Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, B

Percentage Accurate: 93.6% → 94.6%

Time: 20.9s

Alternatives: 16

Speedup: 1.0×

• 30.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+
  (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
  (/
   (+
    (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
    0.083333333333333)
   x)))

C

double code(double x, double y, double z) {
	return ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / 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 - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + ((((((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0) * z) + 0.083333333333333d0) / x)
end function

Java

public static double code(double x, double y, double z) {
	return ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
}

Python

def code(x, y, z):
	return ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(Float64(Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(N[(N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]

Initial Program: 93.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+
  (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
  (/
   (+
    (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
    0.083333333333333)
   x)))

C

double code(double x, double y, double z) {
	return ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / 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 - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + ((((((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0) * z) + 0.083333333333333d0) / x)
end function

Java

public static double code(double x, double y, double z) {
	return ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
}

Python

def code(x, y, z):
	return ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(Float64(Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(N[(N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]

Alternative 1: 94.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.5 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(x + -0.5, \log x, 0.91893853320467 - x\right) + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{{z}^{2}}{\frac{x}{y + 0.0007936500793651}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 1.5e+18)
   (+
    (fma (+ x -0.5) (log x) (- 0.91893853320467 x))
    (/
     (fma
      z
      (fma (+ y 0.0007936500793651) z -0.0027777777777778)
      0.083333333333333)
     x))
   (+
    (+ 0.91893853320467 (- (* (log x) (- x 0.5)) x))
    (/ (pow z 2.0) (/ x (+ y 0.0007936500793651))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.5e+18) {
		tmp = fma((x + -0.5), log(x), (0.91893853320467 - x)) + (fma(z, fma((y + 0.0007936500793651), z, -0.0027777777777778), 0.083333333333333) / x);
	} else {
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + (pow(z, 2.0) / (x / (y + 0.0007936500793651)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1.5e+18)
		tmp = Float64(fma(Float64(x + -0.5), log(x), Float64(0.91893853320467 - x)) + Float64(fma(z, fma(Float64(y + 0.0007936500793651), z, -0.0027777777777778), 0.083333333333333) / x));
	else
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(log(x) * Float64(x - 0.5)) - x)) + Float64((z ^ 2.0) / Float64(x / Float64(y + 0.0007936500793651))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 1.5e+18], N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision] + N[(0.91893853320467 - x), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(N[(y + 0.0007936500793651), $MachinePrecision] * z + -0.0027777777777778), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(0.91893853320467 + N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(N[Power[z, 2.0], $MachinePrecision] / N[(x / N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.5e18

   1. Initial program 98.6%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

      1. sub-neg 98.6%

         \[\leadsto \left(\color{blue}{\left(\left(x - 0.5\right) \cdot \log x + \left(-x\right)\right)} + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      2. associate-+l+ 98.6%

         \[\leadsto \color{blue}{\left(\left(x - 0.5\right) \cdot \log x + \left(\left(-x\right) + 0.91893853320467\right)\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      3. fma-def 98.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x - 0.5, \log x, \left(-x\right) + 0.91893853320467\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      4. sub-neg 98.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{x + \left(-0.5\right)}, \log x, \left(-x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      5. metadata-eval 98.7%

         \[\leadsto \mathsf{fma}\left(x + \color{blue}{-0.5}, \log x, \left(-x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      6. +-commutative 98.7%

         \[\leadsto \mathsf{fma}\left(x + -0.5, \log x, \color{blue}{0.91893853320467 + \left(-x\right)}\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      7. unsub-neg 98.7%

         \[\leadsto \mathsf{fma}\left(x + -0.5, \log x, \color{blue}{0.91893853320467 - x}\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      8. *-commutative 98.7%

         \[\leadsto \mathsf{fma}\left(x + -0.5, \log x, 0.91893853320467 - x\right) + \frac{\color{blue}{z \cdot \left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right)} + 0.083333333333333}{x} \]

      9. fma-def 98.7%

         \[\leadsto \mathsf{fma}\left(x + -0.5, \log x, 0.91893853320467 - x\right) + \frac{\color{blue}{\mathsf{fma}\left(z, \left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778, 0.083333333333333\right)}}{x} \]

      10. fma-neg 98.7%

          \[\leadsto \mathsf{fma}\left(x + -0.5, \log x, 0.91893853320467 - x\right) + \frac{\mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right)}, 0.083333333333333\right)}{x} \]

      11. metadata-eval 98.7%

          \[\leadsto \mathsf{fma}\left(x + -0.5, \log x, 0.91893853320467 - x\right) + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, \color{blue}{-0.0027777777777778}\right), 0.083333333333333\right)}{x} \]

   3. Simplified 98.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x + -0.5, \log x, 0.91893853320467 - x\right) + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}{x}} \]
   4. Add Preprocessing

   if 1.5e18 < z

   1. Initial program 91.9%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 91.9%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   4. Step-by-step derivation

      1. associate-/l* 98.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

   5. Simplified 98.5%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.5 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(x + -0.5, \log x, 0.91893853320467 - x\right) + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{{z}^{2}}{\frac{x}{y + 0.0007936500793651}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\\ \mathbf{if}\;z \leq 22000000000000:\\ \;\;\;\;t_0 + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{{z}^{2}}{\frac{x}{y + 0.0007936500793651}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 0.91893853320467 (- (* (log x) (- x 0.5)) x))))
   (if (<= z 22000000000000.0)
     (+
      t_0
      (/
       (+
        0.083333333333333
        (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))
       x))
     (+ t_0 (/ (pow z 2.0) (/ x (+ y 0.0007936500793651)))))))

C

double code(double x, double y, double z) {
	double t_0 = 0.91893853320467 + ((log(x) * (x - 0.5)) - x);
	double tmp;
	if (z <= 22000000000000.0) {
		tmp = t_0 + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = t_0 + (pow(z, 2.0) / (x / (y + 0.0007936500793651)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 0.91893853320467d0 + ((log(x) * (x - 0.5d0)) - x)
    if (z <= 22000000000000.0d0) then
        tmp = t_0 + ((0.083333333333333d0 + (z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0))) / x)
    else
        tmp = t_0 + ((z ** 2.0d0) / (x / (y + 0.0007936500793651d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 0.91893853320467 + ((Math.log(x) * (x - 0.5)) - x);
	double tmp;
	if (z <= 22000000000000.0) {
		tmp = t_0 + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = t_0 + (Math.pow(z, 2.0) / (x / (y + 0.0007936500793651)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 0.91893853320467 + ((math.log(x) * (x - 0.5)) - x)
	tmp = 0
	if z <= 22000000000000.0:
		tmp = t_0 + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x)
	else:
		tmp = t_0 + (math.pow(z, 2.0) / (x / (y + 0.0007936500793651)))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(0.91893853320467 + Float64(Float64(log(x) * Float64(x - 0.5)) - x))
	tmp = 0.0
	if (z <= 22000000000000.0)
		tmp = Float64(t_0 + Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778))) / x));
	else
		tmp = Float64(t_0 + Float64((z ^ 2.0) / Float64(x / Float64(y + 0.0007936500793651))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 0.91893853320467 + ((log(x) * (x - 0.5)) - x);
	tmp = 0.0;
	if (z <= 22000000000000.0)
		tmp = t_0 + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	else
		tmp = t_0 + ((z ^ 2.0) / (x / (y + 0.0007936500793651)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(0.91893853320467 + N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 22000000000000.0], N[(t$95$0 + N[(N[(0.083333333333333 + N[(z * N[(N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(N[Power[z, 2.0], $MachinePrecision] / N[(x / N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 2.2e13

   1. Initial program 98.6%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Add Preprocessing

   if 2.2e13 < z

   1. Initial program 92.0%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 92.0%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   4. Step-by-step derivation

      1. associate-/l* 98.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

   5. Simplified 98.5%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 22000000000000:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{{z}^{2}}{\frac{x}{y + 0.0007936500793651}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+70} \lor \neg \left(z \leq 6.8 \cdot 10^{+78}\right):\\ \;\;\;\;\left(y + 0.0007936500793651\right) \cdot \frac{{z}^{2}}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot 0.0007936500793651 - 0.0027777777777778\right)}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.85e+70) (not (<= z 6.8e+78)))
   (* (+ y 0.0007936500793651) (/ (pow z 2.0) x))
   (+
    (* x (+ (log x) -1.0))
    (/
     (+
      0.083333333333333
      (* z (- (* z 0.0007936500793651) 0.0027777777777778)))
     x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.85e+70) || !(z <= 6.8e+78)) {
		tmp = (y + 0.0007936500793651) * (pow(z, 2.0) / x);
	} else {
		tmp = (x * (log(x) + -1.0)) + ((0.083333333333333 + (z * ((z * 0.0007936500793651) - 0.0027777777777778))) / 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 ((z <= (-1.85d+70)) .or. (.not. (z <= 6.8d+78))) then
        tmp = (y + 0.0007936500793651d0) * ((z ** 2.0d0) / x)
    else
        tmp = (x * (log(x) + (-1.0d0))) + ((0.083333333333333d0 + (z * ((z * 0.0007936500793651d0) - 0.0027777777777778d0))) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.85e+70) || !(z <= 6.8e+78)) {
		tmp = (y + 0.0007936500793651) * (Math.pow(z, 2.0) / x);
	} else {
		tmp = (x * (Math.log(x) + -1.0)) + ((0.083333333333333 + (z * ((z * 0.0007936500793651) - 0.0027777777777778))) / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.85e+70) or not (z <= 6.8e+78):
		tmp = (y + 0.0007936500793651) * (math.pow(z, 2.0) / x)
	else:
		tmp = (x * (math.log(x) + -1.0)) + ((0.083333333333333 + (z * ((z * 0.0007936500793651) - 0.0027777777777778))) / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.85e+70) || !(z <= 6.8e+78))
		tmp = Float64(Float64(y + 0.0007936500793651) * Float64((z ^ 2.0) / x));
	else
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * 0.0007936500793651) - 0.0027777777777778))) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.85e+70) || ~((z <= 6.8e+78)))
		tmp = (y + 0.0007936500793651) * ((z ^ 2.0) / x);
	else
		tmp = (x * (log(x) + -1.0)) + ((0.083333333333333 + (z * ((z * 0.0007936500793651) - 0.0027777777777778))) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.85e+70], N[Not[LessEqual[z, 6.8e+78]], $MachinePrecision]], N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(N[Power[z, 2.0], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(0.083333333333333 + N[(z * N[(N[(z * 0.0007936500793651), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.84999999999999994e70 or 6.80000000000000014e78 < z

   1. Initial program 93.8%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 93.8%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   4. Step-by-step derivation

      1. associate-/l* 96.8%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

   5. Simplified 96.8%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

   6. Taylor expanded in x around 0 88.5%

      \[\leadsto \color{blue}{\left(0.91893853320467 + -0.5 \cdot \log x\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]
   7. Step-by-step derivation

      1. +-commutative 88.5%

         \[\leadsto \color{blue}{\left(-0.5 \cdot \log x + 0.91893853320467\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]

   8. Simplified 88.5%

      \[\leadsto \color{blue}{\left(-0.5 \cdot \log x + 0.91893853320467\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]

   9. Taylor expanded in x around 0 85.5%

      \[\leadsto \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   10. Step-by-step derivation

       1. +-commutative 85.5%

          \[\leadsto \frac{{z}^{2} \cdot \color{blue}{\left(y + 0.0007936500793651\right)}}{x} \]

       2. associate-*l/ 88.6%

          \[\leadsto \color{blue}{\frac{{z}^{2}}{x} \cdot \left(y + 0.0007936500793651\right)} \]

       3. +-commutative 88.6%

          \[\leadsto \frac{{z}^{2}}{x} \cdot \color{blue}{\left(0.0007936500793651 + y\right)} \]

   11. Simplified 88.6%

       \[\leadsto \color{blue}{\frac{{z}^{2}}{x} \cdot \left(0.0007936500793651 + y\right)} \]

   if -1.84999999999999994e70 < z < 6.80000000000000014e78

   1. Initial program 98.4%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 98.1%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   4. Step-by-step derivation

      1. sub-neg 82.3%

         \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) + \left(-1\right)\right)} + \frac{0.083333333333333}{x} \]

      2. mul-1-neg 82.3%

         \[\leadsto x \cdot \left(\color{blue}{\left(-\log \left(\frac{1}{x}\right)\right)} + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

      3. log-rec 82.3%

         \[\leadsto x \cdot \left(\left(-\color{blue}{\left(-\log x\right)}\right) + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

      4. remove-double-neg 82.3%

         \[\leadsto x \cdot \left(\color{blue}{\log x} + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

      5. metadata-eval 82.3%

         \[\leadsto x \cdot \left(\log x + \color{blue}{-1}\right) + \frac{0.083333333333333}{x} \]

   5. Simplified 98.1%

      \[\leadsto \color{blue}{x \cdot \left(\log x + -1\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   6. Taylor expanded in y around 0 89.3%

      \[\leadsto x \cdot \left(\log x + -1\right) + \frac{\left(\color{blue}{0.0007936500793651 \cdot z} - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   7. Step-by-step derivation

      1. *-commutative 89.3%

         \[\leadsto x \cdot \left(\log x + -1\right) + \frac{\left(\color{blue}{z \cdot 0.0007936500793651} - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   8. Simplified 89.3%

      \[\leadsto x \cdot \left(\log x + -1\right) + \frac{\left(\color{blue}{z \cdot 0.0007936500793651} - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+70} \lor \neg \left(z \leq 6.8 \cdot 10^{+78}\right):\\ \;\;\;\;\left(y + 0.0007936500793651\right) \cdot \frac{{z}^{2}}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot 0.0007936500793651 - 0.0027777777777778\right)}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(\log x + -1\right)\\ \mathbf{if}\;y \leq -850000000000 \lor \neg \left(y \leq 1.25 \cdot 10^{-6}\right):\\ \;\;\;\;t_0 + \frac{0.083333333333333 + z \cdot \left(z \cdot y - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{0.083333333333333 + z \cdot \left(z \cdot 0.0007936500793651 - 0.0027777777777778\right)}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ (log x) -1.0))))
   (if (or (<= y -850000000000.0) (not (<= y 1.25e-6)))
     (+ t_0 (/ (+ 0.083333333333333 (* z (- (* z y) 0.0027777777777778))) x))
     (+
      t_0
      (/
       (+
        0.083333333333333
        (* z (- (* z 0.0007936500793651) 0.0027777777777778)))
       x)))))

C

double code(double x, double y, double z) {
	double t_0 = x * (log(x) + -1.0);
	double tmp;
	if ((y <= -850000000000.0) || !(y <= 1.25e-6)) {
		tmp = t_0 + ((0.083333333333333 + (z * ((z * y) - 0.0027777777777778))) / x);
	} else {
		tmp = t_0 + ((0.083333333333333 + (z * ((z * 0.0007936500793651) - 0.0027777777777778))) / 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) :: t_0
    real(8) :: tmp
    t_0 = x * (log(x) + (-1.0d0))
    if ((y <= (-850000000000.0d0)) .or. (.not. (y <= 1.25d-6))) then
        tmp = t_0 + ((0.083333333333333d0 + (z * ((z * y) - 0.0027777777777778d0))) / x)
    else
        tmp = t_0 + ((0.083333333333333d0 + (z * ((z * 0.0007936500793651d0) - 0.0027777777777778d0))) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (Math.log(x) + -1.0);
	double tmp;
	if ((y <= -850000000000.0) || !(y <= 1.25e-6)) {
		tmp = t_0 + ((0.083333333333333 + (z * ((z * y) - 0.0027777777777778))) / x);
	} else {
		tmp = t_0 + ((0.083333333333333 + (z * ((z * 0.0007936500793651) - 0.0027777777777778))) / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (math.log(x) + -1.0)
	tmp = 0
	if (y <= -850000000000.0) or not (y <= 1.25e-6):
		tmp = t_0 + ((0.083333333333333 + (z * ((z * y) - 0.0027777777777778))) / x)
	else:
		tmp = t_0 + ((0.083333333333333 + (z * ((z * 0.0007936500793651) - 0.0027777777777778))) / x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(log(x) + -1.0))
	tmp = 0.0
	if ((y <= -850000000000.0) || !(y <= 1.25e-6))
		tmp = Float64(t_0 + Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * y) - 0.0027777777777778))) / x));
	else
		tmp = Float64(t_0 + Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * 0.0007936500793651) - 0.0027777777777778))) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (log(x) + -1.0);
	tmp = 0.0;
	if ((y <= -850000000000.0) || ~((y <= 1.25e-6)))
		tmp = t_0 + ((0.083333333333333 + (z * ((z * y) - 0.0027777777777778))) / x);
	else
		tmp = t_0 + ((0.083333333333333 + (z * ((z * 0.0007936500793651) - 0.0027777777777778))) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[y, -850000000000.0], N[Not[LessEqual[y, 1.25e-6]], $MachinePrecision]], N[(t$95$0 + N[(N[(0.083333333333333 + N[(z * N[(N[(z * y), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(N[(0.083333333333333 + N[(z * N[(N[(z * 0.0007936500793651), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.5e11 or 1.2500000000000001e-6 < y

   1. Initial program 95.9%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 95.8%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   4. Step-by-step derivation

      1. sub-neg 50.6%

         \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) + \left(-1\right)\right)} + \frac{0.083333333333333}{x} \]

      2. mul-1-neg 50.6%

         \[\leadsto x \cdot \left(\color{blue}{\left(-\log \left(\frac{1}{x}\right)\right)} + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

      3. log-rec 50.6%

         \[\leadsto x \cdot \left(\left(-\color{blue}{\left(-\log x\right)}\right) + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

      4. remove-double-neg 50.6%

         \[\leadsto x \cdot \left(\color{blue}{\log x} + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

      5. metadata-eval 50.6%

         \[\leadsto x \cdot \left(\log x + \color{blue}{-1}\right) + \frac{0.083333333333333}{x} \]

   5. Simplified 95.8%

      \[\leadsto \color{blue}{x \cdot \left(\log x + -1\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   6. Taylor expanded in y around inf 95.8%

      \[\leadsto x \cdot \left(\log x + -1\right) + \frac{\left(\color{blue}{y \cdot z} - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   7. Step-by-step derivation

      1. *-commutative 95.8%

         \[\leadsto x \cdot \left(\log x + -1\right) + \frac{\left(\color{blue}{z \cdot y} - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   8. Simplified 95.8%

      \[\leadsto x \cdot \left(\log x + -1\right) + \frac{\left(\color{blue}{z \cdot y} - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   if -8.5e11 < y < 1.2500000000000001e-6

   1. Initial program 97.6%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 97.3%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   4. Step-by-step derivation

      1. sub-neg 65.1%

         \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) + \left(-1\right)\right)} + \frac{0.083333333333333}{x} \]

      2. mul-1-neg 65.1%

         \[\leadsto x \cdot \left(\color{blue}{\left(-\log \left(\frac{1}{x}\right)\right)} + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

      3. log-rec 65.1%

         \[\leadsto x \cdot \left(\left(-\color{blue}{\left(-\log x\right)}\right) + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

      4. remove-double-neg 65.1%

         \[\leadsto x \cdot \left(\color{blue}{\log x} + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

      5. metadata-eval 65.1%

         \[\leadsto x \cdot \left(\log x + \color{blue}{-1}\right) + \frac{0.083333333333333}{x} \]

   5. Simplified 97.3%

      \[\leadsto \color{blue}{x \cdot \left(\log x + -1\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   6. Taylor expanded in y around 0 97.3%

      \[\leadsto x \cdot \left(\log x + -1\right) + \frac{\left(\color{blue}{0.0007936500793651 \cdot z} - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   7. Step-by-step derivation

      1. *-commutative 97.3%

         \[\leadsto x \cdot \left(\log x + -1\right) + \frac{\left(\color{blue}{z \cdot 0.0007936500793651} - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   8. Simplified 97.3%

      \[\leadsto x \cdot \left(\log x + -1\right) + \frac{\left(\color{blue}{z \cdot 0.0007936500793651} - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -850000000000 \lor \neg \left(y \leq 1.25 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot y - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot 0.0007936500793651 - 0.0027777777777778\right)}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+24}:\\ \;\;\;\;\frac{{z}^{2} \cdot \left(y + 0.0007936500793651\right)}{x}\\ \mathbf{elif}\;z \leq 220000:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{1}{x \cdot 12.000000000000048}\\ \mathbf{else}:\\ \;\;\;\;\left(y + 0.0007936500793651\right) \cdot \frac{{z}^{2}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.35e+24)
   (/ (* (pow z 2.0) (+ y 0.0007936500793651)) x)
   (if (<= z 220000.0)
     (+
      (+ 0.91893853320467 (- (* (log x) (- x 0.5)) x))
      (/ 1.0 (* x 12.000000000000048)))
     (* (+ y 0.0007936500793651) (/ (pow z 2.0) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.35e+24) {
		tmp = (pow(z, 2.0) * (y + 0.0007936500793651)) / x;
	} else if (z <= 220000.0) {
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + (1.0 / (x * 12.000000000000048));
	} else {
		tmp = (y + 0.0007936500793651) * (pow(z, 2.0) / 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 (z <= (-2.35d+24)) then
        tmp = ((z ** 2.0d0) * (y + 0.0007936500793651d0)) / x
    else if (z <= 220000.0d0) then
        tmp = (0.91893853320467d0 + ((log(x) * (x - 0.5d0)) - x)) + (1.0d0 / (x * 12.000000000000048d0))
    else
        tmp = (y + 0.0007936500793651d0) * ((z ** 2.0d0) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.35e+24) {
		tmp = (Math.pow(z, 2.0) * (y + 0.0007936500793651)) / x;
	} else if (z <= 220000.0) {
		tmp = (0.91893853320467 + ((Math.log(x) * (x - 0.5)) - x)) + (1.0 / (x * 12.000000000000048));
	} else {
		tmp = (y + 0.0007936500793651) * (Math.pow(z, 2.0) / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.35e+24:
		tmp = (math.pow(z, 2.0) * (y + 0.0007936500793651)) / x
	elif z <= 220000.0:
		tmp = (0.91893853320467 + ((math.log(x) * (x - 0.5)) - x)) + (1.0 / (x * 12.000000000000048))
	else:
		tmp = (y + 0.0007936500793651) * (math.pow(z, 2.0) / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.35e+24)
		tmp = Float64(Float64((z ^ 2.0) * Float64(y + 0.0007936500793651)) / x);
	elseif (z <= 220000.0)
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(log(x) * Float64(x - 0.5)) - x)) + Float64(1.0 / Float64(x * 12.000000000000048)));
	else
		tmp = Float64(Float64(y + 0.0007936500793651) * Float64((z ^ 2.0) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.35e+24)
		tmp = ((z ^ 2.0) * (y + 0.0007936500793651)) / x;
	elseif (z <= 220000.0)
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + (1.0 / (x * 12.000000000000048));
	else
		tmp = (y + 0.0007936500793651) * ((z ^ 2.0) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.35e+24], N[(N[(N[Power[z, 2.0], $MachinePrecision] * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[z, 220000.0], N[(N[(0.91893853320467 + N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(x * 12.000000000000048), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(N[Power[z, 2.0], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.35e24

   1. Initial program 96.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 96.2%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   4. Step-by-step derivation

      1. associate-/l* 96.1%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

   5. Simplified 96.1%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

   6. Taylor expanded in x around 0 80.4%

      \[\leadsto \color{blue}{\left(0.91893853320467 + -0.5 \cdot \log x\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]
   7. Step-by-step derivation

      1. +-commutative 80.4%

         \[\leadsto \color{blue}{\left(-0.5 \cdot \log x + 0.91893853320467\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]

   8. Simplified 80.4%

      \[\leadsto \color{blue}{\left(-0.5 \cdot \log x + 0.91893853320467\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]

   9. Taylor expanded in x around 0 80.7%

      \[\leadsto \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]

   if -2.35e24 < z < 2.2e5

   1. Initial program 99.5%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{1}{\frac{x}{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}}} \]

      2. inv-pow 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{{\left(\frac{x}{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}\right)}^{-1}} \]

      3. *-commutative 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + {\left(\frac{x}{\color{blue}{z \cdot \left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right)} + 0.083333333333333}\right)}^{-1} \]

      4. fma-udef 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + {\left(\frac{x}{\color{blue}{\mathsf{fma}\left(z, \left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778, 0.083333333333333\right)}}\right)}^{-1} \]

      5. fma-neg 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + {\left(\frac{x}{\mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right)}, 0.083333333333333\right)}\right)}^{-1} \]

      6. metadata-eval 99.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + {\left(\frac{x}{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, \color{blue}{-0.0027777777777778}\right), 0.083333333333333\right)}\right)}^{-1} \]

   4. Applied egg-rr 99.5%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{{\left(\frac{x}{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}\right)}^{-1}} \]

   5. Taylor expanded in z around 0 91.8%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + {\color{blue}{\left(12.000000000000048 \cdot x\right)}}^{-1} \]
   6. Step-by-step derivation

      1. *-commutative 91.8%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + {\color{blue}{\left(x \cdot 12.000000000000048\right)}}^{-1} \]

   7. Simplified 91.8%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + {\color{blue}{\left(x \cdot 12.000000000000048\right)}}^{-1} \]
   8. Step-by-step derivation

      1. unpow-1 91.8%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{1}{x \cdot 12.000000000000048}} \]

   9. Applied egg-rr 91.8%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{1}{x \cdot 12.000000000000048}} \]

   if 2.2e5 < z

   1. Initial program 92.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 91.3%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   4. Step-by-step derivation

      1. associate-/l* 97.7%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

   5. Simplified 97.7%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

   6. Taylor expanded in x around 0 79.4%

      \[\leadsto \color{blue}{\left(0.91893853320467 + -0.5 \cdot \log x\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]
   7. Step-by-step derivation

      1. +-commutative 79.4%

         \[\leadsto \color{blue}{\left(-0.5 \cdot \log x + 0.91893853320467\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]

   8. Simplified 79.4%

      \[\leadsto \color{blue}{\left(-0.5 \cdot \log x + 0.91893853320467\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]

   9. Taylor expanded in x around 0 74.6%

      \[\leadsto \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   10. Step-by-step derivation

       1. +-commutative 74.6%

          \[\leadsto \frac{{z}^{2} \cdot \color{blue}{\left(y + 0.0007936500793651\right)}}{x} \]

       2. associate-*l/ 79.5%

          \[\leadsto \color{blue}{\frac{{z}^{2}}{x} \cdot \left(y + 0.0007936500793651\right)} \]

       3. +-commutative 79.5%

          \[\leadsto \frac{{z}^{2}}{x} \cdot \color{blue}{\left(0.0007936500793651 + y\right)} \]

   11. Simplified 79.5%

       \[\leadsto \color{blue}{\frac{{z}^{2}}{x} \cdot \left(0.0007936500793651 + y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+24}:\\ \;\;\;\;\frac{{z}^{2} \cdot \left(y + 0.0007936500793651\right)}{x}\\ \mathbf{elif}\;z \leq 220000:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{1}{x \cdot 12.000000000000048}\\ \mathbf{else}:\\ \;\;\;\;\left(y + 0.0007936500793651\right) \cdot \frac{{z}^{2}}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+17}:\\ \;\;\;\;\frac{{z}^{2} \cdot \left(y + 0.0007936500793651\right)}{x}\\ \mathbf{elif}\;z \leq 125000000:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(y + 0.0007936500793651\right) \cdot \frac{{z}^{2}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.65e+17)
   (/ (* (pow z 2.0) (+ y 0.0007936500793651)) x)
   (if (<= z 125000000.0)
     (+
      (* x (+ (log x) -1.0))
      (/ (+ 0.083333333333333 (* z -0.0027777777777778)) x))
     (* (+ y 0.0007936500793651) (/ (pow z 2.0) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.65e+17) {
		tmp = (pow(z, 2.0) * (y + 0.0007936500793651)) / x;
	} else if (z <= 125000000.0) {
		tmp = (x * (log(x) + -1.0)) + ((0.083333333333333 + (z * -0.0027777777777778)) / x);
	} else {
		tmp = (y + 0.0007936500793651) * (pow(z, 2.0) / 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 (z <= (-2.65d+17)) then
        tmp = ((z ** 2.0d0) * (y + 0.0007936500793651d0)) / x
    else if (z <= 125000000.0d0) then
        tmp = (x * (log(x) + (-1.0d0))) + ((0.083333333333333d0 + (z * (-0.0027777777777778d0))) / x)
    else
        tmp = (y + 0.0007936500793651d0) * ((z ** 2.0d0) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.65e+17) {
		tmp = (Math.pow(z, 2.0) * (y + 0.0007936500793651)) / x;
	} else if (z <= 125000000.0) {
		tmp = (x * (Math.log(x) + -1.0)) + ((0.083333333333333 + (z * -0.0027777777777778)) / x);
	} else {
		tmp = (y + 0.0007936500793651) * (Math.pow(z, 2.0) / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.65e+17:
		tmp = (math.pow(z, 2.0) * (y + 0.0007936500793651)) / x
	elif z <= 125000000.0:
		tmp = (x * (math.log(x) + -1.0)) + ((0.083333333333333 + (z * -0.0027777777777778)) / x)
	else:
		tmp = (y + 0.0007936500793651) * (math.pow(z, 2.0) / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.65e+17)
		tmp = Float64(Float64((z ^ 2.0) * Float64(y + 0.0007936500793651)) / x);
	elseif (z <= 125000000.0)
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(Float64(0.083333333333333 + Float64(z * -0.0027777777777778)) / x));
	else
		tmp = Float64(Float64(y + 0.0007936500793651) * Float64((z ^ 2.0) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.65e+17)
		tmp = ((z ^ 2.0) * (y + 0.0007936500793651)) / x;
	elseif (z <= 125000000.0)
		tmp = (x * (log(x) + -1.0)) + ((0.083333333333333 + (z * -0.0027777777777778)) / x);
	else
		tmp = (y + 0.0007936500793651) * ((z ^ 2.0) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.65e+17], N[(N[(N[Power[z, 2.0], $MachinePrecision] * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[z, 125000000.0], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(0.083333333333333 + N[(z * -0.0027777777777778), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(N[Power[z, 2.0], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.65e17

   1. Initial program 96.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 96.2%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   4. Step-by-step derivation

      1. associate-/l* 96.1%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

   5. Simplified 96.1%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

   6. Taylor expanded in x around 0 80.4%

      \[\leadsto \color{blue}{\left(0.91893853320467 + -0.5 \cdot \log x\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]
   7. Step-by-step derivation

      1. +-commutative 80.4%

         \[\leadsto \color{blue}{\left(-0.5 \cdot \log x + 0.91893853320467\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]

   8. Simplified 80.4%

      \[\leadsto \color{blue}{\left(-0.5 \cdot \log x + 0.91893853320467\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]

   9. Taylor expanded in x around 0 80.7%

      \[\leadsto \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]

   if -2.65e17 < z < 1.25e8

   1. Initial program 99.5%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 99.1%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   4. Step-by-step derivation

      1. sub-neg 91.4%

         \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) + \left(-1\right)\right)} + \frac{0.083333333333333}{x} \]

      2. mul-1-neg 91.4%

         \[\leadsto x \cdot \left(\color{blue}{\left(-\log \left(\frac{1}{x}\right)\right)} + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

      3. log-rec 91.4%

         \[\leadsto x \cdot \left(\left(-\color{blue}{\left(-\log x\right)}\right) + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

      4. remove-double-neg 91.4%

         \[\leadsto x \cdot \left(\color{blue}{\log x} + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

      5. metadata-eval 91.4%

         \[\leadsto x \cdot \left(\log x + \color{blue}{-1}\right) + \frac{0.083333333333333}{x} \]

   5. Simplified 99.1%

      \[\leadsto \color{blue}{x \cdot \left(\log x + -1\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   6. Taylor expanded in z around 0 91.6%

      \[\leadsto x \cdot \left(\log x + -1\right) + \frac{\color{blue}{-0.0027777777777778 \cdot z} + 0.083333333333333}{x} \]
   7. Step-by-step derivation

      1. *-commutative 91.6%

         \[\leadsto x \cdot \left(\log x + -1\right) + \frac{\color{blue}{z \cdot -0.0027777777777778} + 0.083333333333333}{x} \]

   8. Simplified 91.6%

      \[\leadsto x \cdot \left(\log x + -1\right) + \frac{\color{blue}{z \cdot -0.0027777777777778} + 0.083333333333333}{x} \]

   if 1.25e8 < z

   1. Initial program 92.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 91.3%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   4. Step-by-step derivation

      1. associate-/l* 97.7%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

   5. Simplified 97.7%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

   6. Taylor expanded in x around 0 79.4%

      \[\leadsto \color{blue}{\left(0.91893853320467 + -0.5 \cdot \log x\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]
   7. Step-by-step derivation

      1. +-commutative 79.4%

         \[\leadsto \color{blue}{\left(-0.5 \cdot \log x + 0.91893853320467\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]

   8. Simplified 79.4%

      \[\leadsto \color{blue}{\left(-0.5 \cdot \log x + 0.91893853320467\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]

   9. Taylor expanded in x around 0 74.6%

      \[\leadsto \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   10. Step-by-step derivation

       1. +-commutative 74.6%

          \[\leadsto \frac{{z}^{2} \cdot \color{blue}{\left(y + 0.0007936500793651\right)}}{x} \]

       2. associate-*l/ 79.5%

          \[\leadsto \color{blue}{\frac{{z}^{2}}{x} \cdot \left(y + 0.0007936500793651\right)} \]

       3. +-commutative 79.5%

          \[\leadsto \frac{{z}^{2}}{x} \cdot \color{blue}{\left(0.0007936500793651 + y\right)} \]

   11. Simplified 79.5%

       \[\leadsto \color{blue}{\frac{{z}^{2}}{x} \cdot \left(0.0007936500793651 + y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+17}:\\ \;\;\;\;\frac{{z}^{2} \cdot \left(y + 0.0007936500793651\right)}{x}\\ \mathbf{elif}\;z \leq 125000000:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(y + 0.0007936500793651\right) \cdot \frac{{z}^{2}}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+19}:\\ \;\;\;\;\frac{{z}^{2} \cdot \left(y + 0.0007936500793651\right)}{x}\\ \mathbf{elif}\;z \leq 13500000:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(y + 0.0007936500793651\right) \cdot \frac{{z}^{2}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.55e+19)
   (/ (* (pow z 2.0) (+ y 0.0007936500793651)) x)
   (if (<= z 13500000.0)
     (+
      (+ 0.91893853320467 (- (* (log x) (- x 0.5)) x))
      (/ 0.083333333333333 x))
     (* (+ y 0.0007936500793651) (/ (pow z 2.0) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.55e+19) {
		tmp = (pow(z, 2.0) * (y + 0.0007936500793651)) / x;
	} else if (z <= 13500000.0) {
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + (0.083333333333333 / x);
	} else {
		tmp = (y + 0.0007936500793651) * (pow(z, 2.0) / 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 (z <= (-1.55d+19)) then
        tmp = ((z ** 2.0d0) * (y + 0.0007936500793651d0)) / x
    else if (z <= 13500000.0d0) then
        tmp = (0.91893853320467d0 + ((log(x) * (x - 0.5d0)) - x)) + (0.083333333333333d0 / x)
    else
        tmp = (y + 0.0007936500793651d0) * ((z ** 2.0d0) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.55e+19) {
		tmp = (Math.pow(z, 2.0) * (y + 0.0007936500793651)) / x;
	} else if (z <= 13500000.0) {
		tmp = (0.91893853320467 + ((Math.log(x) * (x - 0.5)) - x)) + (0.083333333333333 / x);
	} else {
		tmp = (y + 0.0007936500793651) * (Math.pow(z, 2.0) / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.55e+19:
		tmp = (math.pow(z, 2.0) * (y + 0.0007936500793651)) / x
	elif z <= 13500000.0:
		tmp = (0.91893853320467 + ((math.log(x) * (x - 0.5)) - x)) + (0.083333333333333 / x)
	else:
		tmp = (y + 0.0007936500793651) * (math.pow(z, 2.0) / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.55e+19)
		tmp = Float64(Float64((z ^ 2.0) * Float64(y + 0.0007936500793651)) / x);
	elseif (z <= 13500000.0)
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(log(x) * Float64(x - 0.5)) - x)) + Float64(0.083333333333333 / x));
	else
		tmp = Float64(Float64(y + 0.0007936500793651) * Float64((z ^ 2.0) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.55e+19)
		tmp = ((z ^ 2.0) * (y + 0.0007936500793651)) / x;
	elseif (z <= 13500000.0)
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + (0.083333333333333 / x);
	else
		tmp = (y + 0.0007936500793651) * ((z ^ 2.0) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.55e+19], N[(N[(N[Power[z, 2.0], $MachinePrecision] * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[z, 13500000.0], N[(N[(0.91893853320467 + N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision], N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(N[Power[z, 2.0], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.55e19

   1. Initial program 96.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 96.2%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   4. Step-by-step derivation

      1. associate-/l* 96.1%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

   5. Simplified 96.1%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

   6. Taylor expanded in x around 0 80.4%

      \[\leadsto \color{blue}{\left(0.91893853320467 + -0.5 \cdot \log x\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]
   7. Step-by-step derivation

      1. +-commutative 80.4%

         \[\leadsto \color{blue}{\left(-0.5 \cdot \log x + 0.91893853320467\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]

   8. Simplified 80.4%

      \[\leadsto \color{blue}{\left(-0.5 \cdot \log x + 0.91893853320467\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]

   9. Taylor expanded in x around 0 80.7%

      \[\leadsto \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]

   if -1.55e19 < z < 1.35e7

   1. Initial program 99.5%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 91.8%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{0.083333333333333}{x}} \]

   if 1.35e7 < z

   1. Initial program 92.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 91.3%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   4. Step-by-step derivation

      1. associate-/l* 97.7%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

   5. Simplified 97.7%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

   6. Taylor expanded in x around 0 79.4%

      \[\leadsto \color{blue}{\left(0.91893853320467 + -0.5 \cdot \log x\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]
   7. Step-by-step derivation

      1. +-commutative 79.4%

         \[\leadsto \color{blue}{\left(-0.5 \cdot \log x + 0.91893853320467\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]

   8. Simplified 79.4%

      \[\leadsto \color{blue}{\left(-0.5 \cdot \log x + 0.91893853320467\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]

   9. Taylor expanded in x around 0 74.6%

      \[\leadsto \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   10. Step-by-step derivation

       1. +-commutative 74.6%

          \[\leadsto \frac{{z}^{2} \cdot \color{blue}{\left(y + 0.0007936500793651\right)}}{x} \]

       2. associate-*l/ 79.5%

          \[\leadsto \color{blue}{\frac{{z}^{2}}{x} \cdot \left(y + 0.0007936500793651\right)} \]

       3. +-commutative 79.5%

          \[\leadsto \frac{{z}^{2}}{x} \cdot \color{blue}{\left(0.0007936500793651 + y\right)} \]

   11. Simplified 79.5%

       \[\leadsto \color{blue}{\frac{{z}^{2}}{x} \cdot \left(0.0007936500793651 + y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+19}:\\ \;\;\;\;\frac{{z}^{2} \cdot \left(y + 0.0007936500793651\right)}{x}\\ \mathbf{elif}\;z \leq 13500000:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(y + 0.0007936500793651\right) \cdot \frac{{z}^{2}}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 93.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+
  (+ 0.91893853320467 (- (* (log x) (- x 0.5)) x))
  (/
   (+
    0.083333333333333
    (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))
   x)))

C

double code(double x, double y, double z) {
	return (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / 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 = (0.91893853320467d0 + ((log(x) * (x - 0.5d0)) - x)) + ((0.083333333333333d0 + (z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0))) / x)
end function

Java

public static double code(double x, double y, double z) {
	return (0.91893853320467 + ((Math.log(x) * (x - 0.5)) - x)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
}

Python

def code(x, y, z):
	return (0.91893853320467 + ((math.log(x) * (x - 0.5)) - x)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x)

Julia

function code(x, y, z)
	return Float64(Float64(0.91893853320467 + Float64(Float64(log(x) * Float64(x - 0.5)) - x)) + Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778))) / x))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
end

Wolfram

code[x_, y_, z_] := N[(N[(0.91893853320467 + N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(N[(0.083333333333333 + N[(z * N[(N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.8%

   \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
2. Add Preprocessing

3. Final simplification 96.8%

   \[\leadsto \left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} \]
4. Add Preprocessing

Alternative 9: 82.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+19}:\\ \;\;\;\;\frac{{z}^{2} \cdot \left(y + 0.0007936500793651\right)}{x}\\ \mathbf{elif}\;z \leq 140000:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(y + 0.0007936500793651\right) \cdot \frac{{z}^{2}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.5e+19)
   (/ (* (pow z 2.0) (+ y 0.0007936500793651)) x)
   (if (<= z 140000.0)
     (+ (* x (+ (log x) -1.0)) (/ 0.083333333333333 x))
     (* (+ y 0.0007936500793651) (/ (pow z 2.0) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.5e+19) {
		tmp = (pow(z, 2.0) * (y + 0.0007936500793651)) / x;
	} else if (z <= 140000.0) {
		tmp = (x * (log(x) + -1.0)) + (0.083333333333333 / x);
	} else {
		tmp = (y + 0.0007936500793651) * (pow(z, 2.0) / 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 (z <= (-3.5d+19)) then
        tmp = ((z ** 2.0d0) * (y + 0.0007936500793651d0)) / x
    else if (z <= 140000.0d0) then
        tmp = (x * (log(x) + (-1.0d0))) + (0.083333333333333d0 / x)
    else
        tmp = (y + 0.0007936500793651d0) * ((z ** 2.0d0) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.5e+19) {
		tmp = (Math.pow(z, 2.0) * (y + 0.0007936500793651)) / x;
	} else if (z <= 140000.0) {
		tmp = (x * (Math.log(x) + -1.0)) + (0.083333333333333 / x);
	} else {
		tmp = (y + 0.0007936500793651) * (Math.pow(z, 2.0) / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.5e+19:
		tmp = (math.pow(z, 2.0) * (y + 0.0007936500793651)) / x
	elif z <= 140000.0:
		tmp = (x * (math.log(x) + -1.0)) + (0.083333333333333 / x)
	else:
		tmp = (y + 0.0007936500793651) * (math.pow(z, 2.0) / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.5e+19)
		tmp = Float64(Float64((z ^ 2.0) * Float64(y + 0.0007936500793651)) / x);
	elseif (z <= 140000.0)
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(0.083333333333333 / x));
	else
		tmp = Float64(Float64(y + 0.0007936500793651) * Float64((z ^ 2.0) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.5e+19)
		tmp = ((z ^ 2.0) * (y + 0.0007936500793651)) / x;
	elseif (z <= 140000.0)
		tmp = (x * (log(x) + -1.0)) + (0.083333333333333 / x);
	else
		tmp = (y + 0.0007936500793651) * ((z ^ 2.0) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.5e+19], N[(N[(N[Power[z, 2.0], $MachinePrecision] * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[z, 140000.0], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision], N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(N[Power[z, 2.0], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.5e19

   1. Initial program 96.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 96.2%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   4. Step-by-step derivation

      1. associate-/l* 96.1%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

   5. Simplified 96.1%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

   6. Taylor expanded in x around 0 80.4%

      \[\leadsto \color{blue}{\left(0.91893853320467 + -0.5 \cdot \log x\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]
   7. Step-by-step derivation

      1. +-commutative 80.4%

         \[\leadsto \color{blue}{\left(-0.5 \cdot \log x + 0.91893853320467\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]

   8. Simplified 80.4%

      \[\leadsto \color{blue}{\left(-0.5 \cdot \log x + 0.91893853320467\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]

   9. Taylor expanded in x around 0 80.7%

      \[\leadsto \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]

   if -3.5e19 < z < 1.4e5

   1. Initial program 99.5%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 91.8%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{0.083333333333333}{x}} \]

   4. Taylor expanded in x around inf 91.4%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right)} + \frac{0.083333333333333}{x} \]
   5. Step-by-step derivation

      1. sub-neg 91.4%

         \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) + \left(-1\right)\right)} + \frac{0.083333333333333}{x} \]

      2. mul-1-neg 91.4%

         \[\leadsto x \cdot \left(\color{blue}{\left(-\log \left(\frac{1}{x}\right)\right)} + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

      3. log-rec 91.4%

         \[\leadsto x \cdot \left(\left(-\color{blue}{\left(-\log x\right)}\right) + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

      4. remove-double-neg 91.4%

         \[\leadsto x \cdot \left(\color{blue}{\log x} + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

      5. metadata-eval 91.4%

         \[\leadsto x \cdot \left(\log x + \color{blue}{-1}\right) + \frac{0.083333333333333}{x} \]

   6. Simplified 91.4%

      \[\leadsto \color{blue}{x \cdot \left(\log x + -1\right)} + \frac{0.083333333333333}{x} \]

   if 1.4e5 < z

   1. Initial program 92.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 91.3%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   4. Step-by-step derivation

      1. associate-/l* 97.7%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

   5. Simplified 97.7%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

   6. Taylor expanded in x around 0 79.4%

      \[\leadsto \color{blue}{\left(0.91893853320467 + -0.5 \cdot \log x\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]
   7. Step-by-step derivation

      1. +-commutative 79.4%

         \[\leadsto \color{blue}{\left(-0.5 \cdot \log x + 0.91893853320467\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]

   8. Simplified 79.4%

      \[\leadsto \color{blue}{\left(-0.5 \cdot \log x + 0.91893853320467\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]

   9. Taylor expanded in x around 0 74.6%

      \[\leadsto \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   10. Step-by-step derivation

       1. +-commutative 74.6%

          \[\leadsto \frac{{z}^{2} \cdot \color{blue}{\left(y + 0.0007936500793651\right)}}{x} \]

       2. associate-*l/ 79.5%

          \[\leadsto \color{blue}{\frac{{z}^{2}}{x} \cdot \left(y + 0.0007936500793651\right)} \]

       3. +-commutative 79.5%

          \[\leadsto \frac{{z}^{2}}{x} \cdot \color{blue}{\left(0.0007936500793651 + y\right)} \]

   11. Simplified 79.5%

       \[\leadsto \color{blue}{\frac{{z}^{2}}{x} \cdot \left(0.0007936500793651 + y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+19}:\\ \;\;\;\;\frac{{z}^{2} \cdot \left(y + 0.0007936500793651\right)}{x}\\ \mathbf{elif}\;z \leq 140000:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(y + 0.0007936500793651\right) \cdot \frac{{z}^{2}}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 92.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} + x \cdot \left(\log x + -1\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+
  (/
   (+
    0.083333333333333
    (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))
   x)
  (* x (+ (log x) -1.0))))

C

double code(double x, double y, double z) {
	return ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) + (x * (log(x) + -1.0));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((0.083333333333333d0 + (z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0))) / x) + (x * (log(x) + (-1.0d0)))
end function

Java

public static double code(double x, double y, double z) {
	return ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) + (x * (Math.log(x) + -1.0));
}

Python

def code(x, y, z):
	return ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) + (x * (math.log(x) + -1.0))

Julia

function code(x, y, z)
	return Float64(Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778))) / x) + Float64(x * Float64(log(x) + -1.0)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) + (x * (log(x) + -1.0));
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(0.083333333333333 + N[(z * N[(N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] + N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.8%

   \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
2. Add Preprocessing

3. Taylor expanded in x around inf 96.6%

   \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
4. Step-by-step derivation

   1. sub-neg 58.4%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) + \left(-1\right)\right)} + \frac{0.083333333333333}{x} \]

   2. mul-1-neg 58.4%

      \[\leadsto x \cdot \left(\color{blue}{\left(-\log \left(\frac{1}{x}\right)\right)} + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

   3. log-rec 58.4%

      \[\leadsto x \cdot \left(\left(-\color{blue}{\left(-\log x\right)}\right) + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

   4. remove-double-neg 58.4%

      \[\leadsto x \cdot \left(\color{blue}{\log x} + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

   5. metadata-eval 58.4%

      \[\leadsto x \cdot \left(\log x + \color{blue}{-1}\right) + \frac{0.083333333333333}{x} \]

5. Simplified 96.6%

   \[\leadsto \color{blue}{x \cdot \left(\log x + -1\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

6. Final simplification 96.6%

   \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} + x \cdot \left(\log x + -1\right) \]
7. Add Preprocessing

Alternative 11: 60.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-9} \lor \neg \left(z \leq 2.3 \cdot 10^{-32}\right):\\ \;\;\;\;\left(y + 0.0007936500793651\right) \cdot \frac{{z}^{2}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.1e-9) (not (<= z 2.3e-32)))
   (* (+ y 0.0007936500793651) (/ (pow z 2.0) x))
   (/ 0.083333333333333 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.1e-9) || !(z <= 2.3e-32)) {
		tmp = (y + 0.0007936500793651) * (pow(z, 2.0) / x);
	} else {
		tmp = 0.083333333333333 / 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 ((z <= (-1.1d-9)) .or. (.not. (z <= 2.3d-32))) then
        tmp = (y + 0.0007936500793651d0) * ((z ** 2.0d0) / x)
    else
        tmp = 0.083333333333333d0 / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.1e-9) || !(z <= 2.3e-32)) {
		tmp = (y + 0.0007936500793651) * (Math.pow(z, 2.0) / x);
	} else {
		tmp = 0.083333333333333 / x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.1e-9) or not (z <= 2.3e-32):
		tmp = (y + 0.0007936500793651) * (math.pow(z, 2.0) / x)
	else:
		tmp = 0.083333333333333 / x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.1e-9) || !(z <= 2.3e-32))
		tmp = Float64(Float64(y + 0.0007936500793651) * Float64((z ^ 2.0) / x));
	else
		tmp = Float64(0.083333333333333 / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.1e-9) || ~((z <= 2.3e-32)))
		tmp = (y + 0.0007936500793651) * ((z ^ 2.0) / x);
	else
		tmp = 0.083333333333333 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.1e-9], N[Not[LessEqual[z, 2.3e-32]], $MachinePrecision]], N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(N[Power[z, 2.0], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(0.083333333333333 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0999999999999999e-9 or 2.3000000000000001e-32 < z

   1. Initial program 94.6%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 93.3%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   4. Step-by-step derivation

      1. associate-/l* 96.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

   5. Simplified 96.5%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

   6. Taylor expanded in x around 0 71.8%

      \[\leadsto \color{blue}{\left(0.91893853320467 + -0.5 \cdot \log x\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]
   7. Step-by-step derivation

      1. +-commutative 71.8%

         \[\leadsto \color{blue}{\left(-0.5 \cdot \log x + 0.91893853320467\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]

   8. Simplified 71.8%

      \[\leadsto \color{blue}{\left(-0.5 \cdot \log x + 0.91893853320467\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]

   9. Taylor expanded in x around 0 69.5%

      \[\leadsto \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   10. Step-by-step derivation

       1. +-commutative 69.5%

          \[\leadsto \frac{{z}^{2} \cdot \color{blue}{\left(y + 0.0007936500793651\right)}}{x} \]

       2. associate-*l/ 72.0%

          \[\leadsto \color{blue}{\frac{{z}^{2}}{x} \cdot \left(y + 0.0007936500793651\right)} \]

       3. +-commutative 72.0%

          \[\leadsto \frac{{z}^{2}}{x} \cdot \color{blue}{\left(0.0007936500793651 + y\right)} \]

   11. Simplified 72.0%

       \[\leadsto \color{blue}{\frac{{z}^{2}}{x} \cdot \left(0.0007936500793651 + y\right)} \]

   if -1.0999999999999999e-9 < z < 2.3000000000000001e-32

   1. Initial program 99.5%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 93.6%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{0.083333333333333}{x}} \]

   4. Taylor expanded in x around inf 93.1%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right)} + \frac{0.083333333333333}{x} \]
   5. Step-by-step derivation

      1. sub-neg 93.1%

         \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) + \left(-1\right)\right)} + \frac{0.083333333333333}{x} \]

      2. mul-1-neg 93.1%

         \[\leadsto x \cdot \left(\color{blue}{\left(-\log \left(\frac{1}{x}\right)\right)} + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

      3. log-rec 93.1%

         \[\leadsto x \cdot \left(\left(-\color{blue}{\left(-\log x\right)}\right) + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

      4. remove-double-neg 93.1%

         \[\leadsto x \cdot \left(\color{blue}{\log x} + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

      5. metadata-eval 93.1%

         \[\leadsto x \cdot \left(\log x + \color{blue}{-1}\right) + \frac{0.083333333333333}{x} \]

   6. Simplified 93.1%

      \[\leadsto \color{blue}{x \cdot \left(\log x + -1\right)} + \frac{0.083333333333333}{x} \]

   7. Taylor expanded in x around 0 46.4%

      \[\leadsto \color{blue}{\frac{0.083333333333333}{x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-9} \lor \neg \left(z \leq 2.3 \cdot 10^{-32}\right):\\ \;\;\;\;\left(y + 0.0007936500793651\right) \cdot \frac{{z}^{2}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-12}:\\ \;\;\;\;\frac{{z}^{2} \cdot \left(y + 0.0007936500793651\right)}{x}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-32}:\\ \;\;\;\;\frac{0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(y + 0.0007936500793651\right) \cdot \frac{{z}^{2}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.15e-12)
   (/ (* (pow z 2.0) (+ y 0.0007936500793651)) x)
   (if (<= z 3e-32)
     (/ 0.083333333333333 x)
     (* (+ y 0.0007936500793651) (/ (pow z 2.0) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.15e-12) {
		tmp = (pow(z, 2.0) * (y + 0.0007936500793651)) / x;
	} else if (z <= 3e-32) {
		tmp = 0.083333333333333 / x;
	} else {
		tmp = (y + 0.0007936500793651) * (pow(z, 2.0) / 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 (z <= (-1.15d-12)) then
        tmp = ((z ** 2.0d0) * (y + 0.0007936500793651d0)) / x
    else if (z <= 3d-32) then
        tmp = 0.083333333333333d0 / x
    else
        tmp = (y + 0.0007936500793651d0) * ((z ** 2.0d0) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.15e-12) {
		tmp = (Math.pow(z, 2.0) * (y + 0.0007936500793651)) / x;
	} else if (z <= 3e-32) {
		tmp = 0.083333333333333 / x;
	} else {
		tmp = (y + 0.0007936500793651) * (Math.pow(z, 2.0) / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.15e-12:
		tmp = (math.pow(z, 2.0) * (y + 0.0007936500793651)) / x
	elif z <= 3e-32:
		tmp = 0.083333333333333 / x
	else:
		tmp = (y + 0.0007936500793651) * (math.pow(z, 2.0) / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.15e-12)
		tmp = Float64(Float64((z ^ 2.0) * Float64(y + 0.0007936500793651)) / x);
	elseif (z <= 3e-32)
		tmp = Float64(0.083333333333333 / x);
	else
		tmp = Float64(Float64(y + 0.0007936500793651) * Float64((z ^ 2.0) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.15e-12)
		tmp = ((z ^ 2.0) * (y + 0.0007936500793651)) / x;
	elseif (z <= 3e-32)
		tmp = 0.083333333333333 / x;
	else
		tmp = (y + 0.0007936500793651) * ((z ^ 2.0) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.15e-12], N[(N[(N[Power[z, 2.0], $MachinePrecision] * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[z, 3e-32], N[(0.083333333333333 / x), $MachinePrecision], N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(N[Power[z, 2.0], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.14999999999999995e-12

   1. Initial program 96.7%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 96.7%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   4. Step-by-step derivation

      1. associate-/l* 96.6%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

   5. Simplified 96.6%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

   6. Taylor expanded in x around 0 70.2%

      \[\leadsto \color{blue}{\left(0.91893853320467 + -0.5 \cdot \log x\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]
   7. Step-by-step derivation

      1. +-commutative 70.2%

         \[\leadsto \color{blue}{\left(-0.5 \cdot \log x + 0.91893853320467\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]

   8. Simplified 70.2%

      \[\leadsto \color{blue}{\left(-0.5 \cdot \log x + 0.91893853320467\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]

   9. Taylor expanded in x around 0 70.5%

      \[\leadsto \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]

   if -1.14999999999999995e-12 < z < 3e-32

   1. Initial program 99.5%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 93.5%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{0.083333333333333}{x}} \]

   4. Taylor expanded in x around inf 93.1%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right)} + \frac{0.083333333333333}{x} \]
   5. Step-by-step derivation

      1. sub-neg 93.1%

         \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) + \left(-1\right)\right)} + \frac{0.083333333333333}{x} \]

      2. mul-1-neg 93.1%

         \[\leadsto x \cdot \left(\color{blue}{\left(-\log \left(\frac{1}{x}\right)\right)} + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

      3. log-rec 93.1%

         \[\leadsto x \cdot \left(\left(-\color{blue}{\left(-\log x\right)}\right) + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

      4. remove-double-neg 93.1%

         \[\leadsto x \cdot \left(\color{blue}{\log x} + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

      5. metadata-eval 93.1%

         \[\leadsto x \cdot \left(\log x + \color{blue}{-1}\right) + \frac{0.083333333333333}{x} \]

   6. Simplified 93.1%

      \[\leadsto \color{blue}{x \cdot \left(\log x + -1\right)} + \frac{0.083333333333333}{x} \]

   7. Taylor expanded in x around 0 46.7%

      \[\leadsto \color{blue}{\frac{0.083333333333333}{x}} \]

   if 3e-32 < z

   1. Initial program 93.1%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 90.9%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   4. Step-by-step derivation

      1. associate-/l* 96.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

   5. Simplified 96.5%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

   6. Taylor expanded in x around 0 72.1%

      \[\leadsto \color{blue}{\left(0.91893853320467 + -0.5 \cdot \log x\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]
   7. Step-by-step derivation

      1. +-commutative 72.1%

         \[\leadsto \color{blue}{\left(-0.5 \cdot \log x + 0.91893853320467\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]

   8. Simplified 72.1%

      \[\leadsto \color{blue}{\left(-0.5 \cdot \log x + 0.91893853320467\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]

   9. Taylor expanded in x around 0 68.0%

      \[\leadsto \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   10. Step-by-step derivation

       1. +-commutative 68.0%

          \[\leadsto \frac{{z}^{2} \cdot \color{blue}{\left(y + 0.0007936500793651\right)}}{x} \]

       2. associate-*l/ 72.3%

          \[\leadsto \color{blue}{\frac{{z}^{2}}{x} \cdot \left(y + 0.0007936500793651\right)} \]

       3. +-commutative 72.3%

          \[\leadsto \frac{{z}^{2}}{x} \cdot \color{blue}{\left(0.0007936500793651 + y\right)} \]

   11. Simplified 72.3%

       \[\leadsto \color{blue}{\frac{{z}^{2}}{x} \cdot \left(0.0007936500793651 + y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-12}:\\ \;\;\;\;\frac{{z}^{2} \cdot \left(y + 0.0007936500793651\right)}{x}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-32}:\\ \;\;\;\;\frac{0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(y + 0.0007936500793651\right) \cdot \frac{{z}^{2}}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-10} \lor \neg \left(z \leq 3 \cdot 10^{-32}\right):\\ \;\;\;\;{z}^{2} \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8.5e-10) (not (<= z 3e-32)))
   (* (pow z 2.0) (/ y x))
   (/ 0.083333333333333 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.5e-10) || !(z <= 3e-32)) {
		tmp = pow(z, 2.0) * (y / x);
	} else {
		tmp = 0.083333333333333 / 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 ((z <= (-8.5d-10)) .or. (.not. (z <= 3d-32))) then
        tmp = (z ** 2.0d0) * (y / x)
    else
        tmp = 0.083333333333333d0 / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.5e-10) || !(z <= 3e-32)) {
		tmp = Math.pow(z, 2.0) * (y / x);
	} else {
		tmp = 0.083333333333333 / x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8.5e-10) or not (z <= 3e-32):
		tmp = math.pow(z, 2.0) * (y / x)
	else:
		tmp = 0.083333333333333 / x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8.5e-10) || !(z <= 3e-32))
		tmp = Float64((z ^ 2.0) * Float64(y / x));
	else
		tmp = Float64(0.083333333333333 / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -8.5e-10) || ~((z <= 3e-32)))
		tmp = (z ^ 2.0) * (y / x);
	else
		tmp = 0.083333333333333 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8.5e-10], N[Not[LessEqual[z, 3e-32]], $MachinePrecision]], N[(N[Power[z, 2.0], $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision], N[(0.083333333333333 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.4999999999999996e-10 or 3e-32 < z

   1. Initial program 94.6%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 93.3%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   4. Step-by-step derivation

      1. associate-/l* 96.6%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

   5. Simplified 96.6%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

   6. Taylor expanded in x around 0 71.3%

      \[\leadsto \color{blue}{\left(0.91893853320467 + -0.5 \cdot \log x\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]
   7. Step-by-step derivation

      1. +-commutative 71.3%

         \[\leadsto \color{blue}{\left(-0.5 \cdot \log x + 0.91893853320467\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]

   8. Simplified 71.3%

      \[\leadsto \color{blue}{\left(-0.5 \cdot \log x + 0.91893853320467\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]

   9. Taylor expanded in y around inf 47.1%

      \[\leadsto \color{blue}{\frac{y \cdot {z}^{2}}{x}} \]
   10. Step-by-step derivation

       1. *-commutative 47.1%

          \[\leadsto \frac{\color{blue}{{z}^{2} \cdot y}}{x} \]

       2. associate-*r/ 49.5%

          \[\leadsto \color{blue}{{z}^{2} \cdot \frac{y}{x}} \]

   11. Simplified 49.5%

       \[\leadsto \color{blue}{{z}^{2} \cdot \frac{y}{x}} \]

   if -8.4999999999999996e-10 < z < 3e-32

   1. Initial program 99.5%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 93.5%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{0.083333333333333}{x}} \]

   4. Taylor expanded in x around inf 93.1%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right)} + \frac{0.083333333333333}{x} \]
   5. Step-by-step derivation

      1. sub-neg 93.1%

         \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) + \left(-1\right)\right)} + \frac{0.083333333333333}{x} \]

      2. mul-1-neg 93.1%

         \[\leadsto x \cdot \left(\color{blue}{\left(-\log \left(\frac{1}{x}\right)\right)} + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

      3. log-rec 93.1%

         \[\leadsto x \cdot \left(\left(-\color{blue}{\left(-\log x\right)}\right) + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

      4. remove-double-neg 93.1%

         \[\leadsto x \cdot \left(\color{blue}{\log x} + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

      5. metadata-eval 93.1%

         \[\leadsto x \cdot \left(\log x + \color{blue}{-1}\right) + \frac{0.083333333333333}{x} \]

   6. Simplified 93.1%

      \[\leadsto \color{blue}{x \cdot \left(\log x + -1\right)} + \frac{0.083333333333333}{x} \]

   7. Taylor expanded in x around 0 46.7%

      \[\leadsto \color{blue}{\frac{0.083333333333333}{x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-10} \lor \neg \left(z \leq 3 \cdot 10^{-32}\right):\\ \;\;\;\;{z}^{2} \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 49.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-9} \lor \neg \left(z \leq 3 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{y}{\frac{x}{{z}^{2}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.1e-9) (not (<= z 3e-32)))
   (/ y (/ x (pow z 2.0)))
   (/ 0.083333333333333 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.1e-9) || !(z <= 3e-32)) {
		tmp = y / (x / pow(z, 2.0));
	} else {
		tmp = 0.083333333333333 / 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 ((z <= (-1.1d-9)) .or. (.not. (z <= 3d-32))) then
        tmp = y / (x / (z ** 2.0d0))
    else
        tmp = 0.083333333333333d0 / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.1e-9) || !(z <= 3e-32)) {
		tmp = y / (x / Math.pow(z, 2.0));
	} else {
		tmp = 0.083333333333333 / x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.1e-9) or not (z <= 3e-32):
		tmp = y / (x / math.pow(z, 2.0))
	else:
		tmp = 0.083333333333333 / x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.1e-9) || !(z <= 3e-32))
		tmp = Float64(y / Float64(x / (z ^ 2.0)));
	else
		tmp = Float64(0.083333333333333 / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.1e-9) || ~((z <= 3e-32)))
		tmp = y / (x / (z ^ 2.0));
	else
		tmp = 0.083333333333333 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.1e-9], N[Not[LessEqual[z, 3e-32]], $MachinePrecision]], N[(y / N[(x / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.083333333333333 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0999999999999999e-9 or 3e-32 < z

   1. Initial program 94.6%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 93.3%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   4. Step-by-step derivation

      1. associate-/l* 96.5%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

   5. Simplified 96.5%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

   6. Taylor expanded in x around 0 71.8%

      \[\leadsto \color{blue}{\left(0.91893853320467 + -0.5 \cdot \log x\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]
   7. Step-by-step derivation

      1. +-commutative 71.8%

         \[\leadsto \color{blue}{\left(-0.5 \cdot \log x + 0.91893853320467\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]

   8. Simplified 71.8%

      \[\leadsto \color{blue}{\left(-0.5 \cdot \log x + 0.91893853320467\right)} + \frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}} \]

   9. Taylor expanded in y around inf 47.4%

      \[\leadsto \color{blue}{\frac{y \cdot {z}^{2}}{x}} \]
   10. Step-by-step derivation

       1. associate-/l* 52.5%

          \[\leadsto \color{blue}{\frac{y}{\frac{x}{{z}^{2}}}} \]

   11. Simplified 52.5%

       \[\leadsto \color{blue}{\frac{y}{\frac{x}{{z}^{2}}}} \]

   if -1.0999999999999999e-9 < z < 3e-32

   1. Initial program 99.5%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 93.6%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{0.083333333333333}{x}} \]

   4. Taylor expanded in x around inf 93.1%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right)} + \frac{0.083333333333333}{x} \]
   5. Step-by-step derivation

      1. sub-neg 93.1%

         \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) + \left(-1\right)\right)} + \frac{0.083333333333333}{x} \]

      2. mul-1-neg 93.1%

         \[\leadsto x \cdot \left(\color{blue}{\left(-\log \left(\frac{1}{x}\right)\right)} + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

      3. log-rec 93.1%

         \[\leadsto x \cdot \left(\left(-\color{blue}{\left(-\log x\right)}\right) + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

      4. remove-double-neg 93.1%

         \[\leadsto x \cdot \left(\color{blue}{\log x} + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

      5. metadata-eval 93.1%

         \[\leadsto x \cdot \left(\log x + \color{blue}{-1}\right) + \frac{0.083333333333333}{x} \]

   6. Simplified 93.1%

      \[\leadsto \color{blue}{x \cdot \left(\log x + -1\right)} + \frac{0.083333333333333}{x} \]

   7. Taylor expanded in x around 0 46.4%

      \[\leadsto \color{blue}{\frac{0.083333333333333}{x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-9} \lor \neg \left(z \leq 3 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{y}{\frac{x}{{z}^{2}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 24.1% accurate, 41.0× speedup

Math

\[\begin{array}{l} \\ \frac{0.083333333333333}{x} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ 0.083333333333333 x))

C

double code(double x, double y, double z) {
	return 0.083333333333333 / 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 = 0.083333333333333d0 / x
end function

Java

public static double code(double x, double y, double z) {
	return 0.083333333333333 / x;
}

Python

def code(x, y, z):
	return 0.083333333333333 / x

Julia

function code(x, y, z)
	return Float64(0.083333333333333 / x)
end

MATLAB

function tmp = code(x, y, z)
	tmp = 0.083333333333333 / x;
end

Wolfram

code[x_, y_, z_] := N[(0.083333333333333 / x), $MachinePrecision]

Derivation

1. Initial program 96.8%

   \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
2. Add Preprocessing

3. Taylor expanded in z around 0 58.5%

   \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{0.083333333333333}{x}} \]

4. Taylor expanded in x around inf 58.4%

   \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right)} + \frac{0.083333333333333}{x} \]
5. Step-by-step derivation

   1. sub-neg 58.4%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) + \left(-1\right)\right)} + \frac{0.083333333333333}{x} \]

   2. mul-1-neg 58.4%

      \[\leadsto x \cdot \left(\color{blue}{\left(-\log \left(\frac{1}{x}\right)\right)} + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

   3. log-rec 58.4%

      \[\leadsto x \cdot \left(\left(-\color{blue}{\left(-\log x\right)}\right) + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

   4. remove-double-neg 58.4%

      \[\leadsto x \cdot \left(\color{blue}{\log x} + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

   5. metadata-eval 58.4%

      \[\leadsto x \cdot \left(\log x + \color{blue}{-1}\right) + \frac{0.083333333333333}{x} \]

6. Simplified 58.4%

   \[\leadsto \color{blue}{x \cdot \left(\log x + -1\right)} + \frac{0.083333333333333}{x} \]

7. Taylor expanded in x around 0 23.0%

   \[\leadsto \color{blue}{\frac{0.083333333333333}{x}} \]

8. Final simplification 23.0%

   \[\leadsto \frac{0.083333333333333}{x} \]
9. Add Preprocessing

Alternative 16: 1.3% accurate, 61.5× 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 Float64(-x)
end

MATLAB

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

Wolfram

code[x_, y_, z_] := (-x)

Derivation

1. Initial program 96.8%

   \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
2. Add Preprocessing

3. Taylor expanded in z around 0 58.5%

   \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{0.083333333333333}{x}} \]

4. Taylor expanded in x around 0 22.1%

   \[\leadsto \left(\left(\color{blue}{-0.5 \cdot \log x} - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

5. Taylor expanded in x around inf 1.2%

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

   1. neg-mul-1 1.2%

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

7. Simplified 1.2%

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

8. Final simplification 1.2%

   \[\leadsto -x \]
9. Add Preprocessing

Developer target: 98.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(x - 0.5\right) \cdot \log x + \left(0.91893853320467 - x\right)\right) + \frac{0.083333333333333}{x}\right) + \frac{z}{x} \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+
  (+ (+ (* (- x 0.5) (log x)) (- 0.91893853320467 x)) (/ 0.083333333333333 x))
  (* (/ z x) (- (* z (+ y 0.0007936500793651)) 0.0027777777777778))))

C

double code(double x, double y, double z) {
	return ((((x - 0.5) * log(x)) + (0.91893853320467 - x)) + (0.083333333333333 / x)) + ((z / x) * ((z * (y + 0.0007936500793651)) - 0.0027777777777778));
}

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 - 0.5d0) * log(x)) + (0.91893853320467d0 - x)) + (0.083333333333333d0 / x)) + ((z / x) * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0))
end function

Java

public static double code(double x, double y, double z) {
	return ((((x - 0.5) * Math.log(x)) + (0.91893853320467 - x)) + (0.083333333333333 / x)) + ((z / x) * ((z * (y + 0.0007936500793651)) - 0.0027777777777778));
}

Python

def code(x, y, z):
	return ((((x - 0.5) * math.log(x)) + (0.91893853320467 - x)) + (0.083333333333333 / x)) + ((z / x) * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))

Julia

function code(x, y, z)
	return Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) + Float64(0.91893853320467 - x)) + Float64(0.083333333333333 / x)) + Float64(Float64(z / x) * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((((x - 0.5) * log(x)) + (0.91893853320467 - x)) + (0.083333333333333 / x)) + ((z / x) * ((z * (y + 0.0007936500793651)) - 0.0027777777777778));
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] + N[(0.91893853320467 - x), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision] + N[(N[(z / x), $MachinePrecision] * N[(N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024018 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (+ (+ (+ (* (- x 0.5) (log x)) (- 0.91893853320467 x)) (/ 0.083333333333333 x)) (* (/ z x) (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))

  (+ (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467) (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)))