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

Percentage Accurate: 84.6% → 99.6%

Time: 11.3s

Alternatives: 10

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: 84.6% 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: 99.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{e^{0 - z}}{y}\\ \mathbf{if}\;y \leq -13600000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-7}:\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (/ (exp (- 0.0 z)) y))))
   (if (<= y -13600000000.0) t_0 (if (<= y 4e-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 <= -13600000000.0) {
		tmp = t_0;
	} else if (y <= 4e-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 <= (-13600000000.0d0)) then
        tmp = t_0
    else if (y <= 4d-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 <= -13600000000.0) {
		tmp = t_0;
	} else if (y <= 4e-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 <= -13600000000.0:
		tmp = t_0
	elif y <= 4e-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 <= -13600000000.0)
		tmp = t_0;
	elseif (y <= 4e-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 <= -13600000000.0)
		tmp = t_0;
	elseif (y <= 4e-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, -13600000000.0], t$95$0, If[LessEqual[y, 4e-7], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.36e10 or 3.9999999999999998e-7 < y

   1. Initial program 83.8%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   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 83.8%

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

   3. Simplified 83.8%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   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 -1.36e10 < y < 3.9999999999999998e-7

   1. Initial program 82.8%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   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 82.8%

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

   3. Simplified 82.8%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   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 99.1%

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

   7. Simplified 99.1%

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

Alternative 2: 88.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{1}{y}\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+133}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1750000:\\ \;\;\;\;\frac{e^{0 - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (/ 1.0 y))))
   (if (<= z -6.2e+133) t_0 (if (<= z -1750000.0) (/ (exp (- 0.0 z)) y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + (1.0 / y);
	double tmp;
	if (z <= -6.2e+133) {
		tmp = t_0;
	} else if (z <= -1750000.0) {
		tmp = exp((0.0 - z)) / 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 + (1.0d0 / y)
    if (z <= (-6.2d+133)) then
        tmp = t_0
    else if (z <= (-1750000.0d0)) then
        tmp = exp((0.0d0 - z)) / 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 + (1.0 / y);
	double tmp;
	if (z <= -6.2e+133) {
		tmp = t_0;
	} else if (z <= -1750000.0) {
		tmp = Math.exp((0.0 - z)) / y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (1.0 / y)
	tmp = 0
	if z <= -6.2e+133:
		tmp = t_0
	elif z <= -1750000.0:
		tmp = math.exp((0.0 - z)) / y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(1.0 / y))
	tmp = 0.0
	if (z <= -6.2e+133)
		tmp = t_0;
	elseif (z <= -1750000.0)
		tmp = Float64(exp(Float64(0.0 - z)) / y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (1.0 / y);
	tmp = 0.0;
	if (z <= -6.2e+133)
		tmp = t_0;
	elseif (z <= -1750000.0)
		tmp = exp((0.0 - z)) / y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.2e+133], t$95$0, If[LessEqual[z, -1750000.0], N[(N[Exp[N[(0.0 - z), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.2e133 or -1.75e6 < z

   1. Initial program 88.3%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   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 88.3%

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

   3. Simplified 88.3%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   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 91.6%

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

   7. Simplified 91.6%

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

   if -6.2e133 < z < -1.75e6

   1. Initial program 40.1%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   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 40.1%

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

   3. Simplified 40.1%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   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 82.1%

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

   7. Simplified 82.1%

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

   8. Taylor expanded in x around 0

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

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

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

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

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

      3. neg-sub0 N/A

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

      4. --lowering--.f64 82.1%

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

   10. Simplified 82.1%

       \[\leadsto \color{blue}{\frac{e^{0 - z}}{y}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 85.6% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.5 + z \cdot -0.16666666666666666\\ t_1 := z \cdot t\_0\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+203}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -13600000000:\\ \;\;\;\;x + \frac{1 + \frac{z \cdot \left(1 - z \cdot \left(t\_0 \cdot t\_1\right)\right)}{-1 - t\_1}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 0.5 (* z -0.16666666666666666))) (t_1 (* z t_0)))
   (if (<= y -6.2e+203)
     x
     (if (<= y -13600000000.0)
       (+ x (/ (+ 1.0 (/ (* z (- 1.0 (* z (* t_0 t_1)))) (- -1.0 t_1))) y))
       (+ x (/ 1.0 y))))))

C

double code(double x, double y, double z) {
	double t_0 = 0.5 + (z * -0.16666666666666666);
	double t_1 = z * t_0;
	double tmp;
	if (y <= -6.2e+203) {
		tmp = x;
	} else if (y <= -13600000000.0) {
		tmp = x + ((1.0 + ((z * (1.0 - (z * (t_0 * t_1)))) / (-1.0 - t_1))) / 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 0.5d0 + (z * (-0.16666666666666666d0))
    t_1 = z * t_0
    if (y <= (-6.2d+203)) then
        tmp = x
    else if (y <= (-13600000000.0d0)) then
        tmp = x + ((1.0d0 + ((z * (1.0d0 - (z * (t_0 * t_1)))) / ((-1.0d0) - t_1))) / 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 t_0 = 0.5 + (z * -0.16666666666666666);
	double t_1 = z * t_0;
	double tmp;
	if (y <= -6.2e+203) {
		tmp = x;
	} else if (y <= -13600000000.0) {
		tmp = x + ((1.0 + ((z * (1.0 - (z * (t_0 * t_1)))) / (-1.0 - t_1))) / y);
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 0.5 + (z * -0.16666666666666666)
	t_1 = z * t_0
	tmp = 0
	if y <= -6.2e+203:
		tmp = x
	elif y <= -13600000000.0:
		tmp = x + ((1.0 + ((z * (1.0 - (z * (t_0 * t_1)))) / (-1.0 - t_1))) / y)
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(0.5 + Float64(z * -0.16666666666666666))
	t_1 = Float64(z * t_0)
	tmp = 0.0
	if (y <= -6.2e+203)
		tmp = x;
	elseif (y <= -13600000000.0)
		tmp = Float64(x + Float64(Float64(1.0 + Float64(Float64(z * Float64(1.0 - Float64(z * Float64(t_0 * t_1)))) / Float64(-1.0 - t_1))) / y));
	else
		tmp = Float64(x + Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 0.5 + (z * -0.16666666666666666);
	t_1 = z * t_0;
	tmp = 0.0;
	if (y <= -6.2e+203)
		tmp = x;
	elseif (y <= -13600000000.0)
		tmp = x + ((1.0 + ((z * (1.0 - (z * (t_0 * t_1)))) / (-1.0 - t_1))) / y);
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(0.5 + N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * t$95$0), $MachinePrecision]}, If[LessEqual[y, -6.2e+203], x, If[LessEqual[y, -13600000000.0], N[(x + N[(N[(1.0 + N[(N[(z * N[(1.0 - N[(z * N[(t$95$0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(-1.0 - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.2e203

   1. Initial program 72.9%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   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 72.9%

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

   3. Simplified 72.9%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 72.3%

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

   if -6.2e203 < y < -1.36e10

   1. Initial program 88.7%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   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 88.7%

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

   3. Simplified 88.7%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   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%

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

   8. Taylor expanded in z around 0

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

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

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

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

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

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

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

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

      9. *-commutative N/A

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

      10. *-lowering-*.f64 85.9%

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

   10. Simplified 85.9%

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

       1. *-commutative N/A

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

       2. flip-+ N/A

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

       3. associate-*l/ N/A

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

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

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

   12. Applied egg-rr 90.1%

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

   if -1.36e10 < y

   1. Initial program 84.0%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   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 84.0%

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

   3. Simplified 84.0%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   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 90.8%

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

   7. Simplified 90.8%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+203}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -13600000000:\\ \;\;\;\;x + \frac{1 + \frac{z \cdot \left(1 - z \cdot \left(\left(0.5 + z \cdot -0.16666666666666666\right) \cdot \left(z \cdot \left(0.5 + z \cdot -0.16666666666666666\right)\right)\right)\right)}{-1 - z \cdot \left(0.5 + z \cdot -0.16666666666666666\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.0% accurate, 7.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -200000000000:\\ \;\;\;\;\frac{1}{y} + x \cdot \left(1 + \left(z \cdot \left(0.5 + z \cdot -0.16666666666666666\right) + -1\right) \cdot \frac{z}{y \cdot x}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -200000000000.0)
   (+
    (/ 1.0 y)
    (*
     x
     (+
      1.0
      (* (+ (* z (+ 0.5 (* z -0.16666666666666666))) -1.0) (/ z (* y x))))))
   (+ x (/ 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -200000000000.0) {
		tmp = (1.0 / y) + (x * (1.0 + (((z * (0.5 + (z * -0.16666666666666666))) + -1.0) * (z / (y * x)))));
	} 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 (y <= (-200000000000.0d0)) then
        tmp = (1.0d0 / y) + (x * (1.0d0 + (((z * (0.5d0 + (z * (-0.16666666666666666d0)))) + (-1.0d0)) * (z / (y * x)))))
    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 (y <= -200000000000.0) {
		tmp = (1.0 / y) + (x * (1.0 + (((z * (0.5 + (z * -0.16666666666666666))) + -1.0) * (z / (y * x)))));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -200000000000.0:
		tmp = (1.0 / y) + (x * (1.0 + (((z * (0.5 + (z * -0.16666666666666666))) + -1.0) * (z / (y * x)))))
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -200000000000.0)
		tmp = Float64(Float64(1.0 / y) + Float64(x * Float64(1.0 + Float64(Float64(Float64(z * Float64(0.5 + Float64(z * -0.16666666666666666))) + -1.0) * Float64(z / Float64(y * x))))));
	else
		tmp = Float64(x + Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -200000000000.0)
		tmp = (1.0 / y) + (x * (1.0 + (((z * (0.5 + (z * -0.16666666666666666))) + -1.0) * (z / (y * x)))));
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -200000000000.0], N[(N[(1.0 / y), $MachinePrecision] + N[(x * N[(1.0 + N[(N[(N[(z * N[(0.5 + N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision] * N[(z / N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2e11

   1. Initial program 82.0%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   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 82.0%

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

   3. Simplified 82.0%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   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%

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

   8. Taylor expanded in z around 0

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

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

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

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

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

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

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

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

      9. *-commutative N/A

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

      10. *-lowering-*.f64 73.7%

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

   10. Simplified 73.7%

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

   11. Taylor expanded in x around inf

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

       1. associate-+r+ N/A

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

       2. +-commutative N/A

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

       3. associate-+l+ N/A

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

       4. distribute-lft-in N/A

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

       5. associate-/r* N/A

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

       6. associate-*r/ N/A

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

       7. rgt-mult-inverse N/A

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

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

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

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

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

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

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

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

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

   13. Simplified 76.3%

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

   if -2e11 < y

   1. Initial program 84.0%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   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 84.0%

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

   3. Simplified 84.0%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   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 90.8%

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

   7. Simplified 90.8%

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

Alternative 5: 87.7% accurate, 7.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+222}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -13600000000:\\ \;\;\;\;x + \frac{\left(1 - z\right) + \left(0.5 + z \cdot -0.16666666666666666\right) \cdot \left(z \cdot z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.8e+222)
   x
   (if (<= y -13600000000.0)
     (+ x (/ (+ (- 1.0 z) (* (+ 0.5 (* z -0.16666666666666666)) (* z z))) y))
     (+ x (/ 1.0 y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.8e+222) {
		tmp = x;
	} else if (y <= -13600000000.0) {
		tmp = x + (((1.0 - z) + ((0.5 + (z * -0.16666666666666666)) * (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 (y <= (-2.8d+222)) then
        tmp = x
    else if (y <= (-13600000000.0d0)) then
        tmp = x + (((1.0d0 - z) + ((0.5d0 + (z * (-0.16666666666666666d0))) * (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 (y <= -2.8e+222) {
		tmp = x;
	} else if (y <= -13600000000.0) {
		tmp = x + (((1.0 - z) + ((0.5 + (z * -0.16666666666666666)) * (z * z))) / y);
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.8e+222:
		tmp = x
	elif y <= -13600000000.0:
		tmp = x + (((1.0 - z) + ((0.5 + (z * -0.16666666666666666)) * (z * z))) / y)
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.8e+222)
		tmp = x;
	elseif (y <= -13600000000.0)
		tmp = Float64(x + Float64(Float64(Float64(1.0 - z) + Float64(Float64(0.5 + Float64(z * -0.16666666666666666)) * 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 (y <= -2.8e+222)
		tmp = x;
	elseif (y <= -13600000000.0)
		tmp = x + (((1.0 - z) + ((0.5 + (z * -0.16666666666666666)) * (z * z))) / y);
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.8e+222], x, If[LessEqual[y, -13600000000.0], N[(x + N[(N[(N[(1.0 - z), $MachinePrecision] + N[(N[(0.5 + N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] * N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.8000000000000001e222

   1. Initial program 74.1%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   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 74.1%

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

   3. Simplified 74.1%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 77.2%

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

   if -2.8000000000000001e222 < y < -1.36e10

   1. Initial program 86.2%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   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 86.2%

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

   3. Simplified 86.2%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   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%

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

   8. Taylor expanded in z around 0

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

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

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

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

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

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

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

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

      9. *-commutative N/A

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

      10. *-lowering-*.f64 83.7%

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

   10. Simplified 83.7%

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

       1. distribute-lft-in N/A

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

       2. associate-+r+ N/A

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

       3. *-commutative N/A

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

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

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

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

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

       6. mul-1-neg N/A

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

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

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

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

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

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

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

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

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

       11. *-lowering-*.f64 83.7%

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

   12. Applied egg-rr 83.7%

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

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

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

       2. sub-neg N/A

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

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

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

       4. associate-*r* N/A

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

       5. *-commutative N/A

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

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

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

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

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

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

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

       9. *-lowering-*.f64 83.7%

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

   14. Applied egg-rr 83.7%

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

   if -1.36e10 < y

   1. Initial program 84.0%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   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 84.0%

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

   3. Simplified 84.0%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   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 90.8%

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

   7. Simplified 90.8%

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

Alternative 6: 87.7% accurate, 7.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+223}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -13600000000:\\ \;\;\;\;x + \frac{1 + z \cdot \left(z \cdot \left(0.5 + z \cdot -0.16666666666666666\right) + -1\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.6e+223)
   x
   (if (<= y -13600000000.0)
     (+
      x
      (/ (+ 1.0 (* z (+ (* z (+ 0.5 (* z -0.16666666666666666))) -1.0))) y))
     (+ x (/ 1.0 y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.6e+223) {
		tmp = x;
	} else if (y <= -13600000000.0) {
		tmp = x + ((1.0 + (z * ((z * (0.5 + (z * -0.16666666666666666))) + -1.0))) / 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 (y <= (-2.6d+223)) then
        tmp = x
    else if (y <= (-13600000000.0d0)) then
        tmp = x + ((1.0d0 + (z * ((z * (0.5d0 + (z * (-0.16666666666666666d0)))) + (-1.0d0)))) / 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 (y <= -2.6e+223) {
		tmp = x;
	} else if (y <= -13600000000.0) {
		tmp = x + ((1.0 + (z * ((z * (0.5 + (z * -0.16666666666666666))) + -1.0))) / y);
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.6e+223:
		tmp = x
	elif y <= -13600000000.0:
		tmp = x + ((1.0 + (z * ((z * (0.5 + (z * -0.16666666666666666))) + -1.0))) / y)
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.6e+223)
		tmp = x;
	elseif (y <= -13600000000.0)
		tmp = Float64(x + Float64(Float64(1.0 + Float64(z * Float64(Float64(z * Float64(0.5 + Float64(z * -0.16666666666666666))) + -1.0))) / 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 (y <= -2.6e+223)
		tmp = x;
	elseif (y <= -13600000000.0)
		tmp = x + ((1.0 + (z * ((z * (0.5 + (z * -0.16666666666666666))) + -1.0))) / y);
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.6e+223], x, If[LessEqual[y, -13600000000.0], N[(x + N[(N[(1.0 + N[(z * N[(N[(z * N[(0.5 + N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6000000000000002e223

   1. Initial program 74.1%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   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 74.1%

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

   3. Simplified 74.1%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 77.2%

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

   if -2.6000000000000002e223 < y < -1.36e10

   1. Initial program 86.2%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   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 86.2%

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

   3. Simplified 86.2%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   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%

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

   8. Taylor expanded in z around 0

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

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

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

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

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

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

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

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

      9. *-commutative N/A

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

      10. *-lowering-*.f64 83.7%

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

   10. Simplified 83.7%

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

   if -1.36e10 < y

   1. Initial program 84.0%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   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 84.0%

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

   3. Simplified 84.0%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   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 90.8%

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

   7. Simplified 90.8%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+223}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -13600000000:\\ \;\;\;\;x + \frac{1 + z \cdot \left(z \cdot \left(0.5 + z \cdot -0.16666666666666666\right) + -1\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.7% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+223}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -15000000000:\\ \;\;\;\;x + \frac{1 + z \cdot \left(-1 + -0.16666666666666666 \cdot \left(z \cdot z\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.5e+223)
   x
   (if (<= y -15000000000.0)
     (+ x (/ (+ 1.0 (* z (+ -1.0 (* -0.16666666666666666 (* z z))))) y))
     (+ x (/ 1.0 y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.5e+223) {
		tmp = x;
	} else if (y <= -15000000000.0) {
		tmp = x + ((1.0 + (z * (-1.0 + (-0.16666666666666666 * (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 (y <= (-3.5d+223)) then
        tmp = x
    else if (y <= (-15000000000.0d0)) then
        tmp = x + ((1.0d0 + (z * ((-1.0d0) + ((-0.16666666666666666d0) * (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 (y <= -3.5e+223) {
		tmp = x;
	} else if (y <= -15000000000.0) {
		tmp = x + ((1.0 + (z * (-1.0 + (-0.16666666666666666 * (z * z))))) / y);
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.5e+223:
		tmp = x
	elif y <= -15000000000.0:
		tmp = x + ((1.0 + (z * (-1.0 + (-0.16666666666666666 * (z * z))))) / y)
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.5e+223)
		tmp = x;
	elseif (y <= -15000000000.0)
		tmp = Float64(x + Float64(Float64(1.0 + Float64(z * Float64(-1.0 + Float64(-0.16666666666666666 * 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 (y <= -3.5e+223)
		tmp = x;
	elseif (y <= -15000000000.0)
		tmp = x + ((1.0 + (z * (-1.0 + (-0.16666666666666666 * (z * z))))) / y);
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.5e+223], x, If[LessEqual[y, -15000000000.0], N[(x + N[(N[(1.0 + N[(z * N[(-1.0 + N[(-0.16666666666666666 * N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.5000000000000001e223

   1. Initial program 74.1%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   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 74.1%

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

   3. Simplified 74.1%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 77.2%

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

   if -3.5000000000000001e223 < y < -1.5e10

   1. Initial program 86.2%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   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 86.2%

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

   3. Simplified 86.2%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   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%

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

   8. Taylor expanded in z around 0

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

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

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

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

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

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

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

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

      9. *-commutative N/A

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

      10. *-lowering-*.f64 83.7%

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

   10. Simplified 83.7%

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

   11. Taylor expanded in z around inf

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

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

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

       2. unpow2 N/A

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

       3. *-lowering-*.f64 83.0%

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

   13. Simplified 83.0%

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

   if -1.5e10 < y

   1. Initial program 84.0%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   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 84.0%

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

   3. Simplified 84.0%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   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 90.8%

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

   7. Simplified 90.8%

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

Alternative 8: 67.7% accurate, 16.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.2e+65) x (if (<= y 7.5e-14) (/ 1.0 y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.2e+65) {
		tmp = x;
	} else if (y <= 7.5e-14) {
		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 <= (-3.2d+65)) then
        tmp = x
    else if (y <= 7.5d-14) 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 <= -3.2e+65) {
		tmp = x;
	} else if (y <= 7.5e-14) {
		tmp = 1.0 / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.2e+65:
		tmp = x
	elif y <= 7.5e-14:
		tmp = 1.0 / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.2e+65)
		tmp = x;
	elseif (y <= 7.5e-14)
		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 <= -3.2e+65)
		tmp = x;
	elseif (y <= 7.5e-14)
		tmp = 1.0 / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.2e+65], x, If[LessEqual[y, 7.5e-14], N[(1.0 / y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -3.20000000000000007e65 or 7.4999999999999996e-14 < y

   1. Initial program 83.1%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   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 83.1%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 71.9%

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

   if -3.20000000000000007e65 < y < 7.4999999999999996e-14

   1. Initial program 83.7%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   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 83.7%

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

   3. Simplified 83.7%

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

   5. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 70.1%

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

   7. Simplified 70.1%

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

Alternative 9: 85.3% 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 83.4%

   \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
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 83.4%

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

3. Simplified 83.4%

   \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
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 84.4%

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

7. Simplified 84.4%

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

Alternative 10: 50.0% 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 83.4%

   \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
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 83.4%

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

3. Simplified 83.4%

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

5. Taylor expanded in x around inf

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

7. Simplified 51.4%

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

Developer Target 1: 91.6% 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 2024158 
(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)))