	if (b <= -1.35e+48) {
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)));
	} else if (b <= -1.05e-274) {
		tmp = x / (a * (((y * y) - ((y * b) * (y * b))) / (y - (y * b))));
	} else if (b <= 4.5e-173) {
		tmp = x / (a * (b * (y + (y / b))));
	} else if (b <= 5.4e-166) {
		tmp = x / t_1;
	} else {
		tmp = x / ((y * a) + (b * ((y * a) + (t_1 * 0.5))));
	}
	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 = a * (y * b)
    if (b <= (-1.35d+48)) then
        tmp = x * ((1.0d0 / (y * a)) - (b / (y * a)))
    else if (b <= (-1.05d-274)) then
        tmp = x / (a * (((y * y) - ((y * b) * (y * b))) / (y - (y * b))))
    else if (b <= 4.5d-173) then
        tmp = x / (a * (b * (y + (y / b))))
    else if (b <= 5.4d-166) then
        tmp = x / t_1
    else
        tmp = x / ((y * a) + (b * ((y * a) + (t_1 * 0.5d0))))
    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 = a * (y * b);
	double tmp;
	if (b <= -1.35e+48) {
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)));
	} else if (b <= -1.05e-274) {
		tmp = x / (a * (((y * y) - ((y * b) * (y * b))) / (y - (y * b))));
	} else if (b <= 4.5e-173) {
		tmp = x / (a * (b * (y + (y / b))));
	} else if (b <= 5.4e-166) {
		tmp = x / t_1;
	} else {
		tmp = x / ((y * a) + (b * ((y * a) + (t_1 * 0.5))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (y * b)
	tmp = 0
	if b <= -1.35e+48:
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)))
	elif b <= -1.05e-274:
		tmp = x / (a * (((y * y) - ((y * b) * (y * b))) / (y - (y * b))))
	elif b <= 4.5e-173:
		tmp = x / (a * (b * (y + (y / b))))
	elif b <= 5.4e-166:
		tmp = x / t_1
	else:
		tmp = x / ((y * a) + (b * ((y * a) + (t_1 * 0.5))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y * b))
	tmp = 0.0
	if (b <= -1.35e+48)
		tmp = Float64(x * Float64(Float64(1.0 / Float64(y * a)) - Float64(b / Float64(y * a))));
	elseif (b <= -1.05e-274)
		tmp = Float64(x / Float64(a * Float64(Float64(Float64(y * y) - Float64(Float64(y * b) * Float64(y * b))) / Float64(y - Float64(y * b)))));
	elseif (b <= 4.5e-173)
		tmp = Float64(x / Float64(a * Float64(b * Float64(y + Float64(y / b)))));
	elseif (b <= 5.4e-166)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(x / Float64(Float64(y * a) + Float64(b * Float64(Float64(y * a) + Float64(t_1 * 0.5)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (y * b);
	tmp = 0.0;
	if (b <= -1.35e+48)
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)));
	elseif (b <= -1.05e-274)
		tmp = x / (a * (((y * y) - ((y * b) * (y * b))) / (y - (y * b))));
	elseif (b <= 4.5e-173)
		tmp = x / (a * (b * (y + (y / b))));
	elseif (b <= 5.4e-166)
		tmp = x / t_1;
	else
		tmp = x / ((y * a) + (b * ((y * a) + (t_1 * 0.5))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.35e+48], N[(x * N[(N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision] - N[(b / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.05e-274], N[(x / N[(a * N[(N[(N[(y * y), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.5e-173], N[(x / N[(a * N[(b * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.4e-166], N[(x / t$95$1), $MachinePrecision], N[(x / N[(N[(y * a), $MachinePrecision] + N[(b * N[(N[(y * a), $MachinePrecision] + N[(t$95$1 * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.35000000000000002e48

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. exp-diff 64.0%

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

      3. associate-/l/ 64.0%

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

      4. exp-sum 64.0%

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

      5. associate-/l* 64.0%

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

      6. *-commutative 64.0%

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

      7. exp-to-pow 64.0%

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

      8. *-commutative 64.0%

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

      9. exp-to-pow 64.0%

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

      10. sub-neg 64.0%

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

      11. metadata-eval 64.0%

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

   3. Simplified 64.0%

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

   5. Taylor expanded in y around 0 72.1%

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

      1. associate-/r* 68.1%

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

      2. exp-to-pow 68.1%

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

      3. sub-neg 68.1%

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

      4. metadata-eval 68.1%

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

      5. metadata-eval 68.1%

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

      6. sub-neg 68.1%

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

   7. Simplified 68.1%

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

   8. Taylor expanded in t around 0 86.2%

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

   9. Taylor expanded in b around 0 38.0%

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

   10. Taylor expanded in x around 0 51.3%

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

   if -1.35000000000000002e48 < b < -1.04999999999999997e-274

   1. Initial program 95.5%

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

      1. associate-/l* 97.2%

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

      2. exp-diff 93.8%

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

      3. associate-/l/ 93.8%

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

      4. exp-sum 82.0%

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

      5. associate-/l* 82.0%

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

      6. *-commutative 82.0%

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

      7. exp-to-pow 82.0%

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

      8. *-commutative 82.0%

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

      9. exp-to-pow 83.0%

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

      10. sub-neg 83.0%

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

      11. metadata-eval 83.0%

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

   3. Simplified 83.0%

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

   5. Taylor expanded in y around 0 70.9%

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

      1. associate-/r* 70.9%

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

      2. exp-to-pow 71.9%

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

      3. sub-neg 71.9%

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

      4. metadata-eval 71.9%

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

      5. metadata-eval 71.9%

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

      6. sub-neg 71.9%

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

   7. Simplified 71.9%

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

   8. Taylor expanded in t around 0 40.9%

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

   9. Taylor expanded in b around 0 30.9%

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

       1. distribute-lft-out 32.6%

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

   11. Simplified 32.6%

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

       1. flip-+ 50.3%

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

       2. *-commutative 50.3%

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

       3. *-commutative 50.3%

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

       4. *-commutative 50.3%

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

   13. Applied egg-rr 50.3%

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

   if -1.04999999999999997e-274 < b < 4.50000000000000018e-173

   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. Step-by-step derivation

      1. associate-/l* 99.1%

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

      2. exp-diff 99.1%

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

      3. associate-/l/ 99.1%

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

      4. exp-sum 91.2%

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

      5. associate-/l* 86.0%

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

      6. *-commutative 86.0%

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

      7. exp-to-pow 86.0%

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

      8. *-commutative 86.0%

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

      9. exp-to-pow 86.8%

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

      10. sub-neg 86.8%

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

      11. metadata-eval 86.8%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in y around 0 63.3%

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

      1. associate-/r* 63.3%

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

      2. exp-to-pow 64.1%

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

      3. sub-neg 64.1%

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

      4. metadata-eval 64.1%

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

      5. metadata-eval 64.1%

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

      6. sub-neg 64.1%

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

   7. Simplified 64.1%

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

   8. Taylor expanded in t around 0 38.5%

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

   9. Taylor expanded in b around 0 38.5%

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

       1. distribute-lft-out 38.5%

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

   11. Simplified 38.5%

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

   12. Taylor expanded in b around inf 53.5%

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

   if 4.50000000000000018e-173 < b < 5.40000000000000013e-166

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. exp-diff 100.0%

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

      3. associate-/l/ 100.0%

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

      4. exp-sum 100.0%

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

      5. associate-/l* 100.0%

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

      6. *-commutative 100.0%

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

      7. exp-to-pow 100.0%

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

      8. *-commutative 100.0%

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

      9. exp-to-pow 100.0%

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

      10. sub-neg 100.0%

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

      11. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 39.8%

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

      1. associate-/r* 39.8%

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

      2. exp-to-pow 39.8%

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

      3. sub-neg 39.8%

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

      4. metadata-eval 39.8%

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

      5. metadata-eval 39.8%

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

      6. sub-neg 39.8%

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

   7. Simplified 39.8%

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

   8. Taylor expanded in t around 0 8.3%

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

   9. Taylor expanded in b around 0 8.3%

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

       1. distribute-lft-out 8.3%

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

   11. Simplified 8.3%

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

   12. Taylor expanded in b around inf 100.0%

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

       1. *-commutative 100.0%

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

   14. Simplified 100.0%

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

   if 5.40000000000000013e-166 < b

   1. Initial program 99.6%

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

      1. associate-/l* 98.8%

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

      2. exp-diff 75.2%

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

      3. associate-/l/ 75.2%

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

      4. exp-sum 63.8%

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

      5. associate-/l* 60.9%

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

      6. *-commutative 60.9%

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

      7. exp-to-pow 60.9%

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

      8. *-commutative 60.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      9. exp-to-pow 61.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      10. sub-neg 61.3%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

      11. metadata-eval 61.3%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

   3. Simplified 61.3%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 61.8%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 58.0%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 58.3%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 58.3%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 58.3%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

      5. metadata-eval 58.3%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)}}{y}}{e^{b}} \]

      6. sub-neg 58.3%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t - 1\right)}}}{y}}{e^{b}} \]

   7. Simplified 58.3%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t - 1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 62.5%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   9. Step-by-step derivation

      1. associate-*r* 54.9%

         \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

      2. *-commutative 54.9%

         \[\leadsto \frac{x}{\color{blue}{e^{b} \cdot \left(a \cdot y\right)}} \]

   10. Simplified 54.9%

       \[\leadsto \color{blue}{\frac{x}{e^{b} \cdot \left(a \cdot y\right)}} \]

   11. Taylor expanded in b around 0 42.4%

       \[\leadsto \frac{x}{\color{blue}{a \cdot y + b \cdot \left(0.5 \cdot \left(a \cdot \left(b \cdot y\right)\right) + a \cdot y\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(\frac{1}{y \cdot a} - \frac{b}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-274}:\\ \;\;\;\;\frac{x}{a \cdot \frac{y \cdot y - \left(y \cdot b\right) \cdot \left(y \cdot b\right)}{y - y \cdot b}}\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-173}:\\ \;\;\;\;\frac{x}{a \cdot \left(b \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{-166}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a + b \cdot \left(y \cdot a + \left(a \cdot \left(y \cdot b\right)\right) \cdot 0.5\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 42.0% accurate, 10.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+104}:\\ \;\;\;\;x \cdot \left(\frac{1}{y \cdot a} - \frac{b}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq -2.9:\\ \;\;\;\;\frac{a \cdot \left(y \cdot \frac{x}{a}\right) + y \cdot \left(x \cdot b\right)}{a \cdot \left(y \cdot \left(-y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(b \cdot \left(y + \frac{y}{b}\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.2e+104)
   (* x (- (/ 1.0 (* y a)) (/ b (* y a))))
   (if (<= b -2.9)
     (/ (+ (* a (* y (/ x a))) (* y (* x b))) (* a (* y (- y))))
     (/ x (* a (* b (+ y (/ y b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.2e+104) {
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)));
	} else if (b <= -2.9) {
		tmp = ((a * (y * (x / a))) + (y * (x * b))) / (a * (y * -y));
	} else {
		tmp = x / (a * (b * (y + (y / b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.2d+104)) then
        tmp = x * ((1.0d0 / (y * a)) - (b / (y * a)))
    else if (b <= (-2.9d0)) then
        tmp = ((a * (y * (x / a))) + (y * (x * b))) / (a * (y * -y))
    else
        tmp = x / (a * (b * (y + (y / b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.2e+104) {
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)));
	} else if (b <= -2.9) {
		tmp = ((a * (y * (x / a))) + (y * (x * b))) / (a * (y * -y));
	} else {
		tmp = x / (a * (b * (y + (y / b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.2e+104:
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)))
	elif b <= -2.9:
		tmp = ((a * (y * (x / a))) + (y * (x * b))) / (a * (y * -y))
	else:
		tmp = x / (a * (b * (y + (y / b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.2e+104)
		tmp = Float64(x * Float64(Float64(1.0 / Float64(y * a)) - Float64(b / Float64(y * a))));
	elseif (b <= -2.9)
		tmp = Float64(Float64(Float64(a * Float64(y * Float64(x / a))) + Float64(y * Float64(x * b))) / Float64(a * Float64(y * Float64(-y))));
	else
		tmp = Float64(x / Float64(a * Float64(b * Float64(y + Float64(y / b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.2e+104)
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)));
	elseif (b <= -2.9)
		tmp = ((a * (y * (x / a))) + (y * (x * b))) / (a * (y * -y));
	else
		tmp = x / (a * (b * (y + (y / b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.2e+104], N[(x * N[(N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision] - N[(b / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.9], N[(N[(N[(a * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * N[(y * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(b * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.2e104

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. exp-diff 66.7%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 66.7%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 66.7%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. associate-/l* 66.7%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right)} \]

      6. *-commutative 66.7%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      7. exp-to-pow 66.7%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      8. *-commutative 66.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      9. exp-to-pow 66.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      10. sub-neg 66.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

      11. metadata-eval 66.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

   3. Simplified 66.7%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 71.9%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 69.4%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 69.4%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 69.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 69.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

      5. metadata-eval 69.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)}}{y}}{e^{b}} \]

      6. sub-neg 69.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t - 1\right)}}}{y}}{e^{b}} \]

   7. Simplified 69.4%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t - 1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 89.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 40.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]

   10. Taylor expanded in x around 0 57.4%

       \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \frac{b}{a \cdot y} + \frac{1}{a \cdot y}\right)} \]

   if -1.2e104 < b < -2.89999999999999991

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. exp-diff 63.2%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 63.2%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 63.2%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. associate-/l* 63.2%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right)} \]

      6. *-commutative 63.2%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      7. exp-to-pow 63.2%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      8. *-commutative 63.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      9. exp-to-pow 63.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      10. sub-neg 63.2%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

      11. metadata-eval 63.2%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

   3. Simplified 63.2%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 68.7%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 63.4%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 63.4%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 63.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 63.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

      5. metadata-eval 63.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)}}{y}}{e^{b}} \]

      6. sub-neg 63.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t - 1\right)}}}{y}}{e^{b}} \]

   7. Simplified 63.4%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t - 1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 68.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 18.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. fma-define 18.5%

          \[\leadsto \color{blue}{\mathsf{fma}\left(-1, \frac{b \cdot x}{a \cdot y}, \frac{x}{a \cdot y}\right)} \]

       2. add-sqr-sqrt 17.7%

          \[\leadsto \mathsf{fma}\left(-1, \frac{b \cdot x}{a \cdot y}, \color{blue}{\sqrt{\frac{x}{a \cdot y}} \cdot \sqrt{\frac{x}{a \cdot y}}}\right) \]

       3. sqrt-unprod 23.5%

          \[\leadsto \mathsf{fma}\left(-1, \frac{b \cdot x}{a \cdot y}, \color{blue}{\sqrt{\frac{x}{a \cdot y} \cdot \frac{x}{a \cdot y}}}\right) \]

       4. sqr-neg 23.5%

          \[\leadsto \mathsf{fma}\left(-1, \frac{b \cdot x}{a \cdot y}, \sqrt{\color{blue}{\left(-\frac{x}{a \cdot y}\right) \cdot \left(-\frac{x}{a \cdot y}\right)}}\right) \]

       5. mul-1-neg 23.5%

          \[\leadsto \mathsf{fma}\left(-1, \frac{b \cdot x}{a \cdot y}, \sqrt{\color{blue}{\left(-1 \cdot \frac{x}{a \cdot y}\right)} \cdot \left(-\frac{x}{a \cdot y}\right)}\right) \]

       6. mul-1-neg 23.5%

          \[\leadsto \mathsf{fma}\left(-1, \frac{b \cdot x}{a \cdot y}, \sqrt{\left(-1 \cdot \frac{x}{a \cdot y}\right) \cdot \color{blue}{\left(-1 \cdot \frac{x}{a \cdot y}\right)}}\right) \]

       7. sqrt-unprod 0.9%

          \[\leadsto \mathsf{fma}\left(-1, \frac{b \cdot x}{a \cdot y}, \color{blue}{\sqrt{-1 \cdot \frac{x}{a \cdot y}} \cdot \sqrt{-1 \cdot \frac{x}{a \cdot y}}}\right) \]

       8. add-sqr-sqrt 7.8%

          \[\leadsto \mathsf{fma}\left(-1, \frac{b \cdot x}{a \cdot y}, \color{blue}{-1 \cdot \frac{x}{a \cdot y}}\right) \]

       9. mul-1-neg 7.8%

          \[\leadsto \mathsf{fma}\left(-1, \frac{b \cdot x}{a \cdot y}, \color{blue}{-\frac{x}{a \cdot y}}\right) \]

       10. fma-neg 7.8%

           \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} - \frac{x}{a \cdot y}} \]

       11. associate-*r/ 7.8%

           \[\leadsto \color{blue}{\frac{-1 \cdot \left(b \cdot x\right)}{a \cdot y}} - \frac{x}{a \cdot y} \]

       12. associate-/r* 7.8%

           \[\leadsto \frac{-1 \cdot \left(b \cdot x\right)}{a \cdot y} - \color{blue}{\frac{\frac{x}{a}}{y}} \]

       13. frac-sub 32.9%

           \[\leadsto \color{blue}{\frac{\left(-1 \cdot \left(b \cdot x\right)\right) \cdot y - \left(a \cdot y\right) \cdot \frac{x}{a}}{\left(a \cdot y\right) \cdot y}} \]

       14. *-commutative 32.9%

           \[\leadsto \frac{\left(-1 \cdot \color{blue}{\left(x \cdot b\right)}\right) \cdot y - \left(a \cdot y\right) \cdot \frac{x}{a}}{\left(a \cdot y\right) \cdot y} \]

       15. *-commutative 32.9%

           \[\leadsto \frac{\left(-1 \cdot \left(x \cdot b\right)\right) \cdot y - \color{blue}{\left(y \cdot a\right)} \cdot \frac{x}{a}}{\left(a \cdot y\right) \cdot y} \]

       16. *-commutative 32.9%

           \[\leadsto \frac{\left(-1 \cdot \left(x \cdot b\right)\right) \cdot y - \left(y \cdot a\right) \cdot \frac{x}{a}}{\color{blue}{\left(y \cdot a\right)} \cdot y} \]

   11. Applied egg-rr 32.9%

       \[\leadsto \color{blue}{\frac{\left(-1 \cdot \left(x \cdot b\right)\right) \cdot y - \left(y \cdot a\right) \cdot \frac{x}{a}}{\left(y \cdot a\right) \cdot y}} \]
   12. Step-by-step derivation

       1. *-commutative 32.9%

          \[\leadsto \frac{\color{blue}{y \cdot \left(-1 \cdot \left(x \cdot b\right)\right)} - \left(y \cdot a\right) \cdot \frac{x}{a}}{\left(y \cdot a\right) \cdot y} \]

       2. neg-mul-1 32.9%

          \[\leadsto \frac{y \cdot \color{blue}{\left(-x \cdot b\right)} - \left(y \cdot a\right) \cdot \frac{x}{a}}{\left(y \cdot a\right) \cdot y} \]

       3. distribute-rgt-neg-in 32.9%

          \[\leadsto \frac{y \cdot \color{blue}{\left(x \cdot \left(-b\right)\right)} - \left(y \cdot a\right) \cdot \frac{x}{a}}{\left(y \cdot a\right) \cdot y} \]

       4. *-commutative 32.9%

          \[\leadsto \frac{y \cdot \left(x \cdot \left(-b\right)\right) - \color{blue}{\frac{x}{a} \cdot \left(y \cdot a\right)}}{\left(y \cdot a\right) \cdot y} \]

       5. associate-*r* 33.0%

          \[\leadsto \frac{y \cdot \left(x \cdot \left(-b\right)\right) - \color{blue}{\left(\frac{x}{a} \cdot y\right) \cdot a}}{\left(y \cdot a\right) \cdot y} \]

       6. *-commutative 33.0%

          \[\leadsto \frac{y \cdot \left(x \cdot \left(-b\right)\right) - \left(\frac{x}{a} \cdot y\right) \cdot a}{\color{blue}{y \cdot \left(y \cdot a\right)}} \]

       7. associate-*r* 43.1%

          \[\leadsto \frac{y \cdot \left(x \cdot \left(-b\right)\right) - \left(\frac{x}{a} \cdot y\right) \cdot a}{\color{blue}{\left(y \cdot y\right) \cdot a}} \]

   13. Simplified 43.1%

       \[\leadsto \color{blue}{\frac{y \cdot \left(x \cdot \left(-b\right)\right) - \left(\frac{x}{a} \cdot y\right) \cdot a}{\left(y \cdot y\right) \cdot a}} \]

   if -2.89999999999999991 < b

   1. Initial program 97.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.3%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. exp-diff 85.7%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 85.7%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 74.6%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. associate-/l* 72.0%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right)} \]

      6. *-commutative 72.0%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      7. exp-to-pow 72.0%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      8. *-commutative 72.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      9. exp-to-pow 72.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      10. sub-neg 72.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

      11. metadata-eval 72.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

   3. Simplified 72.7%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 64.4%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 62.4%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 63.0%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 63.0%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 63.0%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

      5. metadata-eval 63.0%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)}}{y}}{e^{b}} \]

      6. sub-neg 63.0%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t - 1\right)}}}{y}}{e^{b}} \]

   7. Simplified 63.0%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t - 1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 50.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 37.5%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-lft-out 38.0%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

   11. Simplified 38.0%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

   12. Taylor expanded in b around inf 43.2%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(b \cdot \left(y + \frac{y}{b}\right)\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+104}:\\ \;\;\;\;x \cdot \left(\frac{1}{y \cdot a} - \frac{b}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq -2.9:\\ \;\;\;\;\frac{a \cdot \left(y \cdot \frac{x}{a}\right) + y \cdot \left(x \cdot b\right)}{a \cdot \left(y \cdot \left(-y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(b \cdot \left(y + \frac{y}{b}\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 38.4% accurate, 14.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+43}:\\ \;\;\;\;\frac{b \cdot \frac{x}{-a}}{y}\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-83}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+17}:\\ \;\;\;\;\frac{1}{a} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.65e+43)
   (/ (* b (/ x (- a))) y)
   (if (<= b 2.5e-83)
     (/ x (* y a))
     (if (<= b 5.2e+17) (* (/ 1.0 a) (/ x y)) (/ x (* a (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.65e+43) {
		tmp = (b * (x / -a)) / y;
	} else if (b <= 2.5e-83) {
		tmp = x / (y * a);
	} else if (b <= 5.2e+17) {
		tmp = (1.0 / a) * (x / 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 <= (-1.65d+43)) then
        tmp = (b * (x / -a)) / y
    else if (b <= 2.5d-83) then
        tmp = x / (y * a)
    else if (b <= 5.2d+17) then
        tmp = (1.0d0 / a) * (x / 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 <= -1.65e+43) {
		tmp = (b * (x / -a)) / y;
	} else if (b <= 2.5e-83) {
		tmp = x / (y * a);
	} else if (b <= 5.2e+17) {
		tmp = (1.0 / a) * (x / y);
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.65e+43:
		tmp = (b * (x / -a)) / y
	elif b <= 2.5e-83:
		tmp = x / (y * a)
	elif b <= 5.2e+17:
		tmp = (1.0 / a) * (x / y)
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.65e+43)
		tmp = Float64(Float64(b * Float64(x / Float64(-a))) / y);
	elseif (b <= 2.5e-83)
		tmp = Float64(x / Float64(y * a));
	elseif (b <= 5.2e+17)
		tmp = Float64(Float64(1.0 / a) * Float64(x / 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 <= -1.65e+43)
		tmp = (b * (x / -a)) / y;
	elseif (b <= 2.5e-83)
		tmp = x / (y * a);
	elseif (b <= 5.2e+17)
		tmp = (1.0 / a) * (x / y);
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.65e+43], N[(N[(b * N[(x / (-a)), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 2.5e-83], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.2e+17], N[(N[(1.0 / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.6500000000000001e43

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. exp-diff 65.4%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 65.4%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 65.4%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. associate-/l* 65.4%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right)} \]

      6. *-commutative 65.4%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      7. exp-to-pow 65.4%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      8. *-commutative 65.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      9. exp-to-pow 65.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      10. sub-neg 65.4%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

      11. metadata-eval 65.4%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

   3. Simplified 65.4%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 73.2%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 69.4%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 69.4%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 69.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 69.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

      5. metadata-eval 69.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)}}{y}}{e^{b}} \]

      6. sub-neg 69.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t - 1\right)}}}{y}}{e^{b}} \]

   7. Simplified 69.4%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t - 1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 86.7%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 36.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]

   10. Taylor expanded in b around inf 36.7%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]
   11. Step-by-step derivation

       1. associate-*r/ 36.7%

          \[\leadsto \color{blue}{\frac{-1 \cdot \left(b \cdot x\right)}{a \cdot y}} \]

       2. *-commutative 36.7%

          \[\leadsto \frac{-1 \cdot \color{blue}{\left(x \cdot b\right)}}{a \cdot y} \]

       3. *-commutative 36.7%

          \[\leadsto \frac{-1 \cdot \left(x \cdot b\right)}{\color{blue}{y \cdot a}} \]

       4. times-frac 38.7%

          \[\leadsto \color{blue}{\frac{-1}{y} \cdot \frac{x \cdot b}{a}} \]

       5. associate-*l/ 38.7%

          \[\leadsto \color{blue}{\frac{-1 \cdot \frac{x \cdot b}{a}}{y}} \]

       6. neg-mul-1 38.7%

          \[\leadsto \frac{\color{blue}{-\frac{x \cdot b}{a}}}{y} \]

       7. *-commutative 38.7%

          \[\leadsto \frac{-\frac{\color{blue}{b \cdot x}}{a}}{y} \]

       8. associate-/l* 38.6%

          \[\leadsto \frac{-\color{blue}{b \cdot \frac{x}{a}}}{y} \]

       9. distribute-rgt-neg-in 38.6%

          \[\leadsto \frac{\color{blue}{b \cdot \left(-\frac{x}{a}\right)}}{y} \]

       10. distribute-neg-frac 38.6%

           \[\leadsto \frac{b \cdot \color{blue}{\frac{-x}{a}}}{y} \]

   12. Simplified 38.6%

       \[\leadsto \color{blue}{\frac{b \cdot \frac{-x}{a}}{y}} \]

   if -1.6500000000000001e43 < b < 2.5e-83

   1. Initial program 96.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.3%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. exp-diff 96.6%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 96.6%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 85.1%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. associate-/l* 81.8%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right)} \]

      6. *-commutative 81.8%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      7. exp-to-pow 81.8%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      8. *-commutative 81.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      9. exp-to-pow 82.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      10. sub-neg 82.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

      11. metadata-eval 82.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

   3. Simplified 82.8%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 62.8%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 62.8%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 63.6%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 63.6%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 63.6%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

      5. metadata-eval 63.6%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)}}{y}}{e^{b}} \]

      6. sub-neg 63.6%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t - 1\right)}}}{y}}{e^{b}} \]

   7. Simplified 63.6%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t - 1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 35.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 33.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]

   if 2.5e-83 < b < 5.2e17

   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. Step-by-step derivation

      1. associate-/l* 94.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. exp-diff 83.9%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 83.9%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 73.9%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. associate-/l* 68.9%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right)} \]

      6. *-commutative 68.9%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      7. exp-to-pow 68.9%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      8. *-commutative 68.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      9. exp-to-pow 70.1%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      10. sub-neg 70.1%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

      11. metadata-eval 70.1%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

   3. Simplified 70.1%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 64.3%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 64.3%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 65.5%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 65.5%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 65.5%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

      5. metadata-eval 65.5%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)}}{y}}{e^{b}} \]

      6. sub-neg 65.5%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t - 1\right)}}}{y}}{e^{b}} \]

   7. Simplified 65.5%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t - 1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 55.8%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 35.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-un-lft-identity 35.6%

          \[\leadsto \frac{\color{blue}{1 \cdot x}}{a \cdot y} \]

       2. times-frac 40.6%

          \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y}} \]

   11. Applied egg-rr 40.6%

       \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y}} \]

   if 5.2e17 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. exp-diff 62.9%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 62.9%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 53.2%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. associate-/l* 53.2%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right)} \]

      6. *-commutative 53.2%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      7. exp-to-pow 53.2%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      8. *-commutative 53.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      9. exp-to-pow 53.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      10. sub-neg 53.2%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

      11. metadata-eval 53.2%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

   3. Simplified 53.2%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 66.2%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 59.8%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 59.8%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 59.8%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 59.8%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

      5. metadata-eval 59.8%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)}}{y}}{e^{b}} \]

      6. sub-neg 59.8%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t - 1\right)}}}{y}}{e^{b}} \]

   7. Simplified 59.8%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t - 1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 77.8%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 43.6%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-lft-out 43.6%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

   11. Simplified 43.6%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

   12. Taylor expanded in b around inf 43.6%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(b \cdot y\right)}} \]
   13. Step-by-step derivation

       1. *-commutative 43.6%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y \cdot b\right)}} \]

   14. Simplified 43.6%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot b\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+43}:\\ \;\;\;\;\frac{b \cdot \frac{x}{-a}}{y}\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-83}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+17}:\\ \;\;\;\;\frac{1}{a} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 42.4% accurate, 17.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.7:\\ \;\;\;\;x \cdot \left(\frac{1}{y \cdot a} - \frac{b}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(b \cdot \left(y + \frac{y}{b}\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.7)
   (* x (- (/ 1.0 (* y a)) (/ b (* y a))))
   (/ x (* a (* b (+ y (/ y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.7) {
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)));
	} else {
		tmp = x / (a * (b * (y + (y / b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.7d0)) then
        tmp = x * ((1.0d0 / (y * a)) - (b / (y * a)))
    else
        tmp = x / (a * (b * (y + (y / b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.7) {
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)));
	} else {
		tmp = x / (a * (b * (y + (y / b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.7:
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)))
	else:
		tmp = x / (a * (b * (y + (y / b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.7)
		tmp = Float64(x * Float64(Float64(1.0 / Float64(y * a)) - Float64(b / Float64(y * a))));
	else
		tmp = Float64(x / Float64(a * Float64(b * Float64(y + Float64(y / b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.7)
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)));
	else
		tmp = x / (a * (b * (y + (y / b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.7], N[(x * N[(N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision] - N[(b / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(b * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.7000000000000002

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. exp-diff 65.5%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 65.5%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 65.5%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. associate-/l* 65.5%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right)} \]

      6. *-commutative 65.5%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      7. exp-to-pow 65.5%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      8. *-commutative 65.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      9. exp-to-pow 65.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      10. sub-neg 65.5%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

      11. metadata-eval 65.5%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

   3. Simplified 65.5%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 70.9%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 67.4%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 67.4%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 67.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 67.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

      5. metadata-eval 67.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)}}{y}}{e^{b}} \]

      6. sub-neg 67.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t - 1\right)}}}{y}}{e^{b}} \]

   7. Simplified 67.4%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t - 1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 83.0%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 33.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]

   10. Taylor expanded in x around 0 44.7%

       \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \frac{b}{a \cdot y} + \frac{1}{a \cdot y}\right)} \]

   if -2.7000000000000002 < b

   1. Initial program 97.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.3%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. exp-diff 85.7%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 85.7%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 74.6%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. associate-/l* 72.0%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right)} \]

      6. *-commutative 72.0%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      7. exp-to-pow 72.0%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      8. *-commutative 72.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      9. exp-to-pow 72.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      10. sub-neg 72.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

      11. metadata-eval 72.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

   3. Simplified 72.7%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 64.4%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 62.4%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 63.0%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 63.0%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 63.0%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

      5. metadata-eval 63.0%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)}}{y}}{e^{b}} \]

      6. sub-neg 63.0%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t - 1\right)}}}{y}}{e^{b}} \]

   7. Simplified 63.0%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t - 1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 50.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 37.5%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-lft-out 38.0%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

   11. Simplified 38.0%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

   12. Taylor expanded in b around inf 43.2%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(b \cdot \left(y + \frac{y}{b}\right)\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.7:\\ \;\;\;\;x \cdot \left(\frac{1}{y \cdot a} - \frac{b}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(b \cdot \left(y + \frac{y}{b}\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 43.0% accurate, 19.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{-63}:\\ \;\;\;\;\frac{\frac{x}{y} - \frac{x \cdot b}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(b \cdot \left(y + \frac{y}{b}\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -9e-63)
   (/ (- (/ x y) (/ (* x b) y)) a)
   (/ x (* a (* b (+ y (/ y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9e-63) {
		tmp = ((x / y) - ((x * b) / y)) / a;
	} else {
		tmp = x / (a * (b * (y + (y / b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-9d-63)) then
        tmp = ((x / y) - ((x * b) / y)) / a
    else
        tmp = x / (a * (b * (y + (y / b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9e-63) {
		tmp = ((x / y) - ((x * b) / y)) / a;
	} else {
		tmp = x / (a * (b * (y + (y / b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -9e-63:
		tmp = ((x / y) - ((x * b) / y)) / a
	else:
		tmp = x / (a * (b * (y + (y / b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -9e-63)
		tmp = Float64(Float64(Float64(x / y) - Float64(Float64(x * b) / y)) / a);
	else
		tmp = Float64(x / Float64(a * Float64(b * Float64(y + Float64(y / b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -9e-63)
		tmp = ((x / y) - ((x * b) / y)) / a;
	else
		tmp = x / (a * (b * (y + (y / b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -9e-63], N[(N[(N[(x / y), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(a * N[(b * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.9999999999999999e-63

   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* 99.6%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. exp-diff 71.5%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 71.5%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 67.3%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. associate-/l* 67.3%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right)} \]

      6. *-commutative 67.3%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      7. exp-to-pow 67.3%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      8. *-commutative 67.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      9. exp-to-pow 67.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      10. sub-neg 67.5%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

      11. metadata-eval 67.5%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

   3. Simplified 67.5%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 70.4%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 67.6%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 67.9%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 67.9%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 67.9%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

      5. metadata-eval 67.9%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)}}{y}}{e^{b}} \]

      6. sub-neg 67.9%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t - 1\right)}}}{y}}{e^{b}} \]

   7. Simplified 67.9%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t - 1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 75.2%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 34.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]

   10. Taylor expanded in a around 0 40.0%

       \[\leadsto \color{blue}{\frac{-1 \cdot \frac{b \cdot x}{y} + \frac{x}{y}}{a}} \]
   11. Step-by-step derivation

       1. +-commutative 40.0%

          \[\leadsto \frac{\color{blue}{\frac{x}{y} + -1 \cdot \frac{b \cdot x}{y}}}{a} \]

       2. mul-1-neg 40.0%

          \[\leadsto \frac{\frac{x}{y} + \color{blue}{\left(-\frac{b \cdot x}{y}\right)}}{a} \]

       3. unsub-neg 40.0%

          \[\leadsto \frac{\color{blue}{\frac{x}{y} - \frac{b \cdot x}{y}}}{a} \]

       4. *-commutative 40.0%

          \[\leadsto \frac{\frac{x}{y} - \frac{\color{blue}{x \cdot b}}{y}}{a} \]

   12. Simplified 40.0%

       \[\leadsto \color{blue}{\frac{\frac{x}{y} - \frac{x \cdot b}{y}}{a}} \]

   if -8.9999999999999999e-63 < 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. Step-by-step derivation

      1. associate-/l* 98.4%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. exp-diff 84.8%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 84.8%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 74.5%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. associate-/l* 71.8%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right)} \]

      6. *-commutative 71.8%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      7. exp-to-pow 71.8%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      8. *-commutative 71.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      9. exp-to-pow 72.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      10. sub-neg 72.5%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

      11. metadata-eval 72.5%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

   3. Simplified 72.5%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 64.1%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 62.0%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 62.5%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 62.5%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 62.5%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

      5. metadata-eval 62.5%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)}}{y}}{e^{b}} \]

      6. sub-neg 62.5%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t - 1\right)}}}{y}}{e^{b}} \]

   7. Simplified 62.5%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t - 1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 51.3%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 37.3%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-lft-out 37.8%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

   11. Simplified 37.8%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

   12. Taylor expanded in b around inf 43.4%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(b \cdot \left(y + \frac{y}{b}\right)\right)}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 42.7% accurate, 19.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{-19}:\\ \;\;\;\;\frac{\frac{x}{a} - x \cdot \frac{b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(b \cdot \left(y + \frac{y}{b}\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3e-19)
   (/ (- (/ x a) (* x (/ b a))) y)
   (/ x (* a (* b (+ y (/ y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3e-19) {
		tmp = ((x / a) - (x * (b / a))) / y;
	} else {
		tmp = x / (a * (b * (y + (y / b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3d-19)) then
        tmp = ((x / a) - (x * (b / a))) / y
    else
        tmp = x / (a * (b * (y + (y / b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3e-19) {
		tmp = ((x / a) - (x * (b / a))) / y;
	} else {
		tmp = x / (a * (b * (y + (y / b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3e-19:
		tmp = ((x / a) - (x * (b / a))) / y
	else:
		tmp = x / (a * (b * (y + (y / b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3e-19)
		tmp = Float64(Float64(Float64(x / a) - Float64(x * Float64(b / a))) / y);
	else
		tmp = Float64(x / Float64(a * Float64(b * Float64(y + Float64(y / b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3e-19)
		tmp = ((x / a) - (x * (b / a))) / y;
	else
		tmp = x / (a * (b * (y + (y / b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3e-19], N[(N[(N[(x / a), $MachinePrecision] - N[(x * N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(b * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.99999999999999993e-19

   1. Initial program 99.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. exp-diff 67.7%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 67.7%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 67.7%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. associate-/l* 67.7%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right)} \]

      6. *-commutative 67.7%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      7. exp-to-pow 67.7%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      8. *-commutative 67.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      9. exp-to-pow 67.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      10. sub-neg 67.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

      11. metadata-eval 67.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

   3. Simplified 67.7%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 71.1%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 67.9%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 68.0%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 68.0%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 68.0%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

      5. metadata-eval 68.0%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)}}{y}}{e^{b}} \]

      6. sub-neg 68.0%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t - 1\right)}}}{y}}{e^{b}} \]

   7. Simplified 68.0%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t - 1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 81.0%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 34.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]

   10. Taylor expanded in y around 0 36.1%

       \[\leadsto \color{blue}{\frac{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}{y}} \]
   11. Step-by-step derivation

       1. +-commutative 36.1%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

       2. *-commutative 36.1%

          \[\leadsto \frac{\frac{x}{a} + -1 \cdot \frac{\color{blue}{x \cdot b}}{a}}{y} \]

       3. neg-mul-1 36.1%

          \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{x \cdot b}{a}\right)}}{y} \]

       4. unsub-neg 36.1%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{x \cdot b}{a}}}{y} \]

       5. associate-/l* 39.1%

          \[\leadsto \frac{\frac{x}{a} - \color{blue}{x \cdot \frac{b}{a}}}{y} \]

   12. Simplified 39.1%

       \[\leadsto \color{blue}{\frac{\frac{x}{a} - x \cdot \frac{b}{a}}{y}} \]

   if -2.99999999999999993e-19 < b

   1. Initial program 97.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.3%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. exp-diff 85.4%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 85.4%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 74.1%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. associate-/l* 71.5%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right)} \]

      6. *-commutative 71.5%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      7. exp-to-pow 71.5%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      8. *-commutative 71.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      9. exp-to-pow 72.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      10. sub-neg 72.2%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

      11. metadata-eval 72.2%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

   3. Simplified 72.2%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 64.2%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 62.1%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 62.7%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 62.7%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 62.7%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

      5. metadata-eval 62.7%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)}}{y}}{e^{b}} \]

      6. sub-neg 62.7%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t - 1\right)}}}{y}}{e^{b}} \]

   7. Simplified 62.7%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t - 1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 50.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 37.2%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-lft-out 37.7%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

   11. Simplified 37.7%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

   12. Taylor expanded in b around inf 43.0%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(b \cdot \left(y + \frac{y}{b}\right)\right)}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 41.5% accurate, 19.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.8 \cdot 10^{-10}:\\ \;\;\;\;\frac{b \cdot \frac{x}{-a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(b \cdot \left(y + \frac{y}{b}\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -8.8e-10) (/ (* b (/ x (- a))) y) (/ x (* a (* b (+ y (/ y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8.8e-10) {
		tmp = (b * (x / -a)) / y;
	} else {
		tmp = x / (a * (b * (y + (y / b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-8.8d-10)) then
        tmp = (b * (x / -a)) / y
    else
        tmp = x / (a * (b * (y + (y / b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8.8e-10) {
		tmp = (b * (x / -a)) / y;
	} else {
		tmp = x / (a * (b * (y + (y / b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -8.8e-10:
		tmp = (b * (x / -a)) / y
	else:
		tmp = x / (a * (b * (y + (y / b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -8.8e-10)
		tmp = Float64(Float64(b * Float64(x / Float64(-a))) / y);
	else
		tmp = Float64(x / Float64(a * Float64(b * Float64(y + Float64(y / b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -8.8e-10)
		tmp = (b * (x / -a)) / y;
	else
		tmp = x / (a * (b * (y + (y / b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -8.8e-10], N[(N[(b * N[(x / (-a)), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(b * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.7999999999999996e-10

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. exp-diff 67.2%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 67.2%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 67.2%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. associate-/l* 67.2%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right)} \]

      6. *-commutative 67.2%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      7. exp-to-pow 67.2%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      8. *-commutative 67.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      9. exp-to-pow 67.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      10. sub-neg 67.2%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

      11. metadata-eval 67.2%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

   3. Simplified 67.2%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 70.7%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 67.5%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 67.5%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 67.5%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 67.5%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

      5. metadata-eval 67.5%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)}}{y}}{e^{b}} \]

      6. sub-neg 67.5%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t - 1\right)}}}{y}}{e^{b}} \]

   7. Simplified 67.5%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t - 1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 80.7%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 33.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]

   10. Taylor expanded in b around inf 33.4%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]
   11. Step-by-step derivation

       1. associate-*r/ 33.4%

          \[\leadsto \color{blue}{\frac{-1 \cdot \left(b \cdot x\right)}{a \cdot y}} \]

       2. *-commutative 33.4%

          \[\leadsto \frac{-1 \cdot \color{blue}{\left(x \cdot b\right)}}{a \cdot y} \]

       3. *-commutative 33.4%

          \[\leadsto \frac{-1 \cdot \left(x \cdot b\right)}{\color{blue}{y \cdot a}} \]

       4. times-frac 35.1%

          \[\leadsto \color{blue}{\frac{-1}{y} \cdot \frac{x \cdot b}{a}} \]

       5. associate-*l/ 35.1%

          \[\leadsto \color{blue}{\frac{-1 \cdot \frac{x \cdot b}{a}}{y}} \]

       6. neg-mul-1 35.1%

          \[\leadsto \frac{\color{blue}{-\frac{x \cdot b}{a}}}{y} \]

       7. *-commutative 35.1%

          \[\leadsto \frac{-\frac{\color{blue}{b \cdot x}}{a}}{y} \]

       8. associate-/l* 35.0%

          \[\leadsto \frac{-\color{blue}{b \cdot \frac{x}{a}}}{y} \]

       9. distribute-rgt-neg-in 35.0%

          \[\leadsto \frac{\color{blue}{b \cdot \left(-\frac{x}{a}\right)}}{y} \]

       10. distribute-neg-frac 35.0%

           \[\leadsto \frac{b \cdot \color{blue}{\frac{-x}{a}}}{y} \]

   12. Simplified 35.0%

       \[\leadsto \color{blue}{\frac{b \cdot \frac{-x}{a}}{y}} \]

   if -8.7999999999999996e-10 < b

   1. Initial program 97.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.3%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. exp-diff 85.5%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 85.5%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 74.2%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. associate-/l* 71.6%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right)} \]

      6. *-commutative 71.6%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      7. exp-to-pow 71.6%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      8. *-commutative 71.6%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      9. exp-to-pow 72.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      10. sub-neg 72.3%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

      11. metadata-eval 72.3%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

   3. Simplified 72.3%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 64.4%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 62.3%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 62.9%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 62.9%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 62.9%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

      5. metadata-eval 62.9%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)}}{y}}{e^{b}} \]

      6. sub-neg 62.9%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t - 1\right)}}}{y}}{e^{b}} \]

   7. Simplified 62.9%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t - 1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 50.8%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 37.5%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-lft-out 38.0%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

   11. Simplified 38.0%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

   12. Taylor expanded in b around inf 43.3%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(b \cdot \left(y + \frac{y}{b}\right)\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.8 \cdot 10^{-10}:\\ \;\;\;\;\frac{b \cdot \frac{x}{-a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(b \cdot \left(y + \frac{y}{b}\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 37.5% accurate, 19.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+40}:\\ \;\;\;\;\frac{b \cdot \frac{x}{-a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{a} \cdot \frac{x}{y \cdot \left(1 + b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.2e+40)
   (/ (* b (/ x (- a))) y)
   (* (/ 1.0 a) (/ x (* y (+ 1.0 b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.2e+40) {
		tmp = (b * (x / -a)) / y;
	} else {
		tmp = (1.0 / a) * (x / (y * (1.0 + b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.2d+40)) then
        tmp = (b * (x / -a)) / y
    else
        tmp = (1.0d0 / a) * (x / (y * (1.0d0 + b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.2e+40) {
		tmp = (b * (x / -a)) / y;
	} else {
		tmp = (1.0 / a) * (x / (y * (1.0 + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.2e+40:
		tmp = (b * (x / -a)) / y
	else:
		tmp = (1.0 / a) * (x / (y * (1.0 + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.2e+40)
		tmp = Float64(Float64(b * Float64(x / Float64(-a))) / y);
	else
		tmp = Float64(Float64(1.0 / a) * Float64(x / Float64(y * Float64(1.0 + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.2e+40)
		tmp = (b * (x / -a)) / y;
	else
		tmp = (1.0 / a) * (x / (y * (1.0 + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.2e+40], N[(N[(b * N[(x / (-a)), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(1.0 / a), $MachinePrecision] * N[(x / N[(y * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.2e40

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. exp-diff 65.4%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 65.4%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 65.4%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. associate-/l* 65.4%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right)} \]

      6. *-commutative 65.4%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      7. exp-to-pow 65.4%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      8. *-commutative 65.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      9. exp-to-pow 65.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      10. sub-neg 65.4%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

      11. metadata-eval 65.4%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

   3. Simplified 65.4%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 73.2%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 69.4%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 69.4%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 69.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 69.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

      5. metadata-eval 69.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)}}{y}}{e^{b}} \]

      6. sub-neg 69.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t - 1\right)}}}{y}}{e^{b}} \]

   7. Simplified 69.4%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t - 1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 86.7%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 36.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]

   10. Taylor expanded in b around inf 36.7%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]
   11. Step-by-step derivation

       1. associate-*r/ 36.7%

          \[\leadsto \color{blue}{\frac{-1 \cdot \left(b \cdot x\right)}{a \cdot y}} \]

       2. *-commutative 36.7%

          \[\leadsto \frac{-1 \cdot \color{blue}{\left(x \cdot b\right)}}{a \cdot y} \]

       3. *-commutative 36.7%

          \[\leadsto \frac{-1 \cdot \left(x \cdot b\right)}{\color{blue}{y \cdot a}} \]

       4. times-frac 38.7%

          \[\leadsto \color{blue}{\frac{-1}{y} \cdot \frac{x \cdot b}{a}} \]

       5. associate-*l/ 38.7%

          \[\leadsto \color{blue}{\frac{-1 \cdot \frac{x \cdot b}{a}}{y}} \]

       6. neg-mul-1 38.7%

          \[\leadsto \frac{\color{blue}{-\frac{x \cdot b}{a}}}{y} \]

       7. *-commutative 38.7%

          \[\leadsto \frac{-\frac{\color{blue}{b \cdot x}}{a}}{y} \]

       8. associate-/l* 38.6%

          \[\leadsto \frac{-\color{blue}{b \cdot \frac{x}{a}}}{y} \]

       9. distribute-rgt-neg-in 38.6%

          \[\leadsto \frac{\color{blue}{b \cdot \left(-\frac{x}{a}\right)}}{y} \]

       10. distribute-neg-frac 38.6%

           \[\leadsto \frac{b \cdot \color{blue}{\frac{-x}{a}}}{y} \]

   12. Simplified 38.6%

       \[\leadsto \color{blue}{\frac{b \cdot \frac{-x}{a}}{y}} \]

   if -1.2e40 < b

   1. Initial program 97.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.4%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. exp-diff 85.1%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 85.1%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 74.3%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. associate-/l* 71.9%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right)} \]

      6. *-commutative 71.9%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      7. exp-to-pow 71.9%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      8. *-commutative 71.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      9. exp-to-pow 72.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      10. sub-neg 72.5%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

      11. metadata-eval 72.5%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

   3. Simplified 72.5%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 64.0%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 62.0%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 62.6%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 62.6%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 62.6%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

      5. metadata-eval 62.6%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)}}{y}}{e^{b}} \]

      6. sub-neg 62.6%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t - 1\right)}}}{y}}{e^{b}} \]

   7. Simplified 62.6%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t - 1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 50.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 36.4%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-lft-out 36.9%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

   11. Simplified 36.9%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]
   12. Step-by-step derivation

       1. *-un-lft-identity 36.9%

          \[\leadsto \frac{\color{blue}{1 \cdot x}}{a \cdot \left(y + b \cdot y\right)} \]

       2. times-frac 37.3%

          \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y + b \cdot y}} \]

       3. distribute-rgt1-in 37.3%

          \[\leadsto \frac{1}{a} \cdot \frac{x}{\color{blue}{\left(b + 1\right) \cdot y}} \]

   13. Applied egg-rr 37.3%

       \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{\left(b + 1\right) \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+40}:\\ \;\;\;\;\frac{b \cdot \frac{x}{-a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{a} \cdot \frac{x}{y \cdot \left(1 + b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 38.3% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{-12}:\\ \;\;\;\;\frac{b \cdot \frac{x}{-a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.7e-12) (/ (* b (/ 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 (b <= -3.7e-12) {
		tmp = (b * (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 (b <= (-3.7d-12)) then
        tmp = (b * (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 (b <= -3.7e-12) {
		tmp = (b * (x / -a)) / y;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.7e-12:
		tmp = (b * (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 (b <= -3.7e-12)
		tmp = Float64(Float64(b * Float64(x / Float64(-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 (b <= -3.7e-12)
		tmp = (b * (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[b, -3.7e-12], N[(N[(b * N[(x / (-a)), $MachinePrecision]), $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 b < -3.69999999999999999e-12

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. exp-diff 67.2%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 67.2%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 67.2%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. associate-/l* 67.2%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right)} \]

      6. *-commutative 67.2%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      7. exp-to-pow 67.2%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      8. *-commutative 67.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      9. exp-to-pow 67.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      10. sub-neg 67.2%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

      11. metadata-eval 67.2%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

   3. Simplified 67.2%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 70.7%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 67.5%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 67.5%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 67.5%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 67.5%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

      5. metadata-eval 67.5%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)}}{y}}{e^{b}} \]

      6. sub-neg 67.5%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t - 1\right)}}}{y}}{e^{b}} \]

   7. Simplified 67.5%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t - 1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 80.7%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 33.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]

   10. Taylor expanded in b around inf 33.4%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]
   11. Step-by-step derivation

       1. associate-*r/ 33.4%

          \[\leadsto \color{blue}{\frac{-1 \cdot \left(b \cdot x\right)}{a \cdot y}} \]

       2. *-commutative 33.4%

          \[\leadsto \frac{-1 \cdot \color{blue}{\left(x \cdot b\right)}}{a \cdot y} \]

       3. *-commutative 33.4%

          \[\leadsto \frac{-1 \cdot \left(x \cdot b\right)}{\color{blue}{y \cdot a}} \]

       4. times-frac 35.1%

          \[\leadsto \color{blue}{\frac{-1}{y} \cdot \frac{x \cdot b}{a}} \]

       5. associate-*l/ 35.1%

          \[\leadsto \color{blue}{\frac{-1 \cdot \frac{x \cdot b}{a}}{y}} \]

       6. neg-mul-1 35.1%

          \[\leadsto \frac{\color{blue}{-\frac{x \cdot b}{a}}}{y} \]

       7. *-commutative 35.1%

          \[\leadsto \frac{-\frac{\color{blue}{b \cdot x}}{a}}{y} \]

       8. associate-/l* 35.0%

          \[\leadsto \frac{-\color{blue}{b \cdot \frac{x}{a}}}{y} \]

       9. distribute-rgt-neg-in 35.0%

          \[\leadsto \frac{\color{blue}{b \cdot \left(-\frac{x}{a}\right)}}{y} \]

       10. distribute-neg-frac 35.0%

           \[\leadsto \frac{b \cdot \color{blue}{\frac{-x}{a}}}{y} \]

   12. Simplified 35.0%

       \[\leadsto \color{blue}{\frac{b \cdot \frac{-x}{a}}{y}} \]

   if -3.69999999999999999e-12 < b

   1. Initial program 97.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.3%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. exp-diff 85.5%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 85.5%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 74.2%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. associate-/l* 71.6%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right)} \]

      6. *-commutative 71.6%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      7. exp-to-pow 71.6%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      8. *-commutative 71.6%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      9. exp-to-pow 72.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      10. sub-neg 72.3%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

      11. metadata-eval 72.3%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

   3. Simplified 72.3%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 64.4%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 62.3%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 62.9%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 62.9%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 62.9%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

      5. metadata-eval 62.9%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)}}{y}}{e^{b}} \]

      6. sub-neg 62.9%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t - 1\right)}}}{y}}{e^{b}} \]

   7. Simplified 62.9%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t - 1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 50.8%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 37.5%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-lft-out 38.0%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

   11. Simplified 38.0%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{-12}:\\ \;\;\;\;\frac{b \cdot \frac{x}{-a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 34.7% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 3.8 \cdot 10^{+17}:\\ \;\;\;\;\frac{1}{a} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 3.8e+17) (* (/ 1.0 a) (/ x y)) (/ x (* a (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3.8e+17) {
		tmp = (1.0 / a) * (x / 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 <= 3.8d+17) then
        tmp = (1.0d0 / a) * (x / 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 <= 3.8e+17) {
		tmp = (1.0 / a) * (x / y);
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 3.8e+17:
		tmp = (1.0 / a) * (x / y)
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 3.8e+17)
		tmp = Float64(Float64(1.0 / a) * Float64(x / 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 <= 3.8e+17)
		tmp = (1.0 / a) * (x / y);
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 3.8e+17], N[(N[(1.0 / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 3.8e17

   1. Initial program 97.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.3%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. exp-diff 86.9%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 86.9%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 78.7%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. associate-/l* 76.1%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right)} \]

      6. *-commutative 76.1%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      7. exp-to-pow 76.1%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      8. *-commutative 76.1%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      9. exp-to-pow 76.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      10. sub-neg 76.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

      11. metadata-eval 76.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

   3. Simplified 76.8%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 65.8%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 64.7%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 65.4%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 65.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 65.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

      5. metadata-eval 65.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)}}{y}}{e^{b}} \]

      6. sub-neg 65.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t - 1\right)}}}{y}}{e^{b}} \]

   7. Simplified 65.4%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t - 1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 51.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 32.7%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-un-lft-identity 32.7%

          \[\leadsto \frac{\color{blue}{1 \cdot x}}{a \cdot y} \]

       2. times-frac 33.6%

          \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y}} \]

   11. Applied egg-rr 33.6%

       \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y}} \]

   if 3.8e17 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. exp-diff 62.9%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 62.9%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 53.2%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. associate-/l* 53.2%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right)} \]

      6. *-commutative 53.2%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      7. exp-to-pow 53.2%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      8. *-commutative 53.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      9. exp-to-pow 53.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      10. sub-neg 53.2%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

      11. metadata-eval 53.2%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

   3. Simplified 53.2%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 66.2%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 59.8%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 59.8%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 59.8%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 59.8%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

      5. metadata-eval 59.8%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)}}{y}}{e^{b}} \]

      6. sub-neg 59.8%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t - 1\right)}}}{y}}{e^{b}} \]

   7. Simplified 59.8%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t - 1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 77.8%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 43.6%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-lft-out 43.6%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

   11. Simplified 43.6%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

   12. Taylor expanded in b around inf 43.6%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(b \cdot y\right)}} \]
   13. Step-by-step derivation

       1. *-commutative 43.6%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y \cdot b\right)}} \]

   14. Simplified 43.6%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot b\right)}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 25: 31.1% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+87}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{a} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2e+87) (/ (/ x a) y) (* (/ 1.0 a) (/ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2e+87) {
		tmp = (x / a) / y;
	} else {
		tmp = (1.0 / a) * (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2d+87)) then
        tmp = (x / a) / y
    else
        tmp = (1.0d0 / a) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2e+87) {
		tmp = (x / a) / y;
	} else {
		tmp = (1.0 / a) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2e+87:
		tmp = (x / a) / y
	else:
		tmp = (1.0 / a) * (x / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2e+87)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(Float64(1.0 / a) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2e+87)
		tmp = (x / a) / y;
	else
		tmp = (1.0 / a) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2e+87], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(N[(1.0 / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.9999999999999999e87

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. exp-diff 75.0%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 75.0%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 55.0%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. associate-/l* 55.0%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right)} \]

      6. *-commutative 55.0%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      7. exp-to-pow 55.0%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      8. *-commutative 55.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      9. exp-to-pow 55.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      10. sub-neg 55.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

      11. metadata-eval 55.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

   3. Simplified 55.0%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 72.6%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 72.6%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 72.6%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 72.6%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 72.6%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

      5. metadata-eval 72.6%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)}}{y}}{e^{b}} \]

      6. sub-neg 72.6%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t - 1\right)}}}{y}}{e^{b}} \]

   7. Simplified 72.6%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t - 1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 51.3%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 40.2%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. associate-/r* 47.0%

          \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y}} \]

   11. Applied egg-rr 47.0%

       \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y}} \]

   if -1.9999999999999999e87 < t

   1. Initial program 98.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.5%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. exp-diff 82.3%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 82.3%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 75.8%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. associate-/l* 73.4%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right)} \]

      6. *-commutative 73.4%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      7. exp-to-pow 73.4%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      8. *-commutative 73.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      9. exp-to-pow 74.1%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      10. sub-neg 74.1%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

      11. metadata-eval 74.1%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

   3. Simplified 74.1%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 64.6%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 61.9%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 62.4%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 62.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 62.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

      5. metadata-eval 62.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)}}{y}}{e^{b}} \]

      6. sub-neg 62.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t - 1\right)}}}{y}}{e^{b}} \]

   7. Simplified 62.4%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t - 1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 59.2%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 30.0%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-un-lft-identity 30.0%

          \[\leadsto \frac{\color{blue}{1 \cdot x}}{a \cdot y} \]

       2. times-frac 31.6%

          \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y}} \]

   11. Applied egg-rr 31.6%

       \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 26: 30.5% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 5.5 \cdot 10^{-44}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 5.5e-44) (/ (/ x a) y) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 5.5e-44) {
		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 (z <= 5.5d-44) 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 (z <= 5.5e-44) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 5.5e-44:
		tmp = (x / a) / y
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 5.5e-44)
		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 (z <= 5.5e-44)
		tmp = (x / a) / y;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 5.5e-44], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5.49999999999999993e-44

   1. Initial program 99.3%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. exp-diff 75.0%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 75.0%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 66.8%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. associate-/l* 63.5%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right)} \]

      6. *-commutative 63.5%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      7. exp-to-pow 63.5%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      8. *-commutative 63.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      9. exp-to-pow 64.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      10. sub-neg 64.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

      11. metadata-eval 64.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

   3. Simplified 64.0%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 59.5%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 56.2%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 56.6%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 56.6%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 56.6%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

      5. metadata-eval 56.6%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)}}{y}}{e^{b}} \]

      6. sub-neg 56.6%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t - 1\right)}}}{y}}{e^{b}} \]

   7. Simplified 56.6%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t - 1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 58.8%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 30.2%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. associate-/r* 34.7%

          \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y}} \]

   11. Applied egg-rr 34.7%

       \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y}} \]

   if 5.49999999999999993e-44 < z

   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* 99.4%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. exp-diff 86.7%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 86.7%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 77.7%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. associate-/l* 77.0%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right)} \]

      6. *-commutative 77.0%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      7. exp-to-pow 77.0%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      8. *-commutative 77.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      9. exp-to-pow 77.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      10. sub-neg 77.5%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

      11. metadata-eval 77.5%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

   3. Simplified 77.5%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 71.7%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 70.2%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 70.7%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 70.7%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 70.7%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

      5. metadata-eval 70.7%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)}}{y}}{e^{b}} \]

      6. sub-neg 70.7%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t - 1\right)}}}{y}}{e^{b}} \]

   7. Simplified 70.7%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t - 1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 57.2%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 32.8%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 5.5 \cdot 10^{-44}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 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 98.3%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. associate-/l* 98.7%

      \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

   2. exp-diff 81.1%

      \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

   3. associate-/l/ 81.1%

      \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

   4. exp-sum 72.5%

      \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

   5. associate-/l* 70.6%

      \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right)} \]

   6. *-commutative 70.6%

      \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

   7. exp-to-pow 70.6%

      \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

   8. *-commutative 70.6%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

   9. exp-to-pow 71.1%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

   10. sub-neg 71.1%

       \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

   11. metadata-eval 71.1%

       \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

3. Simplified 71.1%

   \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 65.9%

   \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
6. Step-by-step derivation

   1. associate-/r* 63.5%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

   2. exp-to-pow 64.0%

      \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

   3. sub-neg 64.0%

      \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

   4. metadata-eval 64.0%

      \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   5. metadata-eval 64.0%

      \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)}}{y}}{e^{b}} \]

   6. sub-neg 64.0%

      \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t - 1\right)}}}{y}}{e^{b}} \]

7. Simplified 64.0%

   \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t - 1\right)}}{y}}{e^{b}}} \]

8. Taylor expanded in t around 0 57.9%

   \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

9. Taylor expanded in b around 0 31.6%

   \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]

10. Final simplification 31.6%

    \[\leadsto \frac{x}{y \cdot a} \]
11. Add Preprocessing

Developer target: 72.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t - 1\right)}\\ t_2 := \frac{x \cdot \frac{t\_1}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{if}\;t < -0.8845848504127471:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 852031.2288374073:\\ \;\;\;\;\frac{\frac{x}{y} \cdot t\_1}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (- t 1.0)))
        (t_2 (/ (* x (/ t_1 y)) (- (+ b 1.0) (* y (log z))))))
   (if (< t -0.8845848504127471)
     t_2
     (if (< t 852031.2288374073)
       (/ (* (/ x y) t_1) (exp (- b (* (log z) y))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a ** (t - 1.0d0)
    t_2 = (x * (t_1 / y)) / ((b + 1.0d0) - (y * log(z)))
    if (t < (-0.8845848504127471d0)) then
        tmp = t_2
    else if (t < 852031.2288374073d0) then
        tmp = ((x / y) * t_1) / exp((b - (log(z) * y)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * Math.log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / Math.exp((b - (Math.log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, (t - 1.0))
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * math.log(z)))
	tmp = 0
	if t < -0.8845848504127471:
		tmp = t_2
	elif t < 852031.2288374073:
		tmp = ((x / y) * t_1) / math.exp((b - (math.log(z) * y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = a ^ Float64(t - 1.0)
	t_2 = Float64(Float64(x * Float64(t_1 / y)) / Float64(Float64(b + 1.0) - Float64(y * log(z))))
	tmp = 0.0
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = Float64(Float64(Float64(x / y) * t_1) / exp(Float64(b - Float64(log(z) * y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a ^ (t - 1.0);
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	tmp = 0.0;
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] / N[(N[(b + 1.0), $MachinePrecision] - N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -0.8845848504127471], t$95$2, If[Less[t, 852031.2288374073], N[(N[(N[(x / y), $MachinePrecision] * t$95$1), $MachinePrecision] / N[Exp[N[(b - N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024097 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (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))