Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2

Percentage Accurate: 99.8% → 99.9%

Time: 9.8s

Alternatives: 11

Speedup: 1.0×

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

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

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 + Float64(fma(log(y), Float64(-0.5 - y), y) - z))
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[Log[y], $MachinePrecision] * N[(-0.5 - y), $MachinePrecision] + y), $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. sub-neg 99.8%

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

   2. sub-neg 99.8%

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

   3. associate-+l+ 99.8%

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

   4. associate-+l+ 99.8%

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

   5. sub-neg 99.8%

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

   6. neg-sub0 99.8%

      \[\leadsto x + \left(\left(\color{blue}{\left(0 - \left(y + 0.5\right) \cdot \log y\right)} + y\right) - z\right) \]

   7. associate-+l- 99.8%

      \[\leadsto x + \left(\color{blue}{\left(0 - \left(\left(y + 0.5\right) \cdot \log y - y\right)\right)} - z\right) \]

   8. neg-sub0 99.8%

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

   9. neg-mul-1 99.8%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 76.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2 \cdot 10^{+60} \lor \neg \left(y \leq 1.36 \cdot 10^{+160}\right) \land y \leq 3.5 \cdot 10^{+174}:\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \log y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y 2e+60) (and (not (<= y 1.36e+160)) (<= y 3.5e+174)))
   (- x z)
   (+ x (* y (- 1.0 (log y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= 2e+60) || (!(y <= 1.36e+160) && (y <= 3.5e+174))) {
		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 <= 2d+60) .or. (.not. (y <= 1.36d+160)) .and. (y <= 3.5d+174)) 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 <= 2e+60) || (!(y <= 1.36e+160) && (y <= 3.5e+174))) {
		tmp = x - z;
	} else {
		tmp = x + (y * (1.0 - Math.log(y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= 2e+60) or (not (y <= 1.36e+160) and (y <= 3.5e+174)):
		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 <= 2e+60) || (!(y <= 1.36e+160) && (y <= 3.5e+174)))
		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 <= 2e+60) || (~((y <= 1.36e+160)) && (y <= 3.5e+174)))
		tmp = x - z;
	else
		tmp = x + (y * (1.0 - log(y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, 2e+60], And[N[Not[LessEqual[y, 1.36e+160]], $MachinePrecision], LessEqual[y, 3.5e+174]]], N[(x - z), $MachinePrecision], N[(x + N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.9999999999999999e60 or 1.35999999999999997e160 < y < 3.5000000000000001e174

   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. add-cube-cbrt 98.9%

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

      2. pow2 98.9%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + y}\right)}^{2}} \cdot \sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + y} - z \]

      3. +-commutative 98.9%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{y + \left(x - \left(y + 0.5\right) \cdot \log y\right)}}\right)}^{2} \cdot \sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + y} - z \]

      4. *-commutative 98.9%

         \[\leadsto {\left(\sqrt[3]{y + \left(x - \color{blue}{\log y \cdot \left(y + 0.5\right)}\right)}\right)}^{2} \cdot \sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + y} - z \]

      5. +-commutative 98.9%

         \[\leadsto {\left(\sqrt[3]{y + \left(x - \log y \cdot \left(y + 0.5\right)\right)}\right)}^{2} \cdot \sqrt[3]{\color{blue}{y + \left(x - \left(y + 0.5\right) \cdot \log y\right)}} - z \]

      6. *-commutative 98.9%

         \[\leadsto {\left(\sqrt[3]{y + \left(x - \log y \cdot \left(y + 0.5\right)\right)}\right)}^{2} \cdot \sqrt[3]{y + \left(x - \color{blue}{\log y \cdot \left(y + 0.5\right)}\right)} - z \]

   3. Applied egg-rr 98.9%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{y + \left(x - \log y \cdot \left(y + 0.5\right)\right)}\right)}^{2} \cdot \sqrt[3]{y + \left(x - \log y \cdot \left(y + 0.5\right)\right)}} - z \]

   4. Taylor expanded in x around inf 76.7%

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

   if 1.9999999999999999e60 < y < 1.35999999999999997e160 or 3.5000000000000001e174 < 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. add-cbrt-cube 22.1%

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

      2. pow3 22.1%

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

      3. *-commutative 22.1%

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

   3. Applied egg-rr 22.1%

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

   4. Taylor expanded in y around inf 22.1%

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

      1. mul-1-neg 22.1%

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

      2. distribute-rgt-neg-in 22.1%

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

      3. log-rec 22.1%

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

      4. remove-double-neg 22.1%

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

   6. Simplified 22.1%

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

   7. Taylor expanded in y around 0 99.8%

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

   8. Taylor expanded in z around 0 84.9%

      \[\leadsto \color{blue}{\left(1 - \log y\right) \cdot y + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2 \cdot 10^{+60} \lor \neg \left(y \leq 1.36 \cdot 10^{+160}\right) \land y \leq 3.5 \cdot 10^{+174}:\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \log y\right)\\ \end{array} \]

Alternative 3: 89.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 9 \cdot 10^{+55} \lor \neg \left(y \leq 1.26 \cdot 10^{+160}\right) \land y \leq 3 \cdot 10^{+174}:\\ \;\;\;\;x - \left(z + \log y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \log y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y 9e+55) (and (not (<= y 1.26e+160)) (<= y 3e+174)))
   (- x (+ z (* (log y) 0.5)))
   (+ x (* y (- 1.0 (log y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= 9e+55) || (!(y <= 1.26e+160) && (y <= 3e+174))) {
		tmp = x - (z + (log(y) * 0.5));
	} 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 <= 9d+55) .or. (.not. (y <= 1.26d+160)) .and. (y <= 3d+174)) then
        tmp = x - (z + (log(y) * 0.5d0))
    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 <= 9e+55) || (!(y <= 1.26e+160) && (y <= 3e+174))) {
		tmp = x - (z + (Math.log(y) * 0.5));
	} else {
		tmp = x + (y * (1.0 - Math.log(y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= 9e+55) or (not (y <= 1.26e+160) and (y <= 3e+174)):
		tmp = x - (z + (math.log(y) * 0.5))
	else:
		tmp = x + (y * (1.0 - math.log(y)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= 9e+55) || (!(y <= 1.26e+160) && (y <= 3e+174)))
		tmp = Float64(x - Float64(z + Float64(log(y) * 0.5)));
	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 <= 9e+55) || (~((y <= 1.26e+160)) && (y <= 3e+174)))
		tmp = x - (z + (log(y) * 0.5));
	else
		tmp = x + (y * (1.0 - log(y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, 9e+55], And[N[Not[LessEqual[y, 1.26e+160]], $MachinePrecision], LessEqual[y, 3e+174]]], N[(x - N[(z + N[(N[Log[y], $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.99999999999999996e55 or 1.26000000000000001e160 < y < 3e174

   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+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 96.7%

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

   if 8.99999999999999996e55 < y < 1.26000000000000001e160 or 3e174 < 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. add-cbrt-cube 22.1%

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

      2. pow3 22.1%

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

      3. *-commutative 22.1%

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

   3. Applied egg-rr 22.1%

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

   4. Taylor expanded in y around inf 22.1%

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

      1. mul-1-neg 22.1%

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

      2. distribute-rgt-neg-in 22.1%

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

      3. log-rec 22.1%

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

      4. remove-double-neg 22.1%

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

   6. Simplified 22.1%

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

   7. Taylor expanded in y around 0 99.8%

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

   8. Taylor expanded in z around 0 84.9%

      \[\leadsto \color{blue}{\left(1 - \log y\right) \cdot y + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 9 \cdot 10^{+55} \lor \neg \left(y \leq 1.26 \cdot 10^{+160}\right) \land y \leq 3 \cdot 10^{+174}:\\ \;\;\;\;x - \left(z + \log y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \log y\right)\\ \end{array} \]

Alternative 4: 70.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.6 \cdot 10^{+62} \lor \neg \left(y \leq 6 \cdot 10^{+94}\right) \land y \leq 2.6 \cdot 10^{+180}:\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot \log y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y 3.6e+62) (and (not (<= y 6e+94)) (<= y 2.6e+180)))
   (- x z)
   (- y (* y (log y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= 3.6e+62) || (!(y <= 6e+94) && (y <= 2.6e+180))) {
		tmp = x - z;
	} else {
		tmp = y - (y * 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 <= 3.6d+62) .or. (.not. (y <= 6d+94)) .and. (y <= 2.6d+180)) then
        tmp = x - z
    else
        tmp = y - (y * log(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= 3.6e+62) || (!(y <= 6e+94) && (y <= 2.6e+180))) {
		tmp = x - z;
	} else {
		tmp = y - (y * Math.log(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= 3.6e+62) or (not (y <= 6e+94) and (y <= 2.6e+180)):
		tmp = x - z
	else:
		tmp = y - (y * math.log(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= 3.6e+62) || (!(y <= 6e+94) && (y <= 2.6e+180)))
		tmp = Float64(x - z);
	else
		tmp = Float64(y - Float64(y * log(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= 3.6e+62) || (~((y <= 6e+94)) && (y <= 2.6e+180)))
		tmp = x - z;
	else
		tmp = y - (y * log(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, 3.6e+62], And[N[Not[LessEqual[y, 6e+94]], $MachinePrecision], LessEqual[y, 2.6e+180]]], N[(x - z), $MachinePrecision], N[(y - N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.6e62 or 6.0000000000000001e94 < y < 2.60000000000000021e180

   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. add-cube-cbrt 98.7%

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

      2. pow2 98.7%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + y}\right)}^{2}} \cdot \sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + y} - z \]

      3. +-commutative 98.7%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{y + \left(x - \left(y + 0.5\right) \cdot \log y\right)}}\right)}^{2} \cdot \sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + y} - z \]

      4. *-commutative 98.7%

         \[\leadsto {\left(\sqrt[3]{y + \left(x - \color{blue}{\log y \cdot \left(y + 0.5\right)}\right)}\right)}^{2} \cdot \sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + y} - z \]

      5. +-commutative 98.7%

         \[\leadsto {\left(\sqrt[3]{y + \left(x - \log y \cdot \left(y + 0.5\right)\right)}\right)}^{2} \cdot \sqrt[3]{\color{blue}{y + \left(x - \left(y + 0.5\right) \cdot \log y\right)}} - z \]

      6. *-commutative 98.7%

         \[\leadsto {\left(\sqrt[3]{y + \left(x - \log y \cdot \left(y + 0.5\right)\right)}\right)}^{2} \cdot \sqrt[3]{y + \left(x - \color{blue}{\log y \cdot \left(y + 0.5\right)}\right)} - z \]

   3. Applied egg-rr 98.7%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{y + \left(x - \log y \cdot \left(y + 0.5\right)\right)}\right)}^{2} \cdot \sqrt[3]{y + \left(x - \log y \cdot \left(y + 0.5\right)\right)}} - z \]

   4. Taylor expanded in x around inf 73.2%

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

   if 3.6e62 < y < 6.0000000000000001e94 or 2.60000000000000021e180 < y

   1. Initial program 99.5%

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

      1. sub-neg 99.5%

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

      2. sub-neg 99.5%

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

      3. associate-+l+ 99.5%

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

      4. associate-+l+ 99.5%

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

      5. sub-neg 99.5%

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

      6. neg-sub0 99.5%

         \[\leadsto x + \left(\left(\color{blue}{\left(0 - \left(y + 0.5\right) \cdot \log y\right)} + y\right) - z\right) \]

      7. associate-+l- 99.5%

         \[\leadsto x + \left(\color{blue}{\left(0 - \left(\left(y + 0.5\right) \cdot \log y - y\right)\right)} - z\right) \]

      8. neg-sub0 99.5%

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

      9. neg-mul-1 99.5%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 89.8%

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

      1. +-commutative 89.8%

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

      2. mul-1-neg 89.8%

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

      3. sub-neg 89.8%

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

      4. associate--l+ 89.8%

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

      5. +-commutative 89.8%

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

      6. *-commutative 89.8%

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

      7. sub-neg 89.8%

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

      8. +-commutative 89.8%

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

      9. distribute-rgt-neg-in 89.8%

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

      10. fma-def 89.8%

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

      11. +-commutative 89.8%

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

      12. distribute-neg-in 89.8%

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

      13. metadata-eval 89.8%

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

      14. sub-neg 89.8%

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

   6. Simplified 89.8%

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

   7. Taylor expanded in x around 0 78.2%

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

      1. associate-*r* 78.2%

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

      2. +-commutative 78.2%

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

      3. neg-mul-1 78.2%

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

      4. *-commutative 78.2%

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

      5. distribute-neg-in 78.2%

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

      6. metadata-eval 78.2%

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

   9. Simplified 78.2%

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

   10. Taylor expanded in y around inf 78.2%

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

       1. *-commutative 78.2%

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

       2. log-rec 78.2%

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

       3. distribute-lft-neg-in 78.2%

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

       4. distribute-rgt-neg-in 78.2%

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

   12. Simplified 78.2%

       \[\leadsto y + \color{blue}{\log y \cdot \left(-y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.6 \cdot 10^{+62} \lor \neg \left(y \leq 6 \cdot 10^{+94}\right) \land y \leq 2.6 \cdot 10^{+180}:\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot \log y\\ \end{array} \]

Alternative 5: 70.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.6 \cdot 10^{+62}:\\ \;\;\;\;x - z\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{+94}:\\ \;\;\;\;y + \log y \cdot \left(-0.5 - y\right)\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+180}:\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot \log y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 3.6e+62)
   (- x z)
   (if (<= y 5.7e+94)
     (+ y (* (log y) (- -0.5 y)))
     (if (<= y 1.12e+180) (- x z) (- y (* y (log y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 3.6e+62) {
		tmp = x - z;
	} else if (y <= 5.7e+94) {
		tmp = y + (log(y) * (-0.5 - y));
	} else if (y <= 1.12e+180) {
		tmp = x - z;
	} else {
		tmp = y - (y * 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 <= 3.6d+62) then
        tmp = x - z
    else if (y <= 5.7d+94) then
        tmp = y + (log(y) * ((-0.5d0) - y))
    else if (y <= 1.12d+180) then
        tmp = x - z
    else
        tmp = y - (y * log(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 3.6e+62) {
		tmp = x - z;
	} else if (y <= 5.7e+94) {
		tmp = y + (Math.log(y) * (-0.5 - y));
	} else if (y <= 1.12e+180) {
		tmp = x - z;
	} else {
		tmp = y - (y * Math.log(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 3.6e+62:
		tmp = x - z
	elif y <= 5.7e+94:
		tmp = y + (math.log(y) * (-0.5 - y))
	elif y <= 1.12e+180:
		tmp = x - z
	else:
		tmp = y - (y * math.log(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 3.6e+62)
		tmp = Float64(x - z);
	elseif (y <= 5.7e+94)
		tmp = Float64(y + Float64(log(y) * Float64(-0.5 - y)));
	elseif (y <= 1.12e+180)
		tmp = Float64(x - z);
	else
		tmp = Float64(y - Float64(y * log(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 3.6e+62)
		tmp = x - z;
	elseif (y <= 5.7e+94)
		tmp = y + (log(y) * (-0.5 - y));
	elseif (y <= 1.12e+180)
		tmp = x - z;
	else
		tmp = y - (y * log(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 3.6e+62], N[(x - z), $MachinePrecision], If[LessEqual[y, 5.7e+94], N[(y + N[(N[Log[y], $MachinePrecision] * N[(-0.5 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.12e+180], N[(x - z), $MachinePrecision], N[(y - N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 3.6e62 or 5.7000000000000002e94 < y < 1.12e180

   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. add-cube-cbrt 98.7%

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

      2. pow2 98.7%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + y}\right)}^{2}} \cdot \sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + y} - z \]

      3. +-commutative 98.7%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{y + \left(x - \left(y + 0.5\right) \cdot \log y\right)}}\right)}^{2} \cdot \sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + y} - z \]

      4. *-commutative 98.7%

         \[\leadsto {\left(\sqrt[3]{y + \left(x - \color{blue}{\log y \cdot \left(y + 0.5\right)}\right)}\right)}^{2} \cdot \sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + y} - z \]

      5. +-commutative 98.7%

         \[\leadsto {\left(\sqrt[3]{y + \left(x - \log y \cdot \left(y + 0.5\right)\right)}\right)}^{2} \cdot \sqrt[3]{\color{blue}{y + \left(x - \left(y + 0.5\right) \cdot \log y\right)}} - z \]

      6. *-commutative 98.7%

         \[\leadsto {\left(\sqrt[3]{y + \left(x - \log y \cdot \left(y + 0.5\right)\right)}\right)}^{2} \cdot \sqrt[3]{y + \left(x - \color{blue}{\log y \cdot \left(y + 0.5\right)}\right)} - z \]

   3. Applied egg-rr 98.7%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{y + \left(x - \log y \cdot \left(y + 0.5\right)\right)}\right)}^{2} \cdot \sqrt[3]{y + \left(x - \log y \cdot \left(y + 0.5\right)\right)}} - z \]

   4. Taylor expanded in x around inf 73.2%

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

   if 3.6e62 < y < 5.7000000000000002e94

   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. sub-neg 99.6%

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

      2. sub-neg 99.6%

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

      3. associate-+l+ 99.6%

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

      4. associate-+l+ 99.6%

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

      5. sub-neg 99.6%

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

      6. neg-sub0 99.6%

         \[\leadsto x + \left(\left(\color{blue}{\left(0 - \left(y + 0.5\right) \cdot \log y\right)} + y\right) - z\right) \]

      7. associate-+l- 99.6%

         \[\leadsto x + \left(\color{blue}{\left(0 - \left(\left(y + 0.5\right) \cdot \log y - y\right)\right)} - z\right) \]

      8. neg-sub0 99.6%

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

      9. neg-mul-1 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around 0 88.6%

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

      1. +-commutative 88.6%

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

      2. mul-1-neg 88.6%

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

      3. sub-neg 88.6%

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

      4. associate--l+ 88.6%

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

      5. +-commutative 88.6%

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

      6. *-commutative 88.6%

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

      7. sub-neg 88.6%

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

      8. +-commutative 88.6%

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

      9. distribute-rgt-neg-in 88.6%

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

      10. fma-def 88.6%

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

      11. +-commutative 88.6%

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

      12. distribute-neg-in 88.6%

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

      13. metadata-eval 88.6%

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

      14. sub-neg 88.6%

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

   6. Simplified 88.6%

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

   7. Taylor expanded in x around 0 73.3%

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

      1. associate-*r* 73.3%

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

      2. +-commutative 73.3%

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

      3. neg-mul-1 73.3%

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

      4. *-commutative 73.3%

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

      5. distribute-neg-in 73.3%

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

      6. metadata-eval 73.3%

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

   9. Simplified 73.3%

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

   10. Taylor expanded in y around 0 73.3%

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

       1. +-commutative 73.3%

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

       2. fma-def 73.3%

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

       3. mul-1-neg 73.3%

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

       4. fma-neg 73.3%

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

       5. distribute-rgt-out-- 73.3%

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

   12. Simplified 73.3%

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

   if 1.12e180 < y

   1. Initial program 99.5%

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

      1. sub-neg 99.5%

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

      2. sub-neg 99.5%

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

      3. associate-+l+ 99.5%

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

      4. associate-+l+ 99.5%

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

      5. sub-neg 99.5%

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

      6. neg-sub0 99.5%

         \[\leadsto x + \left(\left(\color{blue}{\left(0 - \left(y + 0.5\right) \cdot \log y\right)} + y\right) - z\right) \]

      7. associate-+l- 99.5%

         \[\leadsto x + \left(\color{blue}{\left(0 - \left(\left(y + 0.5\right) \cdot \log y - y\right)\right)} - z\right) \]

      8. neg-sub0 99.5%

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

      9. neg-mul-1 99.5%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 90.1%

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

      1. +-commutative 90.1%

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

      2. mul-1-neg 90.1%

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

      3. sub-neg 90.1%

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

      4. associate--l+ 90.1%

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

      5. +-commutative 90.1%

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

      6. *-commutative 90.1%

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

      7. sub-neg 90.1%

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

      8. +-commutative 90.1%

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

      9. distribute-rgt-neg-in 90.1%

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

      10. fma-def 90.1%

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

      11. +-commutative 90.1%

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

      12. distribute-neg-in 90.1%

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

      13. metadata-eval 90.1%

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

      14. sub-neg 90.1%

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

   6. Simplified 90.1%

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

   7. Taylor expanded in x around 0 79.3%

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

      1. associate-*r* 79.3%

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

      2. +-commutative 79.3%

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

      3. neg-mul-1 79.3%

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

      4. *-commutative 79.3%

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

      5. distribute-neg-in 79.3%

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

      6. metadata-eval 79.3%

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

   9. Simplified 79.3%

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

   10. Taylor expanded in y around inf 79.3%

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

       1. *-commutative 79.3%

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

       2. log-rec 79.3%

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

       3. distribute-lft-neg-in 79.3%

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

       4. distribute-rgt-neg-in 79.3%

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

   12. Simplified 79.3%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.6 \cdot 10^{+62}:\\ \;\;\;\;x - z\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{+94}:\\ \;\;\;\;y + \log y \cdot \left(-0.5 - y\right)\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+180}:\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot \log y\\ \end{array} \]

Alternative 6: 98.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{-25}:\\ \;\;\;\;x - \left(z + \log y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \left(1 - \log y\right) - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 7.5e-25)
   (- x (+ z (* (log y) 0.5)))
   (+ x (- (* y (- 1.0 (log y))) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 7.5e-25) {
		tmp = x - (z + (log(y) * 0.5));
	} else {
		tmp = x + ((y * (1.0 - log(y))) - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 7.5d-25) then
        tmp = x - (z + (log(y) * 0.5d0))
    else
        tmp = x + ((y * (1.0d0 - log(y))) - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 7.5e-25) {
		tmp = x - (z + (Math.log(y) * 0.5));
	} else {
		tmp = x + ((y * (1.0 - Math.log(y))) - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 7.5e-25:
		tmp = x - (z + (math.log(y) * 0.5))
	else:
		tmp = x + ((y * (1.0 - math.log(y))) - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 7.5e-25)
		tmp = Float64(x - Float64(z + Float64(log(y) * 0.5)));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(1.0 - log(y))) - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 7.5e-25)
		tmp = x - (z + (log(y) * 0.5));
	else
		tmp = x + ((y * (1.0 - log(y))) - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 7.5e-25], N[(x - N[(z + N[(N[Log[y], $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.49999999999999989e-25

   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%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

   if 7.49999999999999989e-25 < y

   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. sub-neg 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-+l+ 99.7%

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

      4. associate-+l+ 99.7%

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

      5. sub-neg 99.7%

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

      6. neg-sub0 99.7%

         \[\leadsto x + \left(\left(\color{blue}{\left(0 - \left(y + 0.5\right) \cdot \log y\right)} + y\right) - z\right) \]

      7. associate-+l- 99.7%

         \[\leadsto x + \left(\color{blue}{\left(0 - \left(\left(y + 0.5\right) \cdot \log y - y\right)\right)} - z\right) \]

      8. neg-sub0 99.7%

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

      9. neg-mul-1 99.7%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 99.7%

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

      1. log-rec 99.7%

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

      2. sub-neg 99.7%

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

   6. Simplified 99.7%

      \[\leadsto x + \left(\color{blue}{y \cdot \left(1 - \log y\right)} - z\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{-25}:\\ \;\;\;\;x - \left(z + \log y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \left(1 - \log y\right) - z\right)\\ \end{array} \]

Alternative 7: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x - N[(N[Log[y], $MachinePrecision] * N[(y + 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y - 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. Final simplification 99.8%

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

Alternative 8: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]

2. Final simplification 99.8%

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

Alternative 9: 48.0% accurate, 18.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+64}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+129}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.05e+64) (- z) (if (<= z 2.6e+129) x (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.05e+64) {
		tmp = -z;
	} else if (z <= 2.6e+129) {
		tmp = x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.05d+64)) then
        tmp = -z
    else if (z <= 2.6d+129) then
        tmp = x
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.05e+64) {
		tmp = -z;
	} else if (z <= 2.6e+129) {
		tmp = x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.05e+64:
		tmp = -z
	elif z <= 2.6e+129:
		tmp = x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.05e+64)
		tmp = Float64(-z);
	elseif (z <= 2.6e+129)
		tmp = x;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.05e+64)
		tmp = -z;
	elseif (z <= 2.6e+129)
		tmp = x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.05e+64], (-z), If[LessEqual[z, 2.6e+129], x, (-z)]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05e64 or 2.60000000000000012e129 < z

   1. Initial program 99.9%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]

   2. Taylor expanded in y around inf 88.4%

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

      1. *-commutative 88.4%

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

      2. log-rec 88.4%

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

      3. distribute-lft-neg-in 88.4%

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

      4. distribute-rgt-neg-in 88.4%

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

   4. Simplified 88.4%

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

   5. Taylor expanded in y around 0 68.6%

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

      1. neg-mul-1 68.6%

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

   7. Simplified 68.6%

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

   if -1.05e64 < z < 2.60000000000000012e129

   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. sub-neg 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-+l+ 99.8%

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

      4. associate-+l+ 99.8%

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

      5. sub-neg 99.8%

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

      6. neg-sub0 99.8%

         \[\leadsto x + \left(\left(\color{blue}{\left(0 - \left(y + 0.5\right) \cdot \log y\right)} + y\right) - z\right) \]

      7. associate-+l- 99.8%

         \[\leadsto x + \left(\color{blue}{\left(0 - \left(\left(y + 0.5\right) \cdot \log y - y\right)\right)} - z\right) \]

      8. neg-sub0 99.8%

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

      9. neg-mul-1 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 41.1%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+64}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+129}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 10: 58.1% 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. add-cube-cbrt 98.6%

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

   2. pow2 98.6%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + y}\right)}^{2}} \cdot \sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + y} - z \]

   3. +-commutative 98.6%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{y + \left(x - \left(y + 0.5\right) \cdot \log y\right)}}\right)}^{2} \cdot \sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + y} - z \]

   4. *-commutative 98.6%

      \[\leadsto {\left(\sqrt[3]{y + \left(x - \color{blue}{\log y \cdot \left(y + 0.5\right)}\right)}\right)}^{2} \cdot \sqrt[3]{\left(x - \left(y + 0.5\right) \cdot \log y\right) + y} - z \]

   5. +-commutative 98.6%

      \[\leadsto {\left(\sqrt[3]{y + \left(x - \log y \cdot \left(y + 0.5\right)\right)}\right)}^{2} \cdot \sqrt[3]{\color{blue}{y + \left(x - \left(y + 0.5\right) \cdot \log y\right)}} - z \]

   6. *-commutative 98.6%

      \[\leadsto {\left(\sqrt[3]{y + \left(x - \log y \cdot \left(y + 0.5\right)\right)}\right)}^{2} \cdot \sqrt[3]{y + \left(x - \color{blue}{\log y \cdot \left(y + 0.5\right)}\right)} - z \]

3. Applied egg-rr 98.6%

   \[\leadsto \color{blue}{{\left(\sqrt[3]{y + \left(x - \log y \cdot \left(y + 0.5\right)\right)}\right)}^{2} \cdot \sqrt[3]{y + \left(x - \log y \cdot \left(y + 0.5\right)\right)}} - z \]

4. Taylor expanded in x around inf 59.8%

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

5. Final simplification 59.8%

   \[\leadsto x - z \]

Alternative 11: 30.1% 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. sub-neg 99.8%

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

   2. sub-neg 99.8%

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

   3. associate-+l+ 99.8%

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

   4. associate-+l+ 99.8%

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

   5. sub-neg 99.8%

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

   6. neg-sub0 99.8%

      \[\leadsto x + \left(\left(\color{blue}{\left(0 - \left(y + 0.5\right) \cdot \log y\right)} + y\right) - z\right) \]

   7. associate-+l- 99.8%

      \[\leadsto x + \left(\color{blue}{\left(0 - \left(\left(y + 0.5\right) \cdot \log y - y\right)\right)} - z\right) \]

   8. neg-sub0 99.8%

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

   9. neg-mul-1 99.8%

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

3. Simplified 99.9%

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

4. Taylor expanded in x around inf 30.5%

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

5. Final simplification 30.5%

   \[\leadsto x \]

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 2023228 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (- (- (+ y x) z) (* (+ y 0.5) (log y)))

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