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

Percentage Accurate: 98.5% → 98.5%

Time: 18.0s

Alternatives: 24

Speedup: 1.0×

• 46.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * exp((((y * log(z)) + (log(a) * (t + -1.0))) - 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)) + (log(a) * (t + (-1.0d0)))) - 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)) + (Math.log(a) * (t + -1.0))) - b))) / y;
}

Python

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

Julia

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

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x * exp((((y * log(z)) + (log(a) * (t + -1.0))) - 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[Log[a], $MachinePrecision] * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Derivation

1. Initial program 97.4%

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

3. Final simplification 97.4%

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

Alternative 2: 79.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-19}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-162}:\\ \;\;\;\;\frac{\frac{x \cdot {a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{e^{b} \cdot \left(y \cdot a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{y \cdot \log z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.5e-19)
   (/ (/ (* x (pow z y)) a) y)
   (if (<= y 2.8e-162)
     (/ (/ (* x (pow a (+ t -1.0))) (exp b)) y)
     (if (<= y 1.75e+84)
       (* x (/ (pow a t) (* (exp b) (* y a))))
       (/ (* x (exp (* y (log z)))) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.5e-19) {
		tmp = ((x * pow(z, y)) / a) / y;
	} else if (y <= 2.8e-162) {
		tmp = ((x * pow(a, (t + -1.0))) / exp(b)) / y;
	} else if (y <= 1.75e+84) {
		tmp = x * (pow(a, t) / (exp(b) * (y * a)));
	} else {
		tmp = (x * exp((y * log(z)))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-3.5d-19)) then
        tmp = ((x * (z ** y)) / a) / y
    else if (y <= 2.8d-162) then
        tmp = ((x * (a ** (t + (-1.0d0)))) / exp(b)) / y
    else if (y <= 1.75d+84) then
        tmp = x * ((a ** t) / (exp(b) * (y * a)))
    else
        tmp = (x * exp((y * log(z)))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.5e-19) {
		tmp = ((x * Math.pow(z, y)) / a) / y;
	} else if (y <= 2.8e-162) {
		tmp = ((x * Math.pow(a, (t + -1.0))) / Math.exp(b)) / y;
	} else if (y <= 1.75e+84) {
		tmp = x * (Math.pow(a, t) / (Math.exp(b) * (y * a)));
	} else {
		tmp = (x * Math.exp((y * Math.log(z)))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.5e-19:
		tmp = ((x * math.pow(z, y)) / a) / y
	elif y <= 2.8e-162:
		tmp = ((x * math.pow(a, (t + -1.0))) / math.exp(b)) / y
	elif y <= 1.75e+84:
		tmp = x * (math.pow(a, t) / (math.exp(b) * (y * a)))
	else:
		tmp = (x * math.exp((y * math.log(z)))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.5e-19)
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	elseif (y <= 2.8e-162)
		tmp = Float64(Float64(Float64(x * (a ^ Float64(t + -1.0))) / exp(b)) / y);
	elseif (y <= 1.75e+84)
		tmp = Float64(x * Float64((a ^ t) / Float64(exp(b) * Float64(y * a))));
	else
		tmp = Float64(Float64(x * exp(Float64(y * log(z)))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.5e-19)
		tmp = ((x * (z ^ y)) / a) / y;
	elseif (y <= 2.8e-162)
		tmp = ((x * (a ^ (t + -1.0))) / exp(b)) / y;
	elseif (y <= 1.75e+84)
		tmp = x * ((a ^ t) / (exp(b) * (y * a)));
	else
		tmp = (x * exp((y * log(z)))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.5e-19], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 2.8e-162], N[(N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 1.75e+84], N[(x * N[(N[Power[a, t], $MachinePrecision] / N[(N[Exp[b], $MachinePrecision] * N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Exp[N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.50000000000000015e-19

   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/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 53.9%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 62.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 62.0%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a}{{z}^{y}}\right)}\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. pow-lowering-pow.f64 73.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   10. Simplified 73.2%

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

   11. Taylor expanded in x around 0

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

       1. associate-/r* N/A

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

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot {z}^{y}}{a}\right), \color{blue}{y}\right) \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot {z}^{y}\right), a\right), y\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({z}^{y}\right)\right), a\right), y\right) \]

       5. pow-lowering-pow.f64 81.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(z, y\right)\right), a\right), y\right) \]

   13. Simplified 81.3%

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

   if -3.50000000000000015e-19 < y < 2.80000000000000022e-162

   1. Initial program 95.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot e^{\log a \cdot \left(t - 1\right) - b}\right)}, y\right) \]
   4. Step-by-step derivation

      1. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}\right), y\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{e^{b}}\right), y\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot e^{\log a \cdot \left(t - 1\right)}\right), \left(e^{b}\right)\right), y\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(e^{\log a \cdot \left(t - 1\right)}\right)\right), \left(e^{b}\right)\right), y\right) \]

      5. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({a}^{\left(t - 1\right)}\right)\right), \left(e^{b}\right)\right), y\right) \]

      6. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t - 1\right)\right)\right), \left(e^{b}\right)\right), y\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), \left(e^{b}\right)\right), y\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \left(t + -1\right)\right)\right), \left(e^{b}\right)\right), y\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right)\right), \left(e^{b}\right)\right), y\right) \]

      10. exp-lowering-exp.f64 89.0%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right)\right), \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   5. Simplified 89.0%

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

   if 2.80000000000000022e-162 < y < 1.7499999999999999e84

   1. Initial program 95.0%

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

   3. Taylor expanded in z around inf

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. prod-exp N/A

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

      4. times-frac N/A

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

      5. associate-/l* N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{e^{-1 \cdot \left(y \cdot \log \left(\frac{1}{z}\right)\right)} \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}\right)}\right) \]

      7. associate-/l/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{\frac{e^{-1 \cdot \left(y \cdot \log \left(\frac{1}{z}\right)\right)} \cdot e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}{\color{blue}{y}}\right)\right) \]

   5. Simplified 98.2%

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

      1. exp-diff N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{e^{\log a \cdot \left(t + -1\right) - \left(\mathsf{neg}\left(y \cdot \log z\right)\right)}}{e^{b}}\right), y\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{1}{\frac{e^{b}}{e^{\log a \cdot \left(t + -1\right) - \left(\mathsf{neg}\left(y \cdot \log z\right)\right)}}}\right), y\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{1}{\frac{e^{b}}{e^{\log a \cdot \left(t + -1\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y \cdot \log z\right)\right)\right)\right)}}}\right), y\right)\right) \]

      4. exp-sum N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{1}{\frac{e^{b}}{e^{\log a \cdot \left(t + -1\right)} \cdot e^{\mathsf{neg}\left(\left(\mathsf{neg}\left(y \cdot \log z\right)\right)\right)}}}\right), y\right)\right) \]

      5. pow-to-exp N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{1}{\frac{e^{b}}{{a}^{\left(t + -1\right)} \cdot e^{\mathsf{neg}\left(\left(\mathsf{neg}\left(y \cdot \log z\right)\right)\right)}}}\right), y\right)\right) \]

      6. remove-double-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{1}{\frac{e^{b}}{{a}^{\left(t + -1\right)} \cdot e^{y \cdot \log z}}}\right), y\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{1}{\frac{e^{b}}{{a}^{\left(t + -1\right)} \cdot e^{\log z \cdot y}}}\right), y\right)\right) \]

      8. pow-to-exp N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{1}{\frac{e^{b}}{{a}^{\left(t + -1\right)} \cdot {z}^{y}}}\right), y\right)\right) \]

      9. associate-/l/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{1}{\frac{\frac{e^{b}}{{z}^{y}}}{{a}^{\left(t + -1\right)}}}\right), y\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{1}{\frac{\frac{e^{b}}{{z}^{y}}}{{a}^{\left(-1 + t\right)}}}\right), y\right)\right) \]

      11. unpow-prod-up N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{1}{\frac{\frac{e^{b}}{{z}^{y}}}{{a}^{-1} \cdot {a}^{t}}}\right), y\right)\right) \]

      12. inv-pow N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{1}{\frac{\frac{e^{b}}{{z}^{y}}}{\frac{1}{a} \cdot {a}^{t}}}\right), y\right)\right) \]

      13. associate-/l/ N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{1}{\frac{\frac{\frac{e^{b}}{{z}^{y}}}{{a}^{t}}}{\frac{1}{a}}}\right), y\right)\right) \]

   7. Applied egg-rr 76.8%

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

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{{a}^{t}}{a \cdot \left(y \cdot e^{b}\right)}\right)}\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left({a}^{t}\right), \color{blue}{\left(a \cdot \left(y \cdot e^{b}\right)\right)}\right)\right) \]

      2. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, t\right), \left(\color{blue}{a} \cdot \left(y \cdot e^{b}\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, t\right), \left(\left(y \cdot e^{b}\right) \cdot \color{blue}{a}\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, t\right), \left(\left(e^{b} \cdot y\right) \cdot a\right)\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, t\right), \left(e^{b} \cdot \color{blue}{\left(y \cdot a\right)}\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, t\right), \left(e^{b} \cdot \left(a \cdot \color{blue}{y}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, t\right), \mathsf{*.f64}\left(\left(e^{b}\right), \color{blue}{\left(a \cdot y\right)}\right)\right)\right) \]

      8. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, t\right), \mathsf{*.f64}\left(\mathsf{exp.f64}\left(b\right), \left(\color{blue}{a} \cdot y\right)\right)\right)\right) \]

      9. *-lowering-*.f64 80.9%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, t\right), \mathsf{*.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(a, \color{blue}{y}\right)\right)\right)\right) \]

   10. Simplified 80.9%

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

   if 1.7499999999999999e84 < 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 y around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(y \cdot \log z\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, \log z\right)\right)\right), y\right) \]

      2. log-lowering-log.f64 86.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, \mathsf{log.f64}\left(z\right)\right)\right)\right), y\right) \]

   5. Simplified 86.9%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-19}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-162}:\\ \;\;\;\;\frac{\frac{x \cdot {a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{e^{b} \cdot \left(y \cdot a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{y \cdot \log z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+59}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+85}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{y \cdot \log z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.05e+59)
   (/ (/ (* x (pow z y)) a) y)
   (if (<= y 1.6e+85)
     (/ (* x (exp (- (* (log a) (+ t -1.0)) b))) y)
     (/ (* x (exp (* y (log z)))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.05e+59) {
		tmp = ((x * pow(z, y)) / a) / y;
	} else if (y <= 1.6e+85) {
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	} else {
		tmp = (x * exp((y * log(z)))) / 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 <= (-1.05d+59)) then
        tmp = ((x * (z ** y)) / a) / y
    else if (y <= 1.6d+85) then
        tmp = (x * exp(((log(a) * (t + (-1.0d0))) - b))) / y
    else
        tmp = (x * exp((y * log(z)))) / 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 <= -1.05e+59) {
		tmp = ((x * Math.pow(z, y)) / a) / y;
	} else if (y <= 1.6e+85) {
		tmp = (x * Math.exp(((Math.log(a) * (t + -1.0)) - b))) / y;
	} else {
		tmp = (x * Math.exp((y * Math.log(z)))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.05e+59:
		tmp = ((x * math.pow(z, y)) / a) / y
	elif y <= 1.6e+85:
		tmp = (x * math.exp(((math.log(a) * (t + -1.0)) - b))) / y
	else:
		tmp = (x * math.exp((y * math.log(z)))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.05e+59)
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	elseif (y <= 1.6e+85)
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t + -1.0)) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(y * log(z)))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.05e+59)
		tmp = ((x * (z ^ y)) / a) / y;
	elseif (y <= 1.6e+85)
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	else
		tmp = (x * exp((y * log(z)))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.05e+59], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 1.6e+85], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.04999999999999992e59

   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/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 54.5%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 63.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 63.7%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a}{{z}^{y}}\right)}\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. pow-lowering-pow.f64 79.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   10. Simplified 79.7%

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

   11. Taylor expanded in x around 0

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

       1. associate-/r* N/A

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

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot {z}^{y}}{a}\right), \color{blue}{y}\right) \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot {z}^{y}\right), a\right), y\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({z}^{y}\right)\right), a\right), y\right) \]

       5. pow-lowering-pow.f64 88.8%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(z, y\right)\right), a\right), y\right) \]

   13. Simplified 88.8%

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

   if -1.04999999999999992e59 < y < 1.60000000000000009e85

   1. Initial program 96.1%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(\log a \cdot \left(t - 1\right) - b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\left(\log a \cdot \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\log a, \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      3. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), b\right)\right)\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + -1\right)\right), b\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 91.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \mathsf{+.f64}\left(t, -1\right)\right), b\right)\right)\right), y\right) \]

   5. Simplified 91.1%

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

   if 1.60000000000000009e85 < 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 y around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(y \cdot \log z\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, \log z\right)\right)\right), y\right) \]

      2. log-lowering-log.f64 86.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, \mathsf{log.f64}\left(z\right)\right)\right)\right), y\right) \]

   5. Simplified 86.9%

      \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z}}}{y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 77.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-19}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+85}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{e^{b} \cdot \left(y \cdot a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{y \cdot \log z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.5e-19)
   (/ (/ (* x (pow z y)) a) y)
   (if (<= y 5.1e+85)
     (/ (* x (pow a t)) (* (exp b) (* y a)))
     (/ (* x (exp (* y (log z)))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.5e-19) {
		tmp = ((x * pow(z, y)) / a) / y;
	} else if (y <= 5.1e+85) {
		tmp = (x * pow(a, t)) / (exp(b) * (y * a));
	} else {
		tmp = (x * exp((y * log(z)))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-3.5d-19)) then
        tmp = ((x * (z ** y)) / a) / y
    else if (y <= 5.1d+85) then
        tmp = (x * (a ** t)) / (exp(b) * (y * a))
    else
        tmp = (x * exp((y * log(z)))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.5e-19) {
		tmp = ((x * Math.pow(z, y)) / a) / y;
	} else if (y <= 5.1e+85) {
		tmp = (x * Math.pow(a, t)) / (Math.exp(b) * (y * a));
	} else {
		tmp = (x * Math.exp((y * Math.log(z)))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.5e-19:
		tmp = ((x * math.pow(z, y)) / a) / y
	elif y <= 5.1e+85:
		tmp = (x * math.pow(a, t)) / (math.exp(b) * (y * a))
	else:
		tmp = (x * math.exp((y * math.log(z)))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.5e-19)
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	elseif (y <= 5.1e+85)
		tmp = Float64(Float64(x * (a ^ t)) / Float64(exp(b) * Float64(y * a)));
	else
		tmp = Float64(Float64(x * exp(Float64(y * log(z)))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.5e-19)
		tmp = ((x * (z ^ y)) / a) / y;
	elseif (y <= 5.1e+85)
		tmp = (x * (a ^ t)) / (exp(b) * (y * a));
	else
		tmp = (x * exp((y * log(z)))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.5e-19], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 5.1e+85], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / N[(N[Exp[b], $MachinePrecision] * N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Exp[N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.50000000000000015e-19

   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/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 53.9%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 62.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 62.0%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a}{{z}^{y}}\right)}\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. pow-lowering-pow.f64 73.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   10. Simplified 73.2%

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

   11. Taylor expanded in x around 0

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

       1. associate-/r* N/A

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

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot {z}^{y}}{a}\right), \color{blue}{y}\right) \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot {z}^{y}\right), a\right), y\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({z}^{y}\right)\right), a\right), y\right) \]

       5. pow-lowering-pow.f64 81.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(z, y\right)\right), a\right), y\right) \]

   13. Simplified 81.3%

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

   if -3.50000000000000015e-19 < y < 5.0999999999999998e85

   1. Initial program 95.6%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 78.2%

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

      1. associate-/r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\frac{e^{b}}{{z}^{y}}}{\color{blue}{{a}^{\left(t + -1\right)}}}\right)\right) \]

      2. unpow-prod-up N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\frac{e^{b}}{{z}^{y}}}{{a}^{t} \cdot \color{blue}{{a}^{-1}}}\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\frac{\frac{e^{b}}{{z}^{y}}}{{a}^{t}}}{\color{blue}{{a}^{-1}}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(\frac{\frac{e^{b}}{{z}^{y}}}{{a}^{t}}\right), \color{blue}{\left({a}^{-1}\right)}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\frac{e^{b}}{{z}^{y}}\right), \left({a}^{t}\right)\right), \left({\color{blue}{a}}^{-1}\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(e^{b}\right), \left({z}^{y}\right)\right), \left({a}^{t}\right)\right), \left({a}^{-1}\right)\right)\right) \]

      7. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left({z}^{y}\right)\right), \left({a}^{t}\right)\right), \left({a}^{-1}\right)\right)\right) \]

      8. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{pow.f64}\left(z, y\right)\right), \left({a}^{t}\right)\right), \left({a}^{-1}\right)\right)\right) \]

      9. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{pow.f64}\left(z, y\right)\right), \mathsf{pow.f64}\left(a, t\right)\right), \left({a}^{-1}\right)\right)\right) \]

      10. unpow-1 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{pow.f64}\left(z, y\right)\right), \mathsf{pow.f64}\left(a, t\right)\right), \left(\frac{1}{\color{blue}{a}}\right)\right)\right) \]

      11. /-lowering-/.f64 78.4%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{pow.f64}\left(z, y\right)\right), \mathsf{pow.f64}\left(a, t\right)\right), \mathsf{/.f64}\left(1, \color{blue}{a}\right)\right)\right) \]

   6. Applied egg-rr 78.4%

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

   7. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot {a}^{t}\right), \color{blue}{\left(a \cdot \left(y \cdot e^{b}\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({a}^{t}\right)\right), \left(\color{blue}{a} \cdot \left(y \cdot e^{b}\right)\right)\right) \]

      3. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, t\right)\right), \left(a \cdot \left(y \cdot e^{b}\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, t\right)\right), \left(\left(a \cdot y\right) \cdot \color{blue}{e^{b}}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, t\right)\right), \mathsf{*.f64}\left(\left(a \cdot y\right), \color{blue}{\left(e^{b}\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, t\right)\right), \mathsf{*.f64}\left(\left(y \cdot a\right), \left(e^{\color{blue}{b}}\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, a\right), \left(e^{\color{blue}{b}}\right)\right)\right) \]

      8. exp-lowering-exp.f64 82.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, a\right), \mathsf{exp.f64}\left(b\right)\right)\right) \]

   9. Simplified 82.9%

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

   if 5.0999999999999998e85 < 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 y around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(y \cdot \log z\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, \log z\right)\right)\right), y\right) \]

      2. log-lowering-log.f64 86.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, \mathsf{log.f64}\left(z\right)\right)\right)\right), y\right) \]

   5. Simplified 86.9%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-19}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+85}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{e^{b} \cdot \left(y \cdot a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{y \cdot \log z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-19}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{e^{b} \cdot \left(y \cdot a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{y \cdot \log z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.5e-19)
   (/ (/ (* x (pow z y)) a) y)
   (if (<= y 3.6e+85)
     (* x (/ (pow a t) (* (exp b) (* y a))))
     (/ (* x (exp (* y (log z)))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.5e-19) {
		tmp = ((x * pow(z, y)) / a) / y;
	} else if (y <= 3.6e+85) {
		tmp = x * (pow(a, t) / (exp(b) * (y * a)));
	} else {
		tmp = (x * exp((y * log(z)))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-3.5d-19)) then
        tmp = ((x * (z ** y)) / a) / y
    else if (y <= 3.6d+85) then
        tmp = x * ((a ** t) / (exp(b) * (y * a)))
    else
        tmp = (x * exp((y * log(z)))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.5e-19) {
		tmp = ((x * Math.pow(z, y)) / a) / y;
	} else if (y <= 3.6e+85) {
		tmp = x * (Math.pow(a, t) / (Math.exp(b) * (y * a)));
	} else {
		tmp = (x * Math.exp((y * Math.log(z)))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.5e-19:
		tmp = ((x * math.pow(z, y)) / a) / y
	elif y <= 3.6e+85:
		tmp = x * (math.pow(a, t) / (math.exp(b) * (y * a)))
	else:
		tmp = (x * math.exp((y * math.log(z)))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.5e-19)
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	elseif (y <= 3.6e+85)
		tmp = Float64(x * Float64((a ^ t) / Float64(exp(b) * Float64(y * a))));
	else
		tmp = Float64(Float64(x * exp(Float64(y * log(z)))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.5e-19)
		tmp = ((x * (z ^ y)) / a) / y;
	elseif (y <= 3.6e+85)
		tmp = x * ((a ^ t) / (exp(b) * (y * a)));
	else
		tmp = (x * exp((y * log(z)))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.5e-19], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 3.6e+85], N[(x * N[(N[Power[a, t], $MachinePrecision] / N[(N[Exp[b], $MachinePrecision] * N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Exp[N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.50000000000000015e-19

   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/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 53.9%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 62.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 62.0%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a}{{z}^{y}}\right)}\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. pow-lowering-pow.f64 73.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   10. Simplified 73.2%

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

   11. Taylor expanded in x around 0

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

       1. associate-/r* N/A

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

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot {z}^{y}}{a}\right), \color{blue}{y}\right) \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot {z}^{y}\right), a\right), y\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({z}^{y}\right)\right), a\right), y\right) \]

       5. pow-lowering-pow.f64 81.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(z, y\right)\right), a\right), y\right) \]

   13. Simplified 81.3%

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

   if -3.50000000000000015e-19 < y < 3.5999999999999998e85

   1. Initial program 95.6%

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

   3. Taylor expanded in z around inf

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. prod-exp N/A

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

      4. times-frac N/A

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

      5. associate-/l* N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{e^{-1 \cdot \left(y \cdot \log \left(\frac{1}{z}\right)\right)} \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}\right)}\right) \]

      7. associate-/l/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{\frac{e^{-1 \cdot \left(y \cdot \log \left(\frac{1}{z}\right)\right)} \cdot e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}{\color{blue}{y}}\right)\right) \]

   5. Simplified 95.2%

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

      1. exp-diff N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{e^{\log a \cdot \left(t + -1\right) - \left(\mathsf{neg}\left(y \cdot \log z\right)\right)}}{e^{b}}\right), y\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{1}{\frac{e^{b}}{e^{\log a \cdot \left(t + -1\right) - \left(\mathsf{neg}\left(y \cdot \log z\right)\right)}}}\right), y\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{1}{\frac{e^{b}}{e^{\log a \cdot \left(t + -1\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y \cdot \log z\right)\right)\right)\right)}}}\right), y\right)\right) \]

      4. exp-sum N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{1}{\frac{e^{b}}{e^{\log a \cdot \left(t + -1\right)} \cdot e^{\mathsf{neg}\left(\left(\mathsf{neg}\left(y \cdot \log z\right)\right)\right)}}}\right), y\right)\right) \]

      5. pow-to-exp N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{1}{\frac{e^{b}}{{a}^{\left(t + -1\right)} \cdot e^{\mathsf{neg}\left(\left(\mathsf{neg}\left(y \cdot \log z\right)\right)\right)}}}\right), y\right)\right) \]

      6. remove-double-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{1}{\frac{e^{b}}{{a}^{\left(t + -1\right)} \cdot e^{y \cdot \log z}}}\right), y\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{1}{\frac{e^{b}}{{a}^{\left(t + -1\right)} \cdot e^{\log z \cdot y}}}\right), y\right)\right) \]

      8. pow-to-exp N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{1}{\frac{e^{b}}{{a}^{\left(t + -1\right)} \cdot {z}^{y}}}\right), y\right)\right) \]

      9. associate-/l/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{1}{\frac{\frac{e^{b}}{{z}^{y}}}{{a}^{\left(t + -1\right)}}}\right), y\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{1}{\frac{\frac{e^{b}}{{z}^{y}}}{{a}^{\left(-1 + t\right)}}}\right), y\right)\right) \]

      11. unpow-prod-up N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{1}{\frac{\frac{e^{b}}{{z}^{y}}}{{a}^{-1} \cdot {a}^{t}}}\right), y\right)\right) \]

      12. inv-pow N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{1}{\frac{\frac{e^{b}}{{z}^{y}}}{\frac{1}{a} \cdot {a}^{t}}}\right), y\right)\right) \]

      13. associate-/l/ N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{1}{\frac{\frac{\frac{e^{b}}{{z}^{y}}}{{a}^{t}}}{\frac{1}{a}}}\right), y\right)\right) \]

   7. Applied egg-rr 84.5%

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

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{{a}^{t}}{a \cdot \left(y \cdot e^{b}\right)}\right)}\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left({a}^{t}\right), \color{blue}{\left(a \cdot \left(y \cdot e^{b}\right)\right)}\right)\right) \]

      2. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, t\right), \left(\color{blue}{a} \cdot \left(y \cdot e^{b}\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, t\right), \left(\left(y \cdot e^{b}\right) \cdot \color{blue}{a}\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, t\right), \left(\left(e^{b} \cdot y\right) \cdot a\right)\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, t\right), \left(e^{b} \cdot \color{blue}{\left(y \cdot a\right)}\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, t\right), \left(e^{b} \cdot \left(a \cdot \color{blue}{y}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, t\right), \mathsf{*.f64}\left(\left(e^{b}\right), \color{blue}{\left(a \cdot y\right)}\right)\right)\right) \]

      8. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, t\right), \mathsf{*.f64}\left(\mathsf{exp.f64}\left(b\right), \left(\color{blue}{a} \cdot y\right)\right)\right)\right) \]

      9. *-lowering-*.f64 82.6%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, t\right), \mathsf{*.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(a, \color{blue}{y}\right)\right)\right)\right) \]

   10. Simplified 82.6%

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

   if 3.5999999999999998e85 < 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 y around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(y \cdot \log z\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, \log z\right)\right)\right), y\right) \]

      2. log-lowering-log.f64 86.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, \mathsf{log.f64}\left(z\right)\right)\right)\right), y\right) \]

   5. Simplified 86.9%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-19}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{e^{b} \cdot \left(y \cdot a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{y \cdot \log z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{e^{b}}}{y}\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-182}:\\ \;\;\;\;\frac{x \cdot \left({a}^{\left(t + -1\right)} \cdot \left(1 - b\right)\right)}{y}\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+18}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x (exp b)) y)))
   (if (<= b -2.2e+18)
     t_1
     (if (<= b -1.2e-182)
       (/ (* x (* (pow a (+ t -1.0)) (- 1.0 b))) y)
       (if (<= b 1.2e+18) (/ (/ (* x (pow z y)) a) y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / exp(b)) / y;
	double tmp;
	if (b <= -2.2e+18) {
		tmp = t_1;
	} else if (b <= -1.2e-182) {
		tmp = (x * (pow(a, (t + -1.0)) * (1.0 - b))) / y;
	} else if (b <= 1.2e+18) {
		tmp = ((x * pow(z, y)) / a) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / exp(b)) / y
    if (b <= (-2.2d+18)) then
        tmp = t_1
    else if (b <= (-1.2d-182)) then
        tmp = (x * ((a ** (t + (-1.0d0))) * (1.0d0 - b))) / y
    else if (b <= 1.2d+18) then
        tmp = ((x * (z ** y)) / a) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / Math.exp(b)) / y;
	double tmp;
	if (b <= -2.2e+18) {
		tmp = t_1;
	} else if (b <= -1.2e-182) {
		tmp = (x * (Math.pow(a, (t + -1.0)) * (1.0 - b))) / y;
	} else if (b <= 1.2e+18) {
		tmp = ((x * Math.pow(z, y)) / a) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / math.exp(b)) / y
	tmp = 0
	if b <= -2.2e+18:
		tmp = t_1
	elif b <= -1.2e-182:
		tmp = (x * (math.pow(a, (t + -1.0)) * (1.0 - b))) / y
	elif b <= 1.2e+18:
		tmp = ((x * math.pow(z, y)) / a) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / exp(b)) / y)
	tmp = 0.0
	if (b <= -2.2e+18)
		tmp = t_1;
	elseif (b <= -1.2e-182)
		tmp = Float64(Float64(x * Float64((a ^ Float64(t + -1.0)) * Float64(1.0 - b))) / y);
	elseif (b <= 1.2e+18)
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / exp(b)) / y;
	tmp = 0.0;
	if (b <= -2.2e+18)
		tmp = t_1;
	elseif (b <= -1.2e-182)
		tmp = (x * ((a ^ (t + -1.0)) * (1.0 - b))) / y;
	elseif (b <= 1.2e+18)
		tmp = ((x * (z ^ y)) / a) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -2.2e+18], t$95$1, If[LessEqual[b, -1.2e-182], N[(N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] * N[(1.0 - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 1.2e+18], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.2e18 or 1.2e18 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 88.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 88.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{0 - b}\right), \color{blue}{y}\right) \]

      2. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{0}}{e^{b}}\right), y\right) \]

      3. 1-exp N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(e^{b}\right)\right), y\right) \]

      6. exp-lowering-exp.f64 88.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   7. Applied egg-rr 88.0%

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

   if -2.2e18 < b < -1.1999999999999999e-182

   1. Initial program 95.2%

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

   3. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{\left(e^{y \cdot \log z + \log a \cdot \left(t - 1\right)} + -1 \cdot \left(b \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}\right)\right)}\right), y\right) \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(e^{y \cdot \log z + \log a \cdot \left(t - 1\right)} + \left(-1 \cdot b\right) \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}\right)\right), y\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(e^{y \cdot \log z + \log a \cdot \left(t - 1\right)} + \left(\mathsf{neg}\left(b\right)\right) \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}\right)\right), y\right) \]

      3. distribute-rgt1-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\left(\mathsf{neg}\left(b\right)\right) + 1\right) \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}\right)\right), y\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(\left(\mathsf{neg}\left(b\right)\right) + 1\right), \left(e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}\right)\right)\right), y\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(\mathsf{neg}\left(b\right)\right), 1\right), \left(e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}\right)\right)\right), y\right) \]

      6. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(0 - b\right), 1\right), \left(e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}\right)\right)\right), y\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, b\right), 1\right), \left(e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}\right)\right)\right), y\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, b\right), 1\right), \left(e^{\log a \cdot \left(t - 1\right) + y \cdot \log z}\right)\right)\right), y\right) \]

      9. exp-sum N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, b\right), 1\right), \left(e^{\log a \cdot \left(t - 1\right)} \cdot e^{y \cdot \log z}\right)\right)\right), y\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, b\right), 1\right), \left(e^{\log a \cdot \left(t - 1\right)} \cdot e^{\log z \cdot y}\right)\right)\right), y\right) \]

      11. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, b\right), 1\right), \left(e^{\log a \cdot \left(t - 1\right)} \cdot {z}^{y}\right)\right)\right), y\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, b\right), 1\right), \mathsf{*.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)}\right), \left({z}^{y}\right)\right)\right)\right), y\right) \]

   5. Simplified 84.3%

      \[\leadsto \frac{x \cdot \color{blue}{\left(\left(\left(0 - b\right) + 1\right) \cdot \left({a}^{\left(t + -1\right)} \cdot {z}^{y}\right)\right)}}{y} \]

   6. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(e^{\log a \cdot \left(t - 1\right)} \cdot \left(1 - b\right)\right)\right), \color{blue}{y}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(e^{\log a \cdot \left(t - 1\right)} \cdot \left(1 - b\right)\right)\right), y\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)}\right), \left(1 - b\right)\right)\right), y\right) \]

      4. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left({a}^{\left(t - 1\right)}\right), \left(1 - b\right)\right)\right), y\right) \]

      5. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \left(t - 1\right)\right), \left(1 - b\right)\right)\right), y\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), \left(1 - b\right)\right)\right), y\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \left(t + -1\right)\right), \left(1 - b\right)\right)\right), y\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \left(1 - b\right)\right)\right), y\right) \]

      9. --lowering--.f64 71.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \mathsf{\_.f64}\left(1, b\right)\right)\right), y\right) \]

   8. Simplified 71.3%

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

   if -1.1999999999999999e-182 < b < 1.2e18

   1. Initial program 95.4%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 77.9%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 68.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 68.8%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a}{{z}^{y}}\right)}\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. pow-lowering-pow.f64 70.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   10. Simplified 70.4%

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

   11. Taylor expanded in x around 0

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

       1. associate-/r* N/A

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

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot {z}^{y}}{a}\right), \color{blue}{y}\right) \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot {z}^{y}\right), a\right), y\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({z}^{y}\right)\right), a\right), y\right) \]

       5. pow-lowering-pow.f64 74.1%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(z, y\right)\right), a\right), y\right) \]

   13. Simplified 74.1%

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

Alternative 7: 59.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -1 + b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\\ t_2 := \frac{\frac{x}{e^{b}}}{y}\\ \mathbf{if}\;b \leq -140:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-15}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{elif}\;b \leq 17000000000:\\ \;\;\;\;\frac{\frac{1}{\frac{x + b \cdot \left(x \cdot \left(1 + b \cdot -0.5\right)\right)}{\left(x \cdot \left(1 + b \cdot t\_1\right)\right) \cdot \left(x - t\_1 \cdot \left(x \cdot b\right)\right)}}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ -1.0 (* b (+ 0.5 (* b -0.16666666666666666)))))
        (t_2 (/ (/ x (exp b)) y)))
   (if (<= b -140.0)
     t_2
     (if (<= b 4e-15)
       (/ (/ x y) a)
       (if (<= b 17000000000.0)
         (/
          (/
           1.0
           (/
            (+ x (* b (* x (+ 1.0 (* b -0.5)))))
            (* (* x (+ 1.0 (* b t_1))) (- x (* t_1 (* x b))))))
          y)
         t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -1.0 + (b * (0.5 + (b * -0.16666666666666666)));
	double t_2 = (x / exp(b)) / y;
	double tmp;
	if (b <= -140.0) {
		tmp = t_2;
	} else if (b <= 4e-15) {
		tmp = (x / y) / a;
	} else if (b <= 17000000000.0) {
		tmp = (1.0 / ((x + (b * (x * (1.0 + (b * -0.5))))) / ((x * (1.0 + (b * t_1))) * (x - (t_1 * (x * b)))))) / y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-1.0d0) + (b * (0.5d0 + (b * (-0.16666666666666666d0))))
    t_2 = (x / exp(b)) / y
    if (b <= (-140.0d0)) then
        tmp = t_2
    else if (b <= 4d-15) then
        tmp = (x / y) / a
    else if (b <= 17000000000.0d0) then
        tmp = (1.0d0 / ((x + (b * (x * (1.0d0 + (b * (-0.5d0)))))) / ((x * (1.0d0 + (b * t_1))) * (x - (t_1 * (x * b)))))) / y
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -1.0 + (b * (0.5 + (b * -0.16666666666666666)));
	double t_2 = (x / Math.exp(b)) / y;
	double tmp;
	if (b <= -140.0) {
		tmp = t_2;
	} else if (b <= 4e-15) {
		tmp = (x / y) / a;
	} else if (b <= 17000000000.0) {
		tmp = (1.0 / ((x + (b * (x * (1.0 + (b * -0.5))))) / ((x * (1.0 + (b * t_1))) * (x - (t_1 * (x * b)))))) / y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -1.0 + (b * (0.5 + (b * -0.16666666666666666)))
	t_2 = (x / math.exp(b)) / y
	tmp = 0
	if b <= -140.0:
		tmp = t_2
	elif b <= 4e-15:
		tmp = (x / y) / a
	elif b <= 17000000000.0:
		tmp = (1.0 / ((x + (b * (x * (1.0 + (b * -0.5))))) / ((x * (1.0 + (b * t_1))) * (x - (t_1 * (x * b)))))) / y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(-1.0 + Float64(b * Float64(0.5 + Float64(b * -0.16666666666666666))))
	t_2 = Float64(Float64(x / exp(b)) / y)
	tmp = 0.0
	if (b <= -140.0)
		tmp = t_2;
	elseif (b <= 4e-15)
		tmp = Float64(Float64(x / y) / a);
	elseif (b <= 17000000000.0)
		tmp = Float64(Float64(1.0 / Float64(Float64(x + Float64(b * Float64(x * Float64(1.0 + Float64(b * -0.5))))) / Float64(Float64(x * Float64(1.0 + Float64(b * t_1))) * Float64(x - Float64(t_1 * Float64(x * b)))))) / y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -1.0 + (b * (0.5 + (b * -0.16666666666666666)));
	t_2 = (x / exp(b)) / y;
	tmp = 0.0;
	if (b <= -140.0)
		tmp = t_2;
	elseif (b <= 4e-15)
		tmp = (x / y) / a;
	elseif (b <= 17000000000.0)
		tmp = (1.0 / ((x + (b * (x * (1.0 + (b * -0.5))))) / ((x * (1.0 + (b * t_1))) * (x - (t_1 * (x * b)))))) / y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-1.0 + N[(b * N[(0.5 + N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -140.0], t$95$2, If[LessEqual[b, 4e-15], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, 17000000000.0], N[(N[(1.0 / N[(N[(x + N[(b * N[(x * N[(1.0 + N[(b * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(x * N[(1.0 + N[(b * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - N[(t$95$1 * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -140 or 1.7e10 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 86.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 86.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{0 - b}\right), \color{blue}{y}\right) \]

      2. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{0}}{e^{b}}\right), y\right) \]

      3. 1-exp N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(e^{b}\right)\right), y\right) \]

      6. exp-lowering-exp.f64 86.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   7. Applied egg-rr 86.0%

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

   if -140 < b < 4.0000000000000003e-15

   1. Initial program 94.9%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 80.5%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 67.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 67.4%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a}{{z}^{y}}\right)}\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. pow-lowering-pow.f64 67.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   10. Simplified 67.4%

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

   11. Taylor expanded in y around 0

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{a}\right) \]
   12. Step-by-step derivation

   13. Simplified 40.8%

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

   if 4.0000000000000003e-15 < b < 1.7e10

   1. Initial program 99.5%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 16.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 16.5%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)}\right), y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)\right)\right), y\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + -1\right)\right)\right)\right), y\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right), -1\right)\right)\right)\right), y\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right), -1\right)\right)\right)\right), y\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(\frac{-1}{6} \cdot b\right)\right)\right), -1\right)\right)\right)\right), y\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(b \cdot \frac{-1}{6}\right)\right)\right), -1\right)\right)\right)\right), y\right) \]

      9. *-lowering-*.f64 16.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right)\right)\right)\right), y\right) \]

   8. Simplified 16.1%

      \[\leadsto \frac{x \cdot \color{blue}{\left(1 + b \cdot \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right) + -1\right)\right)}}{y} \]
   9. Step-by-step derivation

      1. distribute-lft-in N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot 1 + x \cdot \left(b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)\right), y\right) \]

      2. *-rgt-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + x \cdot \left(b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)\right), y\right) \]

      3. flip-+ N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot x - \left(x \cdot \left(b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)\right) \cdot \left(x \cdot \left(b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)\right)}{x - x \cdot \left(b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)}\right), y\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{\frac{x - x \cdot \left(b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)}{x \cdot x - \left(x \cdot \left(b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)\right) \cdot \left(x \cdot \left(b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)\right)}}\right), y\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{x - x \cdot \left(b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)}{x \cdot x - \left(x \cdot \left(b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)\right) \cdot \left(x \cdot \left(b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)\right)}\right)\right), y\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(x - x \cdot \left(b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)\right), \left(x \cdot x - \left(x \cdot \left(b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)\right) \cdot \left(x \cdot \left(b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)\right)\right)\right)\right), y\right) \]

   10. Applied egg-rr 51.5%

       \[\leadsto \frac{\color{blue}{\frac{1}{\frac{x - \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right) + -1\right) \cdot \left(b \cdot x\right)}{\left(x \cdot \left(1 + b \cdot \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right) + -1\right)\right)\right) \cdot \left(x - \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right) + -1\right) \cdot \left(b \cdot x\right)\right)}}}}{y} \]

   11. Taylor expanded in b around 0

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\color{blue}{\left(x + b \cdot \left(\frac{-1}{2} \cdot \left(b \cdot x\right) - -1 \cdot x\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right)\right)\right)\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right), \mathsf{*.f64}\left(b, x\right)\right)\right)\right)\right)\right), y\right) \]
   12. Step-by-step derivation

       1. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(\frac{-1}{2} \cdot \left(b \cdot x\right) - -1 \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right)\right)\right)\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right), \mathsf{*.f64}\left(b, x\right)\right)\right)\right)\right)\right), y\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\frac{-1}{2} \cdot \left(b \cdot x\right) - -1 \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right)\right)\right)\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right), \mathsf{*.f64}\left(b, x\right)\right)\right)\right)\right)\right), y\right) \]

       3. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\frac{-1}{2} \cdot \left(b \cdot x\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right)\right)\right)\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right), \mathsf{*.f64}\left(b, x\right)\right)\right)\right)\right)\right), y\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\frac{-1}{2} \cdot b\right) \cdot x + \left(\mathsf{neg}\left(-1\right)\right) \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right)\right)\right)\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right), \mathsf{*.f64}\left(b, x\right)\right)\right)\right)\right)\right), y\right) \]

       5. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\frac{-1}{2} \cdot b\right) \cdot x + 1 \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right)\right)\right)\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right), \mathsf{*.f64}\left(b, x\right)\right)\right)\right)\right)\right), y\right) \]

       6. distribute-rgt-out N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{-1}{2} \cdot b + 1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right)\right)\right)\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right), \mathsf{*.f64}\left(b, x\right)\right)\right)\right)\right)\right), y\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{-1}{2} \cdot b + 1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right)\right)\right)\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right), \mathsf{*.f64}\left(b, x\right)\right)\right)\right)\right)\right), y\right) \]

       8. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{-1}{2} \cdot b\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right)\right)\right)\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right), \mathsf{*.f64}\left(b, x\right)\right)\right)\right)\right)\right), y\right) \]

       9. *-lowering-*.f64 76.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-1}{2}, b\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right)\right)\right)\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right), \mathsf{*.f64}\left(b, x\right)\right)\right)\right)\right)\right), y\right) \]

   13. Simplified 76.5%

       \[\leadsto \frac{\frac{1}{\frac{\color{blue}{x + b \cdot \left(x \cdot \left(-0.5 \cdot b + 1\right)\right)}}{\left(x \cdot \left(1 + b \cdot \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right) + -1\right)\right)\right) \cdot \left(x - \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right) + -1\right) \cdot \left(b \cdot x\right)\right)}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -140:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-15}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{elif}\;b \leq 17000000000:\\ \;\;\;\;\frac{\frac{1}{\frac{x + b \cdot \left(x \cdot \left(1 + b \cdot -0.5\right)\right)}{\left(x \cdot \left(1 + b \cdot \left(-1 + b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right)\right)\right) \cdot \left(x - \left(-1 + b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right) \cdot \left(x \cdot b\right)\right)}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.7% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{e^{b}}}{y}\\ \mathbf{if}\;b \leq -7.4 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 64000000000:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x (exp b)) y)))
   (if (<= b -7.4e+21)
     t_1
     (if (<= b 64000000000.0) (/ (/ (* x (pow z y)) a) y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / exp(b)) / y;
	double tmp;
	if (b <= -7.4e+21) {
		tmp = t_1;
	} else if (b <= 64000000000.0) {
		tmp = ((x * pow(z, y)) / a) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / exp(b)) / y
    if (b <= (-7.4d+21)) then
        tmp = t_1
    else if (b <= 64000000000.0d0) then
        tmp = ((x * (z ** y)) / a) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / Math.exp(b)) / y;
	double tmp;
	if (b <= -7.4e+21) {
		tmp = t_1;
	} else if (b <= 64000000000.0) {
		tmp = ((x * Math.pow(z, y)) / a) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / math.exp(b)) / y
	tmp = 0
	if b <= -7.4e+21:
		tmp = t_1
	elif b <= 64000000000.0:
		tmp = ((x * math.pow(z, y)) / a) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / exp(b)) / y)
	tmp = 0.0
	if (b <= -7.4e+21)
		tmp = t_1;
	elseif (b <= 64000000000.0)
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / exp(b)) / y;
	tmp = 0.0;
	if (b <= -7.4e+21)
		tmp = t_1;
	elseif (b <= 64000000000.0)
		tmp = ((x * (z ^ y)) / a) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -7.4e+21], t$95$1, If[LessEqual[b, 64000000000.0], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -7.4e21 or 6.4e10 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 87.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 87.9%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{0 - b}\right), \color{blue}{y}\right) \]

      2. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{0}}{e^{b}}\right), y\right) \]

      3. 1-exp N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(e^{b}\right)\right), y\right) \]

      6. exp-lowering-exp.f64 87.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   7. Applied egg-rr 87.9%

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

   if -7.4e21 < b < 6.4e10

   1. Initial program 95.4%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 77.3%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 66.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 66.1%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a}{{z}^{y}}\right)}\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. pow-lowering-pow.f64 68.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   10. Simplified 68.0%

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

   11. Taylor expanded in x around 0

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

       1. associate-/r* N/A

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

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot {z}^{y}}{a}\right), \color{blue}{y}\right) \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot {z}^{y}\right), a\right), y\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({z}^{y}\right)\right), a\right), y\right) \]

       5. pow-lowering-pow.f64 70.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(z, y\right)\right), a\right), y\right) \]

   13. Simplified 70.5%

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

Alternative 9: 72.7% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{e^{b}}}{y}\\ \mathbf{if}\;b \leq -7.6 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+25}:\\ \;\;\;\;\frac{\frac{x}{y}}{\frac{a}{{z}^{y}}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x (exp b)) y)))
   (if (<= b -7.6e+21) t_1 (if (<= b 3e+25) (/ (/ x y) (/ a (pow z y))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / exp(b)) / y;
	double tmp;
	if (b <= -7.6e+21) {
		tmp = t_1;
	} else if (b <= 3e+25) {
		tmp = (x / y) / (a / pow(z, y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / exp(b)) / y
    if (b <= (-7.6d+21)) then
        tmp = t_1
    else if (b <= 3d+25) then
        tmp = (x / y) / (a / (z ** y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / Math.exp(b)) / y;
	double tmp;
	if (b <= -7.6e+21) {
		tmp = t_1;
	} else if (b <= 3e+25) {
		tmp = (x / y) / (a / Math.pow(z, y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / math.exp(b)) / y
	tmp = 0
	if b <= -7.6e+21:
		tmp = t_1
	elif b <= 3e+25:
		tmp = (x / y) / (a / math.pow(z, y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / exp(b)) / y)
	tmp = 0.0
	if (b <= -7.6e+21)
		tmp = t_1;
	elseif (b <= 3e+25)
		tmp = Float64(Float64(x / y) / Float64(a / (z ^ y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / exp(b)) / y;
	tmp = 0.0;
	if (b <= -7.6e+21)
		tmp = t_1;
	elseif (b <= 3e+25)
		tmp = (x / y) / (a / (z ^ y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -7.6e+21], t$95$1, If[LessEqual[b, 3e+25], N[(N[(x / y), $MachinePrecision] / N[(a / N[Power[z, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -7.6e21 or 3.00000000000000006e25 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 87.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 87.9%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{0 - b}\right), \color{blue}{y}\right) \]

      2. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{0}}{e^{b}}\right), y\right) \]

      3. 1-exp N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(e^{b}\right)\right), y\right) \]

      6. exp-lowering-exp.f64 87.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   7. Applied egg-rr 87.9%

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

   if -7.6e21 < b < 3.00000000000000006e25

   1. Initial program 95.4%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 77.3%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 66.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 66.1%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a}{{z}^{y}}\right)}\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. pow-lowering-pow.f64 68.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   10. Simplified 68.0%

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

Alternative 10: 72.7% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{e^{b}}}{y}\\ \mathbf{if}\;b \leq -1.35 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 41000000000:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x (exp b)) y)))
   (if (<= b -1.35e+18)
     t_1
     (if (<= b 41000000000.0) (/ (* x (pow z y)) (* y a)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / exp(b)) / y;
	double tmp;
	if (b <= -1.35e+18) {
		tmp = t_1;
	} else if (b <= 41000000000.0) {
		tmp = (x * pow(z, y)) / (y * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / exp(b)) / y
    if (b <= (-1.35d+18)) then
        tmp = t_1
    else if (b <= 41000000000.0d0) then
        tmp = (x * (z ** y)) / (y * a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / Math.exp(b)) / y;
	double tmp;
	if (b <= -1.35e+18) {
		tmp = t_1;
	} else if (b <= 41000000000.0) {
		tmp = (x * Math.pow(z, y)) / (y * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / math.exp(b)) / y
	tmp = 0
	if b <= -1.35e+18:
		tmp = t_1
	elif b <= 41000000000.0:
		tmp = (x * math.pow(z, y)) / (y * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / exp(b)) / y)
	tmp = 0.0
	if (b <= -1.35e+18)
		tmp = t_1;
	elseif (b <= 41000000000.0)
		tmp = Float64(Float64(x * (z ^ y)) / Float64(y * a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / exp(b)) / y;
	tmp = 0.0;
	if (b <= -1.35e+18)
		tmp = t_1;
	elseif (b <= 41000000000.0)
		tmp = (x * (z ^ y)) / (y * a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -1.35e+18], t$95$1, If[LessEqual[b, 41000000000.0], N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.35e18 or 4.1e10 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 87.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 87.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{0 - b}\right), \color{blue}{y}\right) \]

      2. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{0}}{e^{b}}\right), y\right) \]

      3. 1-exp N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(e^{b}\right)\right), y\right) \]

      6. exp-lowering-exp.f64 87.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   7. Applied egg-rr 87.3%

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

   if -1.35e18 < b < 4.1e10

   1. Initial program 95.3%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 78.4%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 66.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 66.4%

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

   8. Taylor expanded in b around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot {z}^{y}\right), \color{blue}{\left(a \cdot y\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({z}^{y}\right)\right), \left(\color{blue}{a} \cdot y\right)\right) \]

      3. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(z, y\right)\right), \left(a \cdot y\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(z, y\right)\right), \left(y \cdot \color{blue}{a}\right)\right) \]

      5. *-lowering-*.f64 63.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(z, y\right)\right), \mathsf{*.f64}\left(y, \color{blue}{a}\right)\right) \]

   10. Simplified 63.5%

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

Alternative 11: 57.9% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 720:\\ \;\;\;\;\frac{\frac{x}{y}}{a \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 720.0) (/ (/ x y) (* a (exp b))) (/ (/ x (exp b)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 720.0) {
		tmp = (x / y) / (a * exp(b));
	} else {
		tmp = (x / exp(b)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 720.0d0) then
        tmp = (x / y) / (a * exp(b))
    else
        tmp = (x / exp(b)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 720.0) {
		tmp = (x / y) / (a * Math.exp(b));
	} else {
		tmp = (x / Math.exp(b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 720.0:
		tmp = (x / y) / (a * math.exp(b))
	else:
		tmp = (x / math.exp(b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 720.0)
		tmp = Float64(Float64(x / y) / Float64(a * exp(b)));
	else
		tmp = Float64(Float64(x / exp(b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 720.0)
		tmp = (x / y) / (a * exp(b));
	else
		tmp = (x / exp(b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 720.0], N[(N[(x / y), $MachinePrecision] / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 720

   1. Initial program 96.5%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 75.4%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 69.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 69.1%

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

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(a \cdot e^{b}\right)}\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(a, \color{blue}{\left(e^{b}\right)}\right)\right) \]

      2. exp-lowering-exp.f64 53.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right) \]

   10. Simplified 53.1%

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

   if 720 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 84.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 84.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{0 - b}\right), \color{blue}{y}\right) \]

      2. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{0}}{e^{b}}\right), y\right) \]

      3. 1-exp N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(e^{b}\right)\right), y\right) \]

      6. exp-lowering-exp.f64 84.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   7. Applied egg-rr 84.1%

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

Alternative 12: 53.2% accurate, 5.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -1 + b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\\ t_2 := 1 + b \cdot t\_1\\ \mathbf{if}\;b \leq -140:\\ \;\;\;\;x \cdot \frac{t\_2}{y}\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-22}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+34}:\\ \;\;\;\;\frac{\frac{1}{\frac{x + b \cdot \left(x \cdot \left(1 + b \cdot -0.5\right)\right)}{\left(x \cdot t\_2\right) \cdot \left(x - t\_1 \cdot \left(x \cdot b\right)\right)}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ -1.0 (* b (+ 0.5 (* b -0.16666666666666666)))))
        (t_2 (+ 1.0 (* b t_1))))
   (if (<= b -140.0)
     (* x (/ t_2 y))
     (if (<= b 2.6e-22)
       (/ (/ x y) a)
       (if (<= b 5.8e+34)
         (/
          (/
           1.0
           (/
            (+ x (* b (* x (+ 1.0 (* b -0.5)))))
            (* (* x t_2) (- x (* t_1 (* x b))))))
          y)
         (/
          (/ x (+ 1.0 (* b (+ 1.0 (* b (+ 0.5 (* b 0.16666666666666666)))))))
          y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -1.0 + (b * (0.5 + (b * -0.16666666666666666)));
	double t_2 = 1.0 + (b * t_1);
	double tmp;
	if (b <= -140.0) {
		tmp = x * (t_2 / y);
	} else if (b <= 2.6e-22) {
		tmp = (x / y) / a;
	} else if (b <= 5.8e+34) {
		tmp = (1.0 / ((x + (b * (x * (1.0 + (b * -0.5))))) / ((x * t_2) * (x - (t_1 * (x * b)))))) / y;
	} else {
		tmp = (x / (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-1.0d0) + (b * (0.5d0 + (b * (-0.16666666666666666d0))))
    t_2 = 1.0d0 + (b * t_1)
    if (b <= (-140.0d0)) then
        tmp = x * (t_2 / y)
    else if (b <= 2.6d-22) then
        tmp = (x / y) / a
    else if (b <= 5.8d+34) then
        tmp = (1.0d0 / ((x + (b * (x * (1.0d0 + (b * (-0.5d0)))))) / ((x * t_2) * (x - (t_1 * (x * b)))))) / y
    else
        tmp = (x / (1.0d0 + (b * (1.0d0 + (b * (0.5d0 + (b * 0.16666666666666666d0))))))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -1.0 + (b * (0.5 + (b * -0.16666666666666666)));
	double t_2 = 1.0 + (b * t_1);
	double tmp;
	if (b <= -140.0) {
		tmp = x * (t_2 / y);
	} else if (b <= 2.6e-22) {
		tmp = (x / y) / a;
	} else if (b <= 5.8e+34) {
		tmp = (1.0 / ((x + (b * (x * (1.0 + (b * -0.5))))) / ((x * t_2) * (x - (t_1 * (x * b)))))) / y;
	} else {
		tmp = (x / (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -1.0 + (b * (0.5 + (b * -0.16666666666666666)))
	t_2 = 1.0 + (b * t_1)
	tmp = 0
	if b <= -140.0:
		tmp = x * (t_2 / y)
	elif b <= 2.6e-22:
		tmp = (x / y) / a
	elif b <= 5.8e+34:
		tmp = (1.0 / ((x + (b * (x * (1.0 + (b * -0.5))))) / ((x * t_2) * (x - (t_1 * (x * b)))))) / y
	else:
		tmp = (x / (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(-1.0 + Float64(b * Float64(0.5 + Float64(b * -0.16666666666666666))))
	t_2 = Float64(1.0 + Float64(b * t_1))
	tmp = 0.0
	if (b <= -140.0)
		tmp = Float64(x * Float64(t_2 / y));
	elseif (b <= 2.6e-22)
		tmp = Float64(Float64(x / y) / a);
	elseif (b <= 5.8e+34)
		tmp = Float64(Float64(1.0 / Float64(Float64(x + Float64(b * Float64(x * Float64(1.0 + Float64(b * -0.5))))) / Float64(Float64(x * t_2) * Float64(x - Float64(t_1 * Float64(x * b)))))) / y);
	else
		tmp = Float64(Float64(x / Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * Float64(0.5 + Float64(b * 0.16666666666666666))))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -1.0 + (b * (0.5 + (b * -0.16666666666666666)));
	t_2 = 1.0 + (b * t_1);
	tmp = 0.0;
	if (b <= -140.0)
		tmp = x * (t_2 / y);
	elseif (b <= 2.6e-22)
		tmp = (x / y) / a;
	elseif (b <= 5.8e+34)
		tmp = (1.0 / ((x + (b * (x * (1.0 + (b * -0.5))))) / ((x * t_2) * (x - (t_1 * (x * b)))))) / y;
	else
		tmp = (x / (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-1.0 + N[(b * N[(0.5 + N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 + N[(b * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -140.0], N[(x * N[(t$95$2 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.6e-22], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, 5.8e+34], N[(N[(1.0 / N[(N[(x + N[(b * N[(x * N[(1.0 + N[(b * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(x * t$95$2), $MachinePrecision] * N[(x - N[(t$95$1 * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(1.0 + N[(b * N[(1.0 + N[(b * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -140

   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 inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 83.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 83.6%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)}\right), y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)\right)\right), y\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + -1\right)\right)\right)\right), y\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right), -1\right)\right)\right)\right), y\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right), -1\right)\right)\right)\right), y\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(\frac{-1}{6} \cdot b\right)\right)\right), -1\right)\right)\right)\right), y\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(b \cdot \frac{-1}{6}\right)\right)\right), -1\right)\right)\right)\right), y\right) \]

      9. *-lowering-*.f64 66.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right)\right)\right)\right), y\right) \]

   8. Simplified 66.2%

      \[\leadsto \frac{x \cdot \color{blue}{\left(1 + b \cdot \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right) + -1\right)\right)}}{y} \]
   9. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto x \cdot \color{blue}{\frac{1 + b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)}{y}} \]

      2. *-commutative N/A

         \[\leadsto \frac{1 + b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)}{y} \cdot \color{blue}{x} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1 + b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)}{y}\right), \color{blue}{x}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(1 + b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right), y\right), x\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \left(b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)\right), y\right), x\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)\right), y\right), x\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right), -1\right)\right)\right), y\right), x\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right), -1\right)\right)\right), y\right), x\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(b \cdot \frac{-1}{6}\right)\right)\right), -1\right)\right)\right), y\right), x\right) \]

      10. *-lowering-*.f64 67.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right)\right)\right), y\right), x\right) \]

   10. Applied egg-rr 67.9%

       \[\leadsto \color{blue}{\frac{1 + b \cdot \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right) + -1\right)}{y} \cdot x} \]

   if -140 < b < 2.6e-22

   1. Initial program 94.9%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 80.5%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 67.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 67.4%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a}{{z}^{y}}\right)}\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. pow-lowering-pow.f64 67.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   10. Simplified 67.4%

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

   11. Taylor expanded in y around 0

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{a}\right) \]
   12. Step-by-step derivation

   13. Simplified 40.8%

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

   if 2.6e-22 < b < 5.8000000000000003e34

   1. Initial program 99.5%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 16.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 16.5%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)}\right), y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)\right)\right), y\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + -1\right)\right)\right)\right), y\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right), -1\right)\right)\right)\right), y\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right), -1\right)\right)\right)\right), y\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(\frac{-1}{6} \cdot b\right)\right)\right), -1\right)\right)\right)\right), y\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(b \cdot \frac{-1}{6}\right)\right)\right), -1\right)\right)\right)\right), y\right) \]

      9. *-lowering-*.f64 16.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right)\right)\right)\right), y\right) \]

   8. Simplified 16.1%

      \[\leadsto \frac{x \cdot \color{blue}{\left(1 + b \cdot \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right) + -1\right)\right)}}{y} \]
   9. Step-by-step derivation

      1. distribute-lft-in N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot 1 + x \cdot \left(b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)\right), y\right) \]

      2. *-rgt-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + x \cdot \left(b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)\right), y\right) \]

      3. flip-+ N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot x - \left(x \cdot \left(b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)\right) \cdot \left(x \cdot \left(b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)\right)}{x - x \cdot \left(b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)}\right), y\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{\frac{x - x \cdot \left(b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)}{x \cdot x - \left(x \cdot \left(b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)\right) \cdot \left(x \cdot \left(b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)\right)}}\right), y\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{x - x \cdot \left(b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)}{x \cdot x - \left(x \cdot \left(b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)\right) \cdot \left(x \cdot \left(b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)\right)}\right)\right), y\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(x - x \cdot \left(b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)\right), \left(x \cdot x - \left(x \cdot \left(b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)\right) \cdot \left(x \cdot \left(b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)\right)\right)\right)\right), y\right) \]

   10. Applied egg-rr 51.5%

       \[\leadsto \frac{\color{blue}{\frac{1}{\frac{x - \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right) + -1\right) \cdot \left(b \cdot x\right)}{\left(x \cdot \left(1 + b \cdot \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right) + -1\right)\right)\right) \cdot \left(x - \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right) + -1\right) \cdot \left(b \cdot x\right)\right)}}}}{y} \]

   11. Taylor expanded in b around 0

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\color{blue}{\left(x + b \cdot \left(\frac{-1}{2} \cdot \left(b \cdot x\right) - -1 \cdot x\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right)\right)\right)\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right), \mathsf{*.f64}\left(b, x\right)\right)\right)\right)\right)\right), y\right) \]
   12. Step-by-step derivation

       1. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(\frac{-1}{2} \cdot \left(b \cdot x\right) - -1 \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right)\right)\right)\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right), \mathsf{*.f64}\left(b, x\right)\right)\right)\right)\right)\right), y\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\frac{-1}{2} \cdot \left(b \cdot x\right) - -1 \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right)\right)\right)\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right), \mathsf{*.f64}\left(b, x\right)\right)\right)\right)\right)\right), y\right) \]

       3. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\frac{-1}{2} \cdot \left(b \cdot x\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right)\right)\right)\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right), \mathsf{*.f64}\left(b, x\right)\right)\right)\right)\right)\right), y\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\frac{-1}{2} \cdot b\right) \cdot x + \left(\mathsf{neg}\left(-1\right)\right) \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right)\right)\right)\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right), \mathsf{*.f64}\left(b, x\right)\right)\right)\right)\right)\right), y\right) \]

       5. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\frac{-1}{2} \cdot b\right) \cdot x + 1 \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right)\right)\right)\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right), \mathsf{*.f64}\left(b, x\right)\right)\right)\right)\right)\right), y\right) \]

       6. distribute-rgt-out N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{-1}{2} \cdot b + 1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right)\right)\right)\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right), \mathsf{*.f64}\left(b, x\right)\right)\right)\right)\right)\right), y\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{-1}{2} \cdot b + 1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right)\right)\right)\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right), \mathsf{*.f64}\left(b, x\right)\right)\right)\right)\right)\right), y\right) \]

       8. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{-1}{2} \cdot b\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right)\right)\right)\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right), \mathsf{*.f64}\left(b, x\right)\right)\right)\right)\right)\right), y\right) \]

       9. *-lowering-*.f64 76.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-1}{2}, b\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right)\right)\right)\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right), \mathsf{*.f64}\left(b, x\right)\right)\right)\right)\right)\right), y\right) \]

   13. Simplified 76.5%

       \[\leadsto \frac{\frac{1}{\frac{\color{blue}{x + b \cdot \left(x \cdot \left(-0.5 \cdot b + 1\right)\right)}}{\left(x \cdot \left(1 + b \cdot \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right) + -1\right)\right)\right) \cdot \left(x - \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right) + -1\right) \cdot \left(b \cdot x\right)\right)}}}{y} \]

   if 5.8000000000000003e34 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 87.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 87.9%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{0 - b}\right), \color{blue}{y}\right) \]

      2. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{0}}{e^{b}}\right), y\right) \]

      3. 1-exp N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(e^{b}\right)\right), y\right) \]

      6. exp-lowering-exp.f64 87.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   7. Applied egg-rr 87.9%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)\right)}\right), y\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \left(b \cdot \left(1 + b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(1 + b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)\right)\right)\right), y\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \left(b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)\right)\right)\right)\right), y\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)\right)\right)\right)\right), y\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(\frac{1}{6} \cdot b\right)\right)\right)\right)\right)\right)\right), y\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(b \cdot \frac{1}{6}\right)\right)\right)\right)\right)\right)\right), y\right) \]

      7. *-lowering-*.f64 74.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{1}{6}\right)\right)\right)\right)\right)\right)\right), y\right) \]

   10. Simplified 74.6%

       \[\leadsto \frac{\frac{x}{\color{blue}{1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)}}}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -140:\\ \;\;\;\;x \cdot \frac{1 + b \cdot \left(-1 + b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right)}{y}\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-22}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+34}:\\ \;\;\;\;\frac{\frac{1}{\frac{x + b \cdot \left(x \cdot \left(1 + b \cdot -0.5\right)\right)}{\left(x \cdot \left(1 + b \cdot \left(-1 + b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right)\right)\right) \cdot \left(x - \left(-1 + b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right) \cdot \left(x \cdot b\right)\right)}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 53.0% accurate, 11.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -140:\\ \;\;\;\;x \cdot \frac{1 + b \cdot \left(-1 + b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right)}{y}\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+55}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -140.0)
   (* x (/ (+ 1.0 (* b (+ -1.0 (* b (+ 0.5 (* b -0.16666666666666666)))))) y))
   (if (<= b 2.15e+55)
     (/ (/ x y) a)
     (/
      (/ x (+ 1.0 (* b (+ 1.0 (* b (+ 0.5 (* b 0.16666666666666666)))))))
      y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -140.0) {
		tmp = x * ((1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y);
	} else if (b <= 2.15e+55) {
		tmp = (x / y) / a;
	} else {
		tmp = (x / (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))) / 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 <= (-140.0d0)) then
        tmp = x * ((1.0d0 + (b * ((-1.0d0) + (b * (0.5d0 + (b * (-0.16666666666666666d0))))))) / y)
    else if (b <= 2.15d+55) then
        tmp = (x / y) / a
    else
        tmp = (x / (1.0d0 + (b * (1.0d0 + (b * (0.5d0 + (b * 0.16666666666666666d0))))))) / 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 <= -140.0) {
		tmp = x * ((1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y);
	} else if (b <= 2.15e+55) {
		tmp = (x / y) / a;
	} else {
		tmp = (x / (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -140.0:
		tmp = x * ((1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y)
	elif b <= 2.15e+55:
		tmp = (x / y) / a
	else:
		tmp = (x / (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -140.0)
		tmp = Float64(x * Float64(Float64(1.0 + Float64(b * Float64(-1.0 + Float64(b * Float64(0.5 + Float64(b * -0.16666666666666666)))))) / y));
	elseif (b <= 2.15e+55)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(Float64(x / Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * Float64(0.5 + Float64(b * 0.16666666666666666))))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -140.0)
		tmp = x * ((1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y);
	elseif (b <= 2.15e+55)
		tmp = (x / y) / a;
	else
		tmp = (x / (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -140.0], N[(x * N[(N[(1.0 + N[(b * N[(-1.0 + N[(b * N[(0.5 + N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.15e+55], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / N[(1.0 + N[(b * N[(1.0 + N[(b * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -140

   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 inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 83.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 83.6%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)}\right), y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)\right)\right), y\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + -1\right)\right)\right)\right), y\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right), -1\right)\right)\right)\right), y\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right), -1\right)\right)\right)\right), y\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(\frac{-1}{6} \cdot b\right)\right)\right), -1\right)\right)\right)\right), y\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(b \cdot \frac{-1}{6}\right)\right)\right), -1\right)\right)\right)\right), y\right) \]

      9. *-lowering-*.f64 66.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right)\right)\right)\right), y\right) \]

   8. Simplified 66.2%

      \[\leadsto \frac{x \cdot \color{blue}{\left(1 + b \cdot \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right) + -1\right)\right)}}{y} \]
   9. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto x \cdot \color{blue}{\frac{1 + b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)}{y}} \]

      2. *-commutative N/A

         \[\leadsto \frac{1 + b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)}{y} \cdot \color{blue}{x} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1 + b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)}{y}\right), \color{blue}{x}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(1 + b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right), y\right), x\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \left(b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)\right), y\right), x\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)\right), y\right), x\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right), -1\right)\right)\right), y\right), x\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right), -1\right)\right)\right), y\right), x\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(b \cdot \frac{-1}{6}\right)\right)\right), -1\right)\right)\right), y\right), x\right) \]

      10. *-lowering-*.f64 67.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right)\right)\right), y\right), x\right) \]

   10. Applied egg-rr 67.9%

       \[\leadsto \color{blue}{\frac{1 + b \cdot \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right) + -1\right)}{y} \cdot x} \]

   if -140 < b < 2.1499999999999999e55

   1. Initial program 95.3%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 79.0%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 67.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 67.6%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a}{{z}^{y}}\right)}\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. pow-lowering-pow.f64 68.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   10. Simplified 68.0%

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

   11. Taylor expanded in y around 0

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{a}\right) \]
   12. Step-by-step derivation

   13. Simplified 40.0%

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

   if 2.1499999999999999e55 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 87.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 87.5%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{0 - b}\right), \color{blue}{y}\right) \]

      2. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{0}}{e^{b}}\right), y\right) \]

      3. 1-exp N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(e^{b}\right)\right), y\right) \]

      6. exp-lowering-exp.f64 87.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   7. Applied egg-rr 87.5%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)\right)}\right), y\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \left(b \cdot \left(1 + b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(1 + b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)\right)\right)\right), y\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \left(b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)\right)\right)\right)\right), y\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)\right)\right)\right)\right), y\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(\frac{1}{6} \cdot b\right)\right)\right)\right)\right)\right)\right), y\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(b \cdot \frac{1}{6}\right)\right)\right)\right)\right)\right)\right), y\right) \]

      7. *-lowering-*.f64 75.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{1}{6}\right)\right)\right)\right)\right)\right)\right), y\right) \]

   10. Simplified 75.4%

       \[\leadsto \frac{\frac{x}{\color{blue}{1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -140:\\ \;\;\;\;x \cdot \frac{1 + b \cdot \left(-1 + b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right)}{y}\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+55}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.1% accurate, 13.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -140:\\ \;\;\;\;x \cdot \frac{1 + b \cdot \left(-1 + b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right)}{y}\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+55}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 + b \cdot \left(1 + b \cdot 0.5\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -140.0)
   (* x (/ (+ 1.0 (* b (+ -1.0 (* b (+ 0.5 (* b -0.16666666666666666)))))) y))
   (if (<= b 3e+55)
     (/ (/ x y) a)
     (/ (/ x (+ 1.0 (* b (+ 1.0 (* b 0.5))))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -140.0) {
		tmp = x * ((1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y);
	} else if (b <= 3e+55) {
		tmp = (x / y) / a;
	} else {
		tmp = (x / (1.0 + (b * (1.0 + (b * 0.5))))) / 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 <= (-140.0d0)) then
        tmp = x * ((1.0d0 + (b * ((-1.0d0) + (b * (0.5d0 + (b * (-0.16666666666666666d0))))))) / y)
    else if (b <= 3d+55) then
        tmp = (x / y) / a
    else
        tmp = (x / (1.0d0 + (b * (1.0d0 + (b * 0.5d0))))) / 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 <= -140.0) {
		tmp = x * ((1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y);
	} else if (b <= 3e+55) {
		tmp = (x / y) / a;
	} else {
		tmp = (x / (1.0 + (b * (1.0 + (b * 0.5))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -140.0:
		tmp = x * ((1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y)
	elif b <= 3e+55:
		tmp = (x / y) / a
	else:
		tmp = (x / (1.0 + (b * (1.0 + (b * 0.5))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -140.0)
		tmp = Float64(x * Float64(Float64(1.0 + Float64(b * Float64(-1.0 + Float64(b * Float64(0.5 + Float64(b * -0.16666666666666666)))))) / y));
	elseif (b <= 3e+55)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(Float64(x / Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * 0.5))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -140.0)
		tmp = x * ((1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y);
	elseif (b <= 3e+55)
		tmp = (x / y) / a;
	else
		tmp = (x / (1.0 + (b * (1.0 + (b * 0.5))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -140.0], N[(x * N[(N[(1.0 + N[(b * N[(-1.0 + N[(b * N[(0.5 + N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3e+55], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / N[(1.0 + N[(b * N[(1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -140

   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 inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 83.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 83.6%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)}\right), y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)\right)\right), y\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + -1\right)\right)\right)\right), y\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right), -1\right)\right)\right)\right), y\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right), -1\right)\right)\right)\right), y\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(\frac{-1}{6} \cdot b\right)\right)\right), -1\right)\right)\right)\right), y\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(b \cdot \frac{-1}{6}\right)\right)\right), -1\right)\right)\right)\right), y\right) \]

      9. *-lowering-*.f64 66.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right)\right)\right)\right), y\right) \]

   8. Simplified 66.2%

      \[\leadsto \frac{x \cdot \color{blue}{\left(1 + b \cdot \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right) + -1\right)\right)}}{y} \]
   9. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto x \cdot \color{blue}{\frac{1 + b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)}{y}} \]

      2. *-commutative N/A

         \[\leadsto \frac{1 + b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)}{y} \cdot \color{blue}{x} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1 + b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)}{y}\right), \color{blue}{x}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(1 + b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right), y\right), x\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \left(b \cdot \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)\right), y\right), x\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right) + -1\right)\right)\right), y\right), x\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(b \cdot \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right), -1\right)\right)\right), y\right), x\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{1}{2} + b \cdot \frac{-1}{6}\right)\right), -1\right)\right)\right), y\right), x\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(b \cdot \frac{-1}{6}\right)\right)\right), -1\right)\right)\right), y\right), x\right) \]

      10. *-lowering-*.f64 67.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right)\right)\right), y\right), x\right) \]

   10. Applied egg-rr 67.9%

       \[\leadsto \color{blue}{\frac{1 + b \cdot \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right) + -1\right)}{y} \cdot x} \]

   if -140 < b < 3.00000000000000017e55

   1. Initial program 95.3%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 79.0%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 67.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 67.6%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a}{{z}^{y}}\right)}\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. pow-lowering-pow.f64 68.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   10. Simplified 68.0%

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

   11. Taylor expanded in y around 0

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{a}\right) \]
   12. Step-by-step derivation

   13. Simplified 40.0%

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

   if 3.00000000000000017e55 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 87.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 87.5%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{0 - b}\right), \color{blue}{y}\right) \]

      2. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{0}}{e^{b}}\right), y\right) \]

      3. 1-exp N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(e^{b}\right)\right), y\right) \]

      6. exp-lowering-exp.f64 87.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   7. Applied egg-rr 87.5%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(1 + \frac{1}{2} \cdot b\right)\right)}\right), y\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \left(b \cdot \left(1 + \frac{1}{2} \cdot b\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(1 + \frac{1}{2} \cdot b\right)\right)\right)\right), y\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \left(\frac{1}{2} \cdot b\right)\right)\right)\right)\right), y\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \left(b \cdot \frac{1}{2}\right)\right)\right)\right)\right), y\right) \]

      5. *-lowering-*.f64 67.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \frac{1}{2}\right)\right)\right)\right)\right), y\right) \]

   10. Simplified 67.7%

       \[\leadsto \frac{\frac{x}{\color{blue}{1 + b \cdot \left(1 + b \cdot 0.5\right)}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -140:\\ \;\;\;\;x \cdot \frac{1 + b \cdot \left(-1 + b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right)}{y}\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+55}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 + b \cdot \left(1 + b \cdot 0.5\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.1% accurate, 13.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.85 \cdot 10^{+80}:\\ \;\;\;\;\frac{-0.16666666666666666 \cdot \left(x \cdot \left(b \cdot \left(b \cdot b\right)\right)\right)}{y}\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+58}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 + b \cdot \left(1 + b \cdot 0.5\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.85e+80)
   (/ (* -0.16666666666666666 (* x (* b (* b b)))) y)
   (if (<= b 6.2e+58)
     (/ (/ x y) a)
     (/ (/ x (+ 1.0 (* b (+ 1.0 (* b 0.5))))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.85e+80) {
		tmp = (-0.16666666666666666 * (x * (b * (b * b)))) / y;
	} else if (b <= 6.2e+58) {
		tmp = (x / y) / a;
	} else {
		tmp = (x / (1.0 + (b * (1.0 + (b * 0.5))))) / 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 <= (-1.85d+80)) then
        tmp = ((-0.16666666666666666d0) * (x * (b * (b * b)))) / y
    else if (b <= 6.2d+58) then
        tmp = (x / y) / a
    else
        tmp = (x / (1.0d0 + (b * (1.0d0 + (b * 0.5d0))))) / 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 <= -1.85e+80) {
		tmp = (-0.16666666666666666 * (x * (b * (b * b)))) / y;
	} else if (b <= 6.2e+58) {
		tmp = (x / y) / a;
	} else {
		tmp = (x / (1.0 + (b * (1.0 + (b * 0.5))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.85e+80:
		tmp = (-0.16666666666666666 * (x * (b * (b * b)))) / y
	elif b <= 6.2e+58:
		tmp = (x / y) / a
	else:
		tmp = (x / (1.0 + (b * (1.0 + (b * 0.5))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.85e+80)
		tmp = Float64(Float64(-0.16666666666666666 * Float64(x * Float64(b * Float64(b * b)))) / y);
	elseif (b <= 6.2e+58)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(Float64(x / Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * 0.5))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.85e+80)
		tmp = (-0.16666666666666666 * (x * (b * (b * b)))) / y;
	elseif (b <= 6.2e+58)
		tmp = (x / y) / a;
	else
		tmp = (x / (1.0 + (b * (1.0 + (b * 0.5))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.85e+80], N[(N[(-0.16666666666666666 * N[(x * N[(b * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 6.2e+58], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / N[(1.0 + N[(b * N[(1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.84999999999999998e80

   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 inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 91.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 91.6%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{0 - b}\right), \color{blue}{y}\right) \]

      2. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{0}}{e^{b}}\right), y\right) \]

      3. 1-exp N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(e^{b}\right)\right), y\right) \]

      6. exp-lowering-exp.f64 91.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   7. Applied egg-rr 91.6%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot x + \frac{1}{2} \cdot x\right) + \left(\frac{-1}{2} \cdot x + \frac{1}{6} \cdot x\right)\right)\right) - \left(-1 \cdot x + \frac{1}{2} \cdot x\right)\right) - x\right)\right)}, y\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot x + \frac{1}{2} \cdot x\right) + \left(\frac{-1}{2} \cdot x + \frac{1}{6} \cdot x\right)\right)\right) - \left(-1 \cdot x + \frac{1}{2} \cdot x\right)\right) - x\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot x + \frac{1}{2} \cdot x\right) + \left(\frac{-1}{2} \cdot x + \frac{1}{6} \cdot x\right)\right)\right) - \left(-1 \cdot x + \frac{1}{2} \cdot x\right)\right) - x\right)\right)\right), y\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot x + \frac{1}{2} \cdot x\right) + \left(\frac{-1}{2} \cdot x + \frac{1}{6} \cdot x\right)\right)\right) - \left(-1 \cdot x + \frac{1}{2} \cdot x\right)\right)\right), x\right)\right)\right), y\right) \]

   10. Simplified 86.2%

       \[\leadsto \frac{\color{blue}{x + b \cdot \left(b \cdot \left(\left(0 - b \cdot \left(x \cdot 0.5 + x \cdot -0.3333333333333333\right)\right) + x \cdot 0.5\right) - x\right)}}{y} \]

   11. Taylor expanded in b around inf

       \[\leadsto \color{blue}{-1 \cdot \frac{{b}^{3} \cdot \left(\frac{-1}{3} \cdot x + \frac{1}{2} \cdot x\right)}{y}} \]
   12. Step-by-step derivation

       1. associate-*r/ N/A

          \[\leadsto \frac{-1 \cdot \left({b}^{3} \cdot \left(\frac{-1}{3} \cdot x + \frac{1}{2} \cdot x\right)\right)}{\color{blue}{y}} \]

       2. *-commutative N/A

          \[\leadsto \frac{-1 \cdot \left(\left(\frac{-1}{3} \cdot x + \frac{1}{2} \cdot x\right) \cdot {b}^{3}\right)}{y} \]

       3. associate-*r* N/A

          \[\leadsto \frac{\left(-1 \cdot \left(\frac{-1}{3} \cdot x + \frac{1}{2} \cdot x\right)\right) \cdot {b}^{3}}{y} \]

       4. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(-1 \cdot \left(\frac{-1}{3} \cdot x + \frac{1}{2} \cdot x\right)\right) \cdot {b}^{3}\right), \color{blue}{y}\right) \]

       5. distribute-rgt-out N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(-1 \cdot \left(x \cdot \left(\frac{-1}{3} + \frac{1}{2}\right)\right)\right) \cdot {b}^{3}\right), y\right) \]

       6. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(-1 \cdot \left(x \cdot \frac{1}{6}\right)\right) \cdot {b}^{3}\right), y\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(-1 \cdot \left(\frac{1}{6} \cdot x\right)\right) \cdot {b}^{3}\right), y\right) \]

       8. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(\left(-1 \cdot \frac{1}{6}\right) \cdot x\right) \cdot {b}^{3}\right), y\right) \]

       9. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(\frac{-1}{6} \cdot x\right) \cdot {b}^{3}\right), y\right) \]

       10. associate-*r* N/A

           \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{6} \cdot \left(x \cdot {b}^{3}\right)\right), y\right) \]

       11. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{6} \cdot \left({b}^{3} \cdot x\right)\right), y\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{6}, \left({b}^{3} \cdot x\right)\right), y\right) \]

       13. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{6}, \left(x \cdot {b}^{3}\right)\right), y\right) \]

       14. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(x, \left({b}^{3}\right)\right)\right), y\right) \]

       15. cube-mult N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(x, \left(b \cdot \left(b \cdot b\right)\right)\right)\right), y\right) \]

       16. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(x, \left(b \cdot {b}^{2}\right)\right)\right), y\right) \]

       17. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \left({b}^{2}\right)\right)\right)\right), y\right) \]

       18. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot b\right)\right)\right)\right), y\right) \]

       19. *-lowering-*.f64 89.0%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, b\right)\right)\right)\right), y\right) \]

   13. Simplified 89.0%

       \[\leadsto \color{blue}{\frac{-0.16666666666666666 \cdot \left(x \cdot \left(b \cdot \left(b \cdot b\right)\right)\right)}{y}} \]

   if -1.84999999999999998e80 < b < 6.1999999999999998e58

   1. Initial program 95.8%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 76.4%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 67.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 67.0%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a}{{z}^{y}}\right)}\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. pow-lowering-pow.f64 67.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   10. Simplified 67.6%

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

   11. Taylor expanded in y around 0

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{a}\right) \]
   12. Step-by-step derivation

   13. Simplified 38.6%

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

   if 6.1999999999999998e58 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 87.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 87.5%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{0 - b}\right), \color{blue}{y}\right) \]

      2. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{0}}{e^{b}}\right), y\right) \]

      3. 1-exp N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(e^{b}\right)\right), y\right) \]

      6. exp-lowering-exp.f64 87.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   7. Applied egg-rr 87.5%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(1 + \frac{1}{2} \cdot b\right)\right)}\right), y\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \left(b \cdot \left(1 + \frac{1}{2} \cdot b\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(1 + \frac{1}{2} \cdot b\right)\right)\right)\right), y\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \left(\frac{1}{2} \cdot b\right)\right)\right)\right)\right), y\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \left(b \cdot \frac{1}{2}\right)\right)\right)\right)\right), y\right) \]

      5. *-lowering-*.f64 67.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \frac{1}{2}\right)\right)\right)\right)\right), y\right) \]

   10. Simplified 67.7%

       \[\leadsto \frac{\frac{x}{\color{blue}{1 + b \cdot \left(1 + b \cdot 0.5\right)}}}{y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 16: 44.5% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.85 \cdot 10^{+80}:\\ \;\;\;\;\frac{-0.16666666666666666 \cdot \left(x \cdot \left(b \cdot \left(b \cdot b\right)\right)\right)}{y}\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+73}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 + b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.85e+80)
   (/ (* -0.16666666666666666 (* x (* b (* b b)))) y)
   (if (<= b 3.4e+73) (/ (/ x y) a) (/ (/ x (+ 1.0 b)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.85e+80) {
		tmp = (-0.16666666666666666 * (x * (b * (b * b)))) / y;
	} else if (b <= 3.4e+73) {
		tmp = (x / y) / a;
	} else {
		tmp = (x / (1.0 + b)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.85d+80)) then
        tmp = ((-0.16666666666666666d0) * (x * (b * (b * b)))) / y
    else if (b <= 3.4d+73) then
        tmp = (x / y) / a
    else
        tmp = (x / (1.0d0 + b)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.85e+80) {
		tmp = (-0.16666666666666666 * (x * (b * (b * b)))) / y;
	} else if (b <= 3.4e+73) {
		tmp = (x / y) / a;
	} else {
		tmp = (x / (1.0 + b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.85e+80:
		tmp = (-0.16666666666666666 * (x * (b * (b * b)))) / y
	elif b <= 3.4e+73:
		tmp = (x / y) / a
	else:
		tmp = (x / (1.0 + b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.85e+80)
		tmp = Float64(Float64(-0.16666666666666666 * Float64(x * Float64(b * Float64(b * b)))) / y);
	elseif (b <= 3.4e+73)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(Float64(x / Float64(1.0 + b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.85e+80)
		tmp = (-0.16666666666666666 * (x * (b * (b * b)))) / y;
	elseif (b <= 3.4e+73)
		tmp = (x / y) / a;
	else
		tmp = (x / (1.0 + b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.85e+80], N[(N[(-0.16666666666666666 * N[(x * N[(b * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 3.4e+73], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / N[(1.0 + b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.84999999999999998e80

   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 inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 91.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 91.6%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{0 - b}\right), \color{blue}{y}\right) \]

      2. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{0}}{e^{b}}\right), y\right) \]

      3. 1-exp N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(e^{b}\right)\right), y\right) \]

      6. exp-lowering-exp.f64 91.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   7. Applied egg-rr 91.6%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot x + \frac{1}{2} \cdot x\right) + \left(\frac{-1}{2} \cdot x + \frac{1}{6} \cdot x\right)\right)\right) - \left(-1 \cdot x + \frac{1}{2} \cdot x\right)\right) - x\right)\right)}, y\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot x + \frac{1}{2} \cdot x\right) + \left(\frac{-1}{2} \cdot x + \frac{1}{6} \cdot x\right)\right)\right) - \left(-1 \cdot x + \frac{1}{2} \cdot x\right)\right) - x\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot x + \frac{1}{2} \cdot x\right) + \left(\frac{-1}{2} \cdot x + \frac{1}{6} \cdot x\right)\right)\right) - \left(-1 \cdot x + \frac{1}{2} \cdot x\right)\right) - x\right)\right)\right), y\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot x + \frac{1}{2} \cdot x\right) + \left(\frac{-1}{2} \cdot x + \frac{1}{6} \cdot x\right)\right)\right) - \left(-1 \cdot x + \frac{1}{2} \cdot x\right)\right)\right), x\right)\right)\right), y\right) \]

   10. Simplified 86.2%

       \[\leadsto \frac{\color{blue}{x + b \cdot \left(b \cdot \left(\left(0 - b \cdot \left(x \cdot 0.5 + x \cdot -0.3333333333333333\right)\right) + x \cdot 0.5\right) - x\right)}}{y} \]

   11. Taylor expanded in b around inf

       \[\leadsto \color{blue}{-1 \cdot \frac{{b}^{3} \cdot \left(\frac{-1}{3} \cdot x + \frac{1}{2} \cdot x\right)}{y}} \]
   12. Step-by-step derivation

       1. associate-*r/ N/A

          \[\leadsto \frac{-1 \cdot \left({b}^{3} \cdot \left(\frac{-1}{3} \cdot x + \frac{1}{2} \cdot x\right)\right)}{\color{blue}{y}} \]

       2. *-commutative N/A

          \[\leadsto \frac{-1 \cdot \left(\left(\frac{-1}{3} \cdot x + \frac{1}{2} \cdot x\right) \cdot {b}^{3}\right)}{y} \]

       3. associate-*r* N/A

          \[\leadsto \frac{\left(-1 \cdot \left(\frac{-1}{3} \cdot x + \frac{1}{2} \cdot x\right)\right) \cdot {b}^{3}}{y} \]

       4. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(-1 \cdot \left(\frac{-1}{3} \cdot x + \frac{1}{2} \cdot x\right)\right) \cdot {b}^{3}\right), \color{blue}{y}\right) \]

       5. distribute-rgt-out N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(-1 \cdot \left(x \cdot \left(\frac{-1}{3} + \frac{1}{2}\right)\right)\right) \cdot {b}^{3}\right), y\right) \]

       6. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(-1 \cdot \left(x \cdot \frac{1}{6}\right)\right) \cdot {b}^{3}\right), y\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(-1 \cdot \left(\frac{1}{6} \cdot x\right)\right) \cdot {b}^{3}\right), y\right) \]

       8. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(\left(-1 \cdot \frac{1}{6}\right) \cdot x\right) \cdot {b}^{3}\right), y\right) \]

       9. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(\frac{-1}{6} \cdot x\right) \cdot {b}^{3}\right), y\right) \]

       10. associate-*r* N/A

           \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{6} \cdot \left(x \cdot {b}^{3}\right)\right), y\right) \]

       11. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{6} \cdot \left({b}^{3} \cdot x\right)\right), y\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{6}, \left({b}^{3} \cdot x\right)\right), y\right) \]

       13. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{6}, \left(x \cdot {b}^{3}\right)\right), y\right) \]

       14. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(x, \left({b}^{3}\right)\right)\right), y\right) \]

       15. cube-mult N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(x, \left(b \cdot \left(b \cdot b\right)\right)\right)\right), y\right) \]

       16. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(x, \left(b \cdot {b}^{2}\right)\right)\right), y\right) \]

       17. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \left({b}^{2}\right)\right)\right)\right), y\right) \]

       18. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot b\right)\right)\right)\right), y\right) \]

       19. *-lowering-*.f64 89.0%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, b\right)\right)\right)\right), y\right) \]

   13. Simplified 89.0%

       \[\leadsto \color{blue}{\frac{-0.16666666666666666 \cdot \left(x \cdot \left(b \cdot \left(b \cdot b\right)\right)\right)}{y}} \]

   if -1.84999999999999998e80 < b < 3.4000000000000002e73

   1. Initial program 96.0%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 75.9%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 67.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 67.4%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a}{{z}^{y}}\right)}\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. pow-lowering-pow.f64 67.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   10. Simplified 67.4%

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

   11. Taylor expanded in y around 0

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{a}\right) \]
   12. Step-by-step derivation

   13. Simplified 37.5%

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

   if 3.4000000000000002e73 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 88.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 88.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{0 - b}\right), \color{blue}{y}\right) \]

      2. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{0}}{e^{b}}\right), y\right) \]

      3. 1-exp N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(e^{b}\right)\right), y\right) \]

      6. exp-lowering-exp.f64 88.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   7. Applied egg-rr 88.1%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \color{blue}{\left(1 + b\right)}\right), y\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(b + 1\right)\right), y\right) \]

      2. +-lowering-+.f64 45.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(b, 1\right)\right), y\right) \]

   10. Simplified 45.1%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.85 \cdot 10^{+80}:\\ \;\;\;\;\frac{-0.16666666666666666 \cdot \left(x \cdot \left(b \cdot \left(b \cdot b\right)\right)\right)}{y}\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+73}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 + b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 42.9% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -105:\\ \;\;\;\;\left(b \cdot \left(b \cdot b\right)\right) \cdot \left(\frac{x}{y} \cdot -0.16666666666666666\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+74}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 + b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -105.0)
   (* (* b (* b b)) (* (/ x y) -0.16666666666666666))
   (if (<= b 1.45e+74) (/ (/ x y) a) (/ (/ x (+ 1.0 b)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -105.0) {
		tmp = (b * (b * b)) * ((x / y) * -0.16666666666666666);
	} else if (b <= 1.45e+74) {
		tmp = (x / y) / a;
	} else {
		tmp = (x / (1.0 + b)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-105.0d0)) then
        tmp = (b * (b * b)) * ((x / y) * (-0.16666666666666666d0))
    else if (b <= 1.45d+74) then
        tmp = (x / y) / a
    else
        tmp = (x / (1.0d0 + b)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -105.0) {
		tmp = (b * (b * b)) * ((x / y) * -0.16666666666666666);
	} else if (b <= 1.45e+74) {
		tmp = (x / y) / a;
	} else {
		tmp = (x / (1.0 + b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -105.0:
		tmp = (b * (b * b)) * ((x / y) * -0.16666666666666666)
	elif b <= 1.45e+74:
		tmp = (x / y) / a
	else:
		tmp = (x / (1.0 + b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -105.0)
		tmp = Float64(Float64(b * Float64(b * b)) * Float64(Float64(x / y) * -0.16666666666666666));
	elseif (b <= 1.45e+74)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(Float64(x / Float64(1.0 + b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -105.0)
		tmp = (b * (b * b)) * ((x / y) * -0.16666666666666666);
	elseif (b <= 1.45e+74)
		tmp = (x / y) / a;
	else
		tmp = (x / (1.0 + b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -105.0], N[(N[(b * N[(b * b), $MachinePrecision]), $MachinePrecision] * N[(N[(x / y), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.45e+74], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / N[(1.0 + b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -105

   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 inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 83.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 83.6%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)}\right), y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)\right)\right), y\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + -1\right)\right)\right)\right), y\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right), -1\right)\right)\right)\right), y\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right), -1\right)\right)\right)\right), y\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(\frac{-1}{6} \cdot b\right)\right)\right), -1\right)\right)\right)\right), y\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(b \cdot \frac{-1}{6}\right)\right)\right), -1\right)\right)\right)\right), y\right) \]

      9. *-lowering-*.f64 66.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right), -1\right)\right)\right)\right), y\right) \]

   8. Simplified 66.2%

      \[\leadsto \frac{x \cdot \color{blue}{\left(1 + b \cdot \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right) + -1\right)\right)}}{y} \]

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{-1}{6} \cdot \frac{{b}^{3} \cdot x}{y}} \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \frac{{b}^{3} \cdot x}{y} \cdot \color{blue}{\frac{-1}{6}} \]

       2. associate-/l* N/A

          \[\leadsto \left({b}^{3} \cdot \frac{x}{y}\right) \cdot \frac{-1}{6} \]

       3. associate-*r* N/A

          \[\leadsto {b}^{3} \cdot \color{blue}{\left(\frac{x}{y} \cdot \frac{-1}{6}\right)} \]

       4. *-commutative N/A

          \[\leadsto {b}^{3} \cdot \left(\frac{-1}{6} \cdot \color{blue}{\frac{x}{y}}\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({b}^{3}\right), \color{blue}{\left(\frac{-1}{6} \cdot \frac{x}{y}\right)}\right) \]

       6. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(\left(b \cdot \left(b \cdot b\right)\right), \left(\color{blue}{\frac{-1}{6}} \cdot \frac{x}{y}\right)\right) \]

       7. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(b \cdot {b}^{2}\right), \left(\frac{-1}{6} \cdot \frac{x}{y}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left({b}^{2}\right)\right), \left(\color{blue}{\frac{-1}{6}} \cdot \frac{x}{y}\right)\right) \]

       9. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(b \cdot b\right)\right), \left(\frac{-1}{6} \cdot \frac{x}{y}\right)\right) \]

       10. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, b\right)\right), \left(\frac{-1}{6} \cdot \frac{x}{y}\right)\right) \]

       11. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, b\right)\right), \left(\frac{x}{y} \cdot \color{blue}{\frac{-1}{6}}\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, b\right)\right), \mathsf{*.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\frac{-1}{6}}\right)\right) \]

       13. /-lowering-/.f64 66.3%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, b\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \frac{-1}{6}\right)\right) \]

   11. Simplified 66.3%

       \[\leadsto \color{blue}{\left(b \cdot \left(b \cdot b\right)\right) \cdot \left(\frac{x}{y} \cdot -0.16666666666666666\right)} \]

   if -105 < b < 1.4500000000000001e74

   1. Initial program 95.4%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 78.3%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 68.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 68.0%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a}{{z}^{y}}\right)}\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. pow-lowering-pow.f64 67.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   10. Simplified 67.8%

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

   11. Taylor expanded in y around 0

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{a}\right) \]
   12. Step-by-step derivation

   13. Simplified 38.7%

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

   if 1.4500000000000001e74 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 88.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 88.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{0 - b}\right), \color{blue}{y}\right) \]

      2. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{0}}{e^{b}}\right), y\right) \]

      3. 1-exp N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(e^{b}\right)\right), y\right) \]

      6. exp-lowering-exp.f64 88.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   7. Applied egg-rr 88.1%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \color{blue}{\left(1 + b\right)}\right), y\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(b + 1\right)\right), y\right) \]

      2. +-lowering-+.f64 45.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(b, 1\right)\right), y\right) \]

   10. Simplified 45.1%

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

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -105:\\ \;\;\;\;\left(b \cdot \left(b \cdot b\right)\right) \cdot \left(\frac{x}{y} \cdot -0.16666666666666666\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+74}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 + b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 43.0% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+80}:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{+74}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 + b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.5e+80)
   (/ (* 0.5 (* x (* b b))) y)
   (if (<= b 1.85e+74) (/ (/ x y) a) (/ (/ x (+ 1.0 b)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.5e+80) {
		tmp = (0.5 * (x * (b * b))) / y;
	} else if (b <= 1.85e+74) {
		tmp = (x / y) / a;
	} else {
		tmp = (x / (1.0 + b)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-5.5d+80)) then
        tmp = (0.5d0 * (x * (b * b))) / y
    else if (b <= 1.85d+74) then
        tmp = (x / y) / a
    else
        tmp = (x / (1.0d0 + b)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.5e+80) {
		tmp = (0.5 * (x * (b * b))) / y;
	} else if (b <= 1.85e+74) {
		tmp = (x / y) / a;
	} else {
		tmp = (x / (1.0 + b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5.5e+80:
		tmp = (0.5 * (x * (b * b))) / y
	elif b <= 1.85e+74:
		tmp = (x / y) / a
	else:
		tmp = (x / (1.0 + b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.5e+80)
		tmp = Float64(Float64(0.5 * Float64(x * Float64(b * b))) / y);
	elseif (b <= 1.85e+74)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(Float64(x / Float64(1.0 + b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5.5e+80)
		tmp = (0.5 * (x * (b * b))) / y;
	elseif (b <= 1.85e+74)
		tmp = (x / y) / a;
	else
		tmp = (x / (1.0 + b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5.5e+80], N[(N[(0.5 * N[(x * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 1.85e+74], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / N[(1.0 + b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.49999999999999967e80

   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 inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 91.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 91.6%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + b \cdot \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)}, y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot \left(b \cdot x\right) + -1 \cdot x\right)\right)\right), y\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\frac{1}{2} \cdot b\right) \cdot x + -1 \cdot x\right)\right)\right), y\right) \]

      5. distribute-rgt-out N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{1}{2} \cdot b\right), -1\right)\right)\right)\right), y\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(b \cdot \frac{1}{2}\right), -1\right)\right)\right)\right), y\right) \]

      13. *-lowering-*.f64 75.4%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \frac{1}{2}\right), -1\right)\right)\right)\right), y\right) \]

   8. Simplified 75.4%

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

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{{b}^{2} \cdot x}{y}} \]
   10. Step-by-step derivation

       1. associate-*r/ N/A

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

       2. *-commutative N/A

          \[\leadsto \frac{\left({b}^{2} \cdot x\right) \cdot \frac{1}{2}}{y} \]

       3. associate-*r* N/A

          \[\leadsto \frac{{b}^{2} \cdot \left(x \cdot \frac{1}{2}\right)}{y} \]

       4. *-commutative N/A

          \[\leadsto \frac{{b}^{2} \cdot \left(\frac{1}{2} \cdot x\right)}{y} \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left({b}^{2} \cdot \left(\frac{1}{2} \cdot x\right)\right), \color{blue}{y}\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left({b}^{2} \cdot \left(x \cdot \frac{1}{2}\right)\right), y\right) \]

       7. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left({b}^{2} \cdot x\right) \cdot \frac{1}{2}\right), y\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot \left({b}^{2} \cdot x\right)\right), y\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({b}^{2} \cdot x\right)\right), y\right) \]

       10. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(x \cdot {b}^{2}\right)\right), y\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \left({b}^{2}\right)\right)\right), y\right) \]

       12. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \left(b \cdot b\right)\right)\right), y\right) \]

       13. *-lowering-*.f64 80.6%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, b\right)\right)\right), y\right) \]

   11. Simplified 80.6%

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

   if -5.49999999999999967e80 < b < 1.8500000000000001e74

   1. Initial program 96.0%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 75.9%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 67.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 67.4%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a}{{z}^{y}}\right)}\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. pow-lowering-pow.f64 67.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   10. Simplified 67.4%

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

   11. Taylor expanded in y around 0

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{a}\right) \]
   12. Step-by-step derivation

   13. Simplified 37.5%

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

   if 1.8500000000000001e74 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 88.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 88.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{0 - b}\right), \color{blue}{y}\right) \]

      2. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{0}}{e^{b}}\right), y\right) \]

      3. 1-exp N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(e^{b}\right)\right), y\right) \]

      6. exp-lowering-exp.f64 88.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   7. Applied egg-rr 88.1%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \color{blue}{\left(1 + b\right)}\right), y\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(b + 1\right)\right), y\right) \]

      2. +-lowering-+.f64 45.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(b, 1\right)\right), y\right) \]

   10. Simplified 45.1%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+80}:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{+74}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 + b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 37.1% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+81}:\\ \;\;\;\;\frac{x \cdot \left(1 - b\right)}{y}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+73}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 + b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.3e+81)
   (/ (* x (- 1.0 b)) y)
   (if (<= b 3.5e+73) (/ (/ x y) a) (/ (/ x (+ 1.0 b)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.3e+81) {
		tmp = (x * (1.0 - b)) / y;
	} else if (b <= 3.5e+73) {
		tmp = (x / y) / a;
	} else {
		tmp = (x / (1.0 + b)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.3d+81)) then
        tmp = (x * (1.0d0 - b)) / y
    else if (b <= 3.5d+73) then
        tmp = (x / y) / a
    else
        tmp = (x / (1.0d0 + b)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.3e+81) {
		tmp = (x * (1.0 - b)) / y;
	} else if (b <= 3.5e+73) {
		tmp = (x / y) / a;
	} else {
		tmp = (x / (1.0 + b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.3e+81:
		tmp = (x * (1.0 - b)) / y
	elif b <= 3.5e+73:
		tmp = (x / y) / a
	else:
		tmp = (x / (1.0 + b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.3e+81)
		tmp = Float64(Float64(x * Float64(1.0 - b)) / y);
	elseif (b <= 3.5e+73)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(Float64(x / Float64(1.0 + b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.3e+81)
		tmp = (x * (1.0 - b)) / y;
	elseif (b <= 3.5e+73)
		tmp = (x / y) / a;
	else
		tmp = (x / (1.0 + b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.3e+81], N[(N[(x * N[(1.0 - b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 3.5e+73], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / N[(1.0 + b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.2999999999999999e81

   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 inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 91.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 91.6%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + -1 \cdot \left(b \cdot x\right)\right)}, y\right) \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \left(-1 \cdot b\right) \cdot x\right), y\right) \]

      2. neg-mul-1 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \left(\mathsf{neg}\left(b\right)\right) \cdot x\right), y\right) \]

      3. distribute-rgt1-in N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\left(\mathsf{neg}\left(b\right)\right) + 1\right) \cdot x\right), y\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(1 + \left(\mathsf{neg}\left(b\right)\right)\right) \cdot x\right), y\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(1 - b\right) \cdot x\right), y\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(1 - b\right), x\right), y\right) \]

      7. --lowering--.f64 64.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, b\right), x\right), y\right) \]

   8. Simplified 64.1%

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

   if -2.2999999999999999e81 < b < 3.50000000000000002e73

   1. Initial program 96.0%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 75.9%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 67.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 67.4%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a}{{z}^{y}}\right)}\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. pow-lowering-pow.f64 67.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   10. Simplified 67.4%

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

   11. Taylor expanded in y around 0

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{a}\right) \]
   12. Step-by-step derivation

   13. Simplified 37.5%

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

   if 3.50000000000000002e73 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 88.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 88.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{0 - b}\right), \color{blue}{y}\right) \]

      2. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{0}}{e^{b}}\right), y\right) \]

      3. 1-exp N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(e^{b}\right)\right), y\right) \]

      6. exp-lowering-exp.f64 88.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   7. Applied egg-rr 88.1%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \color{blue}{\left(1 + b\right)}\right), y\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(b + 1\right)\right), y\right) \]

      2. +-lowering-+.f64 45.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(b, 1\right)\right), y\right) \]

   10. Simplified 45.1%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+81}:\\ \;\;\;\;\frac{x \cdot \left(1 - b\right)}{y}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+73}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 + b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 33.6% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.42 \cdot 10^{+82}:\\ \;\;\;\;\frac{x \cdot \left(1 - b\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.42e+82) (/ (* x (- 1.0 b)) y) (/ (/ x y) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.42e+82) {
		tmp = (x * (1.0 - b)) / 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 (b <= (-1.42d+82)) then
        tmp = (x * (1.0d0 - b)) / 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 (b <= -1.42e+82) {
		tmp = (x * (1.0 - b)) / y;
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.42e+82:
		tmp = (x * (1.0 - b)) / y
	else:
		tmp = (x / y) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.42e+82)
		tmp = Float64(Float64(x * Float64(1.0 - b)) / y);
	else
		tmp = Float64(Float64(x / y) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.42e+82)
		tmp = (x * (1.0 - b)) / y;
	else
		tmp = (x / y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.42e+82], N[(N[(x * N[(1.0 - b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.41999999999999993e82

   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 inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 91.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 91.6%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + -1 \cdot \left(b \cdot x\right)\right)}, y\right) \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \left(-1 \cdot b\right) \cdot x\right), y\right) \]

      2. neg-mul-1 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \left(\mathsf{neg}\left(b\right)\right) \cdot x\right), y\right) \]

      3. distribute-rgt1-in N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\left(\mathsf{neg}\left(b\right)\right) + 1\right) \cdot x\right), y\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(1 + \left(\mathsf{neg}\left(b\right)\right)\right) \cdot x\right), y\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(1 - b\right) \cdot x\right), y\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(1 - b\right), x\right), y\right) \]

      7. --lowering--.f64 64.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, b\right), x\right), y\right) \]

   8. Simplified 64.1%

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

   if -1.41999999999999993e82 < b

   1. Initial program 97.0%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 69.6%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 65.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 65.6%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a}{{z}^{y}}\right)}\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. pow-lowering-pow.f64 56.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   10. Simplified 56.5%

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

   11. Taylor expanded in y around 0

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{a}\right) \]
   12. Step-by-step derivation

   13. Simplified 32.8%

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

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.42 \cdot 10^{+82}:\\ \;\;\;\;\frac{x \cdot \left(1 - b\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 31.5% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 66000:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 66000.0) (/ x (* y a)) (/ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 66000.0) {
		tmp = x / (y * a);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= 66000.0d0) then
        tmp = x / (y * a)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 66000.0) {
		tmp = x / (y * a);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 66000.0:
		tmp = x / (y * a)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 66000.0)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 66000.0)
		tmp = x / (y * a);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 66000.0], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 66000

   1. Initial program 96.7%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 72.1%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 70.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 70.5%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a}{{z}^{y}}\right)}\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. pow-lowering-pow.f64 60.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   10. Simplified 60.4%

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

   11. Taylor expanded in y around 0

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

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot y\right)}\right) \]

       2. *-lowering-*.f64 35.2%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{y}\right)\right) \]

   13. Simplified 35.2%

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

   if 66000 < 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 b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 43.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 43.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

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

      1. /-lowering-/.f64 20.0%

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{y}\right) \]

   8. Simplified 20.0%

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

4. Final simplification 31.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 66000:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 31.1% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{x}{y}}{a} \end{array} \]

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(Float64(x / 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[(N[(x / y), $MachinePrecision] / a), $MachinePrecision]

Derivation

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/ N/A

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

   2. exp-diff N/A

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

   3. associate-*r/ N/A

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

   4. associate-*l/ N/A

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

   5. associate-/r/ N/A

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

   6. exp-diff N/A

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

   7. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

   8. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

   9. exp-diff N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

   10. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

   11. exp-lowering-exp.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

   12. exp-sum N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

   13. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

   14. *-commutative N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

   15. exp-to-pow N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   16. pow-lowering-pow.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

3. Simplified 69.1%

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

5. Taylor expanded in t around 0

   \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
6. Step-by-step derivation

   1. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

   3. exp-lowering-exp.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

   4. pow-lowering-pow.f64 66.8%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

7. Simplified 66.8%

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

8. Taylor expanded in b around 0

   \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a}{{z}^{y}}\right)}\right) \]
9. Step-by-step derivation

   1. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \color{blue}{\left({z}^{y}\right)}\right)\right) \]

   2. pow-lowering-pow.f64 57.1%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(a, \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

10. Simplified 57.1%

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

11. Taylor expanded in y around 0

    \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{a}\right) \]
12. Step-by-step derivation

13. Simplified 33.5%

    \[\leadsto \frac{\frac{x}{y}}{\color{blue}{a}} \]
14. Add Preprocessing

Alternative 23: 16.4% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\frac{y}{x}} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ 1.0 (/ y x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return 1.0 / (y / x);
}

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 = 1.0d0 / (y / x)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return 1.0 / (y / x);
}

Python

def code(x, y, z, t, a, b):
	return 1.0 / (y / x)

Julia

function code(x, y, z, t, a, b)
	return Float64(1.0 / Float64(y / x))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = 1.0 / (y / x);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(1.0 / N[(y / x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.4%

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

3. Taylor expanded in b around inf

   \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
4. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

   2. neg-sub0 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

   3. --lowering--.f64 48.2%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

5. Simplified 48.2%

   \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

6. Taylor expanded in b around 0

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

   1. /-lowering-/.f64 16.7%

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{y}\right) \]

8. Simplified 16.7%

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

   1. clear-num N/A

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

   2. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{y}{x}\right)}\right) \]

   3. /-lowering-/.f64 16.8%

      \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{x}\right)\right) \]

10. Applied egg-rr 16.8%

    \[\leadsto \color{blue}{\frac{1}{\frac{y}{x}}} \]
11. Add Preprocessing

Alternative 24: 16.1% accurate, 105.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y, z, t, a, b):
	return x / y

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.4%

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

3. Taylor expanded in b around inf

   \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
4. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

   2. neg-sub0 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

   3. --lowering--.f64 48.2%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

5. Simplified 48.2%

   \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

6. Taylor expanded in b around 0

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

   1. /-lowering-/.f64 16.7%

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{y}\right) \]

8. Simplified 16.7%

   \[\leadsto \color{blue}{\frac{x}{y}} \]
9. Add Preprocessing

Developer Target 1: 72.1% 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 2024138 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -8845848504127471/10000000000000000) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z)))) (if (< t 8520312288374073/10000000000) (/ (* (/ x y) (pow a (- t 1))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z)))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))