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

Percentage Accurate: 84.9% → 99.7%

Time: 15.2s

Alternatives: 12

Speedup: 17.6×

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: 84.9% 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

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+50}:\\ \;\;\;\;x + \frac{e^{-z}}{y}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-7}:\\ \;\;\;\;x + \frac{{\left(e^{y}\right)}^{\log \left(\frac{y}{y + z}\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y \cdot e^{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.3e+50)
   (+ x (/ (exp (- z)) y))
   (if (<= y 5.5e-7)
     (+ 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 <= -3.3e+50) {
		tmp = x + (exp(-z) / y);
	} else if (y <= 5.5e-7) {
		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 <= (-3.3d+50)) then
        tmp = x + (exp(-z) / y)
    else if (y <= 5.5d-7) 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 <= -3.3e+50) {
		tmp = x + (Math.exp(-z) / y);
	} else if (y <= 5.5e-7) {
		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 <= -3.3e+50:
		tmp = x + (math.exp(-z) / y)
	elif y <= 5.5e-7:
		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 <= -3.3e+50)
		tmp = Float64(x + Float64(exp(Float64(-z)) / y));
	elseif (y <= 5.5e-7)
		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 <= -3.3e+50)
		tmp = x + (exp(-z) / y);
	elseif (y <= 5.5e-7)
		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, -3.3e+50], N[(x + N[(N[Exp[(-z)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e-7], 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 < -3.3e50

   1. Initial program 74.8%

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

      1. *-commutative 74.8%

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

      2. exp-to-pow 74.8%

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

      3. +-commutative 74.8%

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

   3. Simplified 74.8%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   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 -3.3e50 < y < 5.5000000000000003e-7

   1. Initial program 89.7%

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

      1. exp-prod 99.7%

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

      2. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   if 5.5000000000000003e-7 < y

   1. Initial program 82.8%

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

      1. *-commutative 82.8%

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

      2. exp-to-pow 82.8%

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

      3. +-commutative 82.8%

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

   3. Simplified 82.8%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   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 53.2%

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

      5. sqrt-unprod 79.3%

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

      6. sqr-neg 79.3%

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

      7. sqrt-unprod 26.1%

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

      8. add-sqr-sqrt 66.6%

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

      9. exp-neg 66.6%

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

      10. add-sqr-sqrt 40.5%

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

      11. sqrt-unprod 87.3%

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

      12. sqr-neg 87.3%

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

      13. sqrt-unprod 46.8%

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

      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 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+50}:\\ \;\;\;\;x + \frac{e^{-z}}{y}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-7}:\\ \;\;\;\;x + \frac{{\left(e^{y}\right)}^{\log \left(\frac{y}{y + z}\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y \cdot e^{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1220:\\ \;\;\;\;x + \frac{e^{-z}}{y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-7}:\\ \;\;\;\;\frac{1 + y \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y \cdot e^{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1220.0)
   (+ x (/ (exp (- z)) y))
   (if (<= y 5.8e-7) (/ (+ 1.0 (* y x)) y) (+ x (/ 1.0 (* y (exp z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1220.0) {
		tmp = x + (exp(-z) / y);
	} else if (y <= 5.8e-7) {
		tmp = (1.0 + (y * x)) / 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 <= (-1220.0d0)) then
        tmp = x + (exp(-z) / y)
    else if (y <= 5.8d-7) then
        tmp = (1.0d0 + (y * x)) / 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 <= -1220.0) {
		tmp = x + (Math.exp(-z) / y);
	} else if (y <= 5.8e-7) {
		tmp = (1.0 + (y * x)) / y;
	} else {
		tmp = x + (1.0 / (y * Math.exp(z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1220.0:
		tmp = x + (math.exp(-z) / y)
	elif y <= 5.8e-7:
		tmp = (1.0 + (y * x)) / y
	else:
		tmp = x + (1.0 / (y * math.exp(z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1220.0)
		tmp = Float64(x + Float64(exp(Float64(-z)) / y));
	elseif (y <= 5.8e-7)
		tmp = Float64(Float64(1.0 + Float64(y * x)) / 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 <= -1220.0)
		tmp = x + (exp(-z) / y);
	elseif (y <= 5.8e-7)
		tmp = (1.0 + (y * x)) / y;
	else
		tmp = x + (1.0 / (y * exp(z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1220.0], N[(x + N[(N[Exp[(-z)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e-7], N[(N[(1.0 + N[(y * x), $MachinePrecision]), $MachinePrecision] / y), $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 < -1220

   1. Initial program 78.3%

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

      1. *-commutative 78.3%

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

      2. exp-to-pow 78.3%

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

      3. +-commutative 78.3%

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

   3. Simplified 78.3%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   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 -1220 < y < 5.7999999999999995e-7

   1. Initial program 88.4%

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

      1. exp-prod 99.6%

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

      2. +-commutative 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 99.0%

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

      1. +-commutative 99.0%

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

   7. Simplified 99.0%

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

   8. Taylor expanded in y around 0 99.0%

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

      1. *-commutative 99.0%

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

   10. Simplified 99.0%

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

   if 5.7999999999999995e-7 < y

   1. Initial program 82.8%

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

      1. *-commutative 82.8%

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

      2. exp-to-pow 82.8%

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

      3. +-commutative 82.8%

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

   3. Simplified 82.8%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   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 53.2%

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

      5. sqrt-unprod 79.3%

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

      6. sqr-neg 79.3%

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

      7. sqrt-unprod 26.1%

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

      8. add-sqr-sqrt 66.6%

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

      9. exp-neg 66.6%

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

      10. add-sqr-sqrt 40.5%

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

      11. sqrt-unprod 87.3%

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

      12. sqr-neg 87.3%

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

      13. sqrt-unprod 46.8%

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

      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 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1220:\\ \;\;\;\;x + \frac{e^{-z}}{y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-7}:\\ \;\;\;\;\frac{1 + y \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y \cdot e^{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1220 \lor \neg \left(y \leq 2.25 \cdot 10^{-7}\right):\\ \;\;\;\;x + \frac{e^{-z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + y \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1220.0) (not (<= y 2.25e-7)))
   (+ x (/ (exp (- z)) y))
   (/ (+ 1.0 (* y x)) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1220.0) || !(y <= 2.25e-7)) {
		tmp = x + (exp(-z) / y);
	} else {
		tmp = (1.0 + (y * x)) / 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 <= (-1220.0d0)) .or. (.not. (y <= 2.25d-7))) then
        tmp = x + (exp(-z) / y)
    else
        tmp = (1.0d0 + (y * x)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1220.0) || !(y <= 2.25e-7)) {
		tmp = x + (Math.exp(-z) / y);
	} else {
		tmp = (1.0 + (y * x)) / y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1220.0) or not (y <= 2.25e-7):
		tmp = x + (math.exp(-z) / y)
	else:
		tmp = (1.0 + (y * x)) / y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1220.0) || !(y <= 2.25e-7))
		tmp = Float64(x + Float64(exp(Float64(-z)) / y));
	else
		tmp = Float64(Float64(1.0 + Float64(y * x)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1220.0) || ~((y <= 2.25e-7)))
		tmp = x + (exp(-z) / y);
	else
		tmp = (1.0 + (y * x)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1220.0], N[Not[LessEqual[y, 2.25e-7]], $MachinePrecision]], N[(x + N[(N[Exp[(-z)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(y * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1220 or 2.2499999999999999e-7 < y

   1. Initial program 80.1%

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

      1. *-commutative 80.1%

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

      2. exp-to-pow 80.1%

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

      3. +-commutative 80.1%

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

   3. Simplified 80.1%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   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 -1220 < y < 2.2499999999999999e-7

   1. Initial program 88.4%

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

      1. exp-prod 99.6%

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

      2. +-commutative 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 99.0%

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

      1. +-commutative 99.0%

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

   7. Simplified 99.0%

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

   8. Taylor expanded in y around 0 99.0%

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

      1. *-commutative 99.0%

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

   10. Simplified 99.0%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1220 \lor \neg \left(y \leq 2.25 \cdot 10^{-7}\right):\\ \;\;\;\;x + \frac{e^{-z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + y \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1200:\\ \;\;\;\;\frac{e^{-z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1200.0) (/ (exp (- z)) y) (+ x (/ 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1200.0) {
		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 <= (-1200.0d0)) 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 <= -1200.0) {
		tmp = Math.exp(-z) / y;
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1200.0:
		tmp = math.exp(-z) / y
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1200.0)
		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 <= -1200.0)
		tmp = exp(-z) / y;
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1200.0], 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 < -1200

   1. Initial program 44.3%

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

      1. *-commutative 44.3%

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

      2. exp-to-pow 44.3%

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

      3. +-commutative 44.3%

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

   3. Simplified 44.3%

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

   5. Taylor expanded in y around inf 82.2%

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

      1. mul-1-neg 82.2%

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

   7. Simplified 82.2%

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

      1. clear-num 82.2%

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

      2. inv-pow 82.2%

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

      3. div-inv 82.2%

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

      4. add-sqr-sqrt 82.2%

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

      5. sqrt-unprod 82.2%

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

      6. sqr-neg 82.2%

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

      7. sqrt-unprod 0.0%

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

      8. add-sqr-sqrt 5.9%

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

      9. exp-neg 5.9%

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

      10. add-sqr-sqrt 5.9%

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

      11. sqrt-unprod 5.9%

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

      12. sqr-neg 5.9%

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

      13. sqrt-unprod 0.0%

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

      14. add-sqr-sqrt 82.2%

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

   9. Applied egg-rr 82.2%

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

       1. unpow-1 82.2%

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

   11. Simplified 82.2%

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

   12. Taylor expanded in x around 0 82.2%

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

       1. *-commutative 82.2%

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

       2. associate-/r* 82.2%

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

       3. rec-exp 82.2%

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

   14. Simplified 82.2%

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

   if -1200 < z

   1. Initial program 93.8%

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

      1. exp-prod 97.0%

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

      2. +-commutative 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in y around inf 95.7%

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

      1. +-commutative 95.7%

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

   7. Simplified 95.7%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1200:\\ \;\;\;\;\frac{e^{-z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.3% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+14}:\\ \;\;\;\;x + \frac{x \cdot \left(\frac{1}{x} + \frac{z \cdot \left(z \cdot 0.5 + -1\right)}{x}\right)}{y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-7}:\\ \;\;\;\;\frac{1 + y \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y + y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1e+14)
   (+ x (/ (* x (+ (/ 1.0 x) (/ (* z (+ (* z 0.5) -1.0)) x))) y))
   (if (<= y 5.8e-7) (/ (+ 1.0 (* y x)) y) (+ x (/ 1.0 (+ y (* y z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1e+14) {
		tmp = x + ((x * ((1.0 / x) + ((z * ((z * 0.5) + -1.0)) / x))) / y);
	} else if (y <= 5.8e-7) {
		tmp = (1.0 + (y * x)) / y;
	} else {
		tmp = x + (1.0 / (y + (y * 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 <= (-1d+14)) then
        tmp = x + ((x * ((1.0d0 / x) + ((z * ((z * 0.5d0) + (-1.0d0))) / x))) / y)
    else if (y <= 5.8d-7) then
        tmp = (1.0d0 + (y * x)) / y
    else
        tmp = x + (1.0d0 / (y + (y * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1e+14) {
		tmp = x + ((x * ((1.0 / x) + ((z * ((z * 0.5) + -1.0)) / x))) / y);
	} else if (y <= 5.8e-7) {
		tmp = (1.0 + (y * x)) / y;
	} else {
		tmp = x + (1.0 / (y + (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1e+14:
		tmp = x + ((x * ((1.0 / x) + ((z * ((z * 0.5) + -1.0)) / x))) / y)
	elif y <= 5.8e-7:
		tmp = (1.0 + (y * x)) / y
	else:
		tmp = x + (1.0 / (y + (y * z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1e+14)
		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 <= 5.8e-7)
		tmp = Float64(Float64(1.0 + Float64(y * x)) / y);
	else
		tmp = Float64(x + Float64(1.0 / Float64(y + Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1e+14)
		tmp = x + ((x * ((1.0 / x) + ((z * ((z * 0.5) + -1.0)) / x))) / y);
	elseif (y <= 5.8e-7)
		tmp = (1.0 + (y * x)) / y;
	else
		tmp = x + (1.0 / (y + (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1e+14], 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, 5.8e-7], N[(N[(1.0 + N[(y * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x + N[(1.0 / N[(y + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1e14

   1. Initial program 78.3%

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

      1. exp-prod 78.3%

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

      2. +-commutative 78.3%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in z around 0 70.0%

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

   6. Taylor expanded in x around inf 68.8%

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

   7. Taylor expanded in y around inf 73.1%

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

   if -1e14 < y < 5.7999999999999995e-7

   1. Initial program 88.4%

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

      1. exp-prod 99.6%

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

      2. +-commutative 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 99.0%

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

      1. +-commutative 99.0%

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

   7. Simplified 99.0%

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

   8. Taylor expanded in y around 0 99.0%

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

      1. *-commutative 99.0%

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

   10. Simplified 99.0%

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

   if 5.7999999999999995e-7 < y

   1. Initial program 82.8%

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

      1. *-commutative 82.8%

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

      2. exp-to-pow 82.8%

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

      3. +-commutative 82.8%

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

   3. Simplified 82.8%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   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 53.2%

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

      5. sqrt-unprod 79.3%

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

      6. sqr-neg 79.3%

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

      7. sqrt-unprod 26.1%

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

      8. add-sqr-sqrt 66.6%

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

      9. exp-neg 66.6%

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

      10. add-sqr-sqrt 40.5%

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

      11. sqrt-unprod 87.3%

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

      12. sqr-neg 87.3%

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

      13. sqrt-unprod 46.8%

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

      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 84.6%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+14}:\\ \;\;\;\;x + \frac{x \cdot \left(\frac{1}{x} + \frac{z \cdot \left(z \cdot 0.5 + -1\right)}{x}\right)}{y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-7}:\\ \;\;\;\;\frac{1 + y \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y + y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.1% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1220:\\ \;\;\;\;x + \frac{1 + z \cdot \left(\frac{z \cdot \left(y \cdot 0.5\right)}{y} + -1\right)}{y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-7}:\\ \;\;\;\;\frac{1 + y \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y + y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1220.0)
   (+ x (/ (+ 1.0 (* z (+ (/ (* z (* y 0.5)) y) -1.0))) y))
   (if (<= y 5.8e-7) (/ (+ 1.0 (* y x)) y) (+ x (/ 1.0 (+ y (* y z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1220.0) {
		tmp = x + ((1.0 + (z * (((z * (y * 0.5)) / y) + -1.0))) / y);
	} else if (y <= 5.8e-7) {
		tmp = (1.0 + (y * x)) / y;
	} else {
		tmp = x + (1.0 / (y + (y * 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 <= (-1220.0d0)) then
        tmp = x + ((1.0d0 + (z * (((z * (y * 0.5d0)) / y) + (-1.0d0)))) / y)
    else if (y <= 5.8d-7) then
        tmp = (1.0d0 + (y * x)) / y
    else
        tmp = x + (1.0d0 / (y + (y * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1220.0) {
		tmp = x + ((1.0 + (z * (((z * (y * 0.5)) / y) + -1.0))) / y);
	} else if (y <= 5.8e-7) {
		tmp = (1.0 + (y * x)) / y;
	} else {
		tmp = x + (1.0 / (y + (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1220.0:
		tmp = x + ((1.0 + (z * (((z * (y * 0.5)) / y) + -1.0))) / y)
	elif y <= 5.8e-7:
		tmp = (1.0 + (y * x)) / y
	else:
		tmp = x + (1.0 / (y + (y * z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1220.0)
		tmp = Float64(x + Float64(Float64(1.0 + Float64(z * Float64(Float64(Float64(z * Float64(y * 0.5)) / y) + -1.0))) / y));
	elseif (y <= 5.8e-7)
		tmp = Float64(Float64(1.0 + Float64(y * x)) / y);
	else
		tmp = Float64(x + Float64(1.0 / Float64(y + Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1220.0)
		tmp = x + ((1.0 + (z * (((z * (y * 0.5)) / y) + -1.0))) / y);
	elseif (y <= 5.8e-7)
		tmp = (1.0 + (y * x)) / y;
	else
		tmp = x + (1.0 / (y + (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1220.0], 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, 5.8e-7], N[(N[(1.0 + N[(y * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x + N[(1.0 / N[(y + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1220

   1. Initial program 78.3%

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

      1. exp-prod 78.3%

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

      2. +-commutative 78.3%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in z around 0 70.0%

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

   6. Taylor expanded in y around 0 71.1%

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

      1. associate-*r* 71.1%

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

      2. distribute-rgt-out 71.1%

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

   8. Simplified 71.1%

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

   9. Taylor expanded in y around inf 71.1%

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

       1. *-commutative 71.1%

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

       2. *-commutative 71.1%

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

       3. associate-*r* 71.1%

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

   11. Simplified 71.1%

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

   if -1220 < y < 5.7999999999999995e-7

   1. Initial program 88.4%

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

      1. exp-prod 99.6%

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

      2. +-commutative 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 99.0%

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

      1. +-commutative 99.0%

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

   7. Simplified 99.0%

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

   8. Taylor expanded in y around 0 99.0%

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

      1. *-commutative 99.0%

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

   10. Simplified 99.0%

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

   if 5.7999999999999995e-7 < y

   1. Initial program 82.8%

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

      1. *-commutative 82.8%

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

      2. exp-to-pow 82.8%

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

      3. +-commutative 82.8%

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

   3. Simplified 82.8%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   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 53.2%

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

      5. sqrt-unprod 79.3%

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

      6. sqr-neg 79.3%

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

      7. sqrt-unprod 26.1%

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

      8. add-sqr-sqrt 66.6%

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

      9. exp-neg 66.6%

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

      10. add-sqr-sqrt 40.5%

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

      11. sqrt-unprod 87.3%

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

      12. sqr-neg 87.3%

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

      13. sqrt-unprod 46.8%

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

      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 84.6%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1220:\\ \;\;\;\;x + \frac{1 + z \cdot \left(\frac{z \cdot \left(y \cdot 0.5\right)}{y} + -1\right)}{y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-7}:\\ \;\;\;\;\frac{1 + y \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y + y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.6% accurate, 11.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1220:\\ \;\;\;\;x + \frac{1 + z \cdot \left(z \cdot 0.5 + -1\right)}{y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-7}:\\ \;\;\;\;\frac{1 + y \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y + y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1220.0)
   (+ x (/ (+ 1.0 (* z (+ (* z 0.5) -1.0))) y))
   (if (<= y 5.8e-7) (/ (+ 1.0 (* y x)) y) (+ x (/ 1.0 (+ y (* y z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1220.0) {
		tmp = x + ((1.0 + (z * ((z * 0.5) + -1.0))) / y);
	} else if (y <= 5.8e-7) {
		tmp = (1.0 + (y * x)) / y;
	} else {
		tmp = x + (1.0 / (y + (y * 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 <= (-1220.0d0)) then
        tmp = x + ((1.0d0 + (z * ((z * 0.5d0) + (-1.0d0)))) / y)
    else if (y <= 5.8d-7) then
        tmp = (1.0d0 + (y * x)) / y
    else
        tmp = x + (1.0d0 / (y + (y * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1220.0) {
		tmp = x + ((1.0 + (z * ((z * 0.5) + -1.0))) / y);
	} else if (y <= 5.8e-7) {
		tmp = (1.0 + (y * x)) / y;
	} else {
		tmp = x + (1.0 / (y + (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1220.0:
		tmp = x + ((1.0 + (z * ((z * 0.5) + -1.0))) / y)
	elif y <= 5.8e-7:
		tmp = (1.0 + (y * x)) / y
	else:
		tmp = x + (1.0 / (y + (y * z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1220.0)
		tmp = Float64(x + Float64(Float64(1.0 + Float64(z * Float64(Float64(z * 0.5) + -1.0))) / y));
	elseif (y <= 5.8e-7)
		tmp = Float64(Float64(1.0 + Float64(y * x)) / y);
	else
		tmp = Float64(x + Float64(1.0 / Float64(y + Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1220.0)
		tmp = x + ((1.0 + (z * ((z * 0.5) + -1.0))) / y);
	elseif (y <= 5.8e-7)
		tmp = (1.0 + (y * x)) / y;
	else
		tmp = x + (1.0 / (y + (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1220.0], N[(x + N[(N[(1.0 + N[(z * N[(N[(z * 0.5), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e-7], N[(N[(1.0 + N[(y * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x + N[(1.0 / N[(y + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1220

   1. Initial program 78.3%

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

      1. exp-prod 78.3%

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

      2. +-commutative 78.3%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in z around 0 70.0%

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

   6. Taylor expanded in y around inf 70.0%

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

      1. *-commutative 70.0%

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

   8. Simplified 70.0%

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

   if -1220 < y < 5.7999999999999995e-7

   1. Initial program 88.4%

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

      1. exp-prod 99.6%

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

      2. +-commutative 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 99.0%

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

      1. +-commutative 99.0%

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

   7. Simplified 99.0%

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

   8. Taylor expanded in y around 0 99.0%

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

      1. *-commutative 99.0%

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

   10. Simplified 99.0%

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

   if 5.7999999999999995e-7 < y

   1. Initial program 82.8%

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

      1. *-commutative 82.8%

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

      2. exp-to-pow 82.8%

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

      3. +-commutative 82.8%

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

   3. Simplified 82.8%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   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 53.2%

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

      5. sqrt-unprod 79.3%

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

      6. sqr-neg 79.3%

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

      7. sqrt-unprod 26.1%

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

      8. add-sqr-sqrt 66.6%

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

      9. exp-neg 66.6%

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

      10. add-sqr-sqrt 40.5%

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

      11. sqrt-unprod 87.3%

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

      12. sqr-neg 87.3%

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

      13. sqrt-unprod 46.8%

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

      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 84.6%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1220:\\ \;\;\;\;x + \frac{1 + z \cdot \left(z \cdot 0.5 + -1\right)}{y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-7}:\\ \;\;\;\;\frac{1 + y \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y + y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.1% accurate, 15.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 10^{-7}:\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y + y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1e-7) (+ x (/ 1.0 y)) (+ x (/ 1.0 (+ y (* y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1e-7) {
		tmp = x + (1.0 / y);
	} else {
		tmp = x + (1.0 / (y + (y * 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 <= 1d-7) then
        tmp = x + (1.0d0 / y)
    else
        tmp = x + (1.0d0 / (y + (y * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1e-7) {
		tmp = x + (1.0 / y);
	} else {
		tmp = x + (1.0 / (y + (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1e-7:
		tmp = x + (1.0 / y)
	else:
		tmp = x + (1.0 / (y + (y * z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1e-7)
		tmp = Float64(x + Float64(1.0 / y));
	else
		tmp = Float64(x + Float64(1.0 / Float64(y + Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1e-7)
		tmp = x + (1.0 / y);
	else
		tmp = x + (1.0 / (y + (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1e-7], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / N[(y + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 9.9999999999999995e-8

   1. Initial program 83.5%

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

      1. exp-prod 89.3%

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

      2. +-commutative 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in y around inf 80.9%

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

      1. +-commutative 80.9%

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

   7. Simplified 80.9%

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

   if 9.9999999999999995e-8 < y

   1. Initial program 82.8%

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

      1. *-commutative 82.8%

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

      2. exp-to-pow 82.8%

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

      3. +-commutative 82.8%

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

   3. Simplified 82.8%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   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 53.2%

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

      5. sqrt-unprod 79.3%

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

      6. sqr-neg 79.3%

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

      7. sqrt-unprod 26.1%

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

      8. add-sqr-sqrt 66.6%

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

      9. exp-neg 66.6%

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

      10. add-sqr-sqrt 40.5%

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

      11. sqrt-unprod 87.3%

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

      12. sqr-neg 87.3%

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

      13. sqrt-unprod 46.8%

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

      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 84.6%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 10^{-7}:\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y + y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.6% accurate, 16.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-69}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8.8e-17) x (if (<= y 1.1e-69) (/ 1.0 y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.8e-17) {
		tmp = x;
	} else if (y <= 1.1e-69) {
		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 <= (-8.8d-17)) then
        tmp = x
    else if (y <= 1.1d-69) 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 <= -8.8e-17) {
		tmp = x;
	} else if (y <= 1.1e-69) {
		tmp = 1.0 / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8.8e-17:
		tmp = x
	elif y <= 1.1e-69:
		tmp = 1.0 / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.8e-17)
		tmp = x;
	elseif (y <= 1.1e-69)
		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 <= -8.8e-17)
		tmp = x;
	elseif (y <= 1.1e-69)
		tmp = 1.0 / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.8e-17], x, If[LessEqual[y, 1.1e-69], N[(1.0 / y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -8.8e-17 or 1.1e-69 < y

   1. Initial program 82.3%

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

      1. exp-prod 82.2%

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

      2. +-commutative 82.2%

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

   3. Simplified 82.2%

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

   5. Taylor expanded in x around inf 57.0%

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

   if -8.8e-17 < y < 1.1e-69

   1. Initial program 85.5%

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

      1. exp-prod 99.9%

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

      2. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 80.7%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-69}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 86.1% accurate, 17.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+23}:\\ \;\;\;\;\frac{1 + y \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6e+23) (/ (+ 1.0 (* y x)) y) (+ x (/ 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6e+23) {
		tmp = (1.0 + (y * x)) / 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 <= (-6d+23)) then
        tmp = (1.0d0 + (y * x)) / 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 <= -6e+23) {
		tmp = (1.0 + (y * x)) / y;
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6e+23:
		tmp = (1.0 + (y * x)) / y
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6e+23)
		tmp = Float64(Float64(1.0 + Float64(y * x)) / 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 <= -6e+23)
		tmp = (1.0 + (y * x)) / y;
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6e+23], N[(N[(1.0 + N[(y * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.0000000000000002e23

   1. Initial program 46.6%

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

      1. exp-prod 56.3%

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

      2. +-commutative 56.3%

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

   3. Simplified 56.3%

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

   5. Taylor expanded in y around inf 22.3%

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

      1. +-commutative 22.3%

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

   7. Simplified 22.3%

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

   8. Taylor expanded in y around 0 31.8%

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

      1. *-commutative 31.8%

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

   10. Simplified 31.8%

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

   if -6.0000000000000002e23 < z

   1. Initial program 92.0%

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

      1. exp-prod 95.2%

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

      2. +-commutative 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in y around inf 93.4%

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

      1. +-commutative 93.4%

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

   7. Simplified 93.4%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+23}:\\ \;\;\;\;\frac{1 + y \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 84.6% 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 83.3%

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

   1. exp-prod 87.7%

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

   2. +-commutative 87.7%

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

3. Simplified 87.7%

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

5. Taylor expanded in y around inf 79.8%

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

   1. +-commutative 79.8%

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

7. Simplified 79.8%

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

8. Final simplification 79.8%

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

Alternative 12: 49.9% 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 83.3%

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

   1. exp-prod 87.7%

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

   2. +-commutative 87.7%

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

3. Simplified 87.7%

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

5. Taylor expanded in x around inf 45.1%

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

6. Final simplification 45.1%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 91.5% 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 2024079 
(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)))