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

Percentage Accurate: 93.7% → 96.9%

Time: 14.5s

Alternatives: 14

Speedup: 1.0×

• 27.5% 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: 93.7% 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: 96.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.8 \cdot 10^{+193}:\\ \;\;\;\;\left(0.91893853320467 - \mathsf{fma}\left(\log x, 0.5 - x, x\right)\right) + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + y \cdot \frac{z}{\frac{x}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.8e+193)
   (+
    (- 0.91893853320467 (fma (log x) (- 0.5 x) x))
    (/
     (fma
      z
      (fma (+ y 0.0007936500793651) z -0.0027777777777778)
      0.083333333333333)
     x))
   (+ (+ 0.91893853320467 (- (* (log x) (- x 0.5)) x)) (* y (/ z (/ x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.8e+193) {
		tmp = (0.91893853320467 - fma(log(x), (0.5 - x), x)) + (fma(z, fma((y + 0.0007936500793651), z, -0.0027777777777778), 0.083333333333333) / x);
	} else {
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + (y * (z / (x / z)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.8e+193)
		tmp = Float64(Float64(0.91893853320467 - fma(log(x), Float64(0.5 - x), 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(y * Float64(z / Float64(x / z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.8e+193], N[(N[(0.91893853320467 - N[(N[Log[x], $MachinePrecision] * N[(0.5 - x), $MachinePrecision] + 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[(y * N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.8e193

   1. Initial program 97.3%

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

      1. remove-double-neg 97.3%

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

      2. +-commutative 97.3%

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

      3. associate-+r- 97.3%

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

      4. remove-double-neg 97.3%

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

      5. sub-neg 97.3%

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

      6. associate--r+ 97.3%

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

      7. *-commutative 97.3%

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

      8. distribute-rgt-neg-in 97.3%

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

      9. fma-def 97.4%

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

      10. neg-sub0 97.4%

          \[\leadsto \left(0.91893853320467 - \mathsf{fma}\left(\log x, \color{blue}{0 - \left(x - 0.5\right)}, x\right)\right) + \left(-\left(-\frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\right)\right) \]

      11. associate-+l- 97.4%

          \[\leadsto \left(0.91893853320467 - \mathsf{fma}\left(\log x, \color{blue}{\left(0 - x\right) + 0.5}, x\right)\right) + \left(-\left(-\frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\right)\right) \]

      12. neg-sub0 97.4%

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

      13. +-commutative 97.4%

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

      14. unsub-neg 97.4%

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

      15. remove-double-neg 97.4%

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

   3. Simplified 97.4%

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

   if 1.8e193 < x

   1. Initial program 87.0%

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

   2. Taylor expanded in z around inf 87.0%

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

      1. associate-/l* 90.8%

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

      2. +-commutative 90.8%

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

      3. associate-/r/ 90.8%

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

      4. unpow2 90.8%

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

      5. +-commutative 90.8%

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

   4. Simplified 90.8%

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

   5. Taylor expanded in y around inf 86.7%

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

      1. unpow2 86.7%

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

      2. associate-*r/ 90.5%

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

      3. associate-/l* 97.8%

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

   7. Simplified 97.8%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.8 \cdot 10^{+193}:\\ \;\;\;\;\left(0.91893853320467 - \mathsf{fma}\left(\log x, 0.5 - x, x\right)\right) + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + y \cdot \frac{z}{\frac{x}{z}}\\ \end{array} \]

Alternative 2: 97.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\\ \mathbf{if}\;x \leq 5 \cdot 10^{+176}:\\ \;\;\;\;t_0 + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;t_0 + y \cdot \frac{z}{\frac{x}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 0.91893853320467 (- (* (log x) (- x 0.5)) x))))
   (if (<= x 5e+176)
     (+
      t_0
      (/
       (+
        0.083333333333333
        (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))
       x))
     (+ t_0 (* y (/ z (/ x z)))))))

C

double code(double x, double y, double z) {
	double t_0 = 0.91893853320467 + ((log(x) * (x - 0.5)) - x);
	double tmp;
	if (x <= 5e+176) {
		tmp = t_0 + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = t_0 + (y * (z / (x / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 0.91893853320467d0 + ((log(x) * (x - 0.5d0)) - x)
    if (x <= 5d+176) then
        tmp = t_0 + ((0.083333333333333d0 + (z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0))) / x)
    else
        tmp = t_0 + (y * (z / (x / z)))
    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 (x <= 5e+176) {
		tmp = t_0 + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = t_0 + (y * (z / (x / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 0.91893853320467 + ((math.log(x) * (x - 0.5)) - x)
	tmp = 0
	if x <= 5e+176:
		tmp = t_0 + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x)
	else:
		tmp = t_0 + (y * (z / (x / z)))
	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 (x <= 5e+176)
		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(y * Float64(z / Float64(x / z))));
	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 (x <= 5e+176)
		tmp = t_0 + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	else
		tmp = t_0 + (y * (z / (x / z)));
	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[x, 5e+176], 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[(y * N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 5e176

   1. Initial program 97.2%

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

   if 5e176 < x

   1. Initial program 88.4%

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

   2. Taylor expanded in z around inf 88.4%

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

      1. associate-/l* 91.8%

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

      2. +-commutative 91.8%

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

      3. associate-/r/ 91.8%

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

      4. unpow2 91.8%

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

      5. +-commutative 91.8%

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

   4. Simplified 91.8%

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

   5. Taylor expanded in y around inf 88.2%

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

      1. unpow2 88.2%

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

      2. associate-*r/ 91.5%

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

      3. associate-/l* 98.0%

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

   7. Simplified 98.0%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5 \cdot 10^{+176}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + y \cdot \frac{z}{\frac{x}{z}}\\ \end{array} \]

Alternative 3: 97.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.7 \cdot 10^{+176}:\\ \;\;\;\;\left(\log x \cdot \left(x + -0.5\right) + \left(0.91893853320467 - x\right)\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + y \cdot \frac{z}{\frac{x}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 2.7e+176)
   (+
    (+ (* (log x) (+ x -0.5)) (- 0.91893853320467 x))
    (/
     (+
      0.083333333333333
      (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))
     x))
   (+ (+ 0.91893853320467 (- (* (log x) (- x 0.5)) x)) (* y (/ z (/ x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 2.7e+176) {
		tmp = ((log(x) * (x + -0.5)) + (0.91893853320467 - x)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + (y * (z / (x / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 2.7d+176) then
        tmp = ((log(x) * (x + (-0.5d0))) + (0.91893853320467d0 - x)) + ((0.083333333333333d0 + (z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0))) / x)
    else
        tmp = (0.91893853320467d0 + ((log(x) * (x - 0.5d0)) - x)) + (y * (z / (x / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 2.7e+176) {
		tmp = ((Math.log(x) * (x + -0.5)) + (0.91893853320467 - x)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = (0.91893853320467 + ((Math.log(x) * (x - 0.5)) - x)) + (y * (z / (x / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 2.7e+176:
		tmp = ((math.log(x) * (x + -0.5)) + (0.91893853320467 - x)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x)
	else:
		tmp = (0.91893853320467 + ((math.log(x) * (x - 0.5)) - x)) + (y * (z / (x / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 2.7e+176)
		tmp = Float64(Float64(Float64(log(x) * Float64(x + -0.5)) + Float64(0.91893853320467 - x)) + Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778))) / x));
	else
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(log(x) * Float64(x - 0.5)) - x)) + Float64(y * Float64(z / Float64(x / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 2.7e+176)
		tmp = ((log(x) * (x + -0.5)) + (0.91893853320467 - x)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	else
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + (y * (z / (x / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 2.7e+176], N[(N[(N[(N[Log[x], $MachinePrecision] * N[(x + -0.5), $MachinePrecision]), $MachinePrecision] + N[(0.91893853320467 - 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], N[(N[(0.91893853320467 + N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.6999999999999998e176

   1. Initial program 97.2%

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

      1. associate-+l- 97.3%

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

      2. sub-neg 97.3%

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

      3. metadata-eval 97.3%

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

   3. Applied egg-rr 97.3%

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

   if 2.6999999999999998e176 < x

   1. Initial program 88.4%

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

   2. Taylor expanded in z around inf 88.4%

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

      1. associate-/l* 91.8%

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

      2. +-commutative 91.8%

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

      3. associate-/r/ 91.8%

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

      4. unpow2 91.8%

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

      5. +-commutative 91.8%

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

   4. Simplified 91.8%

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

   5. Taylor expanded in y around inf 88.2%

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

      1. unpow2 88.2%

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

      2. associate-*r/ 91.5%

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

      3. associate-/l* 98.0%

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

   7. Simplified 98.0%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.7 \cdot 10^{+176}:\\ \;\;\;\;\left(\log x \cdot \left(x + -0.5\right) + \left(0.91893853320467 - x\right)\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + y \cdot \frac{z}{\frac{x}{z}}\\ \end{array} \]

Alternative 4: 95.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 10^{+192}:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} + x \cdot \left(\log x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + y \cdot \frac{z}{\frac{x}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1e+192)
   (+
    (/
     (+
      0.083333333333333
      (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))
     x)
    (* x (+ (log x) -1.0)))
   (+ (+ 0.91893853320467 (- (* (log x) (- x 0.5)) x)) (* y (/ z (/ x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1e+192) {
		tmp = ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) + (x * (log(x) + -1.0));
	} else {
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + (y * (z / (x / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 1d+192) then
        tmp = ((0.083333333333333d0 + (z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0))) / x) + (x * (log(x) + (-1.0d0)))
    else
        tmp = (0.91893853320467d0 + ((log(x) * (x - 0.5d0)) - x)) + (y * (z / (x / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1e+192) {
		tmp = ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) + (x * (Math.log(x) + -1.0));
	} else {
		tmp = (0.91893853320467 + ((Math.log(x) * (x - 0.5)) - x)) + (y * (z / (x / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1e+192:
		tmp = ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) + (x * (math.log(x) + -1.0))
	else:
		tmp = (0.91893853320467 + ((math.log(x) * (x - 0.5)) - x)) + (y * (z / (x / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1e+192)
		tmp = Float64(Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778))) / x) + Float64(x * Float64(log(x) + -1.0)));
	else
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(log(x) * Float64(x - 0.5)) - x)) + Float64(y * Float64(z / Float64(x / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1e+192)
		tmp = ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) + (x * (log(x) + -1.0));
	else
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + (y * (z / (x / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1e+192], 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], N[(N[(0.91893853320467 + N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.00000000000000004e192

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf 95.1%

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

      1. *-commutative 48.7%

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

      2. mul-1-neg 48.7%

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

      3. log-rec 48.7%

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

      4. remove-double-neg 48.7%

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

      5. sub-neg 48.7%

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

      6. metadata-eval 48.7%

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

   4. Simplified 95.1%

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

   if 1.00000000000000004e192 < x

   1. Initial program 87.0%

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

   2. Taylor expanded in z around inf 87.0%

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

      1. associate-/l* 90.8%

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

      2. +-commutative 90.8%

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

      3. associate-/r/ 90.8%

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

      4. unpow2 90.8%

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

      5. +-commutative 90.8%

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

   4. Simplified 90.8%

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

   5. Taylor expanded in y around inf 86.7%

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

      1. unpow2 86.7%

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

      2. associate-*r/ 90.5%

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

      3. associate-/l* 97.8%

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

   7. Simplified 97.8%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 10^{+192}:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} + x \cdot \left(\log x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + y \cdot \frac{z}{\frac{x}{z}}\\ \end{array} \]

Alternative 5: 91.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-20} \lor \neg \left(z \leq 1.15 \cdot 10^{-33}\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\log x \cdot \left(x + -0.5\right) + \left(0.91893853320467 - x\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.2e-20) (not (<= z 1.15e-33)))
   (+ (* x (+ (log x) -1.0)) (* (+ y 0.0007936500793651) (/ (* z z) x)))
   (+
    (+ (* (log x) (+ x -0.5)) (- 0.91893853320467 x))
    (/ 0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.2e-20) || !(z <= 1.15e-33)) {
		tmp = (x * (log(x) + -1.0)) + ((y + 0.0007936500793651) * ((z * z) / x));
	} else {
		tmp = ((log(x) * (x + -0.5)) + (0.91893853320467 - x)) + (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 <= (-1.2d-20)) .or. (.not. (z <= 1.15d-33))) then
        tmp = (x * (log(x) + (-1.0d0))) + ((y + 0.0007936500793651d0) * ((z * z) / x))
    else
        tmp = ((log(x) * (x + (-0.5d0))) + (0.91893853320467d0 - x)) + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.2e-20) || !(z <= 1.15e-33)) {
		tmp = (x * (Math.log(x) + -1.0)) + ((y + 0.0007936500793651) * ((z * z) / x));
	} else {
		tmp = ((Math.log(x) * (x + -0.5)) + (0.91893853320467 - x)) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.2e-20) or not (z <= 1.15e-33):
		tmp = (x * (math.log(x) + -1.0)) + ((y + 0.0007936500793651) * ((z * z) / x))
	else:
		tmp = ((math.log(x) * (x + -0.5)) + (0.91893853320467 - x)) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.2e-20) || !(z <= 1.15e-33))
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(Float64(y + 0.0007936500793651) * Float64(Float64(z * z) / x)));
	else
		tmp = Float64(Float64(Float64(log(x) * Float64(x + -0.5)) + Float64(0.91893853320467 - x)) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.2e-20) || ~((z <= 1.15e-33)))
		tmp = (x * (log(x) + -1.0)) + ((y + 0.0007936500793651) * ((z * z) / x));
	else
		tmp = ((log(x) * (x + -0.5)) + (0.91893853320467 - x)) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.2e-20], N[Not[LessEqual[z, 1.15e-33]], $MachinePrecision]], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(N[(z * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[Log[x], $MachinePrecision] * N[(x + -0.5), $MachinePrecision]), $MachinePrecision] + N[(0.91893853320467 - x), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.19999999999999996e-20 or 1.14999999999999993e-33 < 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. Taylor expanded in z around inf 90.6%

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

      1. associate-/l* 92.1%

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

      2. +-commutative 92.1%

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

      3. associate-/r/ 92.1%

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

      4. unpow2 92.1%

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

      5. +-commutative 92.1%

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

   4. Simplified 92.1%

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

   5. Taylor expanded in x around inf 92.1%

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

      1. *-commutative 24.0%

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

      2. mul-1-neg 24.0%

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

      3. log-rec 24.0%

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

      4. remove-double-neg 24.0%

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

      5. sub-neg 24.0%

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

      6. metadata-eval 24.0%

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

   7. Simplified 92.1%

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

   if -1.19999999999999996e-20 < z < 1.14999999999999993e-33

   1. Initial program 99.3%

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

      1. associate-+l- 99.4%

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

      2. sub-neg 99.4%

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

      3. metadata-eval 99.4%

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

   3. Applied egg-rr 99.4%

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

   4. Taylor expanded in z around 0 96.8%

      \[\leadsto \left(\left(x + -0.5\right) \cdot \log x - \left(x - 0.91893853320467\right)\right) + \color{blue}{\frac{0.083333333333333}{x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-20} \lor \neg \left(z \leq 1.15 \cdot 10^{-33}\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\log x \cdot \left(x + -0.5\right) + \left(0.91893853320467 - x\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 6: 91.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(\log x + -1\right)\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{-19}:\\ \;\;\;\;t_0 + \left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-37}:\\ \;\;\;\;\left(\log x \cdot \left(x + -0.5\right) + \left(0.91893853320467 - x\right)\right) + \frac{0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{z \cdot z}{\frac{x}{y + 0.0007936500793651}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ (log x) -1.0))))
   (if (<= z -3.2e-19)
     (+ t_0 (* (+ y 0.0007936500793651) (/ (* z z) x)))
     (if (<= z 1.3e-37)
       (+
        (+ (* (log x) (+ x -0.5)) (- 0.91893853320467 x))
        (/ 0.083333333333333 x))
       (+ t_0 (/ (* z z) (/ x (+ y 0.0007936500793651))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (log(x) + -1.0);
	double tmp;
	if (z <= -3.2e-19) {
		tmp = t_0 + ((y + 0.0007936500793651) * ((z * z) / x));
	} else if (z <= 1.3e-37) {
		tmp = ((log(x) * (x + -0.5)) + (0.91893853320467 - x)) + (0.083333333333333 / x);
	} else {
		tmp = t_0 + ((z * z) / (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 = x * (log(x) + (-1.0d0))
    if (z <= (-3.2d-19)) then
        tmp = t_0 + ((y + 0.0007936500793651d0) * ((z * z) / x))
    else if (z <= 1.3d-37) then
        tmp = ((log(x) * (x + (-0.5d0))) + (0.91893853320467d0 - x)) + (0.083333333333333d0 / x)
    else
        tmp = t_0 + ((z * z) / (x / (y + 0.0007936500793651d0)))
    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 (z <= -3.2e-19) {
		tmp = t_0 + ((y + 0.0007936500793651) * ((z * z) / x));
	} else if (z <= 1.3e-37) {
		tmp = ((Math.log(x) * (x + -0.5)) + (0.91893853320467 - x)) + (0.083333333333333 / x);
	} else {
		tmp = t_0 + ((z * z) / (x / (y + 0.0007936500793651)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (math.log(x) + -1.0)
	tmp = 0
	if z <= -3.2e-19:
		tmp = t_0 + ((y + 0.0007936500793651) * ((z * z) / x))
	elif z <= 1.3e-37:
		tmp = ((math.log(x) * (x + -0.5)) + (0.91893853320467 - x)) + (0.083333333333333 / x)
	else:
		tmp = t_0 + ((z * z) / (x / (y + 0.0007936500793651)))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(log(x) + -1.0))
	tmp = 0.0
	if (z <= -3.2e-19)
		tmp = Float64(t_0 + Float64(Float64(y + 0.0007936500793651) * Float64(Float64(z * z) / x)));
	elseif (z <= 1.3e-37)
		tmp = Float64(Float64(Float64(log(x) * Float64(x + -0.5)) + Float64(0.91893853320467 - x)) + Float64(0.083333333333333 / x));
	else
		tmp = Float64(t_0 + Float64(Float64(z * z) / Float64(x / Float64(y + 0.0007936500793651))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (log(x) + -1.0);
	tmp = 0.0;
	if (z <= -3.2e-19)
		tmp = t_0 + ((y + 0.0007936500793651) * ((z * z) / x));
	elseif (z <= 1.3e-37)
		tmp = ((log(x) * (x + -0.5)) + (0.91893853320467 - x)) + (0.083333333333333 / x);
	else
		tmp = t_0 + ((z * z) / (x / (y + 0.0007936500793651)));
	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[LessEqual[z, -3.2e-19], N[(t$95$0 + N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(N[(z * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e-37], N[(N[(N[(N[Log[x], $MachinePrecision] * N[(x + -0.5), $MachinePrecision]), $MachinePrecision] + N[(0.91893853320467 - x), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(N[(z * z), $MachinePrecision] / N[(x / N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.19999999999999982e-19

   1. Initial program 91.0%

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

   2. Taylor expanded in z around inf 89.7%

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

      1. associate-/l* 92.4%

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

      2. +-commutative 92.4%

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

      3. associate-/r/ 92.4%

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

      4. unpow2 92.4%

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

      5. +-commutative 92.4%

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

   4. Simplified 92.4%

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

   5. Taylor expanded in x around inf 92.4%

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

      1. *-commutative 25.0%

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

      2. mul-1-neg 25.0%

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

      3. log-rec 25.0%

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

      4. remove-double-neg 25.0%

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

      5. sub-neg 25.0%

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

      6. metadata-eval 25.0%

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

   7. Simplified 92.4%

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

   if -3.19999999999999982e-19 < z < 1.2999999999999999e-37

   1. Initial program 99.3%

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

      1. associate-+l- 99.4%

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

      2. sub-neg 99.4%

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

      3. metadata-eval 99.4%

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

   3. Applied egg-rr 99.4%

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

   4. Taylor expanded in z around 0 96.8%

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

   if 1.2999999999999999e-37 < z

   1. Initial program 93.0%

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

      1. associate-+l- 93.0%

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

      2. sub-neg 93.0%

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

      3. metadata-eval 93.0%

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

   3. Applied egg-rr 93.0%

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

   4. Taylor expanded in z around inf 91.7%

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

      1. associate-/l* 91.7%

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

      2. unpow2 91.7%

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

   6. Simplified 91.7%

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

   7. Taylor expanded in x around inf 91.8%

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

      1. *-commutative 76.7%

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

      2. sub-neg 76.7%

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

      3. mul-1-neg 76.7%

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

      4. log-rec 76.7%

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

      5. remove-double-neg 76.7%

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

      6. metadata-eval 76.7%

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

   9. Simplified 91.8%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-37}:\\ \;\;\;\;\left(\log x \cdot \left(x + -0.5\right) + \left(0.91893853320467 - x\right)\right) + \frac{0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{z \cdot z}{\frac{x}{y + 0.0007936500793651}}\\ \end{array} \]

Alternative 7: 79.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-14} \lor \neg \left(z \leq 7 \cdot 10^{-36}\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{y}{\frac{x}{z \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x} + \left(x \cdot \log x + \left(0.91893853320467 - x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.9e-14) (not (<= z 7e-36)))
   (+ (* x (+ (log x) -1.0)) (/ y (/ x (* z z))))
   (+ (/ 0.083333333333333 x) (+ (* x (log x)) (- 0.91893853320467 x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.9e-14) || !(z <= 7e-36)) {
		tmp = (x * (log(x) + -1.0)) + (y / (x / (z * z)));
	} else {
		tmp = (0.083333333333333 / x) + ((x * log(x)) + (0.91893853320467 - 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 <= (-1.9d-14)) .or. (.not. (z <= 7d-36))) then
        tmp = (x * (log(x) + (-1.0d0))) + (y / (x / (z * z)))
    else
        tmp = (0.083333333333333d0 / x) + ((x * log(x)) + (0.91893853320467d0 - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.9e-14) || !(z <= 7e-36)) {
		tmp = (x * (Math.log(x) + -1.0)) + (y / (x / (z * z)));
	} else {
		tmp = (0.083333333333333 / x) + ((x * Math.log(x)) + (0.91893853320467 - x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.9e-14) or not (z <= 7e-36):
		tmp = (x * (math.log(x) + -1.0)) + (y / (x / (z * z)))
	else:
		tmp = (0.083333333333333 / x) + ((x * math.log(x)) + (0.91893853320467 - x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.9e-14) || !(z <= 7e-36))
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(y / Float64(x / Float64(z * z))));
	else
		tmp = Float64(Float64(0.083333333333333 / x) + Float64(Float64(x * log(x)) + Float64(0.91893853320467 - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.9e-14) || ~((z <= 7e-36)))
		tmp = (x * (log(x) + -1.0)) + (y / (x / (z * z)));
	else
		tmp = (0.083333333333333 / x) + ((x * log(x)) + (0.91893853320467 - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.9e-14], N[Not[LessEqual[z, 7e-36]], $MachinePrecision]], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.083333333333333 / x), $MachinePrecision] + N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] + N[(0.91893853320467 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9000000000000001e-14 or 6.9999999999999999e-36 < z

   1. Initial program 91.7%

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

      1. associate-+l- 91.7%

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

      2. sub-neg 91.7%

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

      3. metadata-eval 91.7%

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

   3. Applied egg-rr 91.7%

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

   4. Taylor expanded in y around inf 69.0%

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

      1. associate-/l* 71.8%

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

      2. unpow2 71.8%

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

   6. Simplified 71.8%

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

   7. Taylor expanded in x around inf 71.9%

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

      1. *-commutative 71.9%

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

      2. sub-neg 71.9%

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

      3. mul-1-neg 71.9%

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

      4. log-rec 71.9%

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

      5. remove-double-neg 71.9%

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

      6. metadata-eval 71.9%

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

   9. Simplified 71.9%

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

   if -1.9000000000000001e-14 < z < 6.9999999999999999e-36

   1. Initial program 99.3%

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

      1. associate-+l- 99.4%

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

      2. sub-neg 99.4%

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

      3. metadata-eval 99.4%

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

   3. Applied egg-rr 99.4%

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

   4. Taylor expanded in z around 0 96.0%

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

   5. Taylor expanded in x around inf 92.1%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(\log \left(\frac{1}{x}\right) \cdot x\right)} - \left(x - 0.91893853320467\right)\right) + \frac{0.083333333333333}{x} \]
   6. Step-by-step derivation

      1. mul-1-neg 92.1%

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

      2. distribute-lft-neg-in 92.1%

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

      3. log-rec 92.1%

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

      4. remove-double-neg 92.1%

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

      5. *-commutative 92.1%

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

   7. Simplified 92.1%

      \[\leadsto \left(\color{blue}{x \cdot \log x} - \left(x - 0.91893853320467\right)\right) + \frac{0.083333333333333}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-14} \lor \neg \left(z \leq 7 \cdot 10^{-36}\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{y}{\frac{x}{z \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x} + \left(x \cdot \log x + \left(0.91893853320467 - x\right)\right)\\ \end{array} \]

Alternative 8: 80.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-14} \lor \neg \left(z \leq 2.3 \cdot 10^{-36}\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{y}{\frac{x}{z \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.7e-14) (not (<= z 2.3e-36)))
   (+ (* x (+ (log x) -1.0)) (/ y (/ x (* z z))))
   (+
    (+ 0.91893853320467 (- (* (log x) (- x 0.5)) x))
    (/ 0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.7e-14) || !(z <= 2.3e-36)) {
		tmp = (x * (log(x) + -1.0)) + (y / (x / (z * z)));
	} else {
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + (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 <= (-2.7d-14)) .or. (.not. (z <= 2.3d-36))) then
        tmp = (x * (log(x) + (-1.0d0))) + (y / (x / (z * z)))
    else
        tmp = (0.91893853320467d0 + ((log(x) * (x - 0.5d0)) - x)) + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.7e-14) || !(z <= 2.3e-36)) {
		tmp = (x * (Math.log(x) + -1.0)) + (y / (x / (z * z)));
	} else {
		tmp = (0.91893853320467 + ((Math.log(x) * (x - 0.5)) - x)) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.7e-14) or not (z <= 2.3e-36):
		tmp = (x * (math.log(x) + -1.0)) + (y / (x / (z * z)))
	else:
		tmp = (0.91893853320467 + ((math.log(x) * (x - 0.5)) - x)) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.7e-14) || !(z <= 2.3e-36))
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(y / Float64(x / Float64(z * z))));
	else
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(log(x) * Float64(x - 0.5)) - x)) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.7e-14) || ~((z <= 2.3e-36)))
		tmp = (x * (log(x) + -1.0)) + (y / (x / (z * z)));
	else
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.7e-14], N[Not[LessEqual[z, 2.3e-36]], $MachinePrecision]], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6999999999999999e-14 or 2.29999999999999996e-36 < z

   1. Initial program 91.7%

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

      1. associate-+l- 91.7%

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

      2. sub-neg 91.7%

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

      3. metadata-eval 91.7%

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

   3. Applied egg-rr 91.7%

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

   4. Taylor expanded in y around inf 69.0%

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

      1. associate-/l* 71.8%

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

      2. unpow2 71.8%

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

   6. Simplified 71.8%

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

   7. Taylor expanded in x around inf 71.9%

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

      1. *-commutative 71.9%

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

      2. sub-neg 71.9%

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

      3. mul-1-neg 71.9%

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

      4. log-rec 71.9%

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

      5. remove-double-neg 71.9%

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

      6. metadata-eval 71.9%

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

   9. Simplified 71.9%

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

   if -2.6999999999999999e-14 < z < 2.29999999999999996e-36

   1. Initial program 99.3%

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

   2. Taylor expanded in z around 0 96.0%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{0.083333333333333}{x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-14} \lor \neg \left(z \leq 2.3 \cdot 10^{-36}\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{y}{\frac{x}{z \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 9: 80.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-14} \lor \neg \left(z \leq 1.05 \cdot 10^{-35}\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{y}{\frac{x}{z \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\log x \cdot \left(x + -0.5\right) + \left(0.91893853320467 - x\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.95e-14) (not (<= z 1.05e-35)))
   (+ (* x (+ (log x) -1.0)) (/ y (/ x (* z z))))
   (+
    (+ (* (log x) (+ x -0.5)) (- 0.91893853320467 x))
    (/ 0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.95e-14) || !(z <= 1.05e-35)) {
		tmp = (x * (log(x) + -1.0)) + (y / (x / (z * z)));
	} else {
		tmp = ((log(x) * (x + -0.5)) + (0.91893853320467 - x)) + (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 <= (-1.95d-14)) .or. (.not. (z <= 1.05d-35))) then
        tmp = (x * (log(x) + (-1.0d0))) + (y / (x / (z * z)))
    else
        tmp = ((log(x) * (x + (-0.5d0))) + (0.91893853320467d0 - x)) + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.95e-14) || !(z <= 1.05e-35)) {
		tmp = (x * (Math.log(x) + -1.0)) + (y / (x / (z * z)));
	} else {
		tmp = ((Math.log(x) * (x + -0.5)) + (0.91893853320467 - x)) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.95e-14) or not (z <= 1.05e-35):
		tmp = (x * (math.log(x) + -1.0)) + (y / (x / (z * z)))
	else:
		tmp = ((math.log(x) * (x + -0.5)) + (0.91893853320467 - x)) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.95e-14) || !(z <= 1.05e-35))
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(y / Float64(x / Float64(z * z))));
	else
		tmp = Float64(Float64(Float64(log(x) * Float64(x + -0.5)) + Float64(0.91893853320467 - x)) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.95e-14) || ~((z <= 1.05e-35)))
		tmp = (x * (log(x) + -1.0)) + (y / (x / (z * z)));
	else
		tmp = ((log(x) * (x + -0.5)) + (0.91893853320467 - x)) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.95e-14], N[Not[LessEqual[z, 1.05e-35]], $MachinePrecision]], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[Log[x], $MachinePrecision] * N[(x + -0.5), $MachinePrecision]), $MachinePrecision] + N[(0.91893853320467 - x), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9499999999999999e-14 or 1.05e-35 < z

   1. Initial program 91.7%

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

      1. associate-+l- 91.7%

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

      2. sub-neg 91.7%

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

      3. metadata-eval 91.7%

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

   3. Applied egg-rr 91.7%

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

   4. Taylor expanded in y around inf 69.0%

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

      1. associate-/l* 71.8%

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

      2. unpow2 71.8%

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

   6. Simplified 71.8%

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

   7. Taylor expanded in x around inf 71.9%

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

      1. *-commutative 71.9%

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

      2. sub-neg 71.9%

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

      3. mul-1-neg 71.9%

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

      4. log-rec 71.9%

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

      5. remove-double-neg 71.9%

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

      6. metadata-eval 71.9%

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

   9. Simplified 71.9%

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

   if -1.9499999999999999e-14 < z < 1.05e-35

   1. Initial program 99.3%

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

      1. associate-+l- 99.4%

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

      2. sub-neg 99.4%

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

      3. metadata-eval 99.4%

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

   3. Applied egg-rr 99.4%

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

   4. Taylor expanded in z around 0 96.0%

      \[\leadsto \left(\left(x + -0.5\right) \cdot \log x - \left(x - 0.91893853320467\right)\right) + \color{blue}{\frac{0.083333333333333}{x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-14} \lor \neg \left(z \leq 1.05 \cdot 10^{-35}\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{y}{\frac{x}{z \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\log x \cdot \left(x + -0.5\right) + \left(0.91893853320467 - x\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 10: 56.6% accurate, 1.1× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x * (log(x) + -1.0)) + (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 * (log(x) + (-1.0d0))) + (0.083333333333333d0 / x)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.2%

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

2. Taylor expanded in z around 0 56.1%

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

3. Taylor expanded in x around inf 54.4%

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

   1. *-commutative 54.4%

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

   2. mul-1-neg 54.4%

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

   3. log-rec 54.4%

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

   4. remove-double-neg 54.4%

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

   5. sub-neg 54.4%

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

   6. metadata-eval 54.4%

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

5. Simplified 54.4%

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

6. Final simplification 54.4%

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

Alternative 11: 56.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.75:\\ \;\;\;\;\frac{0.083333333333333}{x} + \left(0.91893853320467 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.75)
   (+ (/ 0.083333333333333 x) (- 0.91893853320467 x))
   (* x (+ (log x) -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.75) {
		tmp = (0.083333333333333 / x) + (0.91893853320467 - x);
	} else {
		tmp = x * (log(x) + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 1.75d0) then
        tmp = (0.083333333333333d0 / x) + (0.91893853320467d0 - x)
    else
        tmp = x * (log(x) + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.75) {
		tmp = (0.083333333333333 / x) + (0.91893853320467 - x);
	} else {
		tmp = x * (Math.log(x) + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1.75:
		tmp = (0.083333333333333 / x) + (0.91893853320467 - x)
	else:
		tmp = x * (math.log(x) + -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.75)
		tmp = Float64(Float64(0.083333333333333 / x) + Float64(0.91893853320467 - x));
	else
		tmp = Float64(x * Float64(log(x) + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1.75)
		tmp = (0.083333333333333 / x) + (0.91893853320467 - x);
	else
		tmp = x * (log(x) + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.75], N[(N[(0.083333333333333 / x), $MachinePrecision] + N[(0.91893853320467 - x), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.75

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 45.2%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{0.083333333333333}{x}} \]
   3. Step-by-step derivation

      1. add-cube-cbrt 45.2%

         \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x} \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right) \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}} - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      2. pow3 45.2%

         \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      3. sub-neg 45.2%

         \[\leadsto \left(\left({\left(\sqrt[3]{\color{blue}{\left(x + \left(-0.5\right)\right)} \cdot \log x}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

      4. metadata-eval 45.2%

         \[\leadsto \left(\left({\left(\sqrt[3]{\left(x + \color{blue}{-0.5}\right) \cdot \log x}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

   4. Applied egg-rr 45.2%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\left(x + -0.5\right) \cdot \log x}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

   5. Taylor expanded in x around inf 44.0%

      \[\leadsto \color{blue}{\left(0.91893853320467 + -1 \cdot x\right)} + \frac{0.083333333333333}{x} \]
   6. Step-by-step derivation

      1. neg-mul-1 44.0%

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

      2. unsub-neg 44.0%

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

   7. Simplified 44.0%

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

   if 1.75 < x

   1. Initial program 90.4%

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

      1. associate-+l- 90.4%

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

      2. sub-neg 90.4%

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

      3. metadata-eval 90.4%

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

   3. Applied egg-rr 90.4%

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

   4. Taylor expanded in z around 0 67.7%

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

   5. Taylor expanded in x around inf 65.5%

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

      1. *-commutative 65.5%

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

      2. sub-neg 65.5%

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

      3. mul-1-neg 65.5%

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

      4. log-rec 65.5%

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

      5. remove-double-neg 65.5%

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

      6. metadata-eval 65.5%

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

      7. +-commutative 65.5%

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

   7. Simplified 65.5%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.75:\\ \;\;\;\;\frac{0.083333333333333}{x} + \left(0.91893853320467 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right)\\ \end{array} \]

Alternative 12: 23.4% accurate, 17.6× speedup

Math

\[\begin{array}{l} \\ \frac{0.083333333333333}{x} + \left(0.91893853320467 - x\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ (/ 0.083333333333333 x) (- 0.91893853320467 x)))

C

double code(double x, double y, double z) {
	return (0.083333333333333 / x) + (0.91893853320467 - 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) + (0.91893853320467d0 - x)
end function

Java

public static double code(double x, double y, double z) {
	return (0.083333333333333 / x) + (0.91893853320467 - x);
}

Python

def code(x, y, z):
	return (0.083333333333333 / x) + (0.91893853320467 - x)

Julia

function code(x, y, z)
	return Float64(Float64(0.083333333333333 / x) + Float64(0.91893853320467 - x))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (0.083333333333333 / x) + (0.91893853320467 - x);
end

Wolfram

code[x_, y_, z_] := N[(N[(0.083333333333333 / x), $MachinePrecision] + N[(0.91893853320467 - x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.2%

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

2. Taylor expanded in z around 0 56.1%

   \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{0.083333333333333}{x}} \]
3. Step-by-step derivation

   1. add-cube-cbrt 55.7%

      \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x} \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right) \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}} - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

   2. pow3 55.7%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

   3. sub-neg 55.7%

      \[\leadsto \left(\left({\left(\sqrt[3]{\color{blue}{\left(x + \left(-0.5\right)\right)} \cdot \log x}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

   4. metadata-eval 55.7%

      \[\leadsto \left(\left({\left(\sqrt[3]{\left(x + \color{blue}{-0.5}\right) \cdot \log x}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

4. Applied egg-rr 55.7%

   \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\left(x + -0.5\right) \cdot \log x}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

5. Taylor expanded in x around inf 23.2%

   \[\leadsto \color{blue}{\left(0.91893853320467 + -1 \cdot x\right)} + \frac{0.083333333333333}{x} \]
6. Step-by-step derivation

   1. neg-mul-1 23.2%

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

   2. unsub-neg 23.2%

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

7. Simplified 23.2%

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

8. Final simplification 23.2%

   \[\leadsto \frac{0.083333333333333}{x} + \left(0.91893853320467 - x\right) \]

Alternative 13: 23.4% accurate, 24.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.2%

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

2. Taylor expanded in z around 0 56.1%

   \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{0.083333333333333}{x}} \]
3. Step-by-step derivation

   1. add-cube-cbrt 55.7%

      \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x} \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right) \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}} - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

   2. pow3 55.7%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

   3. sub-neg 55.7%

      \[\leadsto \left(\left({\left(\sqrt[3]{\color{blue}{\left(x + \left(-0.5\right)\right)} \cdot \log x}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

   4. metadata-eval 55.7%

      \[\leadsto \left(\left({\left(\sqrt[3]{\left(x + \color{blue}{-0.5}\right) \cdot \log x}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

4. Applied egg-rr 55.7%

   \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\left(x + -0.5\right) \cdot \log x}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

5. Taylor expanded in x around inf 23.2%

   \[\leadsto \color{blue}{-1 \cdot x} + \frac{0.083333333333333}{x} \]
6. Step-by-step derivation

   1. neg-mul-1 23.2%

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

7. Simplified 23.2%

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

8. Taylor expanded in x around 0 23.2%

   \[\leadsto \color{blue}{-1 \cdot x + 0.083333333333333 \cdot \frac{1}{x}} \]
9. Step-by-step derivation

   1. neg-mul-1 23.2%

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

   2. associate-*r/ 23.2%

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

   3. metadata-eval 23.2%

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

   4. +-commutative 23.2%

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

   5. unsub-neg 23.2%

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

10. Simplified 23.2%

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

11. Final simplification 23.2%

    \[\leadsto \frac{0.083333333333333}{x} - x \]

Alternative 14: 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 95.2%

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

2. Taylor expanded in z around 0 56.1%

   \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{0.083333333333333}{x}} \]
3. Step-by-step derivation

   1. add-cube-cbrt 55.7%

      \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x} \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right) \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}} - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

   2. pow3 55.7%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

   3. sub-neg 55.7%

      \[\leadsto \left(\left({\left(\sqrt[3]{\color{blue}{\left(x + \left(-0.5\right)\right)} \cdot \log x}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

   4. metadata-eval 55.7%

      \[\leadsto \left(\left({\left(\sqrt[3]{\left(x + \color{blue}{-0.5}\right) \cdot \log x}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

4. Applied egg-rr 55.7%

   \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\left(x + -0.5\right) \cdot \log x}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

5. Taylor expanded in x around inf 23.2%

   \[\leadsto \color{blue}{-1 \cdot x} + \frac{0.083333333333333}{x} \]
6. Step-by-step derivation

   1. neg-mul-1 23.2%

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

7. Simplified 23.2%

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

8. Taylor expanded in x around inf 1.3%

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

   1. neg-mul-1 1.3%

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

10. Simplified 1.3%

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

11. Final simplification 1.3%

    \[\leadsto -x \]

Developer target: 98.4% 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 2023257 
(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)))