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

Percentage Accurate: 85.8% → 99.7%

Time: 13.8s

Alternatives: 14

Speedup: 11.7×

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: 85.8% 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: 99.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1000:\\ \;\;\;\;x + \frac{e^{-z}}{y}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+74}:\\ \;\;\;\;x + \frac{{\left(e^{y}\right)}^{\log \left(\frac{y}{y + z}\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y \cdot e^{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1000.0)
   (+ x (/ (exp (- z)) y))
   (if (<= y 2e+74)
     (+ x (/ (pow (exp y) (log (/ y (+ y z)))) y))
     (+ x (/ 1.0 (* y (exp z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1000.0) {
		tmp = x + (exp(-z) / y);
	} else if (y <= 2e+74) {
		tmp = x + (pow(exp(y), log((y / (y + z)))) / y);
	} else {
		tmp = x + (1.0 / (y * exp(z)));
	}
	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 <= (-1000.0d0)) then
        tmp = x + (exp(-z) / y)
    else if (y <= 2d+74) then
        tmp = x + ((exp(y) ** log((y / (y + z)))) / y)
    else
        tmp = x + (1.0d0 / (y * exp(z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1000.0) {
		tmp = x + (Math.exp(-z) / y);
	} else if (y <= 2e+74) {
		tmp = x + (Math.pow(Math.exp(y), Math.log((y / (y + z)))) / y);
	} else {
		tmp = x + (1.0 / (y * Math.exp(z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1000.0:
		tmp = x + (math.exp(-z) / y)
	elif y <= 2e+74:
		tmp = x + (math.pow(math.exp(y), math.log((y / (y + z)))) / y)
	else:
		tmp = x + (1.0 / (y * math.exp(z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1000.0)
		tmp = Float64(x + Float64(exp(Float64(-z)) / y));
	elseif (y <= 2e+74)
		tmp = Float64(x + Float64((exp(y) ^ log(Float64(y / Float64(y + z)))) / y));
	else
		tmp = Float64(x + Float64(1.0 / Float64(y * exp(z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1000.0)
		tmp = x + (exp(-z) / y);
	elseif (y <= 2e+74)
		tmp = x + ((exp(y) ^ log((y / (y + z)))) / y);
	else
		tmp = x + (1.0 / (y * exp(z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1000.0], N[(x + N[(N[Exp[(-z)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+74], N[(x + N[(N[Power[N[Exp[y], $MachinePrecision], N[Log[N[(y / N[(y + z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / N[(y * N[Exp[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1e3

   1. Initial program 81.3%

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

      1. *-commutative 81.3%

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

      2. exp-to-pow 81.3%

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

      3. +-commutative 81.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

   if -1e3 < y < 1.9999999999999999e74

   1. Initial program 87.3%

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

      1. exp-prod 99.8%

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

      2. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   if 1.9999999999999999e74 < y

   1. Initial program 86.2%

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

      1. *-commutative 86.2%

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

      2. exp-to-pow 86.2%

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

      3. +-commutative 86.2%

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

   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 100.0%

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

      1. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

      1. clear-num 100.0%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{y}{e^{-z}}}} \]

      2. inv-pow 100.0%

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

      3. div-inv 100.0%

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

      4. add-sqr-sqrt 38.0%

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

      5. sqrt-unprod 62.9%

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

      6. sqr-neg 62.9%

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

      7. sqrt-unprod 24.9%

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

      8. add-sqr-sqrt 47.1%

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

      9. exp-neg 47.1%

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

      10. add-sqr-sqrt 22.3%

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

      11. sqrt-unprod 84.3%

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

      12. sqr-neg 84.3%

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

      13. sqrt-unprod 62.0%

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

      14. add-sqr-sqrt 100.0%

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

   9. Applied egg-rr 100.0%

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

       1. unpow-1 100.0%

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

   11. Simplified 100.0%

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

Alternative 2: 99.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5:\\ \;\;\;\;x + \frac{e^{-z}}{y}\\ \mathbf{elif}\;y \leq 2100:\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y \cdot e^{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.5)
   (+ x (/ (exp (- z)) y))
   (if (<= y 2100.0) (+ x (/ 1.0 y)) (+ x (/ 1.0 (* y (exp z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.5) {
		tmp = x + (exp(-z) / y);
	} else if (y <= 2100.0) {
		tmp = x + (1.0 / y);
	} else {
		tmp = x + (1.0 / (y * exp(z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.5d0)) then
        tmp = x + (exp(-z) / y)
    else if (y <= 2100.0d0) then
        tmp = x + (1.0d0 / y)
    else
        tmp = x + (1.0d0 / (y * exp(z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.5) {
		tmp = x + (Math.exp(-z) / y);
	} else if (y <= 2100.0) {
		tmp = x + (1.0 / y);
	} else {
		tmp = x + (1.0 / (y * Math.exp(z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.5:
		tmp = x + (math.exp(-z) / y)
	elif y <= 2100.0:
		tmp = x + (1.0 / y)
	else:
		tmp = x + (1.0 / (y * math.exp(z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.5)
		tmp = Float64(x + Float64(exp(Float64(-z)) / y));
	elseif (y <= 2100.0)
		tmp = Float64(x + Float64(1.0 / y));
	else
		tmp = Float64(x + Float64(1.0 / Float64(y * exp(z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.5)
		tmp = x + (exp(-z) / y);
	elseif (y <= 2100.0)
		tmp = x + (1.0 / y);
	else
		tmp = x + (1.0 / (y * exp(z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.5], N[(x + N[(N[Exp[(-z)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2100.0], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / N[(y * N[Exp[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5

   1. Initial program 81.3%

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

      1. *-commutative 81.3%

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

      2. exp-to-pow 81.3%

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

      3. +-commutative 81.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

   if -1.5 < y < 2100

   1. Initial program 85.9%

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

      1. exp-prod 99.8%

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

      2. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 98.7%

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

      1. +-commutative 98.7%

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

   7. Simplified 98.7%

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

   if 2100 < y

   1. Initial program 88.9%

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

      1. *-commutative 88.9%

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

      2. exp-to-pow 88.9%

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

      3. +-commutative 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

      1. clear-num 100.0%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{y}{e^{-z}}}} \]

      2. inv-pow 100.0%

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

      3. div-inv 100.0%

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

      4. add-sqr-sqrt 35.5%

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

      5. sqrt-unprod 62.1%

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

      6. sqr-neg 62.1%

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

      7. sqrt-unprod 26.7%

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

      8. add-sqr-sqrt 47.9%

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

      9. exp-neg 47.9%

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

      10. add-sqr-sqrt 21.2%

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

      11. sqrt-unprod 85.8%

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

      12. sqr-neg 85.8%

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

      13. sqrt-unprod 64.5%

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

      14. add-sqr-sqrt 100.0%

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

   9. Applied egg-rr 100.0%

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

       1. unpow-1 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5:\\ \;\;\;\;x + \frac{e^{-z}}{y}\\ \mathbf{elif}\;y \leq 2100:\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y \cdot e^{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.55 \lor \neg \left(y \leq 2100\right):\\ \;\;\;\;x + \frac{e^{-z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.55) (not (<= y 2100.0)))
   (+ x (/ (exp (- z)) y))
   (+ x (/ 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.55) || !(y <= 2100.0)) {
		tmp = x + (exp(-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 <= (-0.55d0)) .or. (.not. (y <= 2100.0d0))) then
        tmp = x + (exp(-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 <= -0.55) || !(y <= 2100.0)) {
		tmp = x + (Math.exp(-z) / y);
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.55) or not (y <= 2100.0):
		tmp = x + (math.exp(-z) / y)
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.55) || !(y <= 2100.0))
		tmp = Float64(x + Float64(exp(Float64(-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 <= -0.55) || ~((y <= 2100.0)))
		tmp = x + (exp(-z) / y);
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.55], N[Not[LessEqual[y, 2100.0]], $MachinePrecision]], N[(x + N[(N[Exp[(-z)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.55000000000000004 or 2100 < y

   1. Initial program 84.5%

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

      1. *-commutative 84.5%

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

      2. exp-to-pow 84.5%

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

      3. +-commutative 84.5%

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

   3. Simplified 84.5%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

   if -0.55000000000000004 < y < 2100

   1. Initial program 85.9%

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

      1. exp-prod 99.8%

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

      2. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 98.7%

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

      1. +-commutative 98.7%

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

   7. Simplified 98.7%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.55 \lor \neg \left(y \leq 2100\right):\\ \;\;\;\;x + \frac{e^{-z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1300:\\ \;\;\;\;\frac{e^{-z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1300.0) (/ (exp (- z)) y) (+ x (/ 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1300.0) {
		tmp = exp(-z) / y;
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1300.0d0)) then
        tmp = exp(-z) / y
    else
        tmp = x + (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1300.0) {
		tmp = Math.exp(-z) / y;
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1300.0:
		tmp = math.exp(-z) / y
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1300.0)
		tmp = Float64(exp(Float64(-z)) / y);
	else
		tmp = Float64(x + Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1300.0)
		tmp = exp(-z) / y;
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1300.0], N[(N[Exp[(-z)], $MachinePrecision] / y), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1300

   1. Initial program 48.1%

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

      1. *-commutative 48.1%

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

      2. exp-to-pow 48.1%

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

      3. +-commutative 48.1%

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

   3. Simplified 48.1%

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

   5. Taylor expanded in y around inf 70.5%

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

      1. mul-1-neg 70.5%

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

   7. Simplified 70.5%

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

   8. Taylor expanded in x around 0 70.5%

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

   if -1300 < z

   1. Initial program 95.0%

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

      1. exp-prod 98.8%

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

      2. +-commutative 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in y around inf 95.9%

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

      1. +-commutative 95.9%

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

   7. Simplified 95.9%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1300:\\ \;\;\;\;\frac{e^{-z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 90.2% accurate, 6.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2:\\ \;\;\;\;x + \frac{x \cdot \left(\frac{1}{x} + \frac{z \cdot \left(z \cdot 0.5 + -1\right)}{x}\right)}{y}\\ \mathbf{elif}\;y \leq 2100:\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y + z \cdot \left(y + z \cdot \left(0.16666666666666666 \cdot \left(y \cdot z\right) + y \cdot 0.5\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.2)
   (+ x (/ (* x (+ (/ 1.0 x) (/ (* z (+ (* z 0.5) -1.0)) x))) y))
   (if (<= y 2100.0)
     (+ x (/ 1.0 y))
     (+
      x
      (/
       1.0
       (+
        y
        (* z (+ y (* z (+ (* 0.16666666666666666 (* y z)) (* y 0.5)))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.2) {
		tmp = x + ((x * ((1.0 / x) + ((z * ((z * 0.5) + -1.0)) / x))) / y);
	} else if (y <= 2100.0) {
		tmp = x + (1.0 / y);
	} else {
		tmp = x + (1.0 / (y + (z * (y + (z * ((0.16666666666666666 * (y * z)) + (y * 0.5)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.2d0)) then
        tmp = x + ((x * ((1.0d0 / x) + ((z * ((z * 0.5d0) + (-1.0d0))) / x))) / y)
    else if (y <= 2100.0d0) then
        tmp = x + (1.0d0 / y)
    else
        tmp = x + (1.0d0 / (y + (z * (y + (z * ((0.16666666666666666d0 * (y * z)) + (y * 0.5d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.2) {
		tmp = x + ((x * ((1.0 / x) + ((z * ((z * 0.5) + -1.0)) / x))) / y);
	} else if (y <= 2100.0) {
		tmp = x + (1.0 / y);
	} else {
		tmp = x + (1.0 / (y + (z * (y + (z * ((0.16666666666666666 * (y * z)) + (y * 0.5)))))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.2:
		tmp = x + ((x * ((1.0 / x) + ((z * ((z * 0.5) + -1.0)) / x))) / y)
	elif y <= 2100.0:
		tmp = x + (1.0 / y)
	else:
		tmp = x + (1.0 / (y + (z * (y + (z * ((0.16666666666666666 * (y * z)) + (y * 0.5)))))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.2)
		tmp = Float64(x + Float64(Float64(x * Float64(Float64(1.0 / x) + Float64(Float64(z * Float64(Float64(z * 0.5) + -1.0)) / x))) / y));
	elseif (y <= 2100.0)
		tmp = Float64(x + Float64(1.0 / y));
	else
		tmp = Float64(x + Float64(1.0 / Float64(y + Float64(z * Float64(y + Float64(z * Float64(Float64(0.16666666666666666 * Float64(y * z)) + Float64(y * 0.5))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.2)
		tmp = x + ((x * ((1.0 / x) + ((z * ((z * 0.5) + -1.0)) / x))) / y);
	elseif (y <= 2100.0)
		tmp = x + (1.0 / y);
	else
		tmp = x + (1.0 / (y + (z * (y + (z * ((0.16666666666666666 * (y * z)) + (y * 0.5)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.2], N[(x + N[(N[(x * N[(N[(1.0 / x), $MachinePrecision] + N[(N[(z * N[(N[(z * 0.5), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2100.0], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / N[(y + N[(z * N[(y + N[(z * N[(N[(0.16666666666666666 * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.19999999999999996

   1. Initial program 81.3%

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

      1. exp-prod 81.3%

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

      2. +-commutative 81.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in z around 0 71.0%

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

   6. Taylor expanded in x around inf 66.1%

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

   7. Taylor expanded in y around inf 74.4%

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

   if -1.19999999999999996 < y < 2100

   1. Initial program 85.9%

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

      1. exp-prod 99.8%

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

      2. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 98.7%

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

      1. +-commutative 98.7%

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

   7. Simplified 98.7%

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

   if 2100 < y

   1. Initial program 88.9%

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

      1. *-commutative 88.9%

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

      2. exp-to-pow 88.9%

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

      3. +-commutative 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

      1. clear-num 100.0%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{y}{e^{-z}}}} \]

      2. inv-pow 100.0%

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

      3. div-inv 100.0%

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

      4. add-sqr-sqrt 35.5%

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

      5. sqrt-unprod 62.1%

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

      6. sqr-neg 62.1%

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

      7. sqrt-unprod 26.7%

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

      8. add-sqr-sqrt 47.9%

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

      9. exp-neg 47.9%

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

      10. add-sqr-sqrt 21.2%

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

      11. sqrt-unprod 85.8%

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

      12. sqr-neg 85.8%

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

      13. sqrt-unprod 64.5%

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

      14. add-sqr-sqrt 100.0%

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

   9. Applied egg-rr 100.0%

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

       1. unpow-1 100.0%

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

   11. Simplified 100.0%

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

   12. Taylor expanded in z around 0 85.8%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2:\\ \;\;\;\;x + \frac{x \cdot \left(\frac{1}{x} + \frac{z \cdot \left(z \cdot 0.5 + -1\right)}{x}\right)}{y}\\ \mathbf{elif}\;y \leq 2100:\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y + z \cdot \left(y + z \cdot \left(0.16666666666666666 \cdot \left(y \cdot z\right) + y \cdot 0.5\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 90.2% accurate, 7.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05:\\ \;\;\;\;x + \frac{x \cdot \left(\frac{1}{x} + \frac{z \cdot \left(z \cdot 0.5 + -1\right)}{x}\right)}{y}\\ \mathbf{elif}\;y \leq 4000:\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y \cdot \left(1 + z \cdot \left(1 + z \cdot \left(0.5 + z \cdot 0.16666666666666666\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.05)
   (+ x (/ (* x (+ (/ 1.0 x) (/ (* z (+ (* z 0.5) -1.0)) x))) y))
   (if (<= y 4000.0)
     (+ x (/ 1.0 y))
     (+
      x
      (/
       1.0
       (* y (+ 1.0 (* z (+ 1.0 (* z (+ 0.5 (* z 0.16666666666666666))))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.05) {
		tmp = x + ((x * ((1.0 / x) + ((z * ((z * 0.5) + -1.0)) / x))) / y);
	} else if (y <= 4000.0) {
		tmp = x + (1.0 / y);
	} else {
		tmp = x + (1.0 / (y * (1.0 + (z * (1.0 + (z * (0.5 + (z * 0.16666666666666666))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.05d0)) then
        tmp = x + ((x * ((1.0d0 / x) + ((z * ((z * 0.5d0) + (-1.0d0))) / x))) / y)
    else if (y <= 4000.0d0) then
        tmp = x + (1.0d0 / y)
    else
        tmp = x + (1.0d0 / (y * (1.0d0 + (z * (1.0d0 + (z * (0.5d0 + (z * 0.16666666666666666d0))))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.05) {
		tmp = x + ((x * ((1.0 / x) + ((z * ((z * 0.5) + -1.0)) / x))) / y);
	} else if (y <= 4000.0) {
		tmp = x + (1.0 / y);
	} else {
		tmp = x + (1.0 / (y * (1.0 + (z * (1.0 + (z * (0.5 + (z * 0.16666666666666666))))))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.05:
		tmp = x + ((x * ((1.0 / x) + ((z * ((z * 0.5) + -1.0)) / x))) / y)
	elif y <= 4000.0:
		tmp = x + (1.0 / y)
	else:
		tmp = x + (1.0 / (y * (1.0 + (z * (1.0 + (z * (0.5 + (z * 0.16666666666666666))))))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.05)
		tmp = Float64(x + Float64(Float64(x * Float64(Float64(1.0 / x) + Float64(Float64(z * Float64(Float64(z * 0.5) + -1.0)) / x))) / y));
	elseif (y <= 4000.0)
		tmp = Float64(x + Float64(1.0 / y));
	else
		tmp = Float64(x + Float64(1.0 / Float64(y * Float64(1.0 + Float64(z * Float64(1.0 + Float64(z * Float64(0.5 + Float64(z * 0.16666666666666666)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.05)
		tmp = x + ((x * ((1.0 / x) + ((z * ((z * 0.5) + -1.0)) / x))) / y);
	elseif (y <= 4000.0)
		tmp = x + (1.0 / y);
	else
		tmp = x + (1.0 / (y * (1.0 + (z * (1.0 + (z * (0.5 + (z * 0.16666666666666666))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.05], N[(x + N[(N[(x * N[(N[(1.0 / x), $MachinePrecision] + N[(N[(z * N[(N[(z * 0.5), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4000.0], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / N[(y * N[(1.0 + N[(z * N[(1.0 + N[(z * N[(0.5 + N[(z * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05000000000000004

   1. Initial program 81.3%

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

      1. exp-prod 81.3%

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

      2. +-commutative 81.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in z around 0 71.0%

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

   6. Taylor expanded in x around inf 66.1%

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

   7. Taylor expanded in y around inf 74.4%

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

   if -1.05000000000000004 < y < 4e3

   1. Initial program 85.9%

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

      1. exp-prod 99.8%

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

      2. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 98.7%

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

      1. +-commutative 98.7%

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

   7. Simplified 98.7%

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

   if 4e3 < y

   1. Initial program 88.9%

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

      1. *-commutative 88.9%

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

      2. exp-to-pow 88.9%

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

      3. +-commutative 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

      1. clear-num 100.0%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{y}{e^{-z}}}} \]

      2. inv-pow 100.0%

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

      3. div-inv 100.0%

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

      4. add-sqr-sqrt 35.5%

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

      5. sqrt-unprod 62.1%

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

      6. sqr-neg 62.1%

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

      7. sqrt-unprod 26.7%

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

      8. add-sqr-sqrt 47.9%

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

      9. exp-neg 47.9%

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

      10. add-sqr-sqrt 21.2%

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

      11. sqrt-unprod 85.8%

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

      12. sqr-neg 85.8%

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

      13. sqrt-unprod 64.5%

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

      14. add-sqr-sqrt 100.0%

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

   9. Applied egg-rr 100.0%

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

       1. unpow-1 100.0%

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

   11. Simplified 100.0%

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

   12. Taylor expanded in z around 0 85.8%

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

       1. *-commutative 85.8%

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

   14. Simplified 85.8%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05:\\ \;\;\;\;x + \frac{x \cdot \left(\frac{1}{x} + \frac{z \cdot \left(z \cdot 0.5 + -1\right)}{x}\right)}{y}\\ \mathbf{elif}\;y \leq 4000:\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y \cdot \left(1 + z \cdot \left(1 + z \cdot \left(0.5 + z \cdot 0.16666666666666666\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.5% accurate, 7.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.96:\\ \;\;\;\;x + \frac{1 + z \cdot \left(\frac{z \cdot \left(y \cdot 0.5\right)}{y} + -1\right)}{y}\\ \mathbf{elif}\;y \leq 2100:\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y \cdot \left(1 + z \cdot \left(1 + z \cdot \left(0.5 + z \cdot 0.16666666666666666\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -0.96)
   (+ x (/ (+ 1.0 (* z (+ (/ (* z (* y 0.5)) y) -1.0))) y))
   (if (<= y 2100.0)
     (+ x (/ 1.0 y))
     (+
      x
      (/
       1.0
       (* y (+ 1.0 (* z (+ 1.0 (* z (+ 0.5 (* z 0.16666666666666666))))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.96) {
		tmp = x + ((1.0 + (z * (((z * (y * 0.5)) / y) + -1.0))) / y);
	} else if (y <= 2100.0) {
		tmp = x + (1.0 / y);
	} else {
		tmp = x + (1.0 / (y * (1.0 + (z * (1.0 + (z * (0.5 + (z * 0.16666666666666666))))))));
	}
	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 <= (-0.96d0)) then
        tmp = x + ((1.0d0 + (z * (((z * (y * 0.5d0)) / y) + (-1.0d0)))) / y)
    else if (y <= 2100.0d0) then
        tmp = x + (1.0d0 / y)
    else
        tmp = x + (1.0d0 / (y * (1.0d0 + (z * (1.0d0 + (z * (0.5d0 + (z * 0.16666666666666666d0))))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.96) {
		tmp = x + ((1.0 + (z * (((z * (y * 0.5)) / y) + -1.0))) / y);
	} else if (y <= 2100.0) {
		tmp = x + (1.0 / y);
	} else {
		tmp = x + (1.0 / (y * (1.0 + (z * (1.0 + (z * (0.5 + (z * 0.16666666666666666))))))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -0.96:
		tmp = x + ((1.0 + (z * (((z * (y * 0.5)) / y) + -1.0))) / y)
	elif y <= 2100.0:
		tmp = x + (1.0 / y)
	else:
		tmp = x + (1.0 / (y * (1.0 + (z * (1.0 + (z * (0.5 + (z * 0.16666666666666666))))))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -0.96)
		tmp = Float64(x + Float64(Float64(1.0 + Float64(z * Float64(Float64(Float64(z * Float64(y * 0.5)) / y) + -1.0))) / y));
	elseif (y <= 2100.0)
		tmp = Float64(x + Float64(1.0 / y));
	else
		tmp = Float64(x + Float64(1.0 / Float64(y * Float64(1.0 + Float64(z * Float64(1.0 + Float64(z * Float64(0.5 + Float64(z * 0.16666666666666666)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -0.96)
		tmp = x + ((1.0 + (z * (((z * (y * 0.5)) / y) + -1.0))) / y);
	elseif (y <= 2100.0)
		tmp = x + (1.0 / y);
	else
		tmp = x + (1.0 / (y * (1.0 + (z * (1.0 + (z * (0.5 + (z * 0.16666666666666666))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -0.96], N[(x + N[(N[(1.0 + N[(z * N[(N[(N[(z * N[(y * 0.5), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2100.0], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / N[(y * N[(1.0 + N[(z * N[(1.0 + N[(z * N[(0.5 + N[(z * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.95999999999999996

   1. Initial program 81.3%

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

      1. exp-prod 81.3%

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

      2. +-commutative 81.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in z around 0 71.0%

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

   6. Taylor expanded in y around 0 72.2%

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

      1. associate-*r* 72.2%

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

      2. distribute-rgt-out 72.2%

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

   8. Simplified 72.2%

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

   9. Taylor expanded in y around inf 72.2%

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

       1. associate-*r* 72.2%

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

       2. *-commutative 72.2%

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

       3. *-commutative 72.2%

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

   11. Simplified 72.2%

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

   if -0.95999999999999996 < y < 2100

   1. Initial program 85.9%

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

      1. exp-prod 99.8%

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

      2. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 98.7%

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

      1. +-commutative 98.7%

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

   7. Simplified 98.7%

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

   if 2100 < y

   1. Initial program 88.9%

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

      1. *-commutative 88.9%

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

      2. exp-to-pow 88.9%

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

      3. +-commutative 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

      1. clear-num 100.0%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{y}{e^{-z}}}} \]

      2. inv-pow 100.0%

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

      3. div-inv 100.0%

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

      4. add-sqr-sqrt 35.5%

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

      5. sqrt-unprod 62.1%

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

      6. sqr-neg 62.1%

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

      7. sqrt-unprod 26.7%

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

      8. add-sqr-sqrt 47.9%

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

      9. exp-neg 47.9%

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

      10. add-sqr-sqrt 21.2%

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

      11. sqrt-unprod 85.8%

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

      12. sqr-neg 85.8%

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

      13. sqrt-unprod 64.5%

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

      14. add-sqr-sqrt 100.0%

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

   9. Applied egg-rr 100.0%

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

       1. unpow-1 100.0%

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

   11. Simplified 100.0%

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

   12. Taylor expanded in z around 0 85.8%

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

       1. *-commutative 85.8%

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

   14. Simplified 85.8%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.96:\\ \;\;\;\;x + \frac{1 + z \cdot \left(\frac{z \cdot \left(y \cdot 0.5\right)}{y} + -1\right)}{y}\\ \mathbf{elif}\;y \leq 2100:\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y \cdot \left(1 + z \cdot \left(1 + z \cdot \left(0.5 + z \cdot 0.16666666666666666\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.5% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(y \cdot 0.5\right)\\ \mathbf{if}\;y \leq -1.05:\\ \;\;\;\;x + \frac{1 + z \cdot \left(\frac{t\_0}{y} + -1\right)}{y}\\ \mathbf{elif}\;y \leq 2100:\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y + z \cdot \left(y + t\_0\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* y 0.5))))
   (if (<= y -1.05)
     (+ x (/ (+ 1.0 (* z (+ (/ t_0 y) -1.0))) y))
     (if (<= y 2100.0) (+ x (/ 1.0 y)) (+ x (/ 1.0 (+ y (* z (+ y t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (y * 0.5);
	double tmp;
	if (y <= -1.05) {
		tmp = x + ((1.0 + (z * ((t_0 / y) + -1.0))) / y);
	} else if (y <= 2100.0) {
		tmp = x + (1.0 / y);
	} else {
		tmp = x + (1.0 / (y + (z * (y + 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 = z * (y * 0.5d0)
    if (y <= (-1.05d0)) then
        tmp = x + ((1.0d0 + (z * ((t_0 / y) + (-1.0d0)))) / y)
    else if (y <= 2100.0d0) then
        tmp = x + (1.0d0 / y)
    else
        tmp = x + (1.0d0 / (y + (z * (y + t_0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (y * 0.5);
	double tmp;
	if (y <= -1.05) {
		tmp = x + ((1.0 + (z * ((t_0 / y) + -1.0))) / y);
	} else if (y <= 2100.0) {
		tmp = x + (1.0 / y);
	} else {
		tmp = x + (1.0 / (y + (z * (y + t_0))));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (y * 0.5)
	tmp = 0
	if y <= -1.05:
		tmp = x + ((1.0 + (z * ((t_0 / y) + -1.0))) / y)
	elif y <= 2100.0:
		tmp = x + (1.0 / y)
	else:
		tmp = x + (1.0 / (y + (z * (y + t_0))))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(y * 0.5))
	tmp = 0.0
	if (y <= -1.05)
		tmp = Float64(x + Float64(Float64(1.0 + Float64(z * Float64(Float64(t_0 / y) + -1.0))) / y));
	elseif (y <= 2100.0)
		tmp = Float64(x + Float64(1.0 / y));
	else
		tmp = Float64(x + Float64(1.0 / Float64(y + Float64(z * Float64(y + t_0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (y * 0.5);
	tmp = 0.0;
	if (y <= -1.05)
		tmp = x + ((1.0 + (z * ((t_0 / y) + -1.0))) / y);
	elseif (y <= 2100.0)
		tmp = x + (1.0 / y);
	else
		tmp = x + (1.0 / (y + (z * (y + t_0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(y * 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.05], N[(x + N[(N[(1.0 + N[(z * N[(N[(t$95$0 / y), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2100.0], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / N[(y + N[(z * N[(y + t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05000000000000004

   1. Initial program 81.3%

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

      1. exp-prod 81.3%

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

      2. +-commutative 81.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in z around 0 71.0%

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

   6. Taylor expanded in y around 0 72.2%

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

      1. associate-*r* 72.2%

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

      2. distribute-rgt-out 72.2%

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

   8. Simplified 72.2%

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

   9. Taylor expanded in y around inf 72.2%

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

       1. associate-*r* 72.2%

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

       2. *-commutative 72.2%

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

       3. *-commutative 72.2%

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

   11. Simplified 72.2%

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

   if -1.05000000000000004 < y < 2100

   1. Initial program 85.9%

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

      1. exp-prod 99.8%

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

      2. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 98.7%

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

      1. +-commutative 98.7%

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

   7. Simplified 98.7%

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

   if 2100 < y

   1. Initial program 88.9%

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

      1. *-commutative 88.9%

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

      2. exp-to-pow 88.9%

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

      3. +-commutative 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

      1. clear-num 100.0%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{y}{e^{-z}}}} \]

      2. inv-pow 100.0%

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

      3. div-inv 100.0%

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

      4. add-sqr-sqrt 35.5%

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

      5. sqrt-unprod 62.1%

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

      6. sqr-neg 62.1%

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

      7. sqrt-unprod 26.7%

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

      8. add-sqr-sqrt 47.9%

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

      9. exp-neg 47.9%

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

      10. add-sqr-sqrt 21.2%

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

      11. sqrt-unprod 85.8%

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

      12. sqr-neg 85.8%

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

      13. sqrt-unprod 64.5%

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

      14. add-sqr-sqrt 100.0%

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

   9. Applied egg-rr 100.0%

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

       1. unpow-1 100.0%

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

   11. Simplified 100.0%

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

   12. Taylor expanded in z around 0 85.8%

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

       1. associate-*r* 85.8%

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

       2. *-commutative 85.8%

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

       3. *-commutative 85.8%

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

   14. Simplified 85.8%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05:\\ \;\;\;\;x + \frac{1 + z \cdot \left(\frac{z \cdot \left(y \cdot 0.5\right)}{y} + -1\right)}{y}\\ \mathbf{elif}\;y \leq 2100:\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y + z \cdot \left(y + z \cdot \left(y \cdot 0.5\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.2% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.55:\\ \;\;\;\;x + \left(\frac{1}{y} + \frac{z \cdot \left(z \cdot 0.5 + -1\right)}{y}\right)\\ \mathbf{elif}\;y \leq 2100:\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y + z \cdot \left(y + z \cdot \left(y \cdot 0.5\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -0.55)
   (+ x (+ (/ 1.0 y) (/ (* z (+ (* z 0.5) -1.0)) y)))
   (if (<= y 2100.0)
     (+ x (/ 1.0 y))
     (+ x (/ 1.0 (+ y (* z (+ y (* z (* y 0.5))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.55) {
		tmp = x + ((1.0 / y) + ((z * ((z * 0.5) + -1.0)) / y));
	} else if (y <= 2100.0) {
		tmp = x + (1.0 / y);
	} else {
		tmp = x + (1.0 / (y + (z * (y + (z * (y * 0.5))))));
	}
	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 <= (-0.55d0)) then
        tmp = x + ((1.0d0 / y) + ((z * ((z * 0.5d0) + (-1.0d0))) / y))
    else if (y <= 2100.0d0) then
        tmp = x + (1.0d0 / y)
    else
        tmp = x + (1.0d0 / (y + (z * (y + (z * (y * 0.5d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.55) {
		tmp = x + ((1.0 / y) + ((z * ((z * 0.5) + -1.0)) / y));
	} else if (y <= 2100.0) {
		tmp = x + (1.0 / y);
	} else {
		tmp = x + (1.0 / (y + (z * (y + (z * (y * 0.5))))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -0.55:
		tmp = x + ((1.0 / y) + ((z * ((z * 0.5) + -1.0)) / y))
	elif y <= 2100.0:
		tmp = x + (1.0 / y)
	else:
		tmp = x + (1.0 / (y + (z * (y + (z * (y * 0.5))))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -0.55)
		tmp = Float64(x + Float64(Float64(1.0 / y) + Float64(Float64(z * Float64(Float64(z * 0.5) + -1.0)) / y)));
	elseif (y <= 2100.0)
		tmp = Float64(x + Float64(1.0 / y));
	else
		tmp = Float64(x + Float64(1.0 / Float64(y + Float64(z * Float64(y + Float64(z * Float64(y * 0.5)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -0.55)
		tmp = x + ((1.0 / y) + ((z * ((z * 0.5) + -1.0)) / y));
	elseif (y <= 2100.0)
		tmp = x + (1.0 / y);
	else
		tmp = x + (1.0 / (y + (z * (y + (z * (y * 0.5))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -0.55], N[(x + N[(N[(1.0 / y), $MachinePrecision] + N[(N[(z * N[(N[(z * 0.5), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2100.0], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / N[(y + N[(z * N[(y + N[(z * N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.55000000000000004

   1. Initial program 81.3%

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

      1. exp-prod 81.3%

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

      2. +-commutative 81.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in z around 0 71.0%

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

   6. Taylor expanded in y around inf 71.0%

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

   if -0.55000000000000004 < y < 2100

   1. Initial program 85.9%

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

      1. exp-prod 99.8%

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

      2. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 98.7%

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

      1. +-commutative 98.7%

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

   7. Simplified 98.7%

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

   if 2100 < y

   1. Initial program 88.9%

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

      1. *-commutative 88.9%

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

      2. exp-to-pow 88.9%

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

      3. +-commutative 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

      1. clear-num 100.0%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{y}{e^{-z}}}} \]

      2. inv-pow 100.0%

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

      3. div-inv 100.0%

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

      4. add-sqr-sqrt 35.5%

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

      5. sqrt-unprod 62.1%

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

      6. sqr-neg 62.1%

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

      7. sqrt-unprod 26.7%

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

      8. add-sqr-sqrt 47.9%

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

      9. exp-neg 47.9%

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

      10. add-sqr-sqrt 21.2%

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

      11. sqrt-unprod 85.8%

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

      12. sqr-neg 85.8%

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

      13. sqrt-unprod 64.5%

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

      14. add-sqr-sqrt 100.0%

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

   9. Applied egg-rr 100.0%

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

       1. unpow-1 100.0%

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

   11. Simplified 100.0%

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

   12. Taylor expanded in z around 0 85.8%

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

       1. associate-*r* 85.8%

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

       2. *-commutative 85.8%

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

       3. *-commutative 85.8%

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

   14. Simplified 85.8%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.55:\\ \;\;\;\;x + \left(\frac{1}{y} + \frac{z \cdot \left(z \cdot 0.5 + -1\right)}{y}\right)\\ \mathbf{elif}\;y \leq 2100:\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y + z \cdot \left(y + z \cdot \left(y \cdot 0.5\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 87.7% accurate, 10.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.82:\\ \;\;\;\;x + \left(\frac{1}{y} + \frac{z \cdot \left(z \cdot 0.5 + -1\right)}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -0.82)
   (+ x (+ (/ 1.0 y) (/ (* z (+ (* z 0.5) -1.0)) y)))
   (+ x (/ 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.82) {
		tmp = x + ((1.0 / y) + ((z * ((z * 0.5) + -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 <= (-0.82d0)) then
        tmp = x + ((1.0d0 / y) + ((z * ((z * 0.5d0) + (-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 <= -0.82) {
		tmp = x + ((1.0 / y) + ((z * ((z * 0.5) + -1.0)) / y));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -0.82:
		tmp = x + ((1.0 / y) + ((z * ((z * 0.5) + -1.0)) / y))
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -0.82)
		tmp = Float64(x + Float64(Float64(1.0 / y) + Float64(Float64(z * Float64(Float64(z * 0.5) + -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 <= -0.82)
		tmp = x + ((1.0 / y) + ((z * ((z * 0.5) + -1.0)) / y));
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -0.82], N[(x + N[(N[(1.0 / y), $MachinePrecision] + N[(N[(z * N[(N[(z * 0.5), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.819999999999999951

   1. Initial program 81.3%

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

      1. exp-prod 81.3%

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

      2. +-commutative 81.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in z around 0 71.0%

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

   6. Taylor expanded in y around inf 71.0%

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

   if -0.819999999999999951 < y

   1. Initial program 87.0%

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

      1. exp-prod 95.8%

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

      2. +-commutative 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in y around inf 91.0%

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

      1. +-commutative 91.0%

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

   7. Simplified 91.0%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.82:\\ \;\;\;\;x + \left(\frac{1}{y} + \frac{z \cdot \left(z \cdot 0.5 + -1\right)}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 87.7% accurate, 11.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.96:\\ \;\;\;\;x + \frac{1 + z \cdot \left(z \cdot 0.5 + -1\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -0.96)
   (+ x (/ (+ 1.0 (* z (+ (* z 0.5) -1.0))) y))
   (+ x (/ 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.96) {
		tmp = x + ((1.0 + (z * ((z * 0.5) + -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 <= (-0.96d0)) then
        tmp = x + ((1.0d0 + (z * ((z * 0.5d0) + (-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 <= -0.96) {
		tmp = x + ((1.0 + (z * ((z * 0.5) + -1.0))) / y);
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -0.96:
		tmp = x + ((1.0 + (z * ((z * 0.5) + -1.0))) / y)
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -0.96)
		tmp = Float64(x + Float64(Float64(1.0 + Float64(z * Float64(Float64(z * 0.5) + -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 <= -0.96)
		tmp = x + ((1.0 + (z * ((z * 0.5) + -1.0))) / y);
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -0.96], N[(x + N[(N[(1.0 + N[(z * N[(N[(z * 0.5), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.95999999999999996

   1. Initial program 81.3%

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

      1. exp-prod 81.3%

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

      2. +-commutative 81.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in z around 0 71.0%

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

   6. Taylor expanded in y around inf 71.0%

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

      1. *-commutative 71.0%

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

   8. Simplified 71.0%

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

   if -0.95999999999999996 < y

   1. Initial program 87.0%

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

      1. exp-prod 95.8%

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

      2. +-commutative 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in y around inf 91.0%

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

      1. +-commutative 91.0%

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

   7. Simplified 91.0%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.96:\\ \;\;\;\;x + \frac{1 + z \cdot \left(z \cdot 0.5 + -1\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 67.7% accurate, 16.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -28500000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-67}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -28500000.0) x (if (<= y 1.3e-67) (/ 1.0 y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -28500000.0) {
		tmp = x;
	} else if (y <= 1.3e-67) {
		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 <= (-28500000.0d0)) then
        tmp = x
    else if (y <= 1.3d-67) 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 <= -28500000.0) {
		tmp = x;
	} else if (y <= 1.3e-67) {
		tmp = 1.0 / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -28500000.0:
		tmp = x
	elif y <= 1.3e-67:
		tmp = 1.0 / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -28500000.0)
		tmp = x;
	elseif (y <= 1.3e-67)
		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 <= -28500000.0)
		tmp = x;
	elseif (y <= 1.3e-67)
		tmp = 1.0 / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -28500000.0], x, If[LessEqual[y, 1.3e-67], N[(1.0 / y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -2.85e7 or 1.2999999999999999e-67 < y

   1. Initial program 86.4%

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

      1. exp-prod 86.3%

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

      2. +-commutative 86.3%

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

   3. Simplified 86.3%

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

   5. Taylor expanded in x around inf 68.6%

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

   if -2.85e7 < y < 1.2999999999999999e-67

   1. Initial program 82.6%

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

      1. exp-prod 99.8%

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

      2. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 84.7%

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

Alternative 13: 85.2% 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 85.1%

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

   1. exp-prod 91.0%

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

   2. +-commutative 91.0%

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

3. Simplified 91.0%

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

5. Taylor expanded in y around inf 82.4%

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

   1. +-commutative 82.4%

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

7. Simplified 82.4%

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

8. Final simplification 82.4%

   \[\leadsto x + \frac{1}{y} \]
9. Add Preprocessing

Alternative 14: 49.8% accurate, 211.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 85.1%

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

   1. exp-prod 91.0%

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

   2. +-commutative 91.0%

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

3. Simplified 91.0%

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

5. Taylor expanded in x around inf 50.7%

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

Developer target: 91.9% 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 2024103 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, G"
  :precision binary64

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

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