Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2

Percentage Accurate: 99.8% → 99.9%

Time: 12.5s

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 99.9%

   \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
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. associate-+r- 99.9%

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

   5. *-commutative 99.9%

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

   6. distribute-rgt-neg-in 99.9%

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

   7. fma-def 99.9%

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

   8. +-commutative 99.9%

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

   9. distribute-neg-in 99.9%

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

   10. unsub-neg 99.9%

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

   11. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 70.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log y \cdot -0.5 - z\\ t_1 := y \cdot \left(1 - \log y\right)\\ t_2 := t_1 - z\\ t_3 := x + t_1\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{+139}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-122}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-168}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-114}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-23}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* (log y) -0.5) z))
        (t_1 (* y (- 1.0 (log y))))
        (t_2 (- t_1 z))
        (t_3 (+ x t_1)))
   (if (<= x -2.4e+139)
     t_3
     (if (<= x -1.8e-122)
       t_2
       (if (<= x 1.25e-168)
         t_0
         (if (<= x 1.55e-114) t_2 (if (<= x 5e-23) t_0 t_3)))))))

C

double code(double x, double y, double z) {
	double t_0 = (log(y) * -0.5) - z;
	double t_1 = y * (1.0 - log(y));
	double t_2 = t_1 - z;
	double t_3 = x + t_1;
	double tmp;
	if (x <= -2.4e+139) {
		tmp = t_3;
	} else if (x <= -1.8e-122) {
		tmp = t_2;
	} else if (x <= 1.25e-168) {
		tmp = t_0;
	} else if (x <= 1.55e-114) {
		tmp = t_2;
	} else if (x <= 5e-23) {
		tmp = t_0;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = (log(y) * (-0.5d0)) - z
    t_1 = y * (1.0d0 - log(y))
    t_2 = t_1 - z
    t_3 = x + t_1
    if (x <= (-2.4d+139)) then
        tmp = t_3
    else if (x <= (-1.8d-122)) then
        tmp = t_2
    else if (x <= 1.25d-168) then
        tmp = t_0
    else if (x <= 1.55d-114) then
        tmp = t_2
    else if (x <= 5d-23) then
        tmp = t_0
    else
        tmp = t_3
    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 t_1 = y * (1.0 - Math.log(y));
	double t_2 = t_1 - z;
	double t_3 = x + t_1;
	double tmp;
	if (x <= -2.4e+139) {
		tmp = t_3;
	} else if (x <= -1.8e-122) {
		tmp = t_2;
	} else if (x <= 1.25e-168) {
		tmp = t_0;
	} else if (x <= 1.55e-114) {
		tmp = t_2;
	} else if (x <= 5e-23) {
		tmp = t_0;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (math.log(y) * -0.5) - z
	t_1 = y * (1.0 - math.log(y))
	t_2 = t_1 - z
	t_3 = x + t_1
	tmp = 0
	if x <= -2.4e+139:
		tmp = t_3
	elif x <= -1.8e-122:
		tmp = t_2
	elif x <= 1.25e-168:
		tmp = t_0
	elif x <= 1.55e-114:
		tmp = t_2
	elif x <= 5e-23:
		tmp = t_0
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(log(y) * -0.5) - z)
	t_1 = Float64(y * Float64(1.0 - log(y)))
	t_2 = Float64(t_1 - z)
	t_3 = Float64(x + t_1)
	tmp = 0.0
	if (x <= -2.4e+139)
		tmp = t_3;
	elseif (x <= -1.8e-122)
		tmp = t_2;
	elseif (x <= 1.25e-168)
		tmp = t_0;
	elseif (x <= 1.55e-114)
		tmp = t_2;
	elseif (x <= 5e-23)
		tmp = t_0;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (log(y) * -0.5) - z;
	t_1 = y * (1.0 - log(y));
	t_2 = t_1 - z;
	t_3 = x + t_1;
	tmp = 0.0;
	if (x <= -2.4e+139)
		tmp = t_3;
	elseif (x <= -1.8e-122)
		tmp = t_2;
	elseif (x <= 1.25e-168)
		tmp = t_0;
	elseif (x <= 1.55e-114)
		tmp = t_2;
	elseif (x <= 5e-23)
		tmp = t_0;
	else
		tmp = t_3;
	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]}, Block[{t$95$1 = N[(y * N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - z), $MachinePrecision]}, Block[{t$95$3 = N[(x + t$95$1), $MachinePrecision]}, If[LessEqual[x, -2.4e+139], t$95$3, If[LessEqual[x, -1.8e-122], t$95$2, If[LessEqual[x, 1.25e-168], t$95$0, If[LessEqual[x, 1.55e-114], t$95$2, If[LessEqual[x, 5e-23], t$95$0, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.40000000000000008e139 or 5.0000000000000002e-23 < x

   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. associate-+r- 99.9%

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

      5. *-commutative 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. fma-def 100.0%

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

      8. +-commutative 100.0%

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

      9. distribute-neg-in 100.0%

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

      10. unsub-neg 100.0%

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

      11. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. log-rec 100.0%

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

      2. sub-neg 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around 0 88.8%

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

   if -2.40000000000000008e139 < x < -1.79999999999999997e-122 or 1.25e-168 < x < 1.55e-114

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. distribute-lft-in 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around inf 77.7%

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

      1. sub-neg 77.7%

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

      2. log-rec 77.7%

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

      3. neg-mul-1 77.7%

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

      4. remove-double-neg 77.7%

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

      5. sub-neg 77.7%

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

   7. Simplified 77.7%

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

   if -1.79999999999999997e-122 < x < 1.25e-168 or 1.55e-114 < x < 5.0000000000000002e-23

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. distribute-lft-in 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around 0 99.9%

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

      1. +-commutative 99.9%

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

      2. metadata-eval 99.9%

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

      3. cancel-sign-sub-inv 99.9%

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

      4. distribute-rgt-out-- 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in y around 0 76.1%

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

      1. *-commutative 76.1%

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

   10. Simplified 76.1%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+139}:\\ \;\;\;\;x + y \cdot \left(1 - \log y\right)\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-122}:\\ \;\;\;\;y \cdot \left(1 - \log y\right) - z\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-168}:\\ \;\;\;\;\log y \cdot -0.5 - z\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-114}:\\ \;\;\;\;y \cdot \left(1 - \log y\right) - z\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-23}:\\ \;\;\;\;\log y \cdot -0.5 - z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \log y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(1 - \log y\right)\\ t_1 := t_0 - z\\ t_2 := \left(x - \log y \cdot 0.5\right) - z\\ \mathbf{if}\;y \leq 1.35 \cdot 10^{+37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.72 \cdot 10^{+159}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- 1.0 (log y))))
        (t_1 (- t_0 z))
        (t_2 (- (- x (* (log y) 0.5)) z)))
   (if (<= y 1.35e+37)
     t_2
     (if (<= y 4.8e+49)
       t_1
       (if (<= y 1.02e+103) t_2 (if (<= y 1.72e+159) t_1 (+ x t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (1.0 - log(y));
	double t_1 = t_0 - z;
	double t_2 = (x - (log(y) * 0.5)) - z;
	double tmp;
	if (y <= 1.35e+37) {
		tmp = t_2;
	} else if (y <= 4.8e+49) {
		tmp = t_1;
	} else if (y <= 1.02e+103) {
		tmp = t_2;
	} else if (y <= 1.72e+159) {
		tmp = t_1;
	} else {
		tmp = x + t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = y * (1.0d0 - log(y))
    t_1 = t_0 - z
    t_2 = (x - (log(y) * 0.5d0)) - z
    if (y <= 1.35d+37) then
        tmp = t_2
    else if (y <= 4.8d+49) then
        tmp = t_1
    else if (y <= 1.02d+103) then
        tmp = t_2
    else if (y <= 1.72d+159) then
        tmp = t_1
    else
        tmp = x + t_0
    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 t_1 = t_0 - z;
	double t_2 = (x - (Math.log(y) * 0.5)) - z;
	double tmp;
	if (y <= 1.35e+37) {
		tmp = t_2;
	} else if (y <= 4.8e+49) {
		tmp = t_1;
	} else if (y <= 1.02e+103) {
		tmp = t_2;
	} else if (y <= 1.72e+159) {
		tmp = t_1;
	} else {
		tmp = x + t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (1.0 - math.log(y))
	t_1 = t_0 - z
	t_2 = (x - (math.log(y) * 0.5)) - z
	tmp = 0
	if y <= 1.35e+37:
		tmp = t_2
	elif y <= 4.8e+49:
		tmp = t_1
	elif y <= 1.02e+103:
		tmp = t_2
	elif y <= 1.72e+159:
		tmp = t_1
	else:
		tmp = x + t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(1.0 - log(y)))
	t_1 = Float64(t_0 - z)
	t_2 = Float64(Float64(x - Float64(log(y) * 0.5)) - z)
	tmp = 0.0
	if (y <= 1.35e+37)
		tmp = t_2;
	elseif (y <= 4.8e+49)
		tmp = t_1;
	elseif (y <= 1.02e+103)
		tmp = t_2;
	elseif (y <= 1.72e+159)
		tmp = t_1;
	else
		tmp = Float64(x + t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (1.0 - log(y));
	t_1 = t_0 - z;
	t_2 = (x - (log(y) * 0.5)) - z;
	tmp = 0.0;
	if (y <= 1.35e+37)
		tmp = t_2;
	elseif (y <= 4.8e+49)
		tmp = t_1;
	elseif (y <= 1.02e+103)
		tmp = t_2;
	elseif (y <= 1.72e+159)
		tmp = t_1;
	else
		tmp = x + t_0;
	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]}, Block[{t$95$1 = N[(t$95$0 - z), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(N[Log[y], $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[y, 1.35e+37], t$95$2, If[LessEqual[y, 4.8e+49], t$95$1, If[LessEqual[y, 1.02e+103], t$95$2, If[LessEqual[y, 1.72e+159], t$95$1, N[(x + t$95$0), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.34999999999999993e37 or 4.8e49 < y < 1.01999999999999991e103

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 96.4%

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

   if 1.34999999999999993e37 < y < 4.8e49 or 1.01999999999999991e103 < y < 1.72e159

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. distribute-lft-in 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around inf 83.1%

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

      1. sub-neg 83.1%

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

      2. log-rec 83.1%

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

      3. neg-mul-1 83.1%

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

      4. remove-double-neg 83.1%

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

      5. sub-neg 83.1%

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

   7. Simplified 83.1%

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

   if 1.72e159 < 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. 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. associate-+r- 99.7%

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

      5. *-commutative 99.7%

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

      6. distribute-rgt-neg-in 99.7%

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

      7. fma-def 99.9%

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

      8. +-commutative 99.9%

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

      9. distribute-neg-in 99.9%

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

      10. unsub-neg 99.9%

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

      11. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 99.9%

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

      1. log-rec 99.9%

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

      2. sub-neg 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around 0 89.6%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.35 \cdot 10^{+37}:\\ \;\;\;\;\left(x - \log y \cdot 0.5\right) - z\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \left(1 - \log y\right) - z\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+103}:\\ \;\;\;\;\left(x - \log y \cdot 0.5\right) - z\\ \mathbf{elif}\;y \leq 1.72 \cdot 10^{+159}:\\ \;\;\;\;y \cdot \left(1 - \log y\right) - z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \log y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(1 - \log y\right)\\ t_1 := \left(x - \log y \cdot 0.5\right) - z\\ \mathbf{if}\;y \leq 3.7 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+49}:\\ \;\;\;\;t_0 - z\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+158}:\\ \;\;\;\;\left(y - y \cdot \log y\right) - z\\ \mathbf{else}:\\ \;\;\;\;x + t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- 1.0 (log y)))) (t_1 (- (- x (* (log y) 0.5)) z)))
   (if (<= y 3.7e+37)
     t_1
     (if (<= y 3.5e+49)
       (- t_0 z)
       (if (<= y 1.05e+103)
         t_1
         (if (<= y 5.1e+158) (- (- y (* y (log y))) z) (+ x t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (1.0 - log(y));
	double t_1 = (x - (log(y) * 0.5)) - z;
	double tmp;
	if (y <= 3.7e+37) {
		tmp = t_1;
	} else if (y <= 3.5e+49) {
		tmp = t_0 - z;
	} else if (y <= 1.05e+103) {
		tmp = t_1;
	} else if (y <= 5.1e+158) {
		tmp = (y - (y * log(y))) - z;
	} else {
		tmp = x + t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = y * (1.0d0 - log(y))
    t_1 = (x - (log(y) * 0.5d0)) - z
    if (y <= 3.7d+37) then
        tmp = t_1
    else if (y <= 3.5d+49) then
        tmp = t_0 - z
    else if (y <= 1.05d+103) then
        tmp = t_1
    else if (y <= 5.1d+158) then
        tmp = (y - (y * log(y))) - z
    else
        tmp = x + t_0
    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 t_1 = (x - (Math.log(y) * 0.5)) - z;
	double tmp;
	if (y <= 3.7e+37) {
		tmp = t_1;
	} else if (y <= 3.5e+49) {
		tmp = t_0 - z;
	} else if (y <= 1.05e+103) {
		tmp = t_1;
	} else if (y <= 5.1e+158) {
		tmp = (y - (y * Math.log(y))) - z;
	} else {
		tmp = x + t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (1.0 - math.log(y))
	t_1 = (x - (math.log(y) * 0.5)) - z
	tmp = 0
	if y <= 3.7e+37:
		tmp = t_1
	elif y <= 3.5e+49:
		tmp = t_0 - z
	elif y <= 1.05e+103:
		tmp = t_1
	elif y <= 5.1e+158:
		tmp = (y - (y * math.log(y))) - z
	else:
		tmp = x + t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(1.0 - log(y)))
	t_1 = Float64(Float64(x - Float64(log(y) * 0.5)) - z)
	tmp = 0.0
	if (y <= 3.7e+37)
		tmp = t_1;
	elseif (y <= 3.5e+49)
		tmp = Float64(t_0 - z);
	elseif (y <= 1.05e+103)
		tmp = t_1;
	elseif (y <= 5.1e+158)
		tmp = Float64(Float64(y - Float64(y * log(y))) - z);
	else
		tmp = Float64(x + t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (1.0 - log(y));
	t_1 = (x - (log(y) * 0.5)) - z;
	tmp = 0.0;
	if (y <= 3.7e+37)
		tmp = t_1;
	elseif (y <= 3.5e+49)
		tmp = t_0 - z;
	elseif (y <= 1.05e+103)
		tmp = t_1;
	elseif (y <= 5.1e+158)
		tmp = (y - (y * log(y))) - z;
	else
		tmp = x + t_0;
	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]}, Block[{t$95$1 = N[(N[(x - N[(N[Log[y], $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[y, 3.7e+37], t$95$1, If[LessEqual[y, 3.5e+49], N[(t$95$0 - z), $MachinePrecision], If[LessEqual[y, 1.05e+103], t$95$1, If[LessEqual[y, 5.1e+158], N[(N[(y - N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(x + t$95$0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < 3.6999999999999999e37 or 3.49999999999999975e49 < y < 1.0500000000000001e103

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 96.4%

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

   if 3.6999999999999999e37 < y < 3.49999999999999975e49

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. distribute-lft-in 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around inf 99.7%

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

      1. sub-neg 99.7%

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

      2. log-rec 99.7%

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

      3. neg-mul-1 99.7%

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

      4. remove-double-neg 99.7%

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

      5. sub-neg 99.7%

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

   7. Simplified 99.7%

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

   if 1.0500000000000001e103 < y < 5.09999999999999987e158

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. flip-+ 84.6%

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

      3. associate-*r/ 84.4%

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

      4. fma-neg 84.4%

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

      5. metadata-eval 84.4%

         \[\leadsto \left(\left(x - \frac{\log y \cdot \mathsf{fma}\left(y, y, -\color{blue}{0.25}\right)}{y - 0.5}\right) + y\right) - z \]

      6. metadata-eval 84.4%

         \[\leadsto \left(\left(x - \frac{\log y \cdot \mathsf{fma}\left(y, y, \color{blue}{-0.25}\right)}{y - 0.5}\right) + y\right) - z \]

      7. sub-neg 84.4%

         \[\leadsto \left(\left(x - \frac{\log y \cdot \mathsf{fma}\left(y, y, -0.25\right)}{\color{blue}{y + \left(-0.5\right)}}\right) + y\right) - z \]

      8. metadata-eval 84.4%

         \[\leadsto \left(\left(x - \frac{\log y \cdot \mathsf{fma}\left(y, y, -0.25\right)}{y + \color{blue}{-0.5}}\right) + y\right) - z \]

   4. Applied egg-rr 84.4%

      \[\leadsto \left(\left(x - \color{blue}{\frac{\log y \cdot \mathsf{fma}\left(y, y, -0.25\right)}{y + -0.5}}\right) + y\right) - z \]
   5. Step-by-step derivation

      1. associate-/l* 84.6%

         \[\leadsto \left(\left(x - \color{blue}{\frac{\log y}{\frac{y + -0.5}{\mathsf{fma}\left(y, y, -0.25\right)}}}\right) + y\right) - z \]

      2. +-commutative 84.6%

         \[\leadsto \left(\left(x - \frac{\log y}{\frac{\color{blue}{-0.5 + y}}{\mathsf{fma}\left(y, y, -0.25\right)}}\right) + y\right) - z \]

   6. Simplified 84.6%

      \[\leadsto \left(\left(x - \color{blue}{\frac{\log y}{\frac{-0.5 + y}{\mathsf{fma}\left(y, y, -0.25\right)}}}\right) + y\right) - z \]

   7. Taylor expanded in y around inf 99.7%

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

   8. Taylor expanded in x around 0 79.2%

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

   if 5.09999999999999987e158 < 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. 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. associate-+r- 99.7%

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

      5. *-commutative 99.7%

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

      6. distribute-rgt-neg-in 99.7%

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

      7. fma-def 99.9%

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

      8. +-commutative 99.9%

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

      9. distribute-neg-in 99.9%

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

      10. unsub-neg 99.9%

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

      11. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 99.9%

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

      1. log-rec 99.9%

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

      2. sub-neg 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around 0 89.6%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.7 \cdot 10^{+37}:\\ \;\;\;\;\left(x - \log y \cdot 0.5\right) - z\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \left(1 - \log y\right) - z\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+103}:\\ \;\;\;\;\left(x - \log y \cdot 0.5\right) - z\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+158}:\\ \;\;\;\;\left(y - y \cdot \log y\right) - z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \log y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.42 \cdot 10^{-16} \lor \neg \left(x \leq 2.8 \cdot 10^{-24}\right):\\ \;\;\;\;x + y \cdot \left(1 - \log y\right)\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot -0.5 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.42e-16) (not (<= x 2.8e-24)))
   (+ x (* y (- 1.0 (log y))))
   (- (* (log y) -0.5) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.42e-16) || !(x <= 2.8e-24)) {
		tmp = x + (y * (1.0 - log(y)));
	} else {
		tmp = (log(y) * -0.5) - 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 ((x <= (-1.42d-16)) .or. (.not. (x <= 2.8d-24))) then
        tmp = x + (y * (1.0d0 - log(y)))
    else
        tmp = (log(y) * (-0.5d0)) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.42e-16) || !(x <= 2.8e-24)) {
		tmp = x + (y * (1.0 - Math.log(y)));
	} else {
		tmp = (Math.log(y) * -0.5) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.42e-16) or not (x <= 2.8e-24):
		tmp = x + (y * (1.0 - math.log(y)))
	else:
		tmp = (math.log(y) * -0.5) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.42e-16) || !(x <= 2.8e-24))
		tmp = Float64(x + Float64(y * Float64(1.0 - log(y))));
	else
		tmp = Float64(Float64(log(y) * -0.5) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.42e-16) || ~((x <= 2.8e-24)))
		tmp = x + (y * (1.0 - log(y)));
	else
		tmp = (log(y) * -0.5) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.42e-16], N[Not[LessEqual[x, 2.8e-24]], $MachinePrecision]], 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]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4199999999999999e-16 or 2.8000000000000002e-24 < x

   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+ 99.8%

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

      4. associate-+r- 99.9%

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

      5. *-commutative 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. fma-def 100.0%

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

      8. +-commutative 100.0%

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

      9. distribute-neg-in 100.0%

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

      10. unsub-neg 100.0%

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

      11. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. log-rec 100.0%

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

      2. sub-neg 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around 0 84.0%

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

   if -1.4199999999999999e-16 < x < 2.8000000000000002e-24

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. distribute-lft-in 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around 0 99.9%

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

      1. +-commutative 99.9%

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

      2. metadata-eval 99.9%

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

      3. cancel-sign-sub-inv 99.9%

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

      4. distribute-rgt-out-- 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in y around 0 70.5%

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

      1. *-commutative 70.5%

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

   10. Simplified 70.5%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.42 \cdot 10^{-16} \lor \neg \left(x \leq 2.8 \cdot 10^{-24}\right):\\ \;\;\;\;x + y \cdot \left(1 - \log y\right)\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot -0.5 - z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.021 \lor \neg \left(x \leq 11500000\right):\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot -0.5 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.021) (not (<= x 11500000.0)))
   (- x z)
   (- (* (log y) -0.5) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.021) || !(x <= 11500000.0)) {
		tmp = x - z;
	} else {
		tmp = (log(y) * -0.5) - 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 ((x <= (-0.021d0)) .or. (.not. (x <= 11500000.0d0))) then
        tmp = x - z
    else
        tmp = (log(y) * (-0.5d0)) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.021) || !(x <= 11500000.0)) {
		tmp = x - z;
	} else {
		tmp = (Math.log(y) * -0.5) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.021) or not (x <= 11500000.0):
		tmp = x - z
	else:
		tmp = (math.log(y) * -0.5) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.021) || !(x <= 11500000.0))
		tmp = Float64(x - z);
	else
		tmp = Float64(Float64(log(y) * -0.5) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -0.021) || ~((x <= 11500000.0)))
		tmp = x - z;
	else
		tmp = (log(y) * -0.5) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.021], N[Not[LessEqual[x, 11500000.0]], $MachinePrecision]], N[(x - z), $MachinePrecision], N[(N[(N[Log[y], $MachinePrecision] * -0.5), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0210000000000000013 or 1.15e7 < x

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. distribute-lft-in 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around inf 75.3%

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

   if -0.0210000000000000013 < x < 1.15e7

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. distribute-lft-in 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around 0 99.9%

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

      1. +-commutative 99.9%

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

      2. metadata-eval 99.9%

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

      3. cancel-sign-sub-inv 99.9%

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

      4. distribute-rgt-out-- 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in y around 0 67.9%

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

      1. *-commutative 67.9%

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

   10. Simplified 67.9%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.021 \lor \neg \left(x \leq 11500000\right):\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot -0.5 - z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.6 \cdot 10^{-5}:\\ \;\;\;\;\left(x - \log y \cdot 0.5\right) - z\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \left(1 - \log y\right) - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.6e-5)
   (- (- x (* (log y) 0.5)) z)
   (+ x (- (* y (- 1.0 (log y))) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.6e-5) {
		tmp = (x - (log(y) * 0.5)) - z;
	} 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 <= 1.6d-5) then
        tmp = (x - (log(y) * 0.5d0)) - z
    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 <= 1.6e-5) {
		tmp = (x - (Math.log(y) * 0.5)) - z;
	} else {
		tmp = x + ((y * (1.0 - Math.log(y))) - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.6e-5:
		tmp = (x - (math.log(y) * 0.5)) - z
	else:
		tmp = x + ((y * (1.0 - math.log(y))) - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.6e-5)
		tmp = Float64(Float64(x - Float64(log(y) * 0.5)) - z);
	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 <= 1.6e-5)
		tmp = (x - (log(y) * 0.5)) - z;
	else
		tmp = x + ((y * (1.0 - log(y))) - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.6e-5], N[(N[(x - N[(N[Log[y], $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision] - z), $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 < 1.59999999999999993e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.0%

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

   if 1.59999999999999993e-5 < y

   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+ 99.7%

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

      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. associate-+r- 99.7%

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

      5. *-commutative 99.7%

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

      6. distribute-rgt-neg-in 99.7%

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

      7. fma-def 99.8%

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

      8. +-commutative 99.8%

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

      9. distribute-neg-in 99.8%

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

      10. unsub-neg 99.8%

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

      11. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 99.8%

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

      1. log-rec 99.8%

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

      2. sub-neg 99.8%

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

   7. Simplified 99.8%

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

4. Final simplification 99.4%

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

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 99.9%

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

3. Final simplification 99.9%

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

Alternative 9: 46.9% accurate, 9.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.55 \cdot 10^{+130}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7700000000:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.55e+130) x (if (<= x 7700000000.0) (- z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.55e+130) {
		tmp = x;
	} else if (x <= 7700000000.0) {
		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 <= (-3.55d+130)) then
        tmp = x
    else if (x <= 7700000000.0d0) 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 <= -3.55e+130) {
		tmp = x;
	} else if (x <= 7700000000.0) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.55e+130:
		tmp = x
	elif x <= 7700000000.0:
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.55e+130)
		tmp = x;
	elseif (x <= 7700000000.0)
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.55e+130)
		tmp = x;
	elseif (x <= 7700000000.0)
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.55e+130], x, If[LessEqual[x, 7700000000.0], (-z), x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.5500000000000001e130 or 7.7e9 < x

   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. associate-+r- 99.9%

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

      5. *-commutative 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. fma-def 100.0%

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

      8. +-commutative 100.0%

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

      9. distribute-neg-in 100.0%

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

      10. unsub-neg 100.0%

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

      11. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 66.9%

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

   if -3.5500000000000001e130 < x < 7.7e9

   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. associate-+r- 99.8%

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

      5. *-commutative 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. fma-def 99.9%

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

      8. +-commutative 99.9%

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

      9. distribute-neg-in 99.9%

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

      10. unsub-neg 99.9%

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

      11. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 68.6%

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

      1. log-rec 68.6%

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

      2. sub-neg 68.6%

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

   7. Simplified 68.6%

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

   8. Taylor expanded in z around inf 33.5%

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

      1. neg-mul-1 33.5%

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

   10. Simplified 33.5%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.55 \cdot 10^{+130}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7700000000:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.7% 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 99.9%

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

   1. *-commutative 99.9%

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

   2. distribute-lft-in 99.9%

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

4. Applied egg-rr 99.9%

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

5. Taylor expanded in x around inf 52.6%

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

6. Final simplification 52.6%

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

Alternative 11: 29.3% 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 99.9%

   \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
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. associate-+r- 99.9%

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

   5. *-commutative 99.9%

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

   6. distribute-rgt-neg-in 99.9%

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

   7. fma-def 99.9%

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

   8. +-commutative 99.9%

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

   9. distribute-neg-in 99.9%

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

   10. unsub-neg 99.9%

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

   11. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in x around inf 30.0%

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

6. Final simplification 30.0%

   \[\leadsto x \]
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 2024021 
(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))