Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, G

Percentage Accurate: 84.7% → 99.1%

Time: 11.3s

Alternatives: 9

Speedup: 42.2×

Specification

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (/ (exp (* y (log (/ y (+ z y))))) y)))

C

double code(double x, double y, double z) {
	return x + (exp((y * log((y / (z + y))))) / y);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (exp((y * log((y / (z + y))))) / y)
end function

Java

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

Python

def code(x, y, z):
	return x + (math.exp((y * math.log((y / (z + y))))) / y)

Julia

function code(x, y, z)
	return Float64(x + Float64(exp(Float64(y * log(Float64(y / Float64(z + y))))) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (exp((y * log((y / (z + y))))) / y);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[Exp[N[(y * N[Log[N[(y / N[(z + y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Initial Program: 84.7% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (/ (exp (* y (log (/ y (+ z y))))) y)))

C

double code(double x, double y, double z) {
	return x + (exp((y * log((y / (z + y))))) / y);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (exp((y * log((y / (z + y))))) / y)
end function

Java

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

Python

def code(x, y, z):
	return x + (math.exp((y * math.log((y / (z + y))))) / y)

Julia

function code(x, y, z)
	return Float64(x + Float64(exp(Float64(y * log(Float64(y / Float64(z + y))))) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (exp((y * log((y / (z + y))))) / y);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[Exp[N[(y * N[Log[N[(y / N[(z + y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{e^{0 - z}}{y}\\ \mathbf{if}\;y \leq -1.22 \cdot 10^{+30}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-7}:\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (/ (exp (- 0.0 z)) y))))
   (if (<= y -1.22e+30) t_0 (if (<= y 5e-7) (+ x (/ 1.0 y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + (exp((0.0 - z)) / y);
	double tmp;
	if (y <= -1.22e+30) {
		tmp = t_0;
	} else if (y <= 5e-7) {
		tmp = x + (1.0 / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x + (exp((0.0d0 - z)) / y)
    if (y <= (-1.22d+30)) then
        tmp = t_0
    else if (y <= 5d-7) then
        tmp = x + (1.0d0 / y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (Math.exp((0.0 - z)) / y);
	double tmp;
	if (y <= -1.22e+30) {
		tmp = t_0;
	} else if (y <= 5e-7) {
		tmp = x + (1.0 / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (math.exp((0.0 - z)) / y)
	tmp = 0
	if y <= -1.22e+30:
		tmp = t_0
	elif y <= 5e-7:
		tmp = x + (1.0 / y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(exp(Float64(0.0 - z)) / y))
	tmp = 0.0
	if (y <= -1.22e+30)
		tmp = t_0;
	elseif (y <= 5e-7)
		tmp = Float64(x + Float64(1.0 / y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (exp((0.0 - z)) / y);
	tmp = 0.0;
	if (y <= -1.22e+30)
		tmp = t_0;
	elseif (y <= 5e-7)
		tmp = x + (1.0 / y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(N[Exp[N[(0.0 - z), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.22e+30], t$95$0, If[LessEqual[y, 5e-7], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.22e30 or 4.99999999999999977e-7 < y

   1. Initial program 88.6%

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

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

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

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

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

      3. *-commutative N/A

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

      4. exp-to-pow N/A

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

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

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

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

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

      7. +-commutative N/A

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

      8. +-lowering-+.f64 88.6%

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

   3. Simplified 88.6%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

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

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

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

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

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

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{exp.f64}\left(\left(-1 \cdot z\right)\right), y\right)\right) \]

      4. mul-1-neg N/A

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

      5. neg-sub0 N/A

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

      6. --lowering--.f64 100.0%

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

   7. Simplified 100.0%

      \[\leadsto \color{blue}{x + \frac{e^{0 - z}}{y}} \]

   if -1.22e30 < y < 4.99999999999999977e-7

   1. Initial program 87.0%

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

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

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

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

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

      3. *-commutative N/A

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

      4. exp-to-pow N/A

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

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

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

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

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

      7. +-commutative N/A

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

      8. +-lowering-+.f64 87.0%

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

   3. Simplified 87.0%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

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

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

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{1}{y}\right)}\right) \]

      2. /-lowering-/.f64 99.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(1, \color{blue}{y}\right)\right) \]

   7. Simplified 99.3%

      \[\leadsto \color{blue}{x + \frac{1}{y}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 89.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -320:\\ \;\;\;\;\frac{1}{y \cdot e^{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -320.0) (/ 1.0 (* y (exp z))) (+ x (/ 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -320.0) {
		tmp = 1.0 / (y * exp(z));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-320.0d0)) then
        tmp = 1.0d0 / (y * exp(z))
    else
        tmp = x + (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -320.0) {
		tmp = 1.0 / (y * Math.exp(z));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -320.0:
		tmp = 1.0 / (y * math.exp(z))
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -320.0)
		tmp = Float64(1.0 / Float64(y * exp(z)));
	else
		tmp = Float64(x + Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -320.0)
		tmp = 1.0 / (y * exp(z));
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -320.0], N[(1.0 / N[(y * N[Exp[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -320

   1. Initial program 39.1%

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

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

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

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

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

      3. *-commutative N/A

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

      4. exp-to-pow N/A

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

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

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

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

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

      7. +-commutative N/A

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

      8. +-lowering-+.f64 39.1%

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

   3. Simplified 39.1%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

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

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

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

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

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

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{exp.f64}\left(\left(-1 \cdot z\right)\right), y\right)\right) \]

      4. mul-1-neg N/A

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

      5. neg-sub0 N/A

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

      6. --lowering--.f64 67.7%

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

   7. Simplified 67.7%

      \[\leadsto \color{blue}{x + \frac{e^{0 - z}}{y}} \]

   8. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{e^{\mathsf{neg}\left(z\right)}}{y}} \]
   9. Step-by-step derivation

      1. exp-neg N/A

         \[\leadsto \frac{\frac{1}{e^{z}}}{y} \]

      2. associate-/l/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(y \cdot e^{z}\right)}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{z}\right)}\right)\right) \]

      5. exp-lowering-exp.f64 67.7%

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(z\right)\right)\right) \]

   10. Simplified 67.7%

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

   if -320 < z

   1. Initial program 96.4%

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

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

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

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

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

      3. *-commutative N/A

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

      4. exp-to-pow N/A

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

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

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

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

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

      7. +-commutative N/A

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

      8. +-lowering-+.f64 96.4%

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

   3. Simplified 96.4%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

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

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

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{1}{y}\right)}\right) \]

      2. /-lowering-/.f64 97.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(1, \color{blue}{y}\right)\right) \]

   7. Simplified 97.8%

      \[\leadsto \color{blue}{x + \frac{1}{y}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 87.3% accurate, 7.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{0.3333333333333333 + y \cdot \left(0.5 + y \cdot 0.16666666666666666\right)}{y}}{y} \cdot \frac{z \cdot \left(z \cdot z\right)}{0 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.85e+33)
   (*
    (/ (/ (+ 0.3333333333333333 (* y (+ 0.5 (* y 0.16666666666666666)))) y) y)
    (/ (* z (* z z)) (- 0.0 y)))
   (+ x (/ 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.85e+33) {
		tmp = (((0.3333333333333333 + (y * (0.5 + (y * 0.16666666666666666)))) / y) / y) * ((z * (z * z)) / (0.0 - y));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.85d+33)) then
        tmp = (((0.3333333333333333d0 + (y * (0.5d0 + (y * 0.16666666666666666d0)))) / y) / y) * ((z * (z * z)) / (0.0d0 - y))
    else
        tmp = x + (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.85e+33) {
		tmp = (((0.3333333333333333 + (y * (0.5 + (y * 0.16666666666666666)))) / y) / y) * ((z * (z * z)) / (0.0 - y));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.85e+33:
		tmp = (((0.3333333333333333 + (y * (0.5 + (y * 0.16666666666666666)))) / y) / y) * ((z * (z * z)) / (0.0 - y))
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.85e+33)
		tmp = Float64(Float64(Float64(Float64(0.3333333333333333 + Float64(y * Float64(0.5 + Float64(y * 0.16666666666666666)))) / y) / y) * Float64(Float64(z * Float64(z * z)) / Float64(0.0 - y)));
	else
		tmp = Float64(x + Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.85e+33)
		tmp = (((0.3333333333333333 + (y * (0.5 + (y * 0.16666666666666666)))) / y) / y) * ((z * (z * z)) / (0.0 - y));
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.85e+33], N[(N[(N[(N[(0.3333333333333333 + N[(y * N[(0.5 + N[(y * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] / y), $MachinePrecision] * N[(N[(z * N[(z * z), $MachinePrecision]), $MachinePrecision] / N[(0.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8499999999999999e33

   1. Initial program 35.9%

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

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

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

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

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

      3. *-commutative N/A

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

      4. exp-to-pow N/A

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

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

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

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

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

      7. +-commutative N/A

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

      8. +-lowering-+.f64 35.9%

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

   3. Simplified 35.9%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(z \cdot \left(z \cdot \left(-1 \cdot \frac{z \cdot \left(\frac{1}{6} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{2}} + \frac{1}{2} \cdot \frac{1}{y}\right)\right)}{y} + \left(\frac{1}{2} \cdot \frac{1}{y} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right) - \frac{1}{y}\right) + \frac{1}{y}\right)} \]

   7. Simplified 34.7%

      \[\leadsto \color{blue}{\left(x + \frac{1}{y}\right) + z \cdot \left(z \cdot \left(\left(\frac{0.5}{y} + \frac{0.5}{y \cdot y}\right) - \frac{z \cdot \left(\frac{0.5}{y} + \left(0.16666666666666666 + \frac{0.3333333333333333}{y \cdot y}\right)\right)}{y}\right) + \frac{-1}{y}\right)} \]

   8. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot \left({z}^{3} \cdot \left(\frac{1}{6} \cdot \frac{1}{y} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{3}} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left({z}^{3} \cdot \left(\frac{1}{6} \cdot \frac{1}{y} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{3}} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{{z}^{3} \cdot \left(\frac{1}{6} \cdot \frac{1}{y} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{3}} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right)} \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left({z}^{3} \cdot \left(\frac{1}{6} \cdot \frac{1}{y} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{3}} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\left({z}^{3}\right), \color{blue}{\left(\frac{1}{6} \cdot \frac{1}{y} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{3}} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right)}\right)\right) \]

      5. cube-mult N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\left(z \cdot \left(z \cdot z\right)\right), \left(\color{blue}{\frac{1}{6} \cdot \frac{1}{y}} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{3}} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right)\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\left(z \cdot {z}^{2}\right), \left(\frac{1}{6} \cdot \color{blue}{\frac{1}{y}} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{3}} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \left({z}^{2}\right)\right), \left(\color{blue}{\frac{1}{6} \cdot \frac{1}{y}} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{3}} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right)\right)\right) \]

      8. unpow2 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \left(z \cdot z\right)\right), \left(\frac{1}{6} \cdot \color{blue}{\frac{1}{y}} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{3}} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \left(\frac{1}{6} \cdot \color{blue}{\frac{1}{y}} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{3}} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \left(\frac{1}{6} \cdot \frac{1}{y} + \left(\frac{1}{2} \cdot \frac{1}{{y}^{2}} + \color{blue}{\frac{1}{3} \cdot \frac{1}{{y}^{3}}}\right)\right)\right)\right) \]

      11. associate-+r+ N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \left(\left(\frac{1}{6} \cdot \frac{1}{y} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right) + \color{blue}{\frac{1}{3} \cdot \frac{1}{{y}^{3}}}\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \left(\left(\frac{1}{2} \cdot \frac{1}{{y}^{2}} + \frac{1}{6} \cdot \frac{1}{y}\right) + \color{blue}{\frac{1}{3}} \cdot \frac{1}{{y}^{3}}\right)\right)\right) \]

      13. associate-+l+ N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \left(\frac{1}{2} \cdot \frac{1}{{y}^{2}} + \color{blue}{\left(\frac{1}{6} \cdot \frac{1}{y} + \frac{1}{3} \cdot \frac{1}{{y}^{3}}\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \mathsf{+.f64}\left(\left(\frac{1}{2} \cdot \frac{1}{{y}^{2}}\right), \color{blue}{\left(\frac{1}{6} \cdot \frac{1}{y} + \frac{1}{3} \cdot \frac{1}{{y}^{3}}\right)}\right)\right)\right) \]

   10. Simplified 47.5%

       \[\leadsto \color{blue}{0 - \left(z \cdot \left(z \cdot z\right)\right) \cdot \left(\frac{0.5}{y \cdot y} + \left(\frac{0.16666666666666666}{y} + \frac{0.3333333333333333}{y \cdot \left(y \cdot y\right)}\right)\right)} \]

   11. Taylor expanded in y around 0

       \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \color{blue}{\left(\frac{\frac{1}{3} + y \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot y\right)}{{y}^{3}}\right)}\right)\right) \]
   12. Step-by-step derivation

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

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \mathsf{/.f64}\left(\left(\frac{1}{3} + y \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot y\right)\right), \color{blue}{\left({y}^{3}\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{3}, \left(y \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot y\right)\right)\right), \left({\color{blue}{y}}^{3}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(y, \left(\frac{1}{2} + \frac{1}{6} \cdot y\right)\right)\right), \left({y}^{3}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{1}{2}, \left(\frac{1}{6} \cdot y\right)\right)\right)\right), \left({y}^{3}\right)\right)\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{1}{2}, \left(y \cdot \frac{1}{6}\right)\right)\right)\right), \left({y}^{3}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \frac{1}{6}\right)\right)\right)\right), \left({y}^{3}\right)\right)\right)\right) \]

       7. cube-mult N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \frac{1}{6}\right)\right)\right)\right), \left(y \cdot \color{blue}{\left(y \cdot y\right)}\right)\right)\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \frac{1}{6}\right)\right)\right)\right), \left(y \cdot {y}^{\color{blue}{2}}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \frac{1}{6}\right)\right)\right)\right), \mathsf{*.f64}\left(y, \color{blue}{\left({y}^{2}\right)}\right)\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \frac{1}{6}\right)\right)\right)\right), \mathsf{*.f64}\left(y, \left(y \cdot \color{blue}{y}\right)\right)\right)\right)\right) \]

       11. *-lowering-*.f64 12.1%

           \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \frac{1}{6}\right)\right)\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right)\right)\right) \]

   13. Simplified 12.1%

       \[\leadsto 0 - \left(z \cdot \left(z \cdot z\right)\right) \cdot \color{blue}{\frac{0.3333333333333333 + y \cdot \left(0.5 + y \cdot 0.16666666666666666\right)}{y \cdot \left(y \cdot y\right)}} \]
   14. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(\frac{\frac{1}{3} + y \cdot \left(\frac{1}{2} + y \cdot \frac{1}{6}\right)}{y \cdot \left(y \cdot y\right)} \cdot \color{blue}{\left(z \cdot \left(z \cdot z\right)\right)}\right)\right) \]

       2. associate-/r* N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(\frac{\frac{\frac{1}{3} + y \cdot \left(\frac{1}{2} + y \cdot \frac{1}{6}\right)}{y}}{y \cdot y} \cdot \left(\color{blue}{z} \cdot \left(z \cdot z\right)\right)\right)\right) \]

       3. associate-*l/ N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(\frac{\frac{\frac{1}{3} + y \cdot \left(\frac{1}{2} + y \cdot \frac{1}{6}\right)}{y} \cdot \left(z \cdot \left(z \cdot z\right)\right)}{\color{blue}{y \cdot y}}\right)\right) \]

       4. times-frac N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(\frac{\frac{\frac{1}{3} + y \cdot \left(\frac{1}{2} + y \cdot \frac{1}{6}\right)}{y}}{y} \cdot \color{blue}{\frac{z \cdot \left(z \cdot z\right)}{y}}\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\left(\frac{\frac{\frac{1}{3} + y \cdot \left(\frac{1}{2} + y \cdot \frac{1}{6}\right)}{y}}{y}\right), \color{blue}{\left(\frac{z \cdot \left(z \cdot z\right)}{y}\right)}\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{\frac{1}{3} + y \cdot \left(\frac{1}{2} + y \cdot \frac{1}{6}\right)}{y}\right), y\right), \left(\frac{\color{blue}{z \cdot \left(z \cdot z\right)}}{y}\right)\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{3} + y \cdot \left(\frac{1}{2} + y \cdot \frac{1}{6}\right)\right), y\right), y\right), \left(\frac{\color{blue}{z} \cdot \left(z \cdot z\right)}{y}\right)\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{3}, \left(y \cdot \left(\frac{1}{2} + y \cdot \frac{1}{6}\right)\right)\right), y\right), y\right), \left(\frac{z \cdot \left(z \cdot z\right)}{y}\right)\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(y, \left(\frac{1}{2} + y \cdot \frac{1}{6}\right)\right)\right), y\right), y\right), \left(\frac{z \cdot \left(z \cdot z\right)}{y}\right)\right)\right) \]

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

           \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{1}{2}, \left(y \cdot \frac{1}{6}\right)\right)\right)\right), y\right), y\right), \left(\frac{z \cdot \left(z \cdot z\right)}{y}\right)\right)\right) \]

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

           \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \frac{1}{6}\right)\right)\right)\right), y\right), y\right), \left(\frac{z \cdot \left(z \cdot z\right)}{y}\right)\right)\right) \]

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

           \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \frac{1}{6}\right)\right)\right)\right), y\right), y\right), \mathsf{/.f64}\left(\left(z \cdot \left(z \cdot z\right)\right), \color{blue}{y}\right)\right)\right) \]

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

           \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \frac{1}{6}\right)\right)\right)\right), y\right), y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(z \cdot z\right)\right), y\right)\right)\right) \]

       14. *-lowering-*.f64 58.9%

           \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \frac{1}{6}\right)\right)\right)\right), y\right), y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), y\right)\right)\right) \]

   15. Applied egg-rr 58.9%

       \[\leadsto 0 - \color{blue}{\frac{\frac{0.3333333333333333 + y \cdot \left(0.5 + y \cdot 0.16666666666666666\right)}{y}}{y} \cdot \frac{z \cdot \left(z \cdot z\right)}{y}} \]

   if -1.8499999999999999e33 < z

   1. Initial program 94.8%

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

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

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

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

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

      3. *-commutative N/A

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

      4. exp-to-pow N/A

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

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

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

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

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

      7. +-commutative N/A

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

      8. +-lowering-+.f64 94.8%

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

   3. Simplified 94.8%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

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

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

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{1}{y}\right)}\right) \]

      2. /-lowering-/.f64 96.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(1, \color{blue}{y}\right)\right) \]

   7. Simplified 96.2%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{0.3333333333333333 + y \cdot \left(0.5 + y \cdot 0.16666666666666666\right)}{y}}{y} \cdot \frac{z \cdot \left(z \cdot z\right)}{0 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.7% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+33}:\\ \;\;\;\;x + \frac{1 + \frac{z \cdot \left(z \cdot \left(0.5 + y \cdot 0.5\right)\right)}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.7e+33)
   (+ x (/ (+ 1.0 (/ (* z (* z (+ 0.5 (* y 0.5)))) y)) y))
   (+ x (/ 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.7e+33) {
		tmp = x + ((1.0 + ((z * (z * (0.5 + (y * 0.5)))) / y)) / y);
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-3.7d+33)) then
        tmp = x + ((1.0d0 + ((z * (z * (0.5d0 + (y * 0.5d0)))) / y)) / y)
    else
        tmp = x + (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.7e+33) {
		tmp = x + ((1.0 + ((z * (z * (0.5 + (y * 0.5)))) / y)) / y);
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.7e+33:
		tmp = x + ((1.0 + ((z * (z * (0.5 + (y * 0.5)))) / y)) / y)
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.7e+33)
		tmp = Float64(x + Float64(Float64(1.0 + Float64(Float64(z * Float64(z * Float64(0.5 + Float64(y * 0.5)))) / y)) / y));
	else
		tmp = Float64(x + Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.7e+33)
		tmp = x + ((1.0 + ((z * (z * (0.5 + (y * 0.5)))) / y)) / y);
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.7e+33], N[(x + N[(N[(1.0 + N[(N[(z * N[(z * N[(0.5 + N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6999999999999999e33

   1. Initial program 35.9%

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

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

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

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

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

      3. *-commutative N/A

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

      4. exp-to-pow N/A

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

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

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

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

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

      7. +-commutative N/A

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

      8. +-lowering-+.f64 35.9%

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

   3. Simplified 35.9%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

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

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

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

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

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

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

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

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. /-lowering-/.f64 37.8%

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

   7. Simplified 37.8%

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

   8. Taylor expanded in y around 0

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

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

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

      2. associate-*r* N/A

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

      3. distribute-rgt-out N/A

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

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

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

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

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

      6. *-lowering-*.f64 50.7%

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

   10. Simplified 50.7%

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

   11. Taylor expanded in z around -inf

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

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

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

       2. unpow2 N/A

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

       3. associate-*l* N/A

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

       4. distribute-rgt-in N/A

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

       5. associate-*r* N/A

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

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

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

       7. associate-*r* N/A

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

       8. distribute-rgt-in N/A

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

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

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

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

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

       11. *-commutative N/A

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

       12. *-lowering-*.f64 54.0%

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

   13. Simplified 54.0%

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

   if -3.6999999999999999e33 < z

   1. Initial program 94.8%

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

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

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

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

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

      3. *-commutative N/A

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

      4. exp-to-pow N/A

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

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

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

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

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

      7. +-commutative N/A

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

      8. +-lowering-+.f64 94.8%

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

   3. Simplified 94.8%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

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

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

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{1}{y}\right)}\right) \]

      2. /-lowering-/.f64 96.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(1, \color{blue}{y}\right)\right) \]

   7. Simplified 96.2%

      \[\leadsto \color{blue}{x + \frac{1}{y}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 87.4% accurate, 15.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+103}:\\ \;\;\;\;\frac{z \cdot \left(z \cdot z\right)}{y} \cdot -0.16666666666666666\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -8.2e+103)
   (* (/ (* z (* z z)) y) -0.16666666666666666)
   (+ x (/ 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.2e+103) {
		tmp = ((z * (z * z)) / y) * -0.16666666666666666;
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-8.2d+103)) then
        tmp = ((z * (z * z)) / y) * (-0.16666666666666666d0)
    else
        tmp = x + (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.2e+103) {
		tmp = ((z * (z * z)) / y) * -0.16666666666666666;
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -8.2e+103:
		tmp = ((z * (z * z)) / y) * -0.16666666666666666
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -8.2e+103)
		tmp = Float64(Float64(Float64(z * Float64(z * z)) / y) * -0.16666666666666666);
	else
		tmp = Float64(x + Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -8.2e+103)
		tmp = ((z * (z * z)) / y) * -0.16666666666666666;
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -8.2e+103], N[(N[(N[(z * N[(z * z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] * -0.16666666666666666), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.2000000000000003e103

   1. Initial program 38.9%

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

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

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

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

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

      3. *-commutative N/A

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

      4. exp-to-pow N/A

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

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

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

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

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

      7. +-commutative N/A

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

      8. +-lowering-+.f64 38.9%

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

   3. Simplified 38.9%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(z \cdot \left(z \cdot \left(-1 \cdot \frac{z \cdot \left(\frac{1}{6} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{2}} + \frac{1}{2} \cdot \frac{1}{y}\right)\right)}{y} + \left(\frac{1}{2} \cdot \frac{1}{y} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right) - \frac{1}{y}\right) + \frac{1}{y}\right)} \]

   7. Simplified 46.4%

      \[\leadsto \color{blue}{\left(x + \frac{1}{y}\right) + z \cdot \left(z \cdot \left(\left(\frac{0.5}{y} + \frac{0.5}{y \cdot y}\right) - \frac{z \cdot \left(\frac{0.5}{y} + \left(0.16666666666666666 + \frac{0.3333333333333333}{y \cdot y}\right)\right)}{y}\right) + \frac{-1}{y}\right)} \]

   8. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot \left({z}^{3} \cdot \left(\frac{1}{6} \cdot \frac{1}{y} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{3}} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left({z}^{3} \cdot \left(\frac{1}{6} \cdot \frac{1}{y} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{3}} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{{z}^{3} \cdot \left(\frac{1}{6} \cdot \frac{1}{y} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{3}} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right)} \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left({z}^{3} \cdot \left(\frac{1}{6} \cdot \frac{1}{y} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{3}} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\left({z}^{3}\right), \color{blue}{\left(\frac{1}{6} \cdot \frac{1}{y} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{3}} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right)}\right)\right) \]

      5. cube-mult N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\left(z \cdot \left(z \cdot z\right)\right), \left(\color{blue}{\frac{1}{6} \cdot \frac{1}{y}} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{3}} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right)\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\left(z \cdot {z}^{2}\right), \left(\frac{1}{6} \cdot \color{blue}{\frac{1}{y}} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{3}} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \left({z}^{2}\right)\right), \left(\color{blue}{\frac{1}{6} \cdot \frac{1}{y}} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{3}} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right)\right)\right) \]

      8. unpow2 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \left(z \cdot z\right)\right), \left(\frac{1}{6} \cdot \color{blue}{\frac{1}{y}} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{3}} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \left(\frac{1}{6} \cdot \color{blue}{\frac{1}{y}} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{3}} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \left(\frac{1}{6} \cdot \frac{1}{y} + \left(\frac{1}{2} \cdot \frac{1}{{y}^{2}} + \color{blue}{\frac{1}{3} \cdot \frac{1}{{y}^{3}}}\right)\right)\right)\right) \]

      11. associate-+r+ N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \left(\left(\frac{1}{6} \cdot \frac{1}{y} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right) + \color{blue}{\frac{1}{3} \cdot \frac{1}{{y}^{3}}}\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \left(\left(\frac{1}{2} \cdot \frac{1}{{y}^{2}} + \frac{1}{6} \cdot \frac{1}{y}\right) + \color{blue}{\frac{1}{3}} \cdot \frac{1}{{y}^{3}}\right)\right)\right) \]

      13. associate-+l+ N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \left(\frac{1}{2} \cdot \frac{1}{{y}^{2}} + \color{blue}{\left(\frac{1}{6} \cdot \frac{1}{y} + \frac{1}{3} \cdot \frac{1}{{y}^{3}}\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \mathsf{+.f64}\left(\left(\frac{1}{2} \cdot \frac{1}{{y}^{2}}\right), \color{blue}{\left(\frac{1}{6} \cdot \frac{1}{y} + \frac{1}{3} \cdot \frac{1}{{y}^{3}}\right)}\right)\right)\right) \]

   10. Simplified 63.7%

       \[\leadsto \color{blue}{0 - \left(z \cdot \left(z \cdot z\right)\right) \cdot \left(\frac{0.5}{y \cdot y} + \left(\frac{0.16666666666666666}{y} + \frac{0.3333333333333333}{y \cdot \left(y \cdot y\right)}\right)\right)} \]

   11. Taylor expanded in y around inf

       \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \color{blue}{\left(\frac{\frac{1}{6}}{y}\right)}\right)\right) \]
   12. Step-by-step derivation

       1. /-lowering-/.f64 65.5%

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \mathsf{/.f64}\left(\frac{1}{6}, \color{blue}{y}\right)\right)\right) \]

   13. Simplified 65.5%

       \[\leadsto 0 - \left(z \cdot \left(z \cdot z\right)\right) \cdot \color{blue}{\frac{0.16666666666666666}{y}} \]
   14. Step-by-step derivation

       1. sub0-neg N/A

          \[\leadsto \mathsf{neg}\left(\left(z \cdot \left(z \cdot z\right)\right) \cdot \frac{\frac{1}{6}}{y}\right) \]

       2. associate-*r/ N/A

          \[\leadsto \mathsf{neg}\left(\frac{\left(z \cdot \left(z \cdot z\right)\right) \cdot \frac{1}{6}}{y}\right) \]

       3. distribute-neg-frac2 N/A

          \[\leadsto \frac{\left(z \cdot \left(z \cdot z\right)\right) \cdot \frac{1}{6}}{\color{blue}{\mathsf{neg}\left(y\right)}} \]

       4. *-commutative N/A

          \[\leadsto \frac{\frac{1}{6} \cdot \left(z \cdot \left(z \cdot z\right)\right)}{\mathsf{neg}\left(\color{blue}{y}\right)} \]

       5. neg-mul-1 N/A

          \[\leadsto \frac{\frac{1}{6} \cdot \left(z \cdot \left(z \cdot z\right)\right)}{-1 \cdot \color{blue}{y}} \]

       6. times-frac N/A

          \[\leadsto \frac{\frac{1}{6}}{-1} \cdot \color{blue}{\frac{z \cdot \left(z \cdot z\right)}{y}} \]

       7. metadata-eval N/A

          \[\leadsto \frac{-1}{6} \cdot \frac{\color{blue}{z \cdot \left(z \cdot z\right)}}{y} \]

       8. metadata-eval N/A

          \[\leadsto \left(\mathsf{neg}\left(\frac{1}{6}\right)\right) \cdot \frac{\color{blue}{z \cdot \left(z \cdot z\right)}}{y} \]

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

          \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(\frac{1}{6}\right)\right), \color{blue}{\left(\frac{z \cdot \left(z \cdot z\right)}{y}\right)}\right) \]

       10. metadata-eval N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{-1}{6}, \left(\frac{\color{blue}{z \cdot \left(z \cdot z\right)}}{y}\right)\right) \]

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

           \[\leadsto \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{/.f64}\left(\left(z \cdot \left(z \cdot z\right)\right), \color{blue}{y}\right)\right) \]

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

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

       13. *-lowering-*.f64 65.5%

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

   15. Applied egg-rr 65.5%

       \[\leadsto \color{blue}{-0.16666666666666666 \cdot \frac{z \cdot \left(z \cdot z\right)}{y}} \]

   if -8.2000000000000003e103 < z

   1. Initial program 92.5%

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

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

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

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

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

      3. *-commutative N/A

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

      4. exp-to-pow N/A

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

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

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

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

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

      7. +-commutative N/A

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

      8. +-lowering-+.f64 92.5%

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

   3. Simplified 92.5%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

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

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

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{1}{y}\right)}\right) \]

      2. /-lowering-/.f64 93.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(1, \color{blue}{y}\right)\right) \]

   7. Simplified 93.4%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+103}:\\ \;\;\;\;\frac{z \cdot \left(z \cdot z\right)}{y} \cdot -0.16666666666666666\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.5% accurate, 15.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+156}:\\ \;\;\;\;-0.16666666666666666 \cdot \left(z \cdot \frac{z \cdot z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.3e+156)
   (* -0.16666666666666666 (* z (/ (* z z) y)))
   (+ x (/ 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.3e+156) {
		tmp = -0.16666666666666666 * (z * ((z * z) / y));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-3.3d+156)) then
        tmp = (-0.16666666666666666d0) * (z * ((z * z) / y))
    else
        tmp = x + (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.3e+156) {
		tmp = -0.16666666666666666 * (z * ((z * z) / y));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.3e+156:
		tmp = -0.16666666666666666 * (z * ((z * z) / y))
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.3e+156)
		tmp = Float64(-0.16666666666666666 * Float64(z * Float64(Float64(z * z) / y)));
	else
		tmp = Float64(x + Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.3e+156)
		tmp = -0.16666666666666666 * (z * ((z * z) / y));
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.3e+156], N[(-0.16666666666666666 * N[(z * N[(N[(z * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2999999999999999e156

   1. Initial program 43.6%

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

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

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

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

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

      3. *-commutative N/A

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

      4. exp-to-pow N/A

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

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

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

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

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

      7. +-commutative N/A

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

      8. +-lowering-+.f64 43.6%

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

   3. Simplified 43.6%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(z \cdot \left(z \cdot \left(-1 \cdot \frac{z \cdot \left(\frac{1}{6} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{2}} + \frac{1}{2} \cdot \frac{1}{y}\right)\right)}{y} + \left(\frac{1}{2} \cdot \frac{1}{y} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right) - \frac{1}{y}\right) + \frac{1}{y}\right)} \]

   7. Simplified 59.2%

      \[\leadsto \color{blue}{\left(x + \frac{1}{y}\right) + z \cdot \left(z \cdot \left(\left(\frac{0.5}{y} + \frac{0.5}{y \cdot y}\right) - \frac{z \cdot \left(\frac{0.5}{y} + \left(0.16666666666666666 + \frac{0.3333333333333333}{y \cdot y}\right)\right)}{y}\right) + \frac{-1}{y}\right)} \]

   8. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot \left({z}^{3} \cdot \left(\frac{1}{6} \cdot \frac{1}{y} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{3}} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left({z}^{3} \cdot \left(\frac{1}{6} \cdot \frac{1}{y} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{3}} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{{z}^{3} \cdot \left(\frac{1}{6} \cdot \frac{1}{y} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{3}} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right)} \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left({z}^{3} \cdot \left(\frac{1}{6} \cdot \frac{1}{y} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{3}} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\left({z}^{3}\right), \color{blue}{\left(\frac{1}{6} \cdot \frac{1}{y} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{3}} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right)}\right)\right) \]

      5. cube-mult N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\left(z \cdot \left(z \cdot z\right)\right), \left(\color{blue}{\frac{1}{6} \cdot \frac{1}{y}} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{3}} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right)\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\left(z \cdot {z}^{2}\right), \left(\frac{1}{6} \cdot \color{blue}{\frac{1}{y}} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{3}} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \left({z}^{2}\right)\right), \left(\color{blue}{\frac{1}{6} \cdot \frac{1}{y}} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{3}} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right)\right)\right) \]

      8. unpow2 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \left(z \cdot z\right)\right), \left(\frac{1}{6} \cdot \color{blue}{\frac{1}{y}} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{3}} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \left(\frac{1}{6} \cdot \color{blue}{\frac{1}{y}} + \left(\frac{1}{3} \cdot \frac{1}{{y}^{3}} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right)\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \left(\frac{1}{6} \cdot \frac{1}{y} + \left(\frac{1}{2} \cdot \frac{1}{{y}^{2}} + \color{blue}{\frac{1}{3} \cdot \frac{1}{{y}^{3}}}\right)\right)\right)\right) \]

      11. associate-+r+ N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \left(\left(\frac{1}{6} \cdot \frac{1}{y} + \frac{1}{2} \cdot \frac{1}{{y}^{2}}\right) + \color{blue}{\frac{1}{3} \cdot \frac{1}{{y}^{3}}}\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \left(\left(\frac{1}{2} \cdot \frac{1}{{y}^{2}} + \frac{1}{6} \cdot \frac{1}{y}\right) + \color{blue}{\frac{1}{3}} \cdot \frac{1}{{y}^{3}}\right)\right)\right) \]

      13. associate-+l+ N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \left(\frac{1}{2} \cdot \frac{1}{{y}^{2}} + \color{blue}{\left(\frac{1}{6} \cdot \frac{1}{y} + \frac{1}{3} \cdot \frac{1}{{y}^{3}}\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \mathsf{+.f64}\left(\left(\frac{1}{2} \cdot \frac{1}{{y}^{2}}\right), \color{blue}{\left(\frac{1}{6} \cdot \frac{1}{y} + \frac{1}{3} \cdot \frac{1}{{y}^{3}}\right)}\right)\right)\right) \]

   10. Simplified 64.7%

       \[\leadsto \color{blue}{0 - \left(z \cdot \left(z \cdot z\right)\right) \cdot \left(\frac{0.5}{y \cdot y} + \left(\frac{0.16666666666666666}{y} + \frac{0.3333333333333333}{y \cdot \left(y \cdot y\right)}\right)\right)} \]

   11. Taylor expanded in y around inf

       \[\leadsto \color{blue}{\frac{-1}{6} \cdot \frac{{z}^{3}}{y}} \]
   12. Step-by-step derivation

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

          \[\leadsto \mathsf{*.f64}\left(\frac{-1}{6}, \color{blue}{\left(\frac{{z}^{3}}{y}\right)}\right) \]

       2. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{-1}{6}, \left(\frac{z \cdot \left(z \cdot z\right)}{y}\right)\right) \]

       3. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{-1}{6}, \left(\frac{z \cdot {z}^{2}}{y}\right)\right) \]

       4. associate-/l* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{-1}{6}, \left(z \cdot \color{blue}{\frac{{z}^{2}}{y}}\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{{z}^{2}}{y}\right)}\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left({z}^{2}\right), \color{blue}{y}\right)\right)\right) \]

       7. unpow2 N/A

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

       8. *-lowering-*.f64 66.8%

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

   13. Simplified 66.8%

       \[\leadsto \color{blue}{-0.16666666666666666 \cdot \left(z \cdot \frac{z \cdot z}{y}\right)} \]

   if -3.2999999999999999e156 < z

   1. Initial program 91.0%

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

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

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

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

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

      3. *-commutative N/A

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

      4. exp-to-pow N/A

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

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

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

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

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

      7. +-commutative N/A

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

      8. +-lowering-+.f64 91.0%

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

   3. Simplified 91.0%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

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

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

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{1}{y}\right)}\right) \]

      2. /-lowering-/.f64 92.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(1, \color{blue}{y}\right)\right) \]

   7. Simplified 92.3%

      \[\leadsto \color{blue}{x + \frac{1}{y}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 67.8% accurate, 16.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-101}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-30}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.7e-101) x (if (<= y 7.5e-30) (/ 1.0 y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.7e-101) {
		tmp = x;
	} else if (y <= 7.5e-30) {
		tmp = 1.0 / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.7d-101)) then
        tmp = x
    else if (y <= 7.5d-30) then
        tmp = 1.0d0 / y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.7e-101) {
		tmp = x;
	} else if (y <= 7.5e-30) {
		tmp = 1.0 / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.7e-101:
		tmp = x
	elif y <= 7.5e-30:
		tmp = 1.0 / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.7e-101)
		tmp = x;
	elseif (y <= 7.5e-30)
		tmp = Float64(1.0 / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.7e-101)
		tmp = x;
	elseif (y <= 7.5e-30)
		tmp = 1.0 / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.7e-101], x, If[LessEqual[y, 7.5e-30], N[(1.0 / y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.69999999999999995e-101 or 7.5000000000000006e-30 < y

   1. Initial program 90.5%

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

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

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

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

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

      3. *-commutative N/A

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

      4. exp-to-pow N/A

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

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

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

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

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

      7. +-commutative N/A

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

      8. +-lowering-+.f64 90.5%

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

   3. Simplified 90.5%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 67.1%

      \[\leadsto \color{blue}{x} \]

   if -1.69999999999999995e-101 < y < 7.5000000000000006e-30

   1. Initial program 83.2%

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

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

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

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

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

      3. *-commutative N/A

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

      4. exp-to-pow N/A

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

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

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

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

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

      7. +-commutative N/A

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

      8. +-lowering-+.f64 83.2%

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

   3. Simplified 83.2%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{1}{y}} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 83.5%

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{y}\right) \]

   7. Simplified 83.5%

      \[\leadsto \color{blue}{\frac{1}{y}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 85.7% accurate, 42.2× speedup

Math

\[\begin{array}{l} \\ x + \frac{1}{y} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (/ 1.0 y)))

C

double code(double x, double y, double z) {
	return x + (1.0 / y);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (1.0d0 / y)
end function

Java

public static double code(double x, double y, double z) {
	return x + (1.0 / y);
}

Python

def code(x, y, z):
	return x + (1.0 / y)

Julia

function code(x, y, z)
	return Float64(x + Float64(1.0 / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (1.0 / y);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.9%

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

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

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

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

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

   3. *-commutative N/A

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

   4. exp-to-pow N/A

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

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

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

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

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

   7. +-commutative N/A

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

   8. +-lowering-+.f64 87.9%

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

3. Simplified 87.9%

   \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
4. Add Preprocessing

5. Taylor expanded in z around 0

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

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

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{1}{y}\right)}\right) \]

   2. /-lowering-/.f64 88.6%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(1, \color{blue}{y}\right)\right) \]

7. Simplified 88.6%

   \[\leadsto \color{blue}{x + \frac{1}{y}} \]
8. Add Preprocessing

Alternative 9: 49.8% accurate, 211.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 87.9%

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

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

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

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

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

   3. *-commutative N/A

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

   4. exp-to-pow N/A

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

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

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

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

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

   7. +-commutative N/A

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

   8. +-lowering-+.f64 87.9%

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

3. Simplified 87.9%

   \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
4. Add Preprocessing

5. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
6. Step-by-step derivation

7. Simplified 49.5%

   \[\leadsto \color{blue}{x} \]
8. Add Preprocessing

Developer Target 1: 91.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y}{z + y} < 7.11541576 \cdot 10^{-315}:\\ \;\;\;\;x + \frac{e^{\frac{-1}{z}}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{e^{\log \left({\left(\frac{y}{y + z}\right)}^{y}\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (< (/ y (+ z y)) 7.11541576e-315)
   (+ x (/ (exp (/ -1.0 z)) y))
   (+ x (/ (exp (log (pow (/ y (+ y z)) y))) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y / (z + y)) < 7.11541576e-315) {
		tmp = x + (exp((-1.0 / z)) / y);
	} else {
		tmp = x + (exp(log(pow((y / (y + z)), y))) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y / (z + y)) < 7.11541576d-315) then
        tmp = x + (exp(((-1.0d0) / z)) / y)
    else
        tmp = x + (exp(log(((y / (y + z)) ** y))) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y / (z + y)) < 7.11541576e-315) {
		tmp = x + (Math.exp((-1.0 / z)) / y);
	} else {
		tmp = x + (Math.exp(Math.log(Math.pow((y / (y + z)), y))) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y / (z + y)) < 7.11541576e-315:
		tmp = x + (math.exp((-1.0 / z)) / y)
	else:
		tmp = x + (math.exp(math.log(math.pow((y / (y + z)), y))) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(y / Float64(z + y)) < 7.11541576e-315)
		tmp = Float64(x + Float64(exp(Float64(-1.0 / z)) / y));
	else
		tmp = Float64(x + Float64(exp(log((Float64(y / Float64(y + z)) ^ y))) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y / (z + y)) < 7.11541576e-315)
		tmp = x + (exp((-1.0 / z)) / y);
	else
		tmp = x + (exp(log(((y / (y + z)) ^ y))) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Less[N[(y / N[(z + y), $MachinePrecision]), $MachinePrecision], 7.11541576e-315], N[(x + N[(N[Exp[N[(-1.0 / z), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Exp[N[Log[N[Power[N[(y / N[(y + z), $MachinePrecision]), $MachinePrecision], y], $MachinePrecision]], $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2024138 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, G"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ y (+ z y)) 17788539399477/2500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ x (/ (exp (/ -1 z)) y)) (+ x (/ (exp (log (pow (/ y (+ y z)) y))) y))))

  (+ x (/ (exp (* y (log (/ y (+ z y))))) y)))