Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2

Percentage Accurate: 99.8% → 99.9%

Time: 15.7s

Alternatives: 13

Speedup: 0.5×

Specification

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (+ (- x (* (+ y 0.5) (log y))) y) z))

C

double code(double x, double y, double z) {
	return ((x - ((y + 0.5) * log(y))) + y) - z;
}

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 - ((y + 0.5d0) * log(y))) + y) - z
end function

Java

public static double code(double x, double y, double z) {
	return ((x - ((y + 0.5) * Math.log(y))) + y) - z;
}

Python

def code(x, y, z):
	return ((x - ((y + 0.5) * math.log(y))) + y) - z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x - Float64(Float64(y + 0.5) * log(y))) + y) - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x - ((y + 0.5) * log(y))) + y) - z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x - N[(N[(y + 0.5), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision] - z), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (+ (- x (* (+ y 0.5) (log y))) y) z))

C

double code(double x, double y, double z) {
	return ((x - ((y + 0.5) * log(y))) + y) - z;
}

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 - ((y + 0.5d0) * log(y))) + y) - z
end function

Java

public static double code(double x, double y, double z) {
	return ((x - ((y + 0.5) * Math.log(y))) + y) - z;
}

Python

def code(x, y, z):
	return ((x - ((y + 0.5) * math.log(y))) + y) - z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x - Float64(Float64(y + 0.5) * log(y))) + y) - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x - ((y + 0.5) * log(y))) + y) - z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x - N[(N[(y + 0.5), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision] - z), $MachinePrecision]

Alternative 1: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \left(x + y \cdot \left(1 - \log y\right)\right) - \left(\log y \cdot 0.5 + z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (- (+ x (* y (- 1.0 (log y)))) (+ (* (log y) 0.5) z)))

C

double code(double x, double y, double z) {
	return (x + (y * (1.0 - log(y)))) - ((log(y) * 0.5) + z);
}

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 + (y * (1.0d0 - log(y)))) - ((log(y) * 0.5d0) + z)
end function

Java

public static double code(double x, double y, double z) {
	return (x + (y * (1.0 - Math.log(y)))) - ((Math.log(y) * 0.5) + z);
}

Python

def code(x, y, z):
	return (x + (y * (1.0 - math.log(y)))) - ((math.log(y) * 0.5) + z)

Julia

function code(x, y, z)
	return Float64(Float64(x + Float64(y * Float64(1.0 - log(y)))) - Float64(Float64(log(y) * 0.5) + z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + (y * (1.0 - log(y)))) - ((log(y) * 0.5) + z);
end

Wolfram

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

Derivation

1. Initial program 99.8%

   \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
2. Step-by-step derivation

   1. associate--l+ 99.8%

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

3. Simplified 99.8%

   \[\leadsto \color{blue}{\left(x - \left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 99.9%

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

6. Final simplification 99.9%

   \[\leadsto \left(x + y \cdot \left(1 - \log y\right)\right) - \left(\log y \cdot 0.5 + z\right) \]
7. Add Preprocessing

Alternative 2: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ x + \mathsf{fma}\left(\log y, -0.5 - y, y - z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (fma (log y) (- -0.5 y) (- y z))))

C

double code(double x, double y, double z) {
	return x + fma(log(y), (-0.5 - y), (y - z));
}

Julia

function code(x, y, z)
	return Float64(x + fma(log(y), Float64(-0.5 - y), Float64(y - z)))
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[Log[y], $MachinePrecision] * N[(-0.5 - y), $MachinePrecision] + N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
2. Step-by-step derivation

   1. associate--l+ 99.8%

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

   2. sub-neg 99.8%

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

   3. associate-+l+ 99.8%

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

   4. *-commutative 99.8%

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

   5. distribute-rgt-neg-in 99.8%

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

   6. fma-define 99.9%

      \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -\left(y + 0.5\right), y - z\right)} \]

   7. +-commutative 99.9%

      \[\leadsto x + \mathsf{fma}\left(\log y, -\color{blue}{\left(0.5 + y\right)}, y - z\right) \]

   8. distribute-neg-in 99.9%

      \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) + \left(-y\right)}, y - z\right) \]

   9. unsub-neg 99.9%

      \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) - y}, y - z\right) \]

   10. metadata-eval 99.9%

       \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{-0.5} - y, y - z\right) \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{x + \mathsf{fma}\left(\log y, -0.5 - y, y - z\right)} \]
4. Add Preprocessing

5. Final simplification 99.9%

   \[\leadsto x + \mathsf{fma}\left(\log y, -0.5 - y, y - z\right) \]
6. Add Preprocessing

Alternative 3: 74.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(1 - \log y\right)\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+122}:\\ \;\;\;\;x - z\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+95}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -14:\\ \;\;\;\;x - z\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-210}:\\ \;\;\;\;y + \log y \cdot \left(-0.5 - y\right)\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+65}:\\ \;\;\;\;x + t\_0\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- 1.0 (log y)))))
   (if (<= z -2.1e+122)
     (- x z)
     (if (<= z -1.6e+95)
       t_0
       (if (<= z -14.0)
         (- x z)
         (if (<= z -1.4e-210)
           (+ y (* (log y) (- -0.5 y)))
           (if (<= z 9.2e+65) (+ x t_0) (- x z))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (1.0 - log(y));
	double tmp;
	if (z <= -2.1e+122) {
		tmp = x - z;
	} else if (z <= -1.6e+95) {
		tmp = t_0;
	} else if (z <= -14.0) {
		tmp = x - z;
	} else if (z <= -1.4e-210) {
		tmp = y + (log(y) * (-0.5 - y));
	} else if (z <= 9.2e+65) {
		tmp = x + t_0;
	} else {
		tmp = x - 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) :: t_0
    real(8) :: tmp
    t_0 = y * (1.0d0 - log(y))
    if (z <= (-2.1d+122)) then
        tmp = x - z
    else if (z <= (-1.6d+95)) then
        tmp = t_0
    else if (z <= (-14.0d0)) then
        tmp = x - z
    else if (z <= (-1.4d-210)) then
        tmp = y + (log(y) * ((-0.5d0) - y))
    else if (z <= 9.2d+65) then
        tmp = x + t_0
    else
        tmp = x - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (1.0 - Math.log(y));
	double tmp;
	if (z <= -2.1e+122) {
		tmp = x - z;
	} else if (z <= -1.6e+95) {
		tmp = t_0;
	} else if (z <= -14.0) {
		tmp = x - z;
	} else if (z <= -1.4e-210) {
		tmp = y + (Math.log(y) * (-0.5 - y));
	} else if (z <= 9.2e+65) {
		tmp = x + t_0;
	} else {
		tmp = x - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (1.0 - math.log(y))
	tmp = 0
	if z <= -2.1e+122:
		tmp = x - z
	elif z <= -1.6e+95:
		tmp = t_0
	elif z <= -14.0:
		tmp = x - z
	elif z <= -1.4e-210:
		tmp = y + (math.log(y) * (-0.5 - y))
	elif z <= 9.2e+65:
		tmp = x + t_0
	else:
		tmp = x - z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(1.0 - log(y)))
	tmp = 0.0
	if (z <= -2.1e+122)
		tmp = Float64(x - z);
	elseif (z <= -1.6e+95)
		tmp = t_0;
	elseif (z <= -14.0)
		tmp = Float64(x - z);
	elseif (z <= -1.4e-210)
		tmp = Float64(y + Float64(log(y) * Float64(-0.5 - y)));
	elseif (z <= 9.2e+65)
		tmp = Float64(x + t_0);
	else
		tmp = Float64(x - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (1.0 - log(y));
	tmp = 0.0;
	if (z <= -2.1e+122)
		tmp = x - z;
	elseif (z <= -1.6e+95)
		tmp = t_0;
	elseif (z <= -14.0)
		tmp = x - z;
	elseif (z <= -1.4e-210)
		tmp = y + (log(y) * (-0.5 - y));
	elseif (z <= 9.2e+65)
		tmp = x + t_0;
	else
		tmp = x - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+122], N[(x - z), $MachinePrecision], If[LessEqual[z, -1.6e+95], t$95$0, If[LessEqual[z, -14.0], N[(x - z), $MachinePrecision], If[LessEqual[z, -1.4e-210], N[(y + N[(N[Log[y], $MachinePrecision] * N[(-0.5 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e+65], N[(x + t$95$0), $MachinePrecision], N[(x - z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.10000000000000016e122 or -1.6e95 < z < -14 or 9.2e65 < z

   1. Initial program 99.9%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Step-by-step derivation

      1. associate--l+ 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-+l+ 99.9%

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

      4. *-commutative 99.9%

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

      5. distribute-rgt-neg-in 99.9%

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

      6. fma-define 99.9%

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -\left(y + 0.5\right), y - z\right)} \]

      7. +-commutative 99.9%

         \[\leadsto x + \mathsf{fma}\left(\log y, -\color{blue}{\left(0.5 + y\right)}, y - z\right) \]

      8. distribute-neg-in 99.9%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) + \left(-y\right)}, y - z\right) \]

      9. unsub-neg 99.9%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) - y}, y - z\right) \]

      10. metadata-eval 99.9%

          \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{-0.5} - y, y - z\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(\log y, -0.5 - y, y - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 88.8%

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

      1. +-commutative 88.8%

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

   7. Simplified 88.8%

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

   8. Taylor expanded in x around inf 88.3%

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

   if -2.10000000000000016e122 < z < -1.6e95

   1. Initial program 99.6%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Step-by-step derivation

      1. associate--l+ 99.6%

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

      2. sub-neg 99.6%

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

      3. associate-+l+ 99.6%

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

      4. *-commutative 99.6%

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

      5. distribute-rgt-neg-in 99.6%

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

      6. fma-define 100.0%

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -\left(y + 0.5\right), y - z\right)} \]

      7. +-commutative 100.0%

         \[\leadsto x + \mathsf{fma}\left(\log y, -\color{blue}{\left(0.5 + y\right)}, y - z\right) \]

      8. distribute-neg-in 100.0%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) + \left(-y\right)}, y - z\right) \]

      9. unsub-neg 100.0%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) - y}, y - z\right) \]

      10. metadata-eval 100.0%

          \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{-0.5} - y, y - z\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(\log y, -0.5 - y, y - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 99.6%

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

      1. +-commutative 99.6%

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

      2. mul-1-neg 99.6%

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

      3. distribute-rgt-in 99.6%

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

      4. distribute-neg-in 99.6%

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

      5. distribute-lft-neg-in 99.6%

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

      6. metadata-eval 99.6%

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

      7. distribute-lft-neg-in 99.6%

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

      8. distribute-rgt-in 99.6%

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

      9. sub-neg 99.6%

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

      10. fma-define 100.0%

          \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)} \]

   7. Simplified 100.0%

      \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)} \]

   8. Taylor expanded in x around 0 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*r* 99.6%

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

      3. *-commutative 99.6%

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

      4. rem-square-sqrt 0.0%

         \[\leadsto \left(\log y \cdot \color{blue}{\left(\sqrt{-1} \cdot \sqrt{-1}\right)}\right) \cdot \left(0.5 + y\right) + y \]

      5. unpow2 0.0%

         \[\leadsto \left(\log y \cdot \color{blue}{{\left(\sqrt{-1}\right)}^{2}}\right) \cdot \left(0.5 + y\right) + y \]

      6. associate-*r* 0.0%

         \[\leadsto \color{blue}{\log y \cdot \left({\left(\sqrt{-1}\right)}^{2} \cdot \left(0.5 + y\right)\right)} + y \]

      7. distribute-lft-in 0.0%

         \[\leadsto \log y \cdot \color{blue}{\left({\left(\sqrt{-1}\right)}^{2} \cdot 0.5 + {\left(\sqrt{-1}\right)}^{2} \cdot y\right)} + y \]

      8. unpow2 0.0%

         \[\leadsto \log y \cdot \left(\color{blue}{\left(\sqrt{-1} \cdot \sqrt{-1}\right)} \cdot 0.5 + {\left(\sqrt{-1}\right)}^{2} \cdot y\right) + y \]

      9. rem-square-sqrt 0.0%

         \[\leadsto \log y \cdot \left(\color{blue}{-1} \cdot 0.5 + {\left(\sqrt{-1}\right)}^{2} \cdot y\right) + y \]

      10. metadata-eval 0.0%

          \[\leadsto \log y \cdot \left(\color{blue}{-0.5} + {\left(\sqrt{-1}\right)}^{2} \cdot y\right) + y \]

      11. unpow2 0.0%

          \[\leadsto \log y \cdot \left(-0.5 + \color{blue}{\left(\sqrt{-1} \cdot \sqrt{-1}\right)} \cdot y\right) + y \]

      12. rem-square-sqrt 99.6%

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

      13. neg-mul-1 99.6%

          \[\leadsto \log y \cdot \left(-0.5 + \color{blue}{\left(-y\right)}\right) + y \]

      14. sub-neg 99.6%

          \[\leadsto \log y \cdot \color{blue}{\left(-0.5 - y\right)} + y \]

      15. fma-define 100.0%

          \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)} \]

   10. Simplified 100.0%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)} \]
   11. Step-by-step derivation

       1. fma-undefine 99.6%

          \[\leadsto \color{blue}{\log y \cdot \left(-0.5 - y\right) + y} \]

   12. Applied egg-rr 99.6%

       \[\leadsto \color{blue}{\log y \cdot \left(-0.5 - y\right) + y} \]

   13. Taylor expanded in y around inf 100.0%

       \[\leadsto \color{blue}{y \cdot \left(1 + \log \left(\frac{1}{y}\right)\right)} \]
   14. Step-by-step derivation

       1. log-rec 100.0%

          \[\leadsto y \cdot \left(1 + \color{blue}{\left(-\log y\right)}\right) \]

       2. sub-neg 100.0%

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

   15. Simplified 100.0%

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

   if -14 < z < -1.4e-210

   1. Initial program 99.6%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Step-by-step derivation

      1. associate--l+ 99.6%

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

      2. sub-neg 99.6%

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

      3. associate-+l+ 99.6%

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

      4. *-commutative 99.6%

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

      5. distribute-rgt-neg-in 99.6%

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

      6. fma-define 99.8%

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -\left(y + 0.5\right), y - z\right)} \]

      7. +-commutative 99.8%

         \[\leadsto x + \mathsf{fma}\left(\log y, -\color{blue}{\left(0.5 + y\right)}, y - z\right) \]

      8. distribute-neg-in 99.8%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) + \left(-y\right)}, y - z\right) \]

      9. unsub-neg 99.8%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) - y}, y - z\right) \]

      10. metadata-eval 99.8%

          \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{-0.5} - y, y - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(\log y, -0.5 - y, y - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 99.6%

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

      1. +-commutative 99.6%

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

      2. mul-1-neg 99.6%

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

      3. distribute-rgt-in 99.7%

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

      4. distribute-neg-in 99.7%

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

      5. distribute-lft-neg-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. distribute-lft-neg-in 99.7%

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

      8. distribute-rgt-in 99.6%

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

      9. sub-neg 99.6%

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

      10. fma-define 99.8%

          \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)} \]

   7. Simplified 99.8%

      \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)} \]

   8. Taylor expanded in x around 0 80.9%

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

      1. +-commutative 80.9%

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

      2. associate-*r* 80.9%

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

      3. *-commutative 80.9%

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

      4. rem-square-sqrt 0.0%

         \[\leadsto \left(\log y \cdot \color{blue}{\left(\sqrt{-1} \cdot \sqrt{-1}\right)}\right) \cdot \left(0.5 + y\right) + y \]

      5. unpow2 0.0%

         \[\leadsto \left(\log y \cdot \color{blue}{{\left(\sqrt{-1}\right)}^{2}}\right) \cdot \left(0.5 + y\right) + y \]

      6. associate-*r* 0.0%

         \[\leadsto \color{blue}{\log y \cdot \left({\left(\sqrt{-1}\right)}^{2} \cdot \left(0.5 + y\right)\right)} + y \]

      7. distribute-lft-in 0.0%

         \[\leadsto \log y \cdot \color{blue}{\left({\left(\sqrt{-1}\right)}^{2} \cdot 0.5 + {\left(\sqrt{-1}\right)}^{2} \cdot y\right)} + y \]

      8. unpow2 0.0%

         \[\leadsto \log y \cdot \left(\color{blue}{\left(\sqrt{-1} \cdot \sqrt{-1}\right)} \cdot 0.5 + {\left(\sqrt{-1}\right)}^{2} \cdot y\right) + y \]

      9. rem-square-sqrt 0.0%

         \[\leadsto \log y \cdot \left(\color{blue}{-1} \cdot 0.5 + {\left(\sqrt{-1}\right)}^{2} \cdot y\right) + y \]

      10. metadata-eval 0.0%

          \[\leadsto \log y \cdot \left(\color{blue}{-0.5} + {\left(\sqrt{-1}\right)}^{2} \cdot y\right) + y \]

      11. unpow2 0.0%

          \[\leadsto \log y \cdot \left(-0.5 + \color{blue}{\left(\sqrt{-1} \cdot \sqrt{-1}\right)} \cdot y\right) + y \]

      12. rem-square-sqrt 80.9%

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

      13. neg-mul-1 80.9%

          \[\leadsto \log y \cdot \left(-0.5 + \color{blue}{\left(-y\right)}\right) + y \]

      14. sub-neg 80.9%

          \[\leadsto \log y \cdot \color{blue}{\left(-0.5 - y\right)} + y \]

      15. fma-define 81.1%

          \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)} \]

   10. Simplified 81.1%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)} \]
   11. Step-by-step derivation

       1. fma-undefine 80.9%

          \[\leadsto \color{blue}{\log y \cdot \left(-0.5 - y\right) + y} \]

   12. Applied egg-rr 80.9%

       \[\leadsto \color{blue}{\log y \cdot \left(-0.5 - y\right) + y} \]

   if -1.4e-210 < z < 9.2e65

   1. Initial program 99.7%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Step-by-step derivation

      1. associate--l+ 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-+l+ 99.7%

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

      4. *-commutative 99.7%

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

      5. distribute-rgt-neg-in 99.7%

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

      6. fma-define 99.8%

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -\left(y + 0.5\right), y - z\right)} \]

      7. +-commutative 99.8%

         \[\leadsto x + \mathsf{fma}\left(\log y, -\color{blue}{\left(0.5 + y\right)}, y - z\right) \]

      8. distribute-neg-in 99.8%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) + \left(-y\right)}, y - z\right) \]

      9. unsub-neg 99.8%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) - y}, y - z\right) \]

      10. metadata-eval 99.8%

          \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{-0.5} - y, y - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(\log y, -0.5 - y, y - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 79.9%

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

      1. log-rec 79.9%

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

      2. sub-neg 79.9%

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

   7. Simplified 79.9%

      \[\leadsto x + \color{blue}{y \cdot \left(1 - \log y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+122}:\\ \;\;\;\;x - z\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \left(1 - \log y\right)\\ \mathbf{elif}\;z \leq -14:\\ \;\;\;\;x - z\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-210}:\\ \;\;\;\;y + \log y \cdot \left(-0.5 - y\right)\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+65}:\\ \;\;\;\;x + y \cdot \left(1 - \log y\right)\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.2 \cdot 10^{-103}:\\ \;\;\;\;x - z\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-87}:\\ \;\;\;\;\log y \cdot -0.5\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+128} \lor \neg \left(y \leq 5.2 \cdot 10^{+139}\right) \land y \leq 3.1 \cdot 10^{+158}:\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \log y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 2.2e-103)
   (- x z)
   (if (<= y 4.8e-87)
     (* (log y) -0.5)
     (if (or (<= y 6e+128) (and (not (<= y 5.2e+139)) (<= y 3.1e+158)))
       (- x z)
       (* y (- 1.0 (log y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.2e-103) {
		tmp = x - z;
	} else if (y <= 4.8e-87) {
		tmp = log(y) * -0.5;
	} else if ((y <= 6e+128) || (!(y <= 5.2e+139) && (y <= 3.1e+158))) {
		tmp = x - z;
	} else {
		tmp = y * (1.0 - log(y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 2.2d-103) then
        tmp = x - z
    else if (y <= 4.8d-87) then
        tmp = log(y) * (-0.5d0)
    else if ((y <= 6d+128) .or. (.not. (y <= 5.2d+139)) .and. (y <= 3.1d+158)) then
        tmp = x - z
    else
        tmp = y * (1.0d0 - log(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.2e-103) {
		tmp = x - z;
	} else if (y <= 4.8e-87) {
		tmp = Math.log(y) * -0.5;
	} else if ((y <= 6e+128) || (!(y <= 5.2e+139) && (y <= 3.1e+158))) {
		tmp = x - z;
	} else {
		tmp = y * (1.0 - Math.log(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.2e-103:
		tmp = x - z
	elif y <= 4.8e-87:
		tmp = math.log(y) * -0.5
	elif (y <= 6e+128) or (not (y <= 5.2e+139) and (y <= 3.1e+158)):
		tmp = x - z
	else:
		tmp = y * (1.0 - math.log(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.2e-103)
		tmp = Float64(x - z);
	elseif (y <= 4.8e-87)
		tmp = Float64(log(y) * -0.5);
	elseif ((y <= 6e+128) || (!(y <= 5.2e+139) && (y <= 3.1e+158)))
		tmp = Float64(x - z);
	else
		tmp = Float64(y * Float64(1.0 - log(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.2e-103)
		tmp = x - z;
	elseif (y <= 4.8e-87)
		tmp = log(y) * -0.5;
	elseif ((y <= 6e+128) || (~((y <= 5.2e+139)) && (y <= 3.1e+158)))
		tmp = x - z;
	else
		tmp = y * (1.0 - log(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.2e-103], N[(x - z), $MachinePrecision], If[LessEqual[y, 4.8e-87], N[(N[Log[y], $MachinePrecision] * -0.5), $MachinePrecision], If[Or[LessEqual[y, 6e+128], And[N[Not[LessEqual[y, 5.2e+139]], $MachinePrecision], LessEqual[y, 3.1e+158]]], N[(x - z), $MachinePrecision], N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 2.1999999999999999e-103 or 4.7999999999999999e-87 < y < 5.9999999999999997e128 or 5.20000000000000044e139 < y < 3.1000000000000002e158

   1. Initial program 99.9%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Step-by-step derivation

      1. associate--l+ 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-+l+ 99.9%

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

      4. *-commutative 99.9%

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

      5. distribute-rgt-neg-in 99.9%

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

      6. fma-define 100.0%

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -\left(y + 0.5\right), y - z\right)} \]

      7. +-commutative 100.0%

         \[\leadsto x + \mathsf{fma}\left(\log y, -\color{blue}{\left(0.5 + y\right)}, y - z\right) \]

      8. distribute-neg-in 100.0%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) + \left(-y\right)}, y - z\right) \]

      9. unsub-neg 100.0%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) - y}, y - z\right) \]

      10. metadata-eval 100.0%

          \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{-0.5} - y, y - z\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(\log y, -0.5 - y, y - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 90.7%

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

      1. +-commutative 90.7%

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

   7. Simplified 90.7%

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

   8. Taylor expanded in x around inf 74.0%

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

   if 2.1999999999999999e-103 < y < 4.7999999999999999e-87

   1. Initial program 100.0%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-+l+ 100.0%

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

      4. *-commutative 100.0%

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

      5. distribute-rgt-neg-in 100.0%

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

      6. fma-define 100.0%

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -\left(y + 0.5\right), y - z\right)} \]

      7. +-commutative 100.0%

         \[\leadsto x + \mathsf{fma}\left(\log y, -\color{blue}{\left(0.5 + y\right)}, y - z\right) \]

      8. distribute-neg-in 100.0%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) + \left(-y\right)}, y - z\right) \]

      9. unsub-neg 100.0%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) - y}, y - z\right) \]

      10. metadata-eval 100.0%

          \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{-0.5} - y, y - z\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(\log y, -0.5 - y, y - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. distribute-rgt-in 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. distribute-lft-neg-in 100.0%

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

      6. metadata-eval 100.0%

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

      7. distribute-lft-neg-in 100.0%

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

      8. distribute-rgt-in 100.0%

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

      9. sub-neg 100.0%

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

      10. fma-define 100.0%

          \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)} \]

   7. Simplified 100.0%

      \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)} \]

   8. Taylor expanded in x around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*r* 100.0%

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

      3. *-commutative 100.0%

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

      4. rem-square-sqrt 0.0%

         \[\leadsto \left(\log y \cdot \color{blue}{\left(\sqrt{-1} \cdot \sqrt{-1}\right)}\right) \cdot \left(0.5 + y\right) + y \]

      5. unpow2 0.0%

         \[\leadsto \left(\log y \cdot \color{blue}{{\left(\sqrt{-1}\right)}^{2}}\right) \cdot \left(0.5 + y\right) + y \]

      6. associate-*r* 0.0%

         \[\leadsto \color{blue}{\log y \cdot \left({\left(\sqrt{-1}\right)}^{2} \cdot \left(0.5 + y\right)\right)} + y \]

      7. distribute-lft-in 0.0%

         \[\leadsto \log y \cdot \color{blue}{\left({\left(\sqrt{-1}\right)}^{2} \cdot 0.5 + {\left(\sqrt{-1}\right)}^{2} \cdot y\right)} + y \]

      8. unpow2 0.0%

         \[\leadsto \log y \cdot \left(\color{blue}{\left(\sqrt{-1} \cdot \sqrt{-1}\right)} \cdot 0.5 + {\left(\sqrt{-1}\right)}^{2} \cdot y\right) + y \]

      9. rem-square-sqrt 0.0%

         \[\leadsto \log y \cdot \left(\color{blue}{-1} \cdot 0.5 + {\left(\sqrt{-1}\right)}^{2} \cdot y\right) + y \]

      10. metadata-eval 0.0%

          \[\leadsto \log y \cdot \left(\color{blue}{-0.5} + {\left(\sqrt{-1}\right)}^{2} \cdot y\right) + y \]

      11. unpow2 0.0%

          \[\leadsto \log y \cdot \left(-0.5 + \color{blue}{\left(\sqrt{-1} \cdot \sqrt{-1}\right)} \cdot y\right) + y \]

      12. rem-square-sqrt 100.0%

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

      13. neg-mul-1 100.0%

          \[\leadsto \log y \cdot \left(-0.5 + \color{blue}{\left(-y\right)}\right) + y \]

      14. sub-neg 100.0%

          \[\leadsto \log y \cdot \color{blue}{\left(-0.5 - y\right)} + y \]

      15. fma-define 100.0%

          \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)} \]

   10. Simplified 100.0%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)} \]
   11. Step-by-step derivation

       1. fma-undefine 100.0%

          \[\leadsto \color{blue}{\log y \cdot \left(-0.5 - y\right) + y} \]

   12. Applied egg-rr 100.0%

       \[\leadsto \color{blue}{\log y \cdot \left(-0.5 - y\right) + y} \]

   13. Taylor expanded in y around 0 100.0%

       \[\leadsto \color{blue}{-0.5 \cdot \log y} \]
   14. Step-by-step derivation

       1. *-commutative 100.0%

          \[\leadsto \color{blue}{\log y \cdot -0.5} \]

   15. Simplified 100.0%

       \[\leadsto \color{blue}{\log y \cdot -0.5} \]

   if 5.9999999999999997e128 < y < 5.20000000000000044e139 or 3.1000000000000002e158 < y

   1. Initial program 99.4%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Step-by-step derivation

      1. associate--l+ 99.4%

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

      2. sub-neg 99.4%

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

      3. associate-+l+ 99.5%

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

      4. *-commutative 99.5%

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

      5. distribute-rgt-neg-in 99.5%

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

      6. fma-define 99.6%

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -\left(y + 0.5\right), y - z\right)} \]

      7. +-commutative 99.6%

         \[\leadsto x + \mathsf{fma}\left(\log y, -\color{blue}{\left(0.5 + y\right)}, y - z\right) \]

      8. distribute-neg-in 99.6%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) + \left(-y\right)}, y - z\right) \]

      9. unsub-neg 99.6%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) - y}, y - z\right) \]

      10. metadata-eval 99.6%

          \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{-0.5} - y, y - z\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(\log y, -0.5 - y, y - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 83.5%

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

      1. +-commutative 83.5%

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

      2. mul-1-neg 83.5%

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

      3. distribute-rgt-in 83.5%

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

      4. distribute-neg-in 83.5%

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

      5. distribute-lft-neg-in 83.5%

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

      6. metadata-eval 83.5%

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

      7. distribute-lft-neg-in 83.5%

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

      8. distribute-rgt-in 83.5%

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

      9. sub-neg 83.5%

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

      10. fma-define 83.7%

          \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)} \]

   7. Simplified 83.7%

      \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)} \]

   8. Taylor expanded in x around 0 72.9%

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

      1. +-commutative 72.9%

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

      2. associate-*r* 72.9%

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

      3. *-commutative 72.9%

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

      4. rem-square-sqrt 0.0%

         \[\leadsto \left(\log y \cdot \color{blue}{\left(\sqrt{-1} \cdot \sqrt{-1}\right)}\right) \cdot \left(0.5 + y\right) + y \]

      5. unpow2 0.0%

         \[\leadsto \left(\log y \cdot \color{blue}{{\left(\sqrt{-1}\right)}^{2}}\right) \cdot \left(0.5 + y\right) + y \]

      6. associate-*r* 0.0%

         \[\leadsto \color{blue}{\log y \cdot \left({\left(\sqrt{-1}\right)}^{2} \cdot \left(0.5 + y\right)\right)} + y \]

      7. distribute-lft-in 0.0%

         \[\leadsto \log y \cdot \color{blue}{\left({\left(\sqrt{-1}\right)}^{2} \cdot 0.5 + {\left(\sqrt{-1}\right)}^{2} \cdot y\right)} + y \]

      8. unpow2 0.0%

         \[\leadsto \log y \cdot \left(\color{blue}{\left(\sqrt{-1} \cdot \sqrt{-1}\right)} \cdot 0.5 + {\left(\sqrt{-1}\right)}^{2} \cdot y\right) + y \]

      9. rem-square-sqrt 0.0%

         \[\leadsto \log y \cdot \left(\color{blue}{-1} \cdot 0.5 + {\left(\sqrt{-1}\right)}^{2} \cdot y\right) + y \]

      10. metadata-eval 0.0%

          \[\leadsto \log y \cdot \left(\color{blue}{-0.5} + {\left(\sqrt{-1}\right)}^{2} \cdot y\right) + y \]

      11. unpow2 0.0%

          \[\leadsto \log y \cdot \left(-0.5 + \color{blue}{\left(\sqrt{-1} \cdot \sqrt{-1}\right)} \cdot y\right) + y \]

      12. rem-square-sqrt 72.9%

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

      13. neg-mul-1 72.9%

          \[\leadsto \log y \cdot \left(-0.5 + \color{blue}{\left(-y\right)}\right) + y \]

      14. sub-neg 72.9%

          \[\leadsto \log y \cdot \color{blue}{\left(-0.5 - y\right)} + y \]

      15. fma-define 73.1%

          \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)} \]

   10. Simplified 73.1%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)} \]
   11. Step-by-step derivation

       1. fma-undefine 72.9%

          \[\leadsto \color{blue}{\log y \cdot \left(-0.5 - y\right) + y} \]

   12. Applied egg-rr 72.9%

       \[\leadsto \color{blue}{\log y \cdot \left(-0.5 - y\right) + y} \]

   13. Taylor expanded in y around inf 73.1%

       \[\leadsto \color{blue}{y \cdot \left(1 + \log \left(\frac{1}{y}\right)\right)} \]
   14. Step-by-step derivation

       1. log-rec 73.1%

          \[\leadsto y \cdot \left(1 + \color{blue}{\left(-\log y\right)}\right) \]

       2. sub-neg 73.1%

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

   15. Simplified 73.1%

       \[\leadsto \color{blue}{y \cdot \left(1 - \log y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.2 \cdot 10^{-103}:\\ \;\;\;\;x - z\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-87}:\\ \;\;\;\;\log y \cdot -0.5\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+128} \lor \neg \left(y \leq 5.2 \cdot 10^{+139}\right) \land y \leq 3.1 \cdot 10^{+158}:\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \log y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(1 - \log y\right)\\ \mathbf{if}\;y \leq 1.3 \cdot 10^{-109}:\\ \;\;\;\;x - z\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-86}:\\ \;\;\;\;\log y \cdot -0.5 - z\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+33}:\\ \;\;\;\;x - z\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+170}:\\ \;\;\;\;x + t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- 1.0 (log y)))))
   (if (<= y 1.3e-109)
     (- x z)
     (if (<= y 9e-86)
       (- (* (log y) -0.5) z)
       (if (<= y 2e+33) (- x z) (if (<= y 1.6e+170) (+ x t_0) (- t_0 z)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (1.0 - log(y));
	double tmp;
	if (y <= 1.3e-109) {
		tmp = x - z;
	} else if (y <= 9e-86) {
		tmp = (log(y) * -0.5) - z;
	} else if (y <= 2e+33) {
		tmp = x - z;
	} else if (y <= 1.6e+170) {
		tmp = x + t_0;
	} else {
		tmp = t_0 - 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) :: t_0
    real(8) :: tmp
    t_0 = y * (1.0d0 - log(y))
    if (y <= 1.3d-109) then
        tmp = x - z
    else if (y <= 9d-86) then
        tmp = (log(y) * (-0.5d0)) - z
    else if (y <= 2d+33) then
        tmp = x - z
    else if (y <= 1.6d+170) then
        tmp = x + t_0
    else
        tmp = t_0 - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (1.0 - Math.log(y));
	double tmp;
	if (y <= 1.3e-109) {
		tmp = x - z;
	} else if (y <= 9e-86) {
		tmp = (Math.log(y) * -0.5) - z;
	} else if (y <= 2e+33) {
		tmp = x - z;
	} else if (y <= 1.6e+170) {
		tmp = x + t_0;
	} else {
		tmp = t_0 - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (1.0 - math.log(y))
	tmp = 0
	if y <= 1.3e-109:
		tmp = x - z
	elif y <= 9e-86:
		tmp = (math.log(y) * -0.5) - z
	elif y <= 2e+33:
		tmp = x - z
	elif y <= 1.6e+170:
		tmp = x + t_0
	else:
		tmp = t_0 - z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(1.0 - log(y)))
	tmp = 0.0
	if (y <= 1.3e-109)
		tmp = Float64(x - z);
	elseif (y <= 9e-86)
		tmp = Float64(Float64(log(y) * -0.5) - z);
	elseif (y <= 2e+33)
		tmp = Float64(x - z);
	elseif (y <= 1.6e+170)
		tmp = Float64(x + t_0);
	else
		tmp = Float64(t_0 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (1.0 - log(y));
	tmp = 0.0;
	if (y <= 1.3e-109)
		tmp = x - z;
	elseif (y <= 9e-86)
		tmp = (log(y) * -0.5) - z;
	elseif (y <= 2e+33)
		tmp = x - z;
	elseif (y <= 1.6e+170)
		tmp = x + t_0;
	else
		tmp = t_0 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 1.3e-109], N[(x - z), $MachinePrecision], If[LessEqual[y, 9e-86], N[(N[(N[Log[y], $MachinePrecision] * -0.5), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[y, 2e+33], N[(x - z), $MachinePrecision], If[LessEqual[y, 1.6e+170], N[(x + t$95$0), $MachinePrecision], N[(t$95$0 - z), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < 1.2999999999999999e-109 or 8.9999999999999995e-86 < y < 1.9999999999999999e33

   1. Initial program 100.0%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-+l+ 100.0%

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

      4. *-commutative 100.0%

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

      5. distribute-rgt-neg-in 100.0%

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

      6. fma-define 100.0%

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -\left(y + 0.5\right), y - z\right)} \]

      7. +-commutative 100.0%

         \[\leadsto x + \mathsf{fma}\left(\log y, -\color{blue}{\left(0.5 + y\right)}, y - z\right) \]

      8. distribute-neg-in 100.0%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) + \left(-y\right)}, y - z\right) \]

      9. unsub-neg 100.0%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) - y}, y - z\right) \]

      10. metadata-eval 100.0%

          \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{-0.5} - y, y - z\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(\log y, -0.5 - y, y - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 98.1%

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

      1. +-commutative 98.1%

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

   7. Simplified 98.1%

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

   8. Taylor expanded in x around inf 77.4%

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

   if 1.2999999999999999e-109 < y < 8.9999999999999995e-86

   1. Initial program 100.0%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-+l+ 100.0%

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

      4. *-commutative 100.0%

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

      5. distribute-rgt-neg-in 100.0%

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

      6. fma-define 100.0%

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -\left(y + 0.5\right), y - z\right)} \]

      7. +-commutative 100.0%

         \[\leadsto x + \mathsf{fma}\left(\log y, -\color{blue}{\left(0.5 + y\right)}, y - z\right) \]

      8. distribute-neg-in 100.0%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) + \left(-y\right)}, y - z\right) \]

      9. unsub-neg 100.0%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) - y}, y - z\right) \]

      10. metadata-eval 100.0%

          \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{-0.5} - y, y - z\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(\log y, -0.5 - y, y - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 89.3%

      \[\leadsto \color{blue}{-0.5 \cdot \log y} - z \]
   9. Step-by-step derivation

      1. *-commutative 89.3%

         \[\leadsto \color{blue}{\log y \cdot -0.5} - z \]

   10. Simplified 89.3%

       \[\leadsto \color{blue}{\log y \cdot -0.5} - z \]

   if 1.9999999999999999e33 < y < 1.59999999999999989e170

   1. Initial program 99.8%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Step-by-step derivation

      1. associate--l+ 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-+l+ 99.8%

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

      4. *-commutative 99.8%

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

      5. distribute-rgt-neg-in 99.8%

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

      6. fma-define 99.9%

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -\left(y + 0.5\right), y - z\right)} \]

      7. +-commutative 99.9%

         \[\leadsto x + \mathsf{fma}\left(\log y, -\color{blue}{\left(0.5 + y\right)}, y - z\right) \]

      8. distribute-neg-in 99.9%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) + \left(-y\right)}, y - z\right) \]

      9. unsub-neg 99.9%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) - y}, y - z\right) \]

      10. metadata-eval 99.9%

          \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{-0.5} - y, y - z\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(\log y, -0.5 - y, y - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 89.6%

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

      1. log-rec 89.6%

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

      2. sub-neg 89.6%

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

   7. Simplified 89.6%

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

   if 1.59999999999999989e170 < y

   1. Initial program 99.4%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Step-by-step derivation

      1. associate--l+ 99.4%

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

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\left(x - \left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. add-cube-cbrt 98.6%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x - \left(y + 0.5\right) \cdot \log y} \cdot \sqrt[3]{x - \left(y + 0.5\right) \cdot \log y}\right) \cdot \sqrt[3]{x - \left(y + 0.5\right) \cdot \log y}} + \left(y - z\right) \]

      2. pow3 98.6%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x - \left(y + 0.5\right) \cdot \log y}\right)}^{3}} + \left(y - z\right) \]

      3. sub-neg 98.6%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{x + \left(-\left(y + 0.5\right) \cdot \log y\right)}}\right)}^{3} + \left(y - z\right) \]

      4. *-commutative 98.6%

         \[\leadsto {\left(\sqrt[3]{x + \left(-\color{blue}{\log y \cdot \left(y + 0.5\right)}\right)}\right)}^{3} + \left(y - z\right) \]

      5. distribute-rgt-neg-in 98.6%

         \[\leadsto {\left(\sqrt[3]{x + \color{blue}{\log y \cdot \left(-\left(y + 0.5\right)\right)}}\right)}^{3} + \left(y - z\right) \]

      6. +-commutative 98.6%

         \[\leadsto {\left(\sqrt[3]{x + \log y \cdot \left(-\color{blue}{\left(0.5 + y\right)}\right)}\right)}^{3} + \left(y - z\right) \]

      7. distribute-neg-in 98.6%

         \[\leadsto {\left(\sqrt[3]{x + \log y \cdot \color{blue}{\left(\left(-0.5\right) + \left(-y\right)\right)}}\right)}^{3} + \left(y - z\right) \]

      8. metadata-eval 98.6%

         \[\leadsto {\left(\sqrt[3]{x + \log y \cdot \left(\color{blue}{-0.5} + \left(-y\right)\right)}\right)}^{3} + \left(y - z\right) \]

      9. sub-neg 98.6%

         \[\leadsto {\left(\sqrt[3]{x + \log y \cdot \color{blue}{\left(-0.5 - y\right)}}\right)}^{3} + \left(y - z\right) \]

   6. Applied egg-rr 98.6%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \log y \cdot \left(-0.5 - y\right)}\right)}^{3}} + \left(y - z\right) \]

   7. Taylor expanded in y around inf 98.6%

      \[\leadsto {\left(\sqrt[3]{x + \color{blue}{y \cdot \log \left(\frac{1}{y}\right)}}\right)}^{3} + \left(y - z\right) \]
   8. Step-by-step derivation

      1. log-rec 98.6%

         \[\leadsto {\left(\sqrt[3]{x + y \cdot \color{blue}{\left(-\log y\right)}}\right)}^{3} + \left(y - z\right) \]

   9. Simplified 98.6%

      \[\leadsto {\left(\sqrt[3]{x + \color{blue}{y \cdot \left(-\log y\right)}}\right)}^{3} + \left(y - z\right) \]

   10. Taylor expanded in x around 0 90.1%

       \[\leadsto \color{blue}{\left(y + -1 \cdot \left({1}^{0.3333333333333333} \cdot \left(y \cdot \log y\right)\right)\right) - z} \]
   11. Step-by-step derivation

       1. pow-base-1 90.1%

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

       2. *-lft-identity 90.1%

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

       3. neg-mul-1 90.1%

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

       4. *-lft-identity 90.1%

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

       5. distribute-rgt-neg-in 90.1%

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

       6. log-rec 90.1%

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

       7. *-commutative 90.1%

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

       8. distribute-rgt-in 90.3%

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

       9. log-rec 90.3%

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

       10. sub-neg 90.3%

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

   12. Simplified 90.3%

       \[\leadsto \color{blue}{y \cdot \left(1 - \log y\right) - z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.3 \cdot 10^{-109}:\\ \;\;\;\;x - z\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-86}:\\ \;\;\;\;\log y \cdot -0.5 - z\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+33}:\\ \;\;\;\;x - z\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+170}:\\ \;\;\;\;x + y \cdot \left(1 - \log y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \log y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log y \cdot -0.5 - z\\ \mathbf{if}\;x \leq -355:\\ \;\;\;\;x - z\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-302}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{-257}:\\ \;\;\;\;y \cdot \left(1 - \log y\right)\\ \mathbf{elif}\;x \leq 85000000000000:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* (log y) -0.5) z)))
   (if (<= x -355.0)
     (- x z)
     (if (<= x 1.45e-302)
       t_0
       (if (<= x 2.65e-257)
         (* y (- 1.0 (log y)))
         (if (<= x 85000000000000.0) t_0 (- x z)))))))

C

double code(double x, double y, double z) {
	double t_0 = (log(y) * -0.5) - z;
	double tmp;
	if (x <= -355.0) {
		tmp = x - z;
	} else if (x <= 1.45e-302) {
		tmp = t_0;
	} else if (x <= 2.65e-257) {
		tmp = y * (1.0 - log(y));
	} else if (x <= 85000000000000.0) {
		tmp = t_0;
	} else {
		tmp = x - 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) :: t_0
    real(8) :: tmp
    t_0 = (log(y) * (-0.5d0)) - z
    if (x <= (-355.0d0)) then
        tmp = x - z
    else if (x <= 1.45d-302) then
        tmp = t_0
    else if (x <= 2.65d-257) then
        tmp = y * (1.0d0 - log(y))
    else if (x <= 85000000000000.0d0) then
        tmp = t_0
    else
        tmp = x - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (Math.log(y) * -0.5) - z;
	double tmp;
	if (x <= -355.0) {
		tmp = x - z;
	} else if (x <= 1.45e-302) {
		tmp = t_0;
	} else if (x <= 2.65e-257) {
		tmp = y * (1.0 - Math.log(y));
	} else if (x <= 85000000000000.0) {
		tmp = t_0;
	} else {
		tmp = x - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (math.log(y) * -0.5) - z
	tmp = 0
	if x <= -355.0:
		tmp = x - z
	elif x <= 1.45e-302:
		tmp = t_0
	elif x <= 2.65e-257:
		tmp = y * (1.0 - math.log(y))
	elif x <= 85000000000000.0:
		tmp = t_0
	else:
		tmp = x - z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(log(y) * -0.5) - z)
	tmp = 0.0
	if (x <= -355.0)
		tmp = Float64(x - z);
	elseif (x <= 1.45e-302)
		tmp = t_0;
	elseif (x <= 2.65e-257)
		tmp = Float64(y * Float64(1.0 - log(y)));
	elseif (x <= 85000000000000.0)
		tmp = t_0;
	else
		tmp = Float64(x - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (log(y) * -0.5) - z;
	tmp = 0.0;
	if (x <= -355.0)
		tmp = x - z;
	elseif (x <= 1.45e-302)
		tmp = t_0;
	elseif (x <= 2.65e-257)
		tmp = y * (1.0 - log(y));
	elseif (x <= 85000000000000.0)
		tmp = t_0;
	else
		tmp = x - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[Log[y], $MachinePrecision] * -0.5), $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[x, -355.0], N[(x - z), $MachinePrecision], If[LessEqual[x, 1.45e-302], t$95$0, If[LessEqual[x, 2.65e-257], N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 85000000000000.0], t$95$0, N[(x - z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -355 or 8.5e13 < x

   1. Initial program 99.8%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Step-by-step derivation

      1. associate--l+ 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-+l+ 99.9%

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

      4. *-commutative 99.9%

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

      5. distribute-rgt-neg-in 99.9%

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

      6. fma-define 99.9%

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -\left(y + 0.5\right), y - z\right)} \]

      7. +-commutative 99.9%

         \[\leadsto x + \mathsf{fma}\left(\log y, -\color{blue}{\left(0.5 + y\right)}, y - z\right) \]

      8. distribute-neg-in 99.9%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) + \left(-y\right)}, y - z\right) \]

      9. unsub-neg 99.9%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) - y}, y - z\right) \]

      10. metadata-eval 99.9%

          \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{-0.5} - y, y - z\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(\log y, -0.5 - y, y - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 79.6%

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

      1. +-commutative 79.6%

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

   7. Simplified 79.6%

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

   8. Taylor expanded in x around inf 79.6%

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

   if -355 < x < 1.44999999999999997e-302 or 2.65e-257 < x < 8.5e13

   1. Initial program 99.8%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Step-by-step derivation

      1. associate--l+ 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-+l+ 99.8%

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

      4. *-commutative 99.8%

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

      5. distribute-rgt-neg-in 99.8%

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

      6. fma-define 99.9%

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -\left(y + 0.5\right), y - z\right)} \]

      7. +-commutative 99.9%

         \[\leadsto x + \mathsf{fma}\left(\log y, -\color{blue}{\left(0.5 + y\right)}, y - z\right) \]

      8. distribute-neg-in 99.9%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) + \left(-y\right)}, y - z\right) \]

      9. unsub-neg 99.9%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) - y}, y - z\right) \]

      10. metadata-eval 99.9%

          \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{-0.5} - y, y - z\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(\log y, -0.5 - y, y - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 70.0%

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

      1. +-commutative 70.0%

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

   7. Simplified 70.0%

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

   8. Taylor expanded in x around 0 69.9%

      \[\leadsto \color{blue}{-0.5 \cdot \log y} - z \]
   9. Step-by-step derivation

      1. *-commutative 69.9%

         \[\leadsto \color{blue}{\log y \cdot -0.5} - z \]

   10. Simplified 69.9%

       \[\leadsto \color{blue}{\log y \cdot -0.5} - z \]

   if 1.44999999999999997e-302 < x < 2.65e-257

   1. Initial program 99.2%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Step-by-step derivation

      1. associate--l+ 99.2%

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

      2. sub-neg 99.2%

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

      3. associate-+l+ 99.2%

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

      4. *-commutative 99.2%

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

      5. distribute-rgt-neg-in 99.2%

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

      6. fma-define 99.5%

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -\left(y + 0.5\right), y - z\right)} \]

      7. +-commutative 99.5%

         \[\leadsto x + \mathsf{fma}\left(\log y, -\color{blue}{\left(0.5 + y\right)}, y - z\right) \]

      8. distribute-neg-in 99.5%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) + \left(-y\right)}, y - z\right) \]

      9. unsub-neg 99.5%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) - y}, y - z\right) \]

      10. metadata-eval 99.5%

          \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{-0.5} - y, y - z\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(\log y, -0.5 - y, y - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 89.3%

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

      1. +-commutative 89.3%

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

      2. mul-1-neg 89.3%

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

      3. distribute-rgt-in 89.3%

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

      4. distribute-neg-in 89.3%

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

      5. distribute-lft-neg-in 89.3%

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

      6. metadata-eval 89.3%

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

      7. distribute-lft-neg-in 89.3%

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

      8. distribute-rgt-in 89.3%

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

      9. sub-neg 89.3%

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

      10. fma-define 89.6%

          \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)} \]

   7. Simplified 89.6%

      \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)} \]

   8. Taylor expanded in x around 0 89.3%

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

      1. +-commutative 89.3%

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

      2. associate-*r* 89.3%

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

      3. *-commutative 89.3%

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

      4. rem-square-sqrt 0.0%

         \[\leadsto \left(\log y \cdot \color{blue}{\left(\sqrt{-1} \cdot \sqrt{-1}\right)}\right) \cdot \left(0.5 + y\right) + y \]

      5. unpow2 0.0%

         \[\leadsto \left(\log y \cdot \color{blue}{{\left(\sqrt{-1}\right)}^{2}}\right) \cdot \left(0.5 + y\right) + y \]

      6. associate-*r* 0.0%

         \[\leadsto \color{blue}{\log y \cdot \left({\left(\sqrt{-1}\right)}^{2} \cdot \left(0.5 + y\right)\right)} + y \]

      7. distribute-lft-in 0.0%

         \[\leadsto \log y \cdot \color{blue}{\left({\left(\sqrt{-1}\right)}^{2} \cdot 0.5 + {\left(\sqrt{-1}\right)}^{2} \cdot y\right)} + y \]

      8. unpow2 0.0%

         \[\leadsto \log y \cdot \left(\color{blue}{\left(\sqrt{-1} \cdot \sqrt{-1}\right)} \cdot 0.5 + {\left(\sqrt{-1}\right)}^{2} \cdot y\right) + y \]

      9. rem-square-sqrt 0.0%

         \[\leadsto \log y \cdot \left(\color{blue}{-1} \cdot 0.5 + {\left(\sqrt{-1}\right)}^{2} \cdot y\right) + y \]

      10. metadata-eval 0.0%

          \[\leadsto \log y \cdot \left(\color{blue}{-0.5} + {\left(\sqrt{-1}\right)}^{2} \cdot y\right) + y \]

      11. unpow2 0.0%

          \[\leadsto \log y \cdot \left(-0.5 + \color{blue}{\left(\sqrt{-1} \cdot \sqrt{-1}\right)} \cdot y\right) + y \]

      12. rem-square-sqrt 89.3%

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

      13. neg-mul-1 89.3%

          \[\leadsto \log y \cdot \left(-0.5 + \color{blue}{\left(-y\right)}\right) + y \]

      14. sub-neg 89.3%

          \[\leadsto \log y \cdot \color{blue}{\left(-0.5 - y\right)} + y \]

      15. fma-define 89.6%

          \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)} \]

   10. Simplified 89.6%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)} \]
   11. Step-by-step derivation

       1. fma-undefine 89.3%

          \[\leadsto \color{blue}{\log y \cdot \left(-0.5 - y\right) + y} \]

   12. Applied egg-rr 89.3%

       \[\leadsto \color{blue}{\log y \cdot \left(-0.5 - y\right) + y} \]

   13. Taylor expanded in y around inf 76.1%

       \[\leadsto \color{blue}{y \cdot \left(1 + \log \left(\frac{1}{y}\right)\right)} \]
   14. Step-by-step derivation

       1. log-rec 76.1%

          \[\leadsto y \cdot \left(1 + \color{blue}{\left(-\log y\right)}\right) \]

       2. sub-neg 76.1%

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

   15. Simplified 76.1%

       \[\leadsto \color{blue}{y \cdot \left(1 - \log y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -355:\\ \;\;\;\;x - z\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-302}:\\ \;\;\;\;\log y \cdot -0.5 - z\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{-257}:\\ \;\;\;\;y \cdot \left(1 - \log y\right)\\ \mathbf{elif}\;x \leq 85000000000000:\\ \;\;\;\;\log y \cdot -0.5 - z\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.25 \cdot 10^{-109}:\\ \;\;\;\;x - z\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-86}:\\ \;\;\;\;\log y \cdot -0.5 - z\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+32}:\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \log y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.25e-109)
   (- x z)
   (if (<= y 1.9e-86)
     (- (* (log y) -0.5) z)
     (if (<= y 2.05e+32) (- x z) (+ x (* y (- 1.0 (log y))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.25e-109) {
		tmp = x - z;
	} else if (y <= 1.9e-86) {
		tmp = (log(y) * -0.5) - z;
	} else if (y <= 2.05e+32) {
		tmp = x - z;
	} else {
		tmp = x + (y * (1.0 - log(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 <= 1.25d-109) then
        tmp = x - z
    else if (y <= 1.9d-86) then
        tmp = (log(y) * (-0.5d0)) - z
    else if (y <= 2.05d+32) then
        tmp = x - z
    else
        tmp = x + (y * (1.0d0 - log(y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.25e-109) {
		tmp = x - z;
	} else if (y <= 1.9e-86) {
		tmp = (Math.log(y) * -0.5) - z;
	} else if (y <= 2.05e+32) {
		tmp = x - z;
	} else {
		tmp = x + (y * (1.0 - Math.log(y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.25e-109:
		tmp = x - z
	elif y <= 1.9e-86:
		tmp = (math.log(y) * -0.5) - z
	elif y <= 2.05e+32:
		tmp = x - z
	else:
		tmp = x + (y * (1.0 - math.log(y)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.25e-109)
		tmp = Float64(x - z);
	elseif (y <= 1.9e-86)
		tmp = Float64(Float64(log(y) * -0.5) - z);
	elseif (y <= 2.05e+32)
		tmp = Float64(x - z);
	else
		tmp = Float64(x + Float64(y * Float64(1.0 - log(y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.25e-109)
		tmp = x - z;
	elseif (y <= 1.9e-86)
		tmp = (log(y) * -0.5) - z;
	elseif (y <= 2.05e+32)
		tmp = x - z;
	else
		tmp = x + (y * (1.0 - log(y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.25e-109], N[(x - z), $MachinePrecision], If[LessEqual[y, 1.9e-86], N[(N[(N[Log[y], $MachinePrecision] * -0.5), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[y, 2.05e+32], N[(x - z), $MachinePrecision], N[(x + N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.25000000000000005e-109 or 1.9e-86 < y < 2.0499999999999999e32

   1. Initial program 100.0%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-+l+ 100.0%

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

      4. *-commutative 100.0%

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

      5. distribute-rgt-neg-in 100.0%

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

      6. fma-define 100.0%

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -\left(y + 0.5\right), y - z\right)} \]

      7. +-commutative 100.0%

         \[\leadsto x + \mathsf{fma}\left(\log y, -\color{blue}{\left(0.5 + y\right)}, y - z\right) \]

      8. distribute-neg-in 100.0%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) + \left(-y\right)}, y - z\right) \]

      9. unsub-neg 100.0%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) - y}, y - z\right) \]

      10. metadata-eval 100.0%

          \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{-0.5} - y, y - z\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(\log y, -0.5 - y, y - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 98.1%

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

      1. +-commutative 98.1%

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

   7. Simplified 98.1%

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

   8. Taylor expanded in x around inf 77.4%

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

   if 1.25000000000000005e-109 < y < 1.9e-86

   1. Initial program 100.0%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-+l+ 100.0%

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

      4. *-commutative 100.0%

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

      5. distribute-rgt-neg-in 100.0%

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

      6. fma-define 100.0%

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -\left(y + 0.5\right), y - z\right)} \]

      7. +-commutative 100.0%

         \[\leadsto x + \mathsf{fma}\left(\log y, -\color{blue}{\left(0.5 + y\right)}, y - z\right) \]

      8. distribute-neg-in 100.0%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) + \left(-y\right)}, y - z\right) \]

      9. unsub-neg 100.0%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) - y}, y - z\right) \]

      10. metadata-eval 100.0%

          \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{-0.5} - y, y - z\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(\log y, -0.5 - y, y - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 89.3%

      \[\leadsto \color{blue}{-0.5 \cdot \log y} - z \]
   9. Step-by-step derivation

      1. *-commutative 89.3%

         \[\leadsto \color{blue}{\log y \cdot -0.5} - z \]

   10. Simplified 89.3%

       \[\leadsto \color{blue}{\log y \cdot -0.5} - z \]

   if 2.0499999999999999e32 < y

   1. Initial program 99.6%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Step-by-step derivation

      1. associate--l+ 99.6%

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

      2. sub-neg 99.6%

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

      3. associate-+l+ 99.6%

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

      4. *-commutative 99.6%

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

      5. distribute-rgt-neg-in 99.6%

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

      6. fma-define 99.7%

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -\left(y + 0.5\right), y - z\right)} \]

      7. +-commutative 99.7%

         \[\leadsto x + \mathsf{fma}\left(\log y, -\color{blue}{\left(0.5 + y\right)}, y - z\right) \]

      8. distribute-neg-in 99.7%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) + \left(-y\right)}, y - z\right) \]

      9. unsub-neg 99.7%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) - y}, y - z\right) \]

      10. metadata-eval 99.7%

          \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{-0.5} - y, y - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(\log y, -0.5 - y, y - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 85.0%

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

      1. log-rec 85.0%

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

      2. sub-neg 85.0%

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

   7. Simplified 85.0%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.25 \cdot 10^{-109}:\\ \;\;\;\;x - z\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-86}:\\ \;\;\;\;\log y \cdot -0.5 - z\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+32}:\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \log y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(1 - \log y\right)\\ \mathbf{if}\;y \leq 1.32 \cdot 10^{+42}:\\ \;\;\;\;\left(x + \log y \cdot -0.5\right) - z\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+169}:\\ \;\;\;\;x + t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- 1.0 (log y)))))
   (if (<= y 1.32e+42)
     (- (+ x (* (log y) -0.5)) z)
     (if (<= y 3.6e+169) (+ x t_0) (- t_0 z)))))

C

double code(double x, double y, double z) {
	double t_0 = y * (1.0 - log(y));
	double tmp;
	if (y <= 1.32e+42) {
		tmp = (x + (log(y) * -0.5)) - z;
	} else if (y <= 3.6e+169) {
		tmp = x + t_0;
	} else {
		tmp = t_0 - 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) :: t_0
    real(8) :: tmp
    t_0 = y * (1.0d0 - log(y))
    if (y <= 1.32d+42) then
        tmp = (x + (log(y) * (-0.5d0))) - z
    else if (y <= 3.6d+169) then
        tmp = x + t_0
    else
        tmp = t_0 - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (1.0 - Math.log(y));
	double tmp;
	if (y <= 1.32e+42) {
		tmp = (x + (Math.log(y) * -0.5)) - z;
	} else if (y <= 3.6e+169) {
		tmp = x + t_0;
	} else {
		tmp = t_0 - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (1.0 - math.log(y))
	tmp = 0
	if y <= 1.32e+42:
		tmp = (x + (math.log(y) * -0.5)) - z
	elif y <= 3.6e+169:
		tmp = x + t_0
	else:
		tmp = t_0 - z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(1.0 - log(y)))
	tmp = 0.0
	if (y <= 1.32e+42)
		tmp = Float64(Float64(x + Float64(log(y) * -0.5)) - z);
	elseif (y <= 3.6e+169)
		tmp = Float64(x + t_0);
	else
		tmp = Float64(t_0 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (1.0 - log(y));
	tmp = 0.0;
	if (y <= 1.32e+42)
		tmp = (x + (log(y) * -0.5)) - z;
	elseif (y <= 3.6e+169)
		tmp = x + t_0;
	else
		tmp = t_0 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 1.32e+42], N[(N[(x + N[(N[Log[y], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[y, 3.6e+169], N[(x + t$95$0), $MachinePrecision], N[(t$95$0 - z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.32e42

   1. Initial program 100.0%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-+l+ 100.0%

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

      4. *-commutative 100.0%

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

      5. distribute-rgt-neg-in 100.0%

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

      6. fma-define 100.0%

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -\left(y + 0.5\right), y - z\right)} \]

      7. +-commutative 100.0%

         \[\leadsto x + \mathsf{fma}\left(\log y, -\color{blue}{\left(0.5 + y\right)}, y - z\right) \]

      8. distribute-neg-in 100.0%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) + \left(-y\right)}, y - z\right) \]

      9. unsub-neg 100.0%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) - y}, y - z\right) \]

      10. metadata-eval 100.0%

          \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{-0.5} - y, y - z\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(\log y, -0.5 - y, y - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 98.2%

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

      1. +-commutative 98.2%

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

   7. Simplified 98.2%

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

   if 1.32e42 < y < 3.6000000000000001e169

   1. Initial program 99.8%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Step-by-step derivation

      1. associate--l+ 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-+l+ 99.8%

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

      4. *-commutative 99.8%

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

      5. distribute-rgt-neg-in 99.8%

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

      6. fma-define 99.9%

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -\left(y + 0.5\right), y - z\right)} \]

      7. +-commutative 99.9%

         \[\leadsto x + \mathsf{fma}\left(\log y, -\color{blue}{\left(0.5 + y\right)}, y - z\right) \]

      8. distribute-neg-in 99.9%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) + \left(-y\right)}, y - z\right) \]

      9. unsub-neg 99.9%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) - y}, y - z\right) \]

      10. metadata-eval 99.9%

          \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{-0.5} - y, y - z\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(\log y, -0.5 - y, y - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 89.6%

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

      1. log-rec 89.6%

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

      2. sub-neg 89.6%

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

   7. Simplified 89.6%

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

   if 3.6000000000000001e169 < y

   1. Initial program 99.4%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Step-by-step derivation

      1. associate--l+ 99.4%

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

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\left(x - \left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. add-cube-cbrt 98.6%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x - \left(y + 0.5\right) \cdot \log y} \cdot \sqrt[3]{x - \left(y + 0.5\right) \cdot \log y}\right) \cdot \sqrt[3]{x - \left(y + 0.5\right) \cdot \log y}} + \left(y - z\right) \]

      2. pow3 98.6%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x - \left(y + 0.5\right) \cdot \log y}\right)}^{3}} + \left(y - z\right) \]

      3. sub-neg 98.6%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{x + \left(-\left(y + 0.5\right) \cdot \log y\right)}}\right)}^{3} + \left(y - z\right) \]

      4. *-commutative 98.6%

         \[\leadsto {\left(\sqrt[3]{x + \left(-\color{blue}{\log y \cdot \left(y + 0.5\right)}\right)}\right)}^{3} + \left(y - z\right) \]

      5. distribute-rgt-neg-in 98.6%

         \[\leadsto {\left(\sqrt[3]{x + \color{blue}{\log y \cdot \left(-\left(y + 0.5\right)\right)}}\right)}^{3} + \left(y - z\right) \]

      6. +-commutative 98.6%

         \[\leadsto {\left(\sqrt[3]{x + \log y \cdot \left(-\color{blue}{\left(0.5 + y\right)}\right)}\right)}^{3} + \left(y - z\right) \]

      7. distribute-neg-in 98.6%

         \[\leadsto {\left(\sqrt[3]{x + \log y \cdot \color{blue}{\left(\left(-0.5\right) + \left(-y\right)\right)}}\right)}^{3} + \left(y - z\right) \]

      8. metadata-eval 98.6%

         \[\leadsto {\left(\sqrt[3]{x + \log y \cdot \left(\color{blue}{-0.5} + \left(-y\right)\right)}\right)}^{3} + \left(y - z\right) \]

      9. sub-neg 98.6%

         \[\leadsto {\left(\sqrt[3]{x + \log y \cdot \color{blue}{\left(-0.5 - y\right)}}\right)}^{3} + \left(y - z\right) \]

   6. Applied egg-rr 98.6%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \log y \cdot \left(-0.5 - y\right)}\right)}^{3}} + \left(y - z\right) \]

   7. Taylor expanded in y around inf 98.6%

      \[\leadsto {\left(\sqrt[3]{x + \color{blue}{y \cdot \log \left(\frac{1}{y}\right)}}\right)}^{3} + \left(y - z\right) \]
   8. Step-by-step derivation

      1. log-rec 98.6%

         \[\leadsto {\left(\sqrt[3]{x + y \cdot \color{blue}{\left(-\log y\right)}}\right)}^{3} + \left(y - z\right) \]

   9. Simplified 98.6%

      \[\leadsto {\left(\sqrt[3]{x + \color{blue}{y \cdot \left(-\log y\right)}}\right)}^{3} + \left(y - z\right) \]

   10. Taylor expanded in x around 0 90.1%

       \[\leadsto \color{blue}{\left(y + -1 \cdot \left({1}^{0.3333333333333333} \cdot \left(y \cdot \log y\right)\right)\right) - z} \]
   11. Step-by-step derivation

       1. pow-base-1 90.1%

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

       2. *-lft-identity 90.1%

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

       3. neg-mul-1 90.1%

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

       4. *-lft-identity 90.1%

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

       5. distribute-rgt-neg-in 90.1%

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

       6. log-rec 90.1%

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

       7. *-commutative 90.1%

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

       8. distribute-rgt-in 90.3%

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

       9. log-rec 90.3%

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

       10. sub-neg 90.3%

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

   12. Simplified 90.3%

       \[\leadsto \color{blue}{y \cdot \left(1 - \log y\right) - z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.32 \cdot 10^{+42}:\\ \;\;\;\;\left(x + \log y \cdot -0.5\right) - z\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+169}:\\ \;\;\;\;x + y \cdot \left(1 - \log y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \log y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 55.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.38 \lor \neg \left(z \leq -8.6 \cdot 10^{-224}\right):\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot -0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.38) (not (<= z -8.6e-224))) (- x z) (* (log y) -0.5)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.38) || !(z <= -8.6e-224)) {
		tmp = x - z;
	} else {
		tmp = log(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 ((z <= (-0.38d0)) .or. (.not. (z <= (-8.6d-224)))) then
        tmp = x - z
    else
        tmp = log(y) * (-0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.38) || !(z <= -8.6e-224)) {
		tmp = x - z;
	} else {
		tmp = Math.log(y) * -0.5;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.38) or not (z <= -8.6e-224):
		tmp = x - z
	else:
		tmp = math.log(y) * -0.5
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.38) || !(z <= -8.6e-224))
		tmp = Float64(x - z);
	else
		tmp = Float64(log(y) * -0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.38) || ~((z <= -8.6e-224)))
		tmp = x - z;
	else
		tmp = log(y) * -0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.38], N[Not[LessEqual[z, -8.6e-224]], $MachinePrecision]], N[(x - z), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * -0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.38 or -8.6e-224 < z

   1. Initial program 99.8%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Step-by-step derivation

      1. associate--l+ 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-+l+ 99.8%

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

      4. *-commutative 99.8%

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

      5. distribute-rgt-neg-in 99.8%

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

      6. fma-define 99.9%

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -\left(y + 0.5\right), y - z\right)} \]

      7. +-commutative 99.9%

         \[\leadsto x + \mathsf{fma}\left(\log y, -\color{blue}{\left(0.5 + y\right)}, y - z\right) \]

      8. distribute-neg-in 99.9%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) + \left(-y\right)}, y - z\right) \]

      9. unsub-neg 99.9%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) - y}, y - z\right) \]

      10. metadata-eval 99.9%

          \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{-0.5} - y, y - z\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(\log y, -0.5 - y, y - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 75.7%

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

      1. +-commutative 75.7%

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

   7. Simplified 75.7%

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

   8. Taylor expanded in x around inf 68.2%

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

   if -0.38 < z < -8.6e-224

   1. Initial program 99.6%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Step-by-step derivation

      1. associate--l+ 99.6%

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

      2. sub-neg 99.6%

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

      3. associate-+l+ 99.6%

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

      4. *-commutative 99.6%

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

      5. distribute-rgt-neg-in 99.6%

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

      6. fma-define 99.8%

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -\left(y + 0.5\right), y - z\right)} \]

      7. +-commutative 99.8%

         \[\leadsto x + \mathsf{fma}\left(\log y, -\color{blue}{\left(0.5 + y\right)}, y - z\right) \]

      8. distribute-neg-in 99.8%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) + \left(-y\right)}, y - z\right) \]

      9. unsub-neg 99.8%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) - y}, y - z\right) \]

      10. metadata-eval 99.8%

          \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{-0.5} - y, y - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(\log y, -0.5 - y, y - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 99.6%

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

      1. +-commutative 99.6%

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

      2. mul-1-neg 99.6%

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

      3. distribute-rgt-in 99.7%

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

      4. distribute-neg-in 99.7%

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

      5. distribute-lft-neg-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. distribute-lft-neg-in 99.7%

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

      8. distribute-rgt-in 99.6%

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

      9. sub-neg 99.6%

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

      10. fma-define 99.8%

          \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)} \]

   7. Simplified 99.8%

      \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)} \]

   8. Taylor expanded in x around 0 81.3%

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

      1. +-commutative 81.3%

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

      2. associate-*r* 81.3%

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

      3. *-commutative 81.3%

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

      4. rem-square-sqrt 0.0%

         \[\leadsto \left(\log y \cdot \color{blue}{\left(\sqrt{-1} \cdot \sqrt{-1}\right)}\right) \cdot \left(0.5 + y\right) + y \]

      5. unpow2 0.0%

         \[\leadsto \left(\log y \cdot \color{blue}{{\left(\sqrt{-1}\right)}^{2}}\right) \cdot \left(0.5 + y\right) + y \]

      6. associate-*r* 0.0%

         \[\leadsto \color{blue}{\log y \cdot \left({\left(\sqrt{-1}\right)}^{2} \cdot \left(0.5 + y\right)\right)} + y \]

      7. distribute-lft-in 0.0%

         \[\leadsto \log y \cdot \color{blue}{\left({\left(\sqrt{-1}\right)}^{2} \cdot 0.5 + {\left(\sqrt{-1}\right)}^{2} \cdot y\right)} + y \]

      8. unpow2 0.0%

         \[\leadsto \log y \cdot \left(\color{blue}{\left(\sqrt{-1} \cdot \sqrt{-1}\right)} \cdot 0.5 + {\left(\sqrt{-1}\right)}^{2} \cdot y\right) + y \]

      9. rem-square-sqrt 0.0%

         \[\leadsto \log y \cdot \left(\color{blue}{-1} \cdot 0.5 + {\left(\sqrt{-1}\right)}^{2} \cdot y\right) + y \]

      10. metadata-eval 0.0%

          \[\leadsto \log y \cdot \left(\color{blue}{-0.5} + {\left(\sqrt{-1}\right)}^{2} \cdot y\right) + y \]

      11. unpow2 0.0%

          \[\leadsto \log y \cdot \left(-0.5 + \color{blue}{\left(\sqrt{-1} \cdot \sqrt{-1}\right)} \cdot y\right) + y \]

      12. rem-square-sqrt 81.3%

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

      13. neg-mul-1 81.3%

          \[\leadsto \log y \cdot \left(-0.5 + \color{blue}{\left(-y\right)}\right) + y \]

      14. sub-neg 81.3%

          \[\leadsto \log y \cdot \color{blue}{\left(-0.5 - y\right)} + y \]

      15. fma-define 81.4%

          \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)} \]

   10. Simplified 81.4%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, -0.5 - y, y\right)} \]
   11. Step-by-step derivation

       1. fma-undefine 81.3%

          \[\leadsto \color{blue}{\log y \cdot \left(-0.5 - y\right) + y} \]

   12. Applied egg-rr 81.3%

       \[\leadsto \color{blue}{\log y \cdot \left(-0.5 - y\right) + y} \]

   13. Taylor expanded in y around 0 43.6%

       \[\leadsto \color{blue}{-0.5 \cdot \log y} \]
   14. Step-by-step derivation

       1. *-commutative 43.6%

          \[\leadsto \color{blue}{\log y \cdot -0.5} \]

   15. Simplified 43.6%

       \[\leadsto \color{blue}{\log y \cdot -0.5} \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.38 \lor \neg \left(z \leq -8.6 \cdot 10^{-224}\right):\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot -0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(y - z\right) + \left(x - \log y \cdot \left(y + 0.5\right)\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (- y z) (- x (* (log y) (+ y 0.5)))))

C

double code(double x, double y, double z) {
	return (y - z) + (x - (log(y) * (y + 0.5)));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (y - z) + (x - (log(y) * (y + 0.5d0)))
end function

Java

public static double code(double x, double y, double z) {
	return (y - z) + (x - (Math.log(y) * (y + 0.5)));
}

Python

def code(x, y, z):
	return (y - z) + (x - (math.log(y) * (y + 0.5)))

Julia

function code(x, y, z)
	return Float64(Float64(y - z) + Float64(x - Float64(log(y) * Float64(y + 0.5))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (y - z) + (x - (log(y) * (y + 0.5)));
end

Wolfram

code[x_, y_, z_] := N[(N[(y - z), $MachinePrecision] + N[(x - N[(N[Log[y], $MachinePrecision] * N[(y + 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
2. Step-by-step derivation

   1. associate--l+ 99.8%

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

3. Simplified 99.8%

   \[\leadsto \color{blue}{\left(x - \left(y + 0.5\right) \cdot \log y\right) + \left(y - z\right)} \]
4. Add Preprocessing

5. Final simplification 99.8%

   \[\leadsto \left(y - z\right) + \left(x - \log y \cdot \left(y + 0.5\right)\right) \]
6. Add Preprocessing

Alternative 11: 46.8% accurate, 9.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+106}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+28}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5e+106) x (if (<= x 3.7e+28) (- z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5e+106) {
		tmp = x;
	} else if (x <= 3.7e+28) {
		tmp = -z;
	} 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 (x <= (-5.5d+106)) then
        tmp = x
    else if (x <= 3.7d+28) then
        tmp = -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5e+106) {
		tmp = x;
	} else if (x <= 3.7e+28) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.5e+106:
		tmp = x
	elif x <= 3.7e+28:
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5e+106)
		tmp = x;
	elseif (x <= 3.7e+28)
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.5e+106)
		tmp = x;
	elseif (x <= 3.7e+28)
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5e+106], x, If[LessEqual[x, 3.7e+28], (-z), x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5e106 or 3.6999999999999999e28 < x

   1. Initial program 99.8%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Step-by-step derivation

      1. associate--l+ 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-+l+ 99.9%

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

      4. *-commutative 99.9%

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

      5. distribute-rgt-neg-in 99.9%

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

      6. fma-define 99.9%

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -\left(y + 0.5\right), y - z\right)} \]

      7. +-commutative 99.9%

         \[\leadsto x + \mathsf{fma}\left(\log y, -\color{blue}{\left(0.5 + y\right)}, y - z\right) \]

      8. distribute-neg-in 99.9%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) + \left(-y\right)}, y - z\right) \]

      9. unsub-neg 99.9%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) - y}, y - z\right) \]

      10. metadata-eval 99.9%

          \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{-0.5} - y, y - z\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(\log y, -0.5 - y, y - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 70.0%

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

   if -5.5e106 < x < 3.6999999999999999e28

   1. Initial program 99.7%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Step-by-step derivation

      1. associate--l+ 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-+l+ 99.8%

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

      4. *-commutative 99.8%

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

      5. distribute-rgt-neg-in 99.8%

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

      6. fma-define 99.9%

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -\left(y + 0.5\right), y - z\right)} \]

      7. +-commutative 99.9%

         \[\leadsto x + \mathsf{fma}\left(\log y, -\color{blue}{\left(0.5 + y\right)}, y - z\right) \]

      8. distribute-neg-in 99.9%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) + \left(-y\right)}, y - z\right) \]

      9. unsub-neg 99.9%

         \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) - y}, y - z\right) \]

      10. metadata-eval 99.9%

          \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{-0.5} - y, y - z\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(\log y, -0.5 - y, y - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 67.4%

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

      1. +-commutative 67.4%

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

   7. Simplified 67.4%

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

   8. Taylor expanded in z around inf 40.8%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   9. Step-by-step derivation

      1. neg-mul-1 40.8%

         \[\leadsto \color{blue}{-z} \]

   10. Simplified 40.8%

       \[\leadsto \color{blue}{-z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+106}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+28}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.8% accurate, 37.0× speedup

Math

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

FPCore

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

C

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

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 - z
end function

Java

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

Python

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

Julia

function code(x, y, z)
	return Float64(x - z)
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x - z), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
2. Step-by-step derivation

   1. associate--l+ 99.8%

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

   2. sub-neg 99.8%

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

   3. associate-+l+ 99.8%

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

   4. *-commutative 99.8%

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

   5. distribute-rgt-neg-in 99.8%

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

   6. fma-define 99.9%

      \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -\left(y + 0.5\right), y - z\right)} \]

   7. +-commutative 99.9%

      \[\leadsto x + \mathsf{fma}\left(\log y, -\color{blue}{\left(0.5 + y\right)}, y - z\right) \]

   8. distribute-neg-in 99.9%

      \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) + \left(-y\right)}, y - z\right) \]

   9. unsub-neg 99.9%

      \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) - y}, y - z\right) \]

   10. metadata-eval 99.9%

       \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{-0.5} - y, y - z\right) \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{x + \mathsf{fma}\left(\log y, -0.5 - y, y - z\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 72.9%

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

   1. +-commutative 72.9%

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

7. Simplified 72.9%

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

8. Taylor expanded in x around inf 59.1%

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

9. Final simplification 59.1%

   \[\leadsto x - z \]
10. Add Preprocessing

Alternative 13: 29.5% accurate, 111.0× 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 99.8%

   \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
2. Step-by-step derivation

   1. associate--l+ 99.8%

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

   2. sub-neg 99.8%

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

   3. associate-+l+ 99.8%

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

   4. *-commutative 99.8%

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

   5. distribute-rgt-neg-in 99.8%

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

   6. fma-define 99.9%

      \[\leadsto x + \color{blue}{\mathsf{fma}\left(\log y, -\left(y + 0.5\right), y - z\right)} \]

   7. +-commutative 99.9%

      \[\leadsto x + \mathsf{fma}\left(\log y, -\color{blue}{\left(0.5 + y\right)}, y - z\right) \]

   8. distribute-neg-in 99.9%

      \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) + \left(-y\right)}, y - z\right) \]

   9. unsub-neg 99.9%

      \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{\left(-0.5\right) - y}, y - z\right) \]

   10. metadata-eval 99.9%

       \[\leadsto x + \mathsf{fma}\left(\log y, \color{blue}{-0.5} - y, y - z\right) \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{x + \mathsf{fma}\left(\log y, -0.5 - y, y - z\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 30.5%

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

6. Final simplification 30.5%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(y + x\right) - z\right) - \left(y + 0.5\right) \cdot \log y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (- (+ y x) z) (* (+ y 0.5) (log y))))

C

double code(double x, double y, double z) {
	return ((y + x) - z) - ((y + 0.5) * log(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 = ((y + x) - z) - ((y + 0.5d0) * log(y))
end function

Java

public static double code(double x, double y, double z) {
	return ((y + x) - z) - ((y + 0.5) * Math.log(y));
}

Python

def code(x, y, z):
	return ((y + x) - z) - ((y + 0.5) * math.log(y))

Julia

function code(x, y, z)
	return Float64(Float64(Float64(y + x) - z) - Float64(Float64(y + 0.5) * log(y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((y + x) - z) - ((y + 0.5) * log(y));
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(y + x), $MachinePrecision] - z), $MachinePrecision] - N[(N[(y + 0.5), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024046 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"
  :precision binary64

  :alt
  (- (- (+ y x) z) (* (+ y 0.5) (log y)))

  (- (+ (- x (* (+ y 0.5) (log y))) y) z))