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

Percentage Accurate: 93.7% → 98.1%

Time: 15.7s

Alternatives: 18

Speedup: 1.0×

• 28.4% 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: 98.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) \leq 5 \cdot 10^{+143}:\\ \;\;\;\;\left(\mathsf{fma}\left(x + -0.5, \log x, -x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log x - x\right) + \frac{z}{\frac{x}{z}} \cdot \left(y + 0.0007936500793651\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) 5e+143)
   (+
    (+ (fma (+ x -0.5) (log x) (- x)) 0.91893853320467)
    (/
     (fma
      z
      (fma (+ y 0.0007936500793651) z -0.0027777777777778)
      0.083333333333333)
     x))
   (+ (- (* x (log x)) x) (* (/ z (/ x z)) (+ y 0.0007936500793651)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) <= 5e+143) {
		tmp = (fma((x + -0.5), log(x), -x) + 0.91893853320467) + (fma(z, fma((y + 0.0007936500793651), z, -0.0027777777777778), 0.083333333333333) / x);
	} else {
		tmp = ((x * log(x)) - x) + ((z / (x / z)) * (y + 0.0007936500793651));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778)) <= 5e+143)
		tmp = Float64(Float64(fma(Float64(x + -0.5), log(x), Float64(-x)) + 0.91893853320467) + Float64(fma(z, fma(Float64(y + 0.0007936500793651), z, -0.0027777777777778), 0.083333333333333) / x));
	else
		tmp = Float64(Float64(Float64(x * log(x)) - x) + Float64(Float64(z / Float64(x / z)) * Float64(y + 0.0007936500793651)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(z * N[(N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision], 5e+143], N[(N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision] + (-x)), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(N[(z * N[(N[(y + 0.0007936500793651), $MachinePrecision] * z + -0.0027777777777778), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + N[(N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision] * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) < 5.00000000000000012e143

   1. Initial program 99.5%

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

      1. fma-neg 99.6%

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

      2. sub-neg 99.6%

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

      3. metadata-eval 99.6%

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

      4. *-commutative 99.6%

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

      5. fma-def 99.6%

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

      6. fma-neg 99.6%

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

      7. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   if 5.00000000000000012e143 < (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z)

   1. Initial program 86.4%

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

      1. sub-neg 86.4%

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

      2. metadata-eval 86.4%

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

      3. fma-def 86.4%

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

      4. fma-neg 86.4%

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

      5. metadata-eval 86.4%

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

   3. Simplified 86.4%

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

   4. Taylor expanded in x around inf 86.4%

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

      1. sub-neg 86.4%

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

      2. mul-1-neg 86.4%

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

      3. log-rec 86.4%

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

      4. remove-double-neg 86.4%

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

      5. metadata-eval 86.4%

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

      6. distribute-rgt-in 86.4%

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

      7. *-rgt-identity 86.4%

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

      8. neg-mul-1 86.4%

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

      9. *-rgt-identity 86.4%

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

      10. sub-neg 86.4%

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

      11. *-commutative 86.4%

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

   6. Simplified 86.4%

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

   7. Taylor expanded in x around 0 86.4%

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

   8. Taylor expanded in z around inf 86.4%

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

      1. associate-*l/ 90.1%

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

      2. unpow2 90.1%

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

      3. associate-/l* 99.8%

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

   10. Simplified 99.8%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) \leq 5 \cdot 10^{+143}:\\ \;\;\;\;\left(\mathsf{fma}\left(x + -0.5, \log x, -x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log x - x\right) + \frac{z}{\frac{x}{z}} \cdot \left(y + 0.0007936500793651\right)\\ \end{array} \]

Alternative 2: 98.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) \leq 5 \cdot 10^{+143}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log x - x\right) + \frac{z}{\frac{x}{z}} \cdot \left(y + 0.0007936500793651\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) 5e+143)
   (+
    (+ 0.91893853320467 (- (* (+ x -0.5) (log x)) x))
    (/
     (fma
      (fma (+ y 0.0007936500793651) z -0.0027777777777778)
      z
      0.083333333333333)
     x))
   (+ (- (* x (log x)) x) (* (/ z (/ x z)) (+ y 0.0007936500793651)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) <= 5e+143) {
		tmp = (0.91893853320467 + (((x + -0.5) * log(x)) - x)) + (fma(fma((y + 0.0007936500793651), z, -0.0027777777777778), z, 0.083333333333333) / x);
	} else {
		tmp = ((x * log(x)) - x) + ((z / (x / z)) * (y + 0.0007936500793651));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778)) <= 5e+143)
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(Float64(x + -0.5) * log(x)) - x)) + Float64(fma(fma(Float64(y + 0.0007936500793651), z, -0.0027777777777778), z, 0.083333333333333) / x));
	else
		tmp = Float64(Float64(Float64(x * log(x)) - x) + Float64(Float64(z / Float64(x / z)) * Float64(y + 0.0007936500793651)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(z * N[(N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision], 5e+143], N[(N[(0.91893853320467 + N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z + -0.0027777777777778), $MachinePrecision] * z + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + N[(N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision] * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) < 5.00000000000000012e143

   1. Initial program 99.5%

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

      1. sub-neg 99.5%

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

      2. metadata-eval 99.5%

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

      3. fma-def 99.5%

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

      4. fma-neg 99.5%

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

      5. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   if 5.00000000000000012e143 < (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z)

   1. Initial program 86.4%

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

      1. sub-neg 86.4%

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

      2. metadata-eval 86.4%

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

      3. fma-def 86.4%

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

      4. fma-neg 86.4%

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

      5. metadata-eval 86.4%

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

   3. Simplified 86.4%

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

   4. Taylor expanded in x around inf 86.4%

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

      1. sub-neg 86.4%

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

      2. mul-1-neg 86.4%

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

      3. log-rec 86.4%

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

      4. remove-double-neg 86.4%

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

      5. metadata-eval 86.4%

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

      6. distribute-rgt-in 86.4%

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

      7. *-rgt-identity 86.4%

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

      8. neg-mul-1 86.4%

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

      9. *-rgt-identity 86.4%

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

      10. sub-neg 86.4%

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

      11. *-commutative 86.4%

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

   6. Simplified 86.4%

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

   7. Taylor expanded in x around 0 86.4%

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

   8. Taylor expanded in z around inf 86.4%

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

      1. associate-*l/ 90.1%

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

      2. unpow2 90.1%

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

      3. associate-/l* 99.8%

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

   10. Simplified 99.8%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) \leq 5 \cdot 10^{+143}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log x - x\right) + \frac{z}{\frac{x}{z}} \cdot \left(y + 0.0007936500793651\right)\\ \end{array} \]

Alternative 3: 99.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 128000000000:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log x - x\right) + \mathsf{fma}\left(z, z \cdot \left(\frac{0.0007936500793651}{x} + \frac{y}{x}\right), \frac{\mathsf{fma}\left(-0.0027777777777778, z, 0.083333333333333\right)}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 128000000000.0)
   (+
    (+ 0.91893853320467 (- (* (+ x -0.5) (log x)) x))
    (/
     (fma
      (fma (+ y 0.0007936500793651) z -0.0027777777777778)
      z
      0.083333333333333)
     x))
   (+
    (- (* x (log x)) x)
    (fma
     z
     (* z (+ (/ 0.0007936500793651 x) (/ y x)))
     (/ (fma -0.0027777777777778 z 0.083333333333333) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 128000000000.0) {
		tmp = (0.91893853320467 + (((x + -0.5) * log(x)) - x)) + (fma(fma((y + 0.0007936500793651), z, -0.0027777777777778), z, 0.083333333333333) / x);
	} else {
		tmp = ((x * log(x)) - x) + fma(z, (z * ((0.0007936500793651 / x) + (y / x))), (fma(-0.0027777777777778, z, 0.083333333333333) / x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 128000000000.0)
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(Float64(x + -0.5) * log(x)) - x)) + Float64(fma(fma(Float64(y + 0.0007936500793651), z, -0.0027777777777778), z, 0.083333333333333) / x));
	else
		tmp = Float64(Float64(Float64(x * log(x)) - x) + fma(z, Float64(z * Float64(Float64(0.0007936500793651 / x) + Float64(y / x))), Float64(fma(-0.0027777777777778, z, 0.083333333333333) / x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 128000000000.0], N[(N[(0.91893853320467 + N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z + -0.0027777777777778), $MachinePrecision] * z + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + N[(z * N[(z * N[(N[(0.0007936500793651 / x), $MachinePrecision] + N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-0.0027777777777778 * z + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.28e11

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. metadata-eval 99.6%

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

      3. fma-def 99.7%

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

      4. fma-neg 99.7%

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

      5. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   if 1.28e11 < x

   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. Step-by-step derivation

      1. sub-neg 91.0%

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

      2. metadata-eval 91.0%

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

      3. fma-def 91.0%

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

      4. fma-neg 91.0%

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

      5. metadata-eval 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in x around inf 91.1%

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

      1. sub-neg 91.1%

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

      2. mul-1-neg 91.1%

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

      3. log-rec 91.1%

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

      4. remove-double-neg 91.1%

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

      5. metadata-eval 91.1%

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

      6. distribute-rgt-in 91.0%

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

      7. *-rgt-identity 91.0%

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

      8. neg-mul-1 91.0%

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

      9. *-rgt-identity 91.0%

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

      10. sub-neg 91.0%

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

      11. *-commutative 91.0%

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

   6. Simplified 91.0%

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

   7. Taylor expanded in x around 0 91.0%

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

   8. Taylor expanded in z around 0 93.4%

      \[\leadsto \left(x \cdot \log x - x\right) + \color{blue}{\left(-0.0027777777777778 \cdot \frac{z}{x} + \left({z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) + 0.083333333333333 \cdot \frac{1}{x}\right)\right)} \]
   9. Step-by-step derivation

      1. +-commutative 93.4%

         \[\leadsto \left(x \cdot \log x - x\right) + \color{blue}{\left(\left({z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) + 0.083333333333333 \cdot \frac{1}{x}\right) + -0.0027777777777778 \cdot \frac{z}{x}\right)} \]

      2. associate-*r/ 93.4%

         \[\leadsto \left(x \cdot \log x - x\right) + \left(\left({z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) + \color{blue}{\frac{0.083333333333333 \cdot 1}{x}}\right) + -0.0027777777777778 \cdot \frac{z}{x}\right) \]

      3. metadata-eval 93.4%

         \[\leadsto \left(x \cdot \log x - x\right) + \left(\left({z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) + \frac{\color{blue}{0.083333333333333}}{x}\right) + -0.0027777777777778 \cdot \frac{z}{x}\right) \]

      4. associate-+l+ 93.4%

         \[\leadsto \left(x \cdot \log x - x\right) + \color{blue}{\left({z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) + \left(\frac{0.083333333333333}{x} + -0.0027777777777778 \cdot \frac{z}{x}\right)\right)} \]

      5. unpow2 93.4%

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

      6. associate-*l* 99.6%

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

      7. +-commutative 99.6%

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

      8. metadata-eval 99.6%

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

      9. associate-*r/ 99.6%

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

      10. fma-def 99.6%

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

      11. associate-*r/ 99.6%

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

      12. metadata-eval 99.6%

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

   10. Simplified 99.6%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 128000000000:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log x - x\right) + \mathsf{fma}\left(z, z \cdot \left(\frac{0.0007936500793651}{x} + \frac{y}{x}\right), \frac{\mathsf{fma}\left(-0.0027777777777778, z, 0.083333333333333\right)}{x}\right)\\ \end{array} \]

Alternative 4: 98.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)\\ \mathbf{if}\;t_0 \leq 5 \cdot 10^{+143}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{t_0 + 0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log x - x\right) + \frac{z}{\frac{x}{z}} \cdot \left(y + 0.0007936500793651\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778))))
   (if (<= t_0 5e+143)
     (+
      (+ 0.91893853320467 (- (* (log x) (- x 0.5)) x))
      (/ (+ t_0 0.083333333333333) x))
     (+ (- (* x (log x)) x) (* (/ z (/ x z)) (+ y 0.0007936500793651))))))

C

double code(double x, double y, double z) {
	double t_0 = z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778);
	double tmp;
	if (t_0 <= 5e+143) {
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + ((t_0 + 0.083333333333333) / x);
	} else {
		tmp = ((x * log(x)) - x) + ((z / (x / z)) * (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 = z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0)
    if (t_0 <= 5d+143) then
        tmp = (0.91893853320467d0 + ((log(x) * (x - 0.5d0)) - x)) + ((t_0 + 0.083333333333333d0) / x)
    else
        tmp = ((x * log(x)) - x) + ((z / (x / z)) * (y + 0.0007936500793651d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778);
	double tmp;
	if (t_0 <= 5e+143) {
		tmp = (0.91893853320467 + ((Math.log(x) * (x - 0.5)) - x)) + ((t_0 + 0.083333333333333) / x);
	} else {
		tmp = ((x * Math.log(x)) - x) + ((z / (x / z)) * (y + 0.0007936500793651));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)
	tmp = 0
	if t_0 <= 5e+143:
		tmp = (0.91893853320467 + ((math.log(x) * (x - 0.5)) - x)) + ((t_0 + 0.083333333333333) / x)
	else:
		tmp = ((x * math.log(x)) - x) + ((z / (x / z)) * (y + 0.0007936500793651))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778))
	tmp = 0.0
	if (t_0 <= 5e+143)
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(log(x) * Float64(x - 0.5)) - x)) + Float64(Float64(t_0 + 0.083333333333333) / x));
	else
		tmp = Float64(Float64(Float64(x * log(x)) - x) + Float64(Float64(z / Float64(x / z)) * Float64(y + 0.0007936500793651)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778);
	tmp = 0.0;
	if (t_0 <= 5e+143)
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + ((t_0 + 0.083333333333333) / x);
	else
		tmp = ((x * log(x)) - x) + ((z / (x / z)) * (y + 0.0007936500793651));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 5e+143], N[(N[(0.91893853320467 + N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + N[(N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision] * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) < 5.00000000000000012e143

   1. Initial program 99.5%

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

   if 5.00000000000000012e143 < (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z)

   1. Initial program 86.4%

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

      1. sub-neg 86.4%

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

      2. metadata-eval 86.4%

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

      3. fma-def 86.4%

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

      4. fma-neg 86.4%

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

      5. metadata-eval 86.4%

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

   3. Simplified 86.4%

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

   4. Taylor expanded in x around inf 86.4%

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

      1. sub-neg 86.4%

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

      2. mul-1-neg 86.4%

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

      3. log-rec 86.4%

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

      4. remove-double-neg 86.4%

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

      5. metadata-eval 86.4%

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

      6. distribute-rgt-in 86.4%

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

      7. *-rgt-identity 86.4%

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

      8. neg-mul-1 86.4%

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

      9. *-rgt-identity 86.4%

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

      10. sub-neg 86.4%

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

      11. *-commutative 86.4%

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

   6. Simplified 86.4%

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

   7. Taylor expanded in x around 0 86.4%

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

   8. Taylor expanded in z around inf 86.4%

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

      1. associate-*l/ 90.1%

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

      2. unpow2 90.1%

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

      3. associate-/l* 99.8%

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

   10. Simplified 99.8%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) \leq 5 \cdot 10^{+143}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log x - x\right) + \frac{z}{\frac{x}{z}} \cdot \left(y + 0.0007936500793651\right)\\ \end{array} \]

Alternative 5: 79.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log x - x\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+219}:\\ \;\;\;\;t_0 + z \cdot \left(z \cdot \frac{0.0007936500793651}{x}\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-53}:\\ \;\;\;\;t_0 + \frac{y}{\frac{x}{z \cdot z}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-70}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{1}{x \cdot 12.000000000000048}\\ \mathbf{else}:\\ \;\;\;\;t_0 + z \cdot \left(z \cdot \frac{y}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* x (log x)) x)))
   (if (<= z -5.8e+219)
     (+ t_0 (* z (* z (/ 0.0007936500793651 x))))
     (if (<= z -2.6e-53)
       (+ t_0 (/ y (/ x (* z z))))
       (if (<= z 4.5e-70)
         (+
          (+ 0.91893853320467 (- (* (+ x -0.5) (log x)) x))
          (/ 1.0 (* x 12.000000000000048)))
         (+ t_0 (* z (* z (/ y x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = (x * log(x)) - x;
	double tmp;
	if (z <= -5.8e+219) {
		tmp = t_0 + (z * (z * (0.0007936500793651 / x)));
	} else if (z <= -2.6e-53) {
		tmp = t_0 + (y / (x / (z * z)));
	} else if (z <= 4.5e-70) {
		tmp = (0.91893853320467 + (((x + -0.5) * log(x)) - x)) + (1.0 / (x * 12.000000000000048));
	} else {
		tmp = t_0 + (z * (z * (y / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x * log(x)) - x
    if (z <= (-5.8d+219)) then
        tmp = t_0 + (z * (z * (0.0007936500793651d0 / x)))
    else if (z <= (-2.6d-53)) then
        tmp = t_0 + (y / (x / (z * z)))
    else if (z <= 4.5d-70) then
        tmp = (0.91893853320467d0 + (((x + (-0.5d0)) * log(x)) - x)) + (1.0d0 / (x * 12.000000000000048d0))
    else
        tmp = t_0 + (z * (z * (y / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * Math.log(x)) - x;
	double tmp;
	if (z <= -5.8e+219) {
		tmp = t_0 + (z * (z * (0.0007936500793651 / x)));
	} else if (z <= -2.6e-53) {
		tmp = t_0 + (y / (x / (z * z)));
	} else if (z <= 4.5e-70) {
		tmp = (0.91893853320467 + (((x + -0.5) * Math.log(x)) - x)) + (1.0 / (x * 12.000000000000048));
	} else {
		tmp = t_0 + (z * (z * (y / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * math.log(x)) - x
	tmp = 0
	if z <= -5.8e+219:
		tmp = t_0 + (z * (z * (0.0007936500793651 / x)))
	elif z <= -2.6e-53:
		tmp = t_0 + (y / (x / (z * z)))
	elif z <= 4.5e-70:
		tmp = (0.91893853320467 + (((x + -0.5) * math.log(x)) - x)) + (1.0 / (x * 12.000000000000048))
	else:
		tmp = t_0 + (z * (z * (y / x)))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * log(x)) - x)
	tmp = 0.0
	if (z <= -5.8e+219)
		tmp = Float64(t_0 + Float64(z * Float64(z * Float64(0.0007936500793651 / x))));
	elseif (z <= -2.6e-53)
		tmp = Float64(t_0 + Float64(y / Float64(x / Float64(z * z))));
	elseif (z <= 4.5e-70)
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(Float64(x + -0.5) * log(x)) - x)) + Float64(1.0 / Float64(x * 12.000000000000048)));
	else
		tmp = Float64(t_0 + Float64(z * Float64(z * Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * log(x)) - x;
	tmp = 0.0;
	if (z <= -5.8e+219)
		tmp = t_0 + (z * (z * (0.0007936500793651 / x)));
	elseif (z <= -2.6e-53)
		tmp = t_0 + (y / (x / (z * z)));
	elseif (z <= 4.5e-70)
		tmp = (0.91893853320467 + (((x + -0.5) * log(x)) - x)) + (1.0 / (x * 12.000000000000048));
	else
		tmp = t_0 + (z * (z * (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[z, -5.8e+219], N[(t$95$0 + N[(z * N[(z * N[(0.0007936500793651 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.6e-53], N[(t$95$0 + N[(y / N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-70], N[(N[(0.91893853320467 + N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(x * 12.000000000000048), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(z * N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.79999999999999958e219

   1. Initial program 81.7%

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

      1. sub-neg 81.7%

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

      2. metadata-eval 81.7%

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

      3. fma-def 81.7%

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

      4. fma-neg 81.7%

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

      5. metadata-eval 81.7%

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

   3. Simplified 81.7%

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

   4. Taylor expanded in x around inf 81.7%

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

      1. sub-neg 81.7%

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

      2. mul-1-neg 81.7%

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

      3. log-rec 81.7%

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

      4. remove-double-neg 81.7%

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

      5. metadata-eval 81.7%

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

      6. distribute-rgt-in 81.7%

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

      7. *-rgt-identity 81.7%

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

      8. neg-mul-1 81.7%

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

      9. *-rgt-identity 81.7%

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

      10. sub-neg 81.7%

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

      11. *-commutative 81.7%

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

   6. Simplified 81.7%

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

   7. Taylor expanded in y around 0 68.4%

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

      1. fma-neg 68.4%

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

      2. metadata-eval 68.4%

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

   9. Simplified 68.4%

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

   10. Taylor expanded in z around inf 68.4%

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

       1. *-commutative 68.4%

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

       2. associate-*l/ 68.4%

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

       3. associate-*r/ 68.4%

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

       4. metadata-eval 68.4%

          \[\leadsto \left(x \cdot \log x - x\right) + {z}^{2} \cdot \frac{\color{blue}{0.0007936500793651 \cdot 1}}{x} \]

       5. associate-*r/ 68.4%

          \[\leadsto \left(x \cdot \log x - x\right) + {z}^{2} \cdot \color{blue}{\left(0.0007936500793651 \cdot \frac{1}{x}\right)} \]

       6. unpow2 68.4%

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

       7. associate-*l* 84.9%

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

       8. associate-*r/ 84.9%

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

       9. metadata-eval 84.9%

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

   12. Simplified 84.9%

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

   if -5.79999999999999958e219 < z < -2.59999999999999996e-53

   1. Initial program 94.8%

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

      1. sub-neg 94.8%

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

      2. metadata-eval 94.8%

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

      3. fma-def 94.9%

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

      4. fma-neg 94.9%

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

      5. metadata-eval 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in x around inf 95.0%

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

      1. sub-neg 95.0%

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

      2. mul-1-neg 95.0%

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

      3. log-rec 95.0%

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

      4. remove-double-neg 95.0%

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

      5. metadata-eval 95.0%

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

      6. distribute-rgt-in 94.9%

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

      7. *-rgt-identity 94.9%

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

      8. neg-mul-1 94.9%

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

      9. *-rgt-identity 94.9%

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

      10. sub-neg 94.9%

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

      11. *-commutative 94.9%

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

   6. Simplified 94.9%

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

   7. Taylor expanded in y around inf 72.6%

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

      1. associate-/l* 75.9%

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

      2. unpow2 75.9%

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

   9. Simplified 75.9%

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

   if -2.59999999999999996e-53 < z < 4.50000000000000022e-70

   1. Initial program 99.4%

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

      1. sub-neg 99.4%

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

      2. metadata-eval 99.4%

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

      3. fma-def 99.4%

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

      4. fma-neg 99.4%

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

      5. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 97.8%

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

      1. clear-num 96.8%

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

      2. inv-pow 96.8%

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

      3. div-inv 96.9%

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

      4. metadata-eval 96.9%

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

   6. Applied egg-rr 97.9%

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

      1. unpow-1 96.9%

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

   8. Simplified 97.9%

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

   if 4.50000000000000022e-70 < z

   1. Initial program 93.2%

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

      1. sub-neg 93.2%

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

      2. metadata-eval 93.2%

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

      3. fma-def 93.2%

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

      4. fma-neg 93.1%

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

      5. metadata-eval 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in x around inf 93.1%

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

      1. sub-neg 93.1%

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

      2. mul-1-neg 93.1%

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

      3. log-rec 93.1%

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

      4. remove-double-neg 93.1%

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

      5. metadata-eval 93.1%

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

      6. distribute-rgt-in 93.1%

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

      7. *-rgt-identity 93.1%

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

      8. neg-mul-1 93.1%

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

      9. *-rgt-identity 93.1%

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

      10. sub-neg 93.1%

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

      11. *-commutative 93.1%

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

   6. Simplified 93.1%

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

      1. metadata-eval 93.1%

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

      2. fma-neg 93.2%

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

      3. fma-def 93.2%

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

      4. *-un-lft-identity 93.2%

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

      5. add-sqr-sqrt 93.0%

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

      6. times-frac 93.1%

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

      7. *-commutative 93.1%

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

      8. fma-udef 93.1%

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

      9. fma-neg 93.1%

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

      10. metadata-eval 93.1%

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

   8. Applied egg-rr 93.1%

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

   9. Taylor expanded in y around inf 69.2%

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

       1. unpow2 69.2%

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

       2. *-commutative 69.2%

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

       3. associate-*r/ 70.4%

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

       4. associate-*l* 73.4%

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

   11. Simplified 73.4%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+219}:\\ \;\;\;\;\left(x \cdot \log x - x\right) + z \cdot \left(z \cdot \frac{0.0007936500793651}{x}\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-53}:\\ \;\;\;\;\left(x \cdot \log x - x\right) + \frac{y}{\frac{x}{z \cdot z}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-70}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{1}{x \cdot 12.000000000000048}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log x - x\right) + z \cdot \left(z \cdot \frac{y}{x}\right)\\ \end{array} \]

Alternative 6: 98.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log x - x\\ \mathbf{if}\;x \leq 100000000000:\\ \;\;\;\;t_0 + \frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{z}{\frac{x}{z}} \cdot \left(y + 0.0007936500793651\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* x (log x)) x)))
   (if (<= x 100000000000.0)
     (+
      t_0
      (/
       (+
        (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778))
        0.083333333333333)
       x))
     (+ t_0 (* (/ z (/ x z)) (+ y 0.0007936500793651))))))

C

double code(double x, double y, double z) {
	double t_0 = (x * log(x)) - x;
	double tmp;
	if (x <= 100000000000.0) {
		tmp = t_0 + (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x);
	} else {
		tmp = t_0 + ((z / (x / z)) * (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)) - x
    if (x <= 100000000000.0d0) then
        tmp = t_0 + (((z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0)) + 0.083333333333333d0) / x)
    else
        tmp = t_0 + ((z / (x / z)) * (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)) - x;
	double tmp;
	if (x <= 100000000000.0) {
		tmp = t_0 + (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x);
	} else {
		tmp = t_0 + ((z / (x / z)) * (y + 0.0007936500793651));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * math.log(x)) - x
	tmp = 0
	if x <= 100000000000.0:
		tmp = t_0 + (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x)
	else:
		tmp = t_0 + ((z / (x / z)) * (y + 0.0007936500793651))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * log(x)) - x)
	tmp = 0.0
	if (x <= 100000000000.0)
		tmp = Float64(t_0 + Float64(Float64(Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x));
	else
		tmp = Float64(t_0 + Float64(Float64(z / Float64(x / z)) * Float64(y + 0.0007936500793651)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * log(x)) - x;
	tmp = 0.0;
	if (x <= 100000000000.0)
		tmp = t_0 + (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x);
	else
		tmp = t_0 + ((z / (x / z)) * (y + 0.0007936500793651));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[x, 100000000000.0], N[(t$95$0 + N[(N[(N[(z * N[(N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision] * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 1e11

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. metadata-eval 99.6%

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

      3. fma-def 99.7%

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

      4. fma-neg 99.7%

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

      5. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 98.8%

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

      1. sub-neg 98.8%

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

      2. mul-1-neg 98.8%

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

      3. log-rec 98.8%

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

      4. remove-double-neg 98.8%

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

      5. metadata-eval 98.8%

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

      6. distribute-rgt-in 98.8%

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

      7. *-rgt-identity 98.8%

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

      8. neg-mul-1 98.8%

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

      9. *-rgt-identity 98.8%

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

      10. sub-neg 98.8%

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

      11. *-commutative 98.8%

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

   6. Simplified 98.8%

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

   7. Taylor expanded in x around 0 98.7%

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

   if 1e11 < x

   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. Step-by-step derivation

      1. sub-neg 91.0%

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

      2. metadata-eval 91.0%

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

      3. fma-def 91.0%

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

      4. fma-neg 91.0%

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

      5. metadata-eval 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in x around inf 91.1%

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

      1. sub-neg 91.1%

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

      2. mul-1-neg 91.1%

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

      3. log-rec 91.1%

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

      4. remove-double-neg 91.1%

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

      5. metadata-eval 91.1%

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

      6. distribute-rgt-in 91.0%

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

      7. *-rgt-identity 91.0%

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

      8. neg-mul-1 91.0%

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

      9. *-rgt-identity 91.0%

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

      10. sub-neg 91.0%

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

      11. *-commutative 91.0%

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

   6. Simplified 91.0%

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

   7. Taylor expanded in x around 0 91.0%

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

   8. Taylor expanded in z around inf 91.0%

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

      1. associate-*l/ 93.3%

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

      2. unpow2 93.3%

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

      3. associate-/l* 99.6%

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

   10. Simplified 99.6%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 100000000000:\\ \;\;\;\;\left(x \cdot \log x - x\right) + \frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log x - x\right) + \frac{z}{\frac{x}{z}} \cdot \left(y + 0.0007936500793651\right)\\ \end{array} \]

Alternative 7: 79.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log x - x\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+218}:\\ \;\;\;\;t_0 + z \cdot \left(z \cdot \frac{0.0007936500793651}{x}\right)\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-52} \lor \neg \left(z \leq 6 \cdot 10^{-70}\right):\\ \;\;\;\;t_0 + z \cdot \left(z \cdot \frac{y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* x (log x)) x)))
   (if (<= z -1.65e+218)
     (+ t_0 (* z (* z (/ 0.0007936500793651 x))))
     (if (or (<= z -1.16e-52) (not (<= z 6e-70)))
       (+ t_0 (* z (* z (/ y x))))
       (+
        (+ 0.91893853320467 (- (* (+ x -0.5) (log x)) x))
        (/ 0.083333333333333 x))))))

C

double code(double x, double y, double z) {
	double t_0 = (x * log(x)) - x;
	double tmp;
	if (z <= -1.65e+218) {
		tmp = t_0 + (z * (z * (0.0007936500793651 / x)));
	} else if ((z <= -1.16e-52) || !(z <= 6e-70)) {
		tmp = t_0 + (z * (z * (y / x)));
	} else {
		tmp = (0.91893853320467 + (((x + -0.5) * log(x)) - 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) :: t_0
    real(8) :: tmp
    t_0 = (x * log(x)) - x
    if (z <= (-1.65d+218)) then
        tmp = t_0 + (z * (z * (0.0007936500793651d0 / x)))
    else if ((z <= (-1.16d-52)) .or. (.not. (z <= 6d-70))) then
        tmp = t_0 + (z * (z * (y / x)))
    else
        tmp = (0.91893853320467d0 + (((x + (-0.5d0)) * log(x)) - x)) + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * Math.log(x)) - x;
	double tmp;
	if (z <= -1.65e+218) {
		tmp = t_0 + (z * (z * (0.0007936500793651 / x)));
	} else if ((z <= -1.16e-52) || !(z <= 6e-70)) {
		tmp = t_0 + (z * (z * (y / x)));
	} else {
		tmp = (0.91893853320467 + (((x + -0.5) * Math.log(x)) - x)) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * math.log(x)) - x
	tmp = 0
	if z <= -1.65e+218:
		tmp = t_0 + (z * (z * (0.0007936500793651 / x)))
	elif (z <= -1.16e-52) or not (z <= 6e-70):
		tmp = t_0 + (z * (z * (y / x)))
	else:
		tmp = (0.91893853320467 + (((x + -0.5) * math.log(x)) - x)) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * log(x)) - x)
	tmp = 0.0
	if (z <= -1.65e+218)
		tmp = Float64(t_0 + Float64(z * Float64(z * Float64(0.0007936500793651 / x))));
	elseif ((z <= -1.16e-52) || !(z <= 6e-70))
		tmp = Float64(t_0 + Float64(z * Float64(z * Float64(y / x))));
	else
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(Float64(x + -0.5) * log(x)) - x)) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * log(x)) - x;
	tmp = 0.0;
	if (z <= -1.65e+218)
		tmp = t_0 + (z * (z * (0.0007936500793651 / x)));
	elseif ((z <= -1.16e-52) || ~((z <= 6e-70)))
		tmp = t_0 + (z * (z * (y / x)));
	else
		tmp = (0.91893853320467 + (((x + -0.5) * log(x)) - x)) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[z, -1.65e+218], N[(t$95$0 + N[(z * N[(z * N[(0.0007936500793651 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.16e-52], N[Not[LessEqual[z, 6e-70]], $MachinePrecision]], N[(t$95$0 + N[(z * N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.91893853320467 + N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.64999999999999999e218

   1. Initial program 81.7%

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

      1. sub-neg 81.7%

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

      2. metadata-eval 81.7%

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

      3. fma-def 81.7%

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

      4. fma-neg 81.7%

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

      5. metadata-eval 81.7%

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

   3. Simplified 81.7%

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

   4. Taylor expanded in x around inf 81.7%

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

      1. sub-neg 81.7%

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

      2. mul-1-neg 81.7%

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

      3. log-rec 81.7%

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

      4. remove-double-neg 81.7%

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

      5. metadata-eval 81.7%

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

      6. distribute-rgt-in 81.7%

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

      7. *-rgt-identity 81.7%

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

      8. neg-mul-1 81.7%

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

      9. *-rgt-identity 81.7%

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

      10. sub-neg 81.7%

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

      11. *-commutative 81.7%

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

   6. Simplified 81.7%

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

   7. Taylor expanded in y around 0 68.4%

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

      1. fma-neg 68.4%

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

      2. metadata-eval 68.4%

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

   9. Simplified 68.4%

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

   10. Taylor expanded in z around inf 68.4%

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

       1. *-commutative 68.4%

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

       2. associate-*l/ 68.4%

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

       3. associate-*r/ 68.4%

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

       4. metadata-eval 68.4%

          \[\leadsto \left(x \cdot \log x - x\right) + {z}^{2} \cdot \frac{\color{blue}{0.0007936500793651 \cdot 1}}{x} \]

       5. associate-*r/ 68.4%

          \[\leadsto \left(x \cdot \log x - x\right) + {z}^{2} \cdot \color{blue}{\left(0.0007936500793651 \cdot \frac{1}{x}\right)} \]

       6. unpow2 68.4%

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

       7. associate-*l* 84.9%

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

       8. associate-*r/ 84.9%

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

       9. metadata-eval 84.9%

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

   12. Simplified 84.9%

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

   if -1.64999999999999999e218 < z < -1.1599999999999999e-52 or 6.0000000000000003e-70 < z

   1. Initial program 93.9%

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

      1. sub-neg 93.9%

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

      2. metadata-eval 93.9%

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

      3. fma-def 93.9%

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

      4. fma-neg 93.9%

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

      5. metadata-eval 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in x around inf 94.0%

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

      1. sub-neg 94.0%

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

      2. mul-1-neg 94.0%

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

      3. log-rec 94.0%

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

      4. remove-double-neg 94.0%

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

      5. metadata-eval 94.0%

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

      6. distribute-rgt-in 93.9%

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

      7. *-rgt-identity 93.9%

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

      8. neg-mul-1 93.9%

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

      9. *-rgt-identity 93.9%

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

      10. sub-neg 93.9%

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

      11. *-commutative 93.9%

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

   6. Simplified 93.9%

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

      1. metadata-eval 93.9%

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

      2. fma-neg 93.9%

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

      3. fma-def 93.9%

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

      4. *-un-lft-identity 93.9%

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

      5. add-sqr-sqrt 93.8%

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

      6. times-frac 93.8%

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

      7. *-commutative 93.8%

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

      8. fma-udef 93.8%

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

      9. fma-neg 93.8%

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

      10. metadata-eval 93.8%

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

   8. Applied egg-rr 93.8%

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

   9. Taylor expanded in y around inf 70.7%

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

       1. unpow2 70.7%

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

       2. *-commutative 70.7%

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

       3. associate-*r/ 72.1%

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

       4. associate-*l* 74.5%

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

   11. Simplified 74.5%

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

   if -1.1599999999999999e-52 < z < 6.0000000000000003e-70

   1. Initial program 99.4%

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

      1. sub-neg 99.4%

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

      2. metadata-eval 99.4%

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

      3. fma-def 99.4%

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

      4. fma-neg 99.4%

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

      5. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 97.8%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+218}:\\ \;\;\;\;\left(x \cdot \log x - x\right) + z \cdot \left(z \cdot \frac{0.0007936500793651}{x}\right)\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-52} \lor \neg \left(z \leq 6 \cdot 10^{-70}\right):\\ \;\;\;\;\left(x \cdot \log x - x\right) + z \cdot \left(z \cdot \frac{y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 8: 79.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log x - x\\ \mathbf{if}\;z \leq -3.35 \cdot 10^{+220}:\\ \;\;\;\;t_0 + z \cdot \left(z \cdot \frac{0.0007936500793651}{x}\right)\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-52}:\\ \;\;\;\;t_0 + \frac{y}{\frac{x}{z \cdot z}}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-72}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;t_0 + z \cdot \left(z \cdot \frac{y}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* x (log x)) x)))
   (if (<= z -3.35e+220)
     (+ t_0 (* z (* z (/ 0.0007936500793651 x))))
     (if (<= z -2.15e-52)
       (+ t_0 (/ y (/ x (* z z))))
       (if (<= z 5.4e-72)
         (+
          (+ 0.91893853320467 (- (* (+ x -0.5) (log x)) x))
          (/ 0.083333333333333 x))
         (+ t_0 (* z (* z (/ y x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = (x * log(x)) - x;
	double tmp;
	if (z <= -3.35e+220) {
		tmp = t_0 + (z * (z * (0.0007936500793651 / x)));
	} else if (z <= -2.15e-52) {
		tmp = t_0 + (y / (x / (z * z)));
	} else if (z <= 5.4e-72) {
		tmp = (0.91893853320467 + (((x + -0.5) * log(x)) - x)) + (0.083333333333333 / x);
	} else {
		tmp = t_0 + (z * (z * (y / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x * log(x)) - x
    if (z <= (-3.35d+220)) then
        tmp = t_0 + (z * (z * (0.0007936500793651d0 / x)))
    else if (z <= (-2.15d-52)) then
        tmp = t_0 + (y / (x / (z * z)))
    else if (z <= 5.4d-72) then
        tmp = (0.91893853320467d0 + (((x + (-0.5d0)) * log(x)) - x)) + (0.083333333333333d0 / x)
    else
        tmp = t_0 + (z * (z * (y / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * Math.log(x)) - x;
	double tmp;
	if (z <= -3.35e+220) {
		tmp = t_0 + (z * (z * (0.0007936500793651 / x)));
	} else if (z <= -2.15e-52) {
		tmp = t_0 + (y / (x / (z * z)));
	} else if (z <= 5.4e-72) {
		tmp = (0.91893853320467 + (((x + -0.5) * Math.log(x)) - x)) + (0.083333333333333 / x);
	} else {
		tmp = t_0 + (z * (z * (y / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * math.log(x)) - x
	tmp = 0
	if z <= -3.35e+220:
		tmp = t_0 + (z * (z * (0.0007936500793651 / x)))
	elif z <= -2.15e-52:
		tmp = t_0 + (y / (x / (z * z)))
	elif z <= 5.4e-72:
		tmp = (0.91893853320467 + (((x + -0.5) * math.log(x)) - x)) + (0.083333333333333 / x)
	else:
		tmp = t_0 + (z * (z * (y / x)))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * log(x)) - x)
	tmp = 0.0
	if (z <= -3.35e+220)
		tmp = Float64(t_0 + Float64(z * Float64(z * Float64(0.0007936500793651 / x))));
	elseif (z <= -2.15e-52)
		tmp = Float64(t_0 + Float64(y / Float64(x / Float64(z * z))));
	elseif (z <= 5.4e-72)
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(Float64(x + -0.5) * log(x)) - x)) + Float64(0.083333333333333 / x));
	else
		tmp = Float64(t_0 + Float64(z * Float64(z * Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * log(x)) - x;
	tmp = 0.0;
	if (z <= -3.35e+220)
		tmp = t_0 + (z * (z * (0.0007936500793651 / x)));
	elseif (z <= -2.15e-52)
		tmp = t_0 + (y / (x / (z * z)));
	elseif (z <= 5.4e-72)
		tmp = (0.91893853320467 + (((x + -0.5) * log(x)) - x)) + (0.083333333333333 / x);
	else
		tmp = t_0 + (z * (z * (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[z, -3.35e+220], N[(t$95$0 + N[(z * N[(z * N[(0.0007936500793651 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.15e-52], N[(t$95$0 + N[(y / N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e-72], N[(N[(0.91893853320467 + N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(z * N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.3499999999999999e220

   1. Initial program 81.7%

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

      1. sub-neg 81.7%

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

      2. metadata-eval 81.7%

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

      3. fma-def 81.7%

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

      4. fma-neg 81.7%

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

      5. metadata-eval 81.7%

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

   3. Simplified 81.7%

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

   4. Taylor expanded in x around inf 81.7%

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

      1. sub-neg 81.7%

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

      2. mul-1-neg 81.7%

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

      3. log-rec 81.7%

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

      4. remove-double-neg 81.7%

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

      5. metadata-eval 81.7%

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

      6. distribute-rgt-in 81.7%

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

      7. *-rgt-identity 81.7%

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

      8. neg-mul-1 81.7%

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

      9. *-rgt-identity 81.7%

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

      10. sub-neg 81.7%

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

      11. *-commutative 81.7%

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

   6. Simplified 81.7%

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

   7. Taylor expanded in y around 0 68.4%

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

      1. fma-neg 68.4%

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

      2. metadata-eval 68.4%

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

   9. Simplified 68.4%

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

   10. Taylor expanded in z around inf 68.4%

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

       1. *-commutative 68.4%

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

       2. associate-*l/ 68.4%

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

       3. associate-*r/ 68.4%

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

       4. metadata-eval 68.4%

          \[\leadsto \left(x \cdot \log x - x\right) + {z}^{2} \cdot \frac{\color{blue}{0.0007936500793651 \cdot 1}}{x} \]

       5. associate-*r/ 68.4%

          \[\leadsto \left(x \cdot \log x - x\right) + {z}^{2} \cdot \color{blue}{\left(0.0007936500793651 \cdot \frac{1}{x}\right)} \]

       6. unpow2 68.4%

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

       7. associate-*l* 84.9%

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

       8. associate-*r/ 84.9%

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

       9. metadata-eval 84.9%

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

   12. Simplified 84.9%

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

   if -3.3499999999999999e220 < z < -2.1500000000000002e-52

   1. Initial program 94.8%

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

      1. sub-neg 94.8%

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

      2. metadata-eval 94.8%

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

      3. fma-def 94.9%

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

      4. fma-neg 94.9%

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

      5. metadata-eval 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in x around inf 95.0%

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

      1. sub-neg 95.0%

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

      2. mul-1-neg 95.0%

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

      3. log-rec 95.0%

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

      4. remove-double-neg 95.0%

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

      5. metadata-eval 95.0%

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

      6. distribute-rgt-in 94.9%

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

      7. *-rgt-identity 94.9%

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

      8. neg-mul-1 94.9%

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

      9. *-rgt-identity 94.9%

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

      10. sub-neg 94.9%

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

      11. *-commutative 94.9%

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

   6. Simplified 94.9%

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

   7. Taylor expanded in y around inf 72.6%

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

      1. associate-/l* 75.9%

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

      2. unpow2 75.9%

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

   9. Simplified 75.9%

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

   if -2.1500000000000002e-52 < z < 5.4e-72

   1. Initial program 99.4%

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

      1. sub-neg 99.4%

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

      2. metadata-eval 99.4%

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

      3. fma-def 99.4%

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

      4. fma-neg 99.4%

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

      5. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 97.8%

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

   if 5.4e-72 < z

   1. Initial program 93.2%

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

      1. sub-neg 93.2%

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

      2. metadata-eval 93.2%

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

      3. fma-def 93.2%

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

      4. fma-neg 93.1%

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

      5. metadata-eval 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in x around inf 93.1%

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

      1. sub-neg 93.1%

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

      2. mul-1-neg 93.1%

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

      3. log-rec 93.1%

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

      4. remove-double-neg 93.1%

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

      5. metadata-eval 93.1%

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

      6. distribute-rgt-in 93.1%

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

      7. *-rgt-identity 93.1%

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

      8. neg-mul-1 93.1%

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

      9. *-rgt-identity 93.1%

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

      10. sub-neg 93.1%

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

      11. *-commutative 93.1%

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

   6. Simplified 93.1%

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

      1. metadata-eval 93.1%

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

      2. fma-neg 93.2%

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

      3. fma-def 93.2%

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

      4. *-un-lft-identity 93.2%

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

      5. add-sqr-sqrt 93.0%

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

      6. times-frac 93.1%

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

      7. *-commutative 93.1%

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

      8. fma-udef 93.1%

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

      9. fma-neg 93.1%

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

      10. metadata-eval 93.1%

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

   8. Applied egg-rr 93.1%

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

   9. Taylor expanded in y around inf 69.2%

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

       1. unpow2 69.2%

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

       2. *-commutative 69.2%

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

       3. associate-*r/ 70.4%

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

       4. associate-*l* 73.4%

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

   11. Simplified 73.4%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.35 \cdot 10^{+220}:\\ \;\;\;\;\left(x \cdot \log x - x\right) + z \cdot \left(z \cdot \frac{0.0007936500793651}{x}\right)\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-52}:\\ \;\;\;\;\left(x \cdot \log x - x\right) + \frac{y}{\frac{x}{z \cdot z}}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-72}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log x - x\right) + z \cdot \left(z \cdot \frac{y}{x}\right)\\ \end{array} \]

Alternative 9: 91.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-52} \lor \neg \left(z \leq 8 \cdot 10^{-70}\right):\\ \;\;\;\;\left(x \cdot \log x - x\right) + \left(z \cdot z\right) \cdot \frac{y + 0.0007936500793651}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{1}{x \cdot 12.000000000000048}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.4e-52) (not (<= z 8e-70)))
   (+ (- (* x (log x)) x) (* (* z z) (/ (+ y 0.0007936500793651) x)))
   (+
    (+ 0.91893853320467 (- (* (+ x -0.5) (log x)) x))
    (/ 1.0 (* x 12.000000000000048)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.4e-52) || !(z <= 8e-70)) {
		tmp = ((x * log(x)) - x) + ((z * z) * ((y + 0.0007936500793651) / x));
	} else {
		tmp = (0.91893853320467 + (((x + -0.5) * log(x)) - x)) + (1.0 / (x * 12.000000000000048));
	}
	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 <= (-2.4d-52)) .or. (.not. (z <= 8d-70))) then
        tmp = ((x * log(x)) - x) + ((z * z) * ((y + 0.0007936500793651d0) / x))
    else
        tmp = (0.91893853320467d0 + (((x + (-0.5d0)) * log(x)) - x)) + (1.0d0 / (x * 12.000000000000048d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.4e-52) || !(z <= 8e-70)) {
		tmp = ((x * Math.log(x)) - x) + ((z * z) * ((y + 0.0007936500793651) / x));
	} else {
		tmp = (0.91893853320467 + (((x + -0.5) * Math.log(x)) - x)) + (1.0 / (x * 12.000000000000048));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.4e-52) or not (z <= 8e-70):
		tmp = ((x * math.log(x)) - x) + ((z * z) * ((y + 0.0007936500793651) / x))
	else:
		tmp = (0.91893853320467 + (((x + -0.5) * math.log(x)) - x)) + (1.0 / (x * 12.000000000000048))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.4e-52) || !(z <= 8e-70))
		tmp = Float64(Float64(Float64(x * log(x)) - x) + Float64(Float64(z * z) * Float64(Float64(y + 0.0007936500793651) / x)));
	else
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(Float64(x + -0.5) * log(x)) - x)) + Float64(1.0 / Float64(x * 12.000000000000048)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.4e-52) || ~((z <= 8e-70)))
		tmp = ((x * log(x)) - x) + ((z * z) * ((y + 0.0007936500793651) / x));
	else
		tmp = (0.91893853320467 + (((x + -0.5) * log(x)) - x)) + (1.0 / (x * 12.000000000000048));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.4e-52], N[Not[LessEqual[z, 8e-70]], $MachinePrecision]], N[(N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + N[(N[(z * z), $MachinePrecision] * N[(N[(y + 0.0007936500793651), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.91893853320467 + N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(x * 12.000000000000048), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4000000000000002e-52 or 7.99999999999999997e-70 < z

   1. Initial program 92.6%

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

      1. sub-neg 92.6%

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

      2. metadata-eval 92.6%

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

      3. fma-def 92.6%

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

      4. fma-neg 92.6%

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

      5. metadata-eval 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in x around inf 92.7%

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

      1. sub-neg 92.7%

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

      2. mul-1-neg 92.7%

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

      3. log-rec 92.7%

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

      4. remove-double-neg 92.7%

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

      5. metadata-eval 92.7%

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

      6. distribute-rgt-in 92.6%

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

      7. *-rgt-identity 92.6%

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

      8. neg-mul-1 92.6%

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

      9. *-rgt-identity 92.6%

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

      10. sub-neg 92.6%

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

      11. *-commutative 92.6%

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

   6. Simplified 92.6%

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

   7. Taylor expanded in z around inf 90.1%

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

      1. *-lft-identity 90.1%

         \[\leadsto \left(x \cdot \log x - x\right) + \frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{\color{blue}{1 \cdot x}} \]

      2. times-frac 91.4%

         \[\leadsto \left(x \cdot \log x - x\right) + \color{blue}{\frac{{z}^{2}}{1} \cdot \frac{0.0007936500793651 + y}{x}} \]

      3. /-rgt-identity 91.4%

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

      4. unpow2 91.4%

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

   9. Simplified 91.4%

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

   if -2.4000000000000002e-52 < z < 7.99999999999999997e-70

   1. Initial program 99.4%

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

      1. sub-neg 99.4%

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

      2. metadata-eval 99.4%

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

      3. fma-def 99.4%

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

      4. fma-neg 99.4%

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

      5. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 97.8%

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

      1. clear-num 96.8%

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

      2. inv-pow 96.8%

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

      3. div-inv 96.9%

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

      4. metadata-eval 96.9%

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

   6. Applied egg-rr 97.9%

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

      1. unpow-1 96.9%

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

   8. Simplified 97.9%

      \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{1}{x \cdot 12.000000000000048}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-52} \lor \neg \left(z \leq 8 \cdot 10^{-70}\right):\\ \;\;\;\;\left(x \cdot \log x - x\right) + \left(z \cdot z\right) \cdot \frac{y + 0.0007936500793651}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{1}{x \cdot 12.000000000000048}\\ \end{array} \]

Alternative 10: 95.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-53} \lor \neg \left(z \leq 8 \cdot 10^{-70}\right):\\ \;\;\;\;\left(x \cdot \log x - x\right) + \frac{z}{\frac{x}{z}} \cdot \left(y + 0.0007936500793651\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{1}{x \cdot 12.000000000000048}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.5e-53) (not (<= z 8e-70)))
   (+ (- (* x (log x)) x) (* (/ z (/ x z)) (+ y 0.0007936500793651)))
   (+
    (+ 0.91893853320467 (- (* (+ x -0.5) (log x)) x))
    (/ 1.0 (* x 12.000000000000048)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.5e-53) || !(z <= 8e-70)) {
		tmp = ((x * log(x)) - x) + ((z / (x / z)) * (y + 0.0007936500793651));
	} else {
		tmp = (0.91893853320467 + (((x + -0.5) * log(x)) - x)) + (1.0 / (x * 12.000000000000048));
	}
	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 <= (-2.5d-53)) .or. (.not. (z <= 8d-70))) then
        tmp = ((x * log(x)) - x) + ((z / (x / z)) * (y + 0.0007936500793651d0))
    else
        tmp = (0.91893853320467d0 + (((x + (-0.5d0)) * log(x)) - x)) + (1.0d0 / (x * 12.000000000000048d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.5e-53) || !(z <= 8e-70)) {
		tmp = ((x * Math.log(x)) - x) + ((z / (x / z)) * (y + 0.0007936500793651));
	} else {
		tmp = (0.91893853320467 + (((x + -0.5) * Math.log(x)) - x)) + (1.0 / (x * 12.000000000000048));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.5e-53) or not (z <= 8e-70):
		tmp = ((x * math.log(x)) - x) + ((z / (x / z)) * (y + 0.0007936500793651))
	else:
		tmp = (0.91893853320467 + (((x + -0.5) * math.log(x)) - x)) + (1.0 / (x * 12.000000000000048))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.5e-53) || !(z <= 8e-70))
		tmp = Float64(Float64(Float64(x * log(x)) - x) + Float64(Float64(z / Float64(x / z)) * Float64(y + 0.0007936500793651)));
	else
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(Float64(x + -0.5) * log(x)) - x)) + Float64(1.0 / Float64(x * 12.000000000000048)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.5e-53) || ~((z <= 8e-70)))
		tmp = ((x * log(x)) - x) + ((z / (x / z)) * (y + 0.0007936500793651));
	else
		tmp = (0.91893853320467 + (((x + -0.5) * log(x)) - x)) + (1.0 / (x * 12.000000000000048));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.5e-53], N[Not[LessEqual[z, 8e-70]], $MachinePrecision]], N[(N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + N[(N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision] * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.91893853320467 + N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(x * 12.000000000000048), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5e-53 or 7.99999999999999997e-70 < z

   1. Initial program 92.6%

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

      1. sub-neg 92.6%

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

      2. metadata-eval 92.6%

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

      3. fma-def 92.6%

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

      4. fma-neg 92.6%

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

      5. metadata-eval 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in x around inf 92.7%

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

      1. sub-neg 92.7%

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

      2. mul-1-neg 92.7%

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

      3. log-rec 92.7%

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

      4. remove-double-neg 92.7%

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

      5. metadata-eval 92.7%

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

      6. distribute-rgt-in 92.6%

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

      7. *-rgt-identity 92.6%

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

      8. neg-mul-1 92.6%

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

      9. *-rgt-identity 92.6%

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

      10. sub-neg 92.6%

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

      11. *-commutative 92.6%

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

   6. Simplified 92.6%

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

   7. Taylor expanded in x around 0 92.6%

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

   8. Taylor expanded in z around inf 90.1%

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

      1. associate-*l/ 92.1%

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

      2. unpow2 92.1%

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

      3. associate-/l* 97.3%

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

   10. Simplified 97.3%

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

   if -2.5e-53 < z < 7.99999999999999997e-70

   1. Initial program 99.4%

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

      1. sub-neg 99.4%

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

      2. metadata-eval 99.4%

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

      3. fma-def 99.4%

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

      4. fma-neg 99.4%

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

      5. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 97.8%

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

      1. clear-num 96.8%

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

      2. inv-pow 96.8%

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

      3. div-inv 96.9%

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

      4. metadata-eval 96.9%

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

   6. Applied egg-rr 97.9%

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

      1. unpow-1 96.9%

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

   8. Simplified 97.9%

      \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{1}{x \cdot 12.000000000000048}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-53} \lor \neg \left(z \leq 8 \cdot 10^{-70}\right):\\ \;\;\;\;\left(x \cdot \log x - x\right) + \frac{z}{\frac{x}{z}} \cdot \left(y + 0.0007936500793651\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{1}{x \cdot 12.000000000000048}\\ \end{array} \]

Alternative 11: 97.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log x - x\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{-29} \lor \neg \left(z \leq 9.8\right):\\ \;\;\;\;t_0 + \frac{z}{\frac{x}{z}} \cdot \left(y + 0.0007936500793651\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{0.083333333333333 + z \cdot \left(y \cdot z\right)}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* x (log x)) x)))
   (if (or (<= z -6.8e-29) (not (<= z 9.8)))
     (+ t_0 (* (/ z (/ x z)) (+ y 0.0007936500793651)))
     (+ t_0 (/ (+ 0.083333333333333 (* z (* y z))) x)))))

C

double code(double x, double y, double z) {
	double t_0 = (x * log(x)) - x;
	double tmp;
	if ((z <= -6.8e-29) || !(z <= 9.8)) {
		tmp = t_0 + ((z / (x / z)) * (y + 0.0007936500793651));
	} else {
		tmp = t_0 + ((0.083333333333333 + (z * (y * z))) / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x * log(x)) - x
    if ((z <= (-6.8d-29)) .or. (.not. (z <= 9.8d0))) then
        tmp = t_0 + ((z / (x / z)) * (y + 0.0007936500793651d0))
    else
        tmp = t_0 + ((0.083333333333333d0 + (z * (y * z))) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * Math.log(x)) - x;
	double tmp;
	if ((z <= -6.8e-29) || !(z <= 9.8)) {
		tmp = t_0 + ((z / (x / z)) * (y + 0.0007936500793651));
	} else {
		tmp = t_0 + ((0.083333333333333 + (z * (y * z))) / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * math.log(x)) - x
	tmp = 0
	if (z <= -6.8e-29) or not (z <= 9.8):
		tmp = t_0 + ((z / (x / z)) * (y + 0.0007936500793651))
	else:
		tmp = t_0 + ((0.083333333333333 + (z * (y * z))) / x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * log(x)) - x)
	tmp = 0.0
	if ((z <= -6.8e-29) || !(z <= 9.8))
		tmp = Float64(t_0 + Float64(Float64(z / Float64(x / z)) * Float64(y + 0.0007936500793651)));
	else
		tmp = Float64(t_0 + Float64(Float64(0.083333333333333 + Float64(z * Float64(y * z))) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * log(x)) - x;
	tmp = 0.0;
	if ((z <= -6.8e-29) || ~((z <= 9.8)))
		tmp = t_0 + ((z / (x / z)) * (y + 0.0007936500793651));
	else
		tmp = t_0 + ((0.083333333333333 + (z * (y * z))) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]}, If[Or[LessEqual[z, -6.8e-29], N[Not[LessEqual[z, 9.8]], $MachinePrecision]], N[(t$95$0 + N[(N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision] * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(N[(0.083333333333333 + N[(z * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.79999999999999945e-29 or 9.8000000000000007 < z

   1. Initial program 92.0%

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

      1. sub-neg 92.0%

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

      2. metadata-eval 92.0%

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

      3. fma-def 92.0%

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

      4. fma-neg 92.0%

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

      5. metadata-eval 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in x around inf 92.0%

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

      1. sub-neg 92.0%

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

      2. mul-1-neg 92.0%

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

      3. log-rec 92.0%

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

      4. remove-double-neg 92.0%

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

      5. metadata-eval 92.0%

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

      6. distribute-rgt-in 92.0%

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

      7. *-rgt-identity 92.0%

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

      8. neg-mul-1 92.0%

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

      9. *-rgt-identity 92.0%

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

      10. sub-neg 92.0%

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

      11. *-commutative 92.0%

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

   6. Simplified 92.0%

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

   7. Taylor expanded in x around 0 92.0%

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

   8. Taylor expanded in z around inf 90.6%

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

      1. associate-*l/ 92.8%

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

      2. unpow2 92.8%

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

      3. associate-/l* 98.4%

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

   10. Simplified 98.4%

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

   if -6.79999999999999945e-29 < z < 9.8000000000000007

   1. Initial program 99.4%

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

      1. sub-neg 99.4%

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

      2. metadata-eval 99.4%

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

      3. fma-def 99.4%

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

      4. fma-neg 99.4%

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

      5. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around inf 98.5%

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

      1. sub-neg 98.5%

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

      2. mul-1-neg 98.5%

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

      3. log-rec 98.5%

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

      4. remove-double-neg 98.5%

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

      5. metadata-eval 98.5%

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

      6. distribute-rgt-in 98.5%

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

      7. *-rgt-identity 98.5%

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

      8. neg-mul-1 98.5%

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

      9. *-rgt-identity 98.5%

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

      10. sub-neg 98.5%

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

      11. *-commutative 98.5%

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

   6. Simplified 98.5%

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

   7. Taylor expanded in x around 0 98.5%

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

   8. Taylor expanded in y around inf 98.0%

      \[\leadsto \left(x \cdot \log x - x\right) + \frac{0.083333333333333 + \color{blue}{y \cdot {z}^{2}}}{x} \]
   9. Step-by-step derivation

      1. *-commutative 98.0%

         \[\leadsto \left(x \cdot \log x - x\right) + \frac{0.083333333333333 + \color{blue}{{z}^{2} \cdot y}}{x} \]

      2. unpow2 98.0%

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

      3. associate-*l* 98.0%

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

   10. Simplified 98.0%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-29} \lor \neg \left(z \leq 9.8\right):\\ \;\;\;\;\left(x \cdot \log x - x\right) + \frac{z}{\frac{x}{z}} \cdot \left(y + 0.0007936500793651\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log x - x\right) + \frac{0.083333333333333 + z \cdot \left(y \cdot z\right)}{x}\\ \end{array} \]

Alternative 12: 62.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -36 \lor \neg \left(z \leq 2.5 \cdot 10^{+14}\right):\\ \;\;\;\;\left(x \cdot \log x - x\right) + -0.0027777777777778 \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -36.0) (not (<= z 2.5e+14)))
   (+ (- (* x (log x)) x) (* -0.0027777777777778 (/ z x)))
   (+
    (+ 0.91893853320467 (- (* (+ x -0.5) (log x)) x))
    (/ 0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -36.0) || !(z <= 2.5e+14)) {
		tmp = ((x * log(x)) - x) + (-0.0027777777777778 * (z / x));
	} else {
		tmp = (0.91893853320467 + (((x + -0.5) * log(x)) - 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 <= (-36.0d0)) .or. (.not. (z <= 2.5d+14))) then
        tmp = ((x * log(x)) - x) + ((-0.0027777777777778d0) * (z / x))
    else
        tmp = (0.91893853320467d0 + (((x + (-0.5d0)) * log(x)) - 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 <= -36.0) || !(z <= 2.5e+14)) {
		tmp = ((x * Math.log(x)) - x) + (-0.0027777777777778 * (z / x));
	} else {
		tmp = (0.91893853320467 + (((x + -0.5) * Math.log(x)) - x)) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -36.0) or not (z <= 2.5e+14):
		tmp = ((x * math.log(x)) - x) + (-0.0027777777777778 * (z / x))
	else:
		tmp = (0.91893853320467 + (((x + -0.5) * math.log(x)) - x)) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -36.0) || !(z <= 2.5e+14))
		tmp = Float64(Float64(Float64(x * log(x)) - x) + Float64(-0.0027777777777778 * Float64(z / x)));
	else
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(Float64(x + -0.5) * log(x)) - x)) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -36.0) || ~((z <= 2.5e+14)))
		tmp = ((x * log(x)) - x) + (-0.0027777777777778 * (z / x));
	else
		tmp = (0.91893853320467 + (((x + -0.5) * log(x)) - x)) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -36.0], N[Not[LessEqual[z, 2.5e+14]], $MachinePrecision]], N[(N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + N[(-0.0027777777777778 * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.91893853320467 + N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -36 or 2.5e14 < z

   1. Initial program 91.3%

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

      1. sub-neg 91.3%

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

      2. metadata-eval 91.3%

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

      3. fma-def 91.3%

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

      4. fma-neg 91.3%

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

      5. metadata-eval 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in x around inf 91.3%

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

      1. sub-neg 91.3%

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

      2. mul-1-neg 91.3%

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

      3. log-rec 91.3%

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

      4. remove-double-neg 91.3%

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

      5. metadata-eval 91.3%

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

      6. distribute-rgt-in 91.3%

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

      7. *-rgt-identity 91.3%

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

      8. neg-mul-1 91.3%

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

      9. *-rgt-identity 91.3%

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

      10. sub-neg 91.3%

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

      11. *-commutative 91.3%

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

   6. Simplified 91.3%

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

   7. Taylor expanded in z around 0 32.3%

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

      1. *-commutative 32.3%

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

   9. Simplified 32.3%

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

   10. Taylor expanded in z around inf 33.7%

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

   if -36 < z < 2.5e14

   1. Initial program 99.4%

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

      1. sub-neg 99.4%

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

      2. metadata-eval 99.4%

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

      3. fma-def 99.4%

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

      4. fma-neg 99.4%

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

      5. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 85.9%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -36 \lor \neg \left(z \leq 2.5 \cdot 10^{+14}\right):\\ \;\;\;\;\left(x \cdot \log x - x\right) + -0.0027777777777778 \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 13: 78.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -21 \lor \neg \left(z \leq 140\right):\\ \;\;\;\;\left(x \cdot \log x - x\right) + 0.0007936500793651 \cdot \frac{z \cdot z}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -21.0) (not (<= z 140.0)))
   (+ (- (* x (log x)) x) (* 0.0007936500793651 (/ (* z z) x)))
   (+
    (+ 0.91893853320467 (- (* (+ x -0.5) (log x)) x))
    (/ 0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -21.0) || !(z <= 140.0)) {
		tmp = ((x * log(x)) - x) + (0.0007936500793651 * ((z * z) / x));
	} else {
		tmp = (0.91893853320467 + (((x + -0.5) * log(x)) - 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 <= (-21.0d0)) .or. (.not. (z <= 140.0d0))) then
        tmp = ((x * log(x)) - x) + (0.0007936500793651d0 * ((z * z) / x))
    else
        tmp = (0.91893853320467d0 + (((x + (-0.5d0)) * log(x)) - 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 <= -21.0) || !(z <= 140.0)) {
		tmp = ((x * Math.log(x)) - x) + (0.0007936500793651 * ((z * z) / x));
	} else {
		tmp = (0.91893853320467 + (((x + -0.5) * Math.log(x)) - x)) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -21.0) or not (z <= 140.0):
		tmp = ((x * math.log(x)) - x) + (0.0007936500793651 * ((z * z) / x))
	else:
		tmp = (0.91893853320467 + (((x + -0.5) * math.log(x)) - x)) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -21.0) || !(z <= 140.0))
		tmp = Float64(Float64(Float64(x * log(x)) - x) + Float64(0.0007936500793651 * Float64(Float64(z * z) / x)));
	else
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(Float64(x + -0.5) * log(x)) - x)) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -21.0) || ~((z <= 140.0)))
		tmp = ((x * log(x)) - x) + (0.0007936500793651 * ((z * z) / x));
	else
		tmp = (0.91893853320467 + (((x + -0.5) * log(x)) - x)) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -21.0], N[Not[LessEqual[z, 140.0]], $MachinePrecision]], N[(N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + N[(0.0007936500793651 * N[(N[(z * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.91893853320467 + N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -21 or 140 < z

   1. Initial program 91.4%

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

      1. sub-neg 91.4%

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

      2. metadata-eval 91.4%

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

      3. fma-def 91.4%

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

      4. fma-neg 91.4%

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

      5. metadata-eval 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in x around inf 91.4%

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

      1. sub-neg 91.4%

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

      2. mul-1-neg 91.4%

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

      3. log-rec 91.4%

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

      4. remove-double-neg 91.4%

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

      5. metadata-eval 91.4%

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

      6. distribute-rgt-in 91.4%

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

      7. *-rgt-identity 91.4%

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

      8. neg-mul-1 91.4%

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

      9. *-rgt-identity 91.4%

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

      10. sub-neg 91.4%

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

      11. *-commutative 91.4%

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

   6. Simplified 91.4%

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

   7. Taylor expanded in y around 0 64.3%

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

      1. fma-neg 64.3%

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

      2. metadata-eval 64.3%

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

   9. Simplified 64.3%

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

   10. Taylor expanded in z around inf 63.5%

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

       1. unpow2 63.5%

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

   12. Simplified 63.5%

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

   if -21 < z < 140

   1. Initial program 99.4%

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

      1. sub-neg 99.4%

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

      2. metadata-eval 99.4%

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

      3. fma-def 99.4%

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

      4. fma-neg 99.5%

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

      5. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in z around 0 86.4%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -21 \lor \neg \left(z \leq 140\right):\\ \;\;\;\;\left(x \cdot \log x - x\right) + 0.0007936500793651 \cdot \frac{z \cdot z}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 14: 80.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -12.5 \lor \neg \left(z \leq 140\right):\\ \;\;\;\;\left(x \cdot \log x - x\right) + z \cdot \left(z \cdot \frac{0.0007936500793651}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -12.5) (not (<= z 140.0)))
   (+ (- (* x (log x)) x) (* z (* z (/ 0.0007936500793651 x))))
   (+
    (+ 0.91893853320467 (- (* (+ x -0.5) (log x)) x))
    (/ 0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -12.5) || !(z <= 140.0)) {
		tmp = ((x * log(x)) - x) + (z * (z * (0.0007936500793651 / x)));
	} else {
		tmp = (0.91893853320467 + (((x + -0.5) * log(x)) - 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 <= (-12.5d0)) .or. (.not. (z <= 140.0d0))) then
        tmp = ((x * log(x)) - x) + (z * (z * (0.0007936500793651d0 / x)))
    else
        tmp = (0.91893853320467d0 + (((x + (-0.5d0)) * log(x)) - 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 <= -12.5) || !(z <= 140.0)) {
		tmp = ((x * Math.log(x)) - x) + (z * (z * (0.0007936500793651 / x)));
	} else {
		tmp = (0.91893853320467 + (((x + -0.5) * Math.log(x)) - x)) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -12.5) or not (z <= 140.0):
		tmp = ((x * math.log(x)) - x) + (z * (z * (0.0007936500793651 / x)))
	else:
		tmp = (0.91893853320467 + (((x + -0.5) * math.log(x)) - x)) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -12.5) || !(z <= 140.0))
		tmp = Float64(Float64(Float64(x * log(x)) - x) + Float64(z * Float64(z * Float64(0.0007936500793651 / x))));
	else
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(Float64(x + -0.5) * log(x)) - x)) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -12.5) || ~((z <= 140.0)))
		tmp = ((x * log(x)) - x) + (z * (z * (0.0007936500793651 / x)));
	else
		tmp = (0.91893853320467 + (((x + -0.5) * log(x)) - x)) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -12.5], N[Not[LessEqual[z, 140.0]], $MachinePrecision]], N[(N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + N[(z * N[(z * N[(0.0007936500793651 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.91893853320467 + N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -12.5 or 140 < z

   1. Initial program 91.4%

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

      1. sub-neg 91.4%

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

      2. metadata-eval 91.4%

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

      3. fma-def 91.4%

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

      4. fma-neg 91.4%

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

      5. metadata-eval 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in x around inf 91.4%

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

      1. sub-neg 91.4%

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

      2. mul-1-neg 91.4%

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

      3. log-rec 91.4%

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

      4. remove-double-neg 91.4%

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

      5. metadata-eval 91.4%

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

      6. distribute-rgt-in 91.4%

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

      7. *-rgt-identity 91.4%

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

      8. neg-mul-1 91.4%

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

      9. *-rgt-identity 91.4%

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

      10. sub-neg 91.4%

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

      11. *-commutative 91.4%

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

   6. Simplified 91.4%

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

   7. Taylor expanded in y around 0 64.3%

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

      1. fma-neg 64.3%

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

      2. metadata-eval 64.3%

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

   9. Simplified 64.3%

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

   10. Taylor expanded in z around inf 63.5%

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

       1. *-commutative 63.5%

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

       2. associate-*l/ 63.5%

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

       3. associate-*r/ 63.5%

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

       4. metadata-eval 63.5%

          \[\leadsto \left(x \cdot \log x - x\right) + {z}^{2} \cdot \frac{\color{blue}{0.0007936500793651 \cdot 1}}{x} \]

       5. associate-*r/ 63.5%

          \[\leadsto \left(x \cdot \log x - x\right) + {z}^{2} \cdot \color{blue}{\left(0.0007936500793651 \cdot \frac{1}{x}\right)} \]

       6. unpow2 63.5%

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

       7. associate-*l* 65.5%

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

       8. associate-*r/ 65.6%

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

       9. metadata-eval 65.6%

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

   12. Simplified 65.6%

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

   if -12.5 < z < 140

   1. Initial program 99.4%

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

      1. sub-neg 99.4%

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

      2. metadata-eval 99.4%

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

      3. fma-def 99.4%

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

      4. fma-neg 99.5%

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

      5. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in z around 0 86.4%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -12.5 \lor \neg \left(z \leq 140\right):\\ \;\;\;\;\left(x \cdot \log x - x\right) + z \cdot \left(z \cdot \frac{0.0007936500793651}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 15: 61.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1600 \lor \neg \left(z \leq 5.4 \cdot 10^{+31}\right):\\ \;\;\;\;\left(x \cdot \log x - x\right) + -0.0027777777777778 \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x \cdot 12.000000000000048} + x \cdot \left(\log x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1600.0) (not (<= z 5.4e+31)))
   (+ (- (* x (log x)) x) (* -0.0027777777777778 (/ z x)))
   (+ (/ 1.0 (* x 12.000000000000048)) (* x (+ (log x) -1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1600.0) || !(z <= 5.4e+31)) {
		tmp = ((x * log(x)) - x) + (-0.0027777777777778 * (z / x));
	} else {
		tmp = (1.0 / (x * 12.000000000000048)) + (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 ((z <= (-1600.0d0)) .or. (.not. (z <= 5.4d+31))) then
        tmp = ((x * log(x)) - x) + ((-0.0027777777777778d0) * (z / x))
    else
        tmp = (1.0d0 / (x * 12.000000000000048d0)) + (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 ((z <= -1600.0) || !(z <= 5.4e+31)) {
		tmp = ((x * Math.log(x)) - x) + (-0.0027777777777778 * (z / x));
	} else {
		tmp = (1.0 / (x * 12.000000000000048)) + (x * (Math.log(x) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1600.0) or not (z <= 5.4e+31):
		tmp = ((x * math.log(x)) - x) + (-0.0027777777777778 * (z / x))
	else:
		tmp = (1.0 / (x * 12.000000000000048)) + (x * (math.log(x) + -1.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1600.0) || !(z <= 5.4e+31))
		tmp = Float64(Float64(Float64(x * log(x)) - x) + Float64(-0.0027777777777778 * Float64(z / x)));
	else
		tmp = Float64(Float64(1.0 / Float64(x * 12.000000000000048)) + Float64(x * Float64(log(x) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1600.0) || ~((z <= 5.4e+31)))
		tmp = ((x * log(x)) - x) + (-0.0027777777777778 * (z / x));
	else
		tmp = (1.0 / (x * 12.000000000000048)) + (x * (log(x) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1600.0], N[Not[LessEqual[z, 5.4e+31]], $MachinePrecision]], N[(N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + N[(-0.0027777777777778 * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[(x * 12.000000000000048), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1600 or 5.39999999999999971e31 < z

   1. Initial program 91.2%

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

      1. sub-neg 91.2%

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

      2. metadata-eval 91.2%

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

      3. fma-def 91.2%

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

      4. fma-neg 91.2%

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

      5. metadata-eval 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in x around inf 91.3%

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

      1. sub-neg 91.3%

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

      2. mul-1-neg 91.3%

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

      3. log-rec 91.3%

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

      4. remove-double-neg 91.3%

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

      5. metadata-eval 91.3%

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

      6. distribute-rgt-in 91.2%

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

      7. *-rgt-identity 91.2%

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

      8. neg-mul-1 91.2%

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

      9. *-rgt-identity 91.2%

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

      10. sub-neg 91.2%

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

      11. *-commutative 91.2%

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

   6. Simplified 91.2%

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

   7. Taylor expanded in z around 0 31.8%

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

      1. *-commutative 31.8%

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

   9. Simplified 31.8%

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

   10. Taylor expanded in z around inf 33.2%

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

   if -1600 < z < 5.39999999999999971e31

   1. Initial program 99.4%

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

      1. sub-neg 99.4%

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

      2. metadata-eval 99.4%

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

      3. fma-def 99.4%

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

      4. fma-neg 99.4%

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

      5. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 85.9%

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

   5. Taylor expanded in x around inf 85.1%

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

      1. sub-neg 85.1%

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

      2. mul-1-neg 85.1%

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

      3. log-rec 85.1%

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

      4. remove-double-neg 85.1%

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

      5. metadata-eval 85.1%

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

   7. Simplified 85.1%

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

      1. clear-num 85.1%

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

      2. inv-pow 85.1%

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

      3. div-inv 85.2%

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

      4. metadata-eval 85.2%

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

   9. Applied egg-rr 85.2%

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

       1. unpow-1 85.2%

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

   11. Simplified 85.2%

       \[\leadsto x \cdot \left(\log x + -1\right) + \color{blue}{\frac{1}{x \cdot 12.000000000000048}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1600 \lor \neg \left(z \leq 5.4 \cdot 10^{+31}\right):\\ \;\;\;\;\left(x \cdot \log x - x\right) + -0.0027777777777778 \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x \cdot 12.000000000000048} + x \cdot \left(\log x + -1\right)\\ \end{array} \]

Alternative 16: 55.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \frac{1}{x \cdot 12.000000000000048} + x \cdot \left(\log x + -1\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ (/ 1.0 (* x 12.000000000000048)) (* x (+ (log x) -1.0))))

C

double code(double x, double y, double z) {
	return (1.0 / (x * 12.000000000000048)) + (x * (log(x) + -1.0));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (1.0d0 / (x * 12.000000000000048d0)) + (x * (log(x) + (-1.0d0)))
end function

Java

public static double code(double x, double y, double z) {
	return (1.0 / (x * 12.000000000000048)) + (x * (Math.log(x) + -1.0));
}

Python

def code(x, y, z):
	return (1.0 / (x * 12.000000000000048)) + (x * (math.log(x) + -1.0))

Julia

function code(x, y, z)
	return Float64(Float64(1.0 / Float64(x * 12.000000000000048)) + Float64(x * Float64(log(x) + -1.0)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (1.0 / (x * 12.000000000000048)) + (x * (log(x) + -1.0));
end

Wolfram

code[x_, y_, z_] := N[(N[(1.0 / N[(x * 12.000000000000048), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.7%

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

   1. sub-neg 95.7%

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

   2. metadata-eval 95.7%

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

   3. fma-def 95.7%

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

   4. fma-neg 95.7%

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

   5. metadata-eval 95.7%

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

3. Simplified 95.7%

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

4. Taylor expanded in z around 0 55.7%

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

5. Taylor expanded in x around inf 55.2%

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

   1. sub-neg 55.2%

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

   2. mul-1-neg 55.2%

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

   3. log-rec 55.2%

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

   4. remove-double-neg 55.2%

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

   5. metadata-eval 55.2%

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

7. Simplified 55.2%

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

   1. clear-num 55.2%

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

   2. inv-pow 55.2%

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

   3. div-inv 55.2%

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

   4. metadata-eval 55.2%

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

9. Applied egg-rr 55.2%

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

    1. unpow-1 55.2%

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

11. Simplified 55.2%

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

12. Final simplification 55.2%

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

Alternative 17: 34.8% 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 95.7%

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

   1. sub-neg 95.7%

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

   2. metadata-eval 95.7%

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

   3. fma-def 95.7%

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

   4. fma-neg 95.7%

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

   5. metadata-eval 95.7%

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

3. Simplified 95.7%

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

4. Taylor expanded in z around 0 55.7%

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

5. Taylor expanded in x around inf 55.2%

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

   1. sub-neg 55.2%

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

   2. mul-1-neg 55.2%

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

   3. log-rec 55.2%

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

   4. remove-double-neg 55.2%

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

   5. metadata-eval 55.2%

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

7. Simplified 55.2%

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

   1. add-sqr-sqrt 55.1%

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

   2. sqrt-unprod 52.6%

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

   3. frac-times 52.6%

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

   4. metadata-eval 52.6%

      \[\leadsto x \cdot \left(\log x + -1\right) + \sqrt{\frac{\color{blue}{0.0069444444444443885}}{x \cdot x}} \]

9. Applied egg-rr 52.6%

   \[\leadsto x \cdot \left(\log x + -1\right) + \color{blue}{\sqrt{\frac{0.0069444444444443885}{x \cdot x}}} \]
10. Step-by-step derivation

    1. associate-/r* 52.6%

       \[\leadsto x \cdot \left(\log x + -1\right) + \sqrt{\color{blue}{\frac{\frac{0.0069444444444443885}{x}}{x}}} \]

11. Simplified 52.6%

    \[\leadsto x \cdot \left(\log x + -1\right) + \color{blue}{\sqrt{\frac{\frac{0.0069444444444443885}{x}}{x}}} \]

12. Taylor expanded in x around -inf 36.3%

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

13. Final simplification 36.3%

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

Alternative 18: 55.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.7%

   \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
2. Step-by-step derivation

   1. sub-neg 95.7%

      \[\leadsto \left(\left(\color{blue}{\left(x + \left(-0.5\right)\right)} \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. metadata-eval 95.7%

      \[\leadsto \left(\left(\left(x + \color{blue}{-0.5}\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   3. fma-def 95.7%

      \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\mathsf{fma}\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778, z, 0.083333333333333\right)}}{x} \]

   4. fma-neg 95.7%

      \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right)}, z, 0.083333333333333\right)}{x} \]

   5. metadata-eval 95.7%

      \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, \color{blue}{-0.0027777777777778}\right), z, 0.083333333333333\right)}{x} \]

3. Simplified 95.7%

   \[\leadsto \color{blue}{\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}} \]

4. Taylor expanded in z around 0 55.7%

   \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{0.083333333333333}{x}} \]

5. Taylor expanded in x around inf 55.2%

   \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right)} + \frac{0.083333333333333}{x} \]
6. Step-by-step derivation

   1. sub-neg 55.2%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) + \left(-1\right)\right)} + \frac{0.083333333333333}{x} \]

   2. mul-1-neg 55.2%

      \[\leadsto x \cdot \left(\color{blue}{\left(-\log \left(\frac{1}{x}\right)\right)} + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

   3. log-rec 55.2%

      \[\leadsto x \cdot \left(\left(-\color{blue}{\left(-\log x\right)}\right) + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

   4. remove-double-neg 55.2%

      \[\leadsto x \cdot \left(\color{blue}{\log x} + \left(-1\right)\right) + \frac{0.083333333333333}{x} \]

   5. metadata-eval 55.2%

      \[\leadsto x \cdot \left(\log x + \color{blue}{-1}\right) + \frac{0.083333333333333}{x} \]

7. Simplified 55.2%

   \[\leadsto \color{blue}{x \cdot \left(\log x + -1\right)} + \frac{0.083333333333333}{x} \]

8. Final simplification 55.2%

   \[\leadsto \frac{0.083333333333333}{x} + x \cdot \left(\log x + -1\right) \]

Developer target: 98.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(x - 0.5\right) \cdot \log x + \left(0.91893853320467 - x\right)\right) + \frac{0.083333333333333}{x}\right) + \frac{z}{x} \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+
  (+ (+ (* (- x 0.5) (log x)) (- 0.91893853320467 x)) (/ 0.083333333333333 x))
  (* (/ z x) (- (* z (+ y 0.0007936500793651)) 0.0027777777777778))))

C

double code(double x, double y, double z) {
	return ((((x - 0.5) * log(x)) + (0.91893853320467 - x)) + (0.083333333333333 / x)) + ((z / x) * ((z * (y + 0.0007936500793651)) - 0.0027777777777778));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((((x - 0.5d0) * log(x)) + (0.91893853320467d0 - x)) + (0.083333333333333d0 / x)) + ((z / x) * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0))
end function

Java

public static double code(double x, double y, double z) {
	return ((((x - 0.5) * Math.log(x)) + (0.91893853320467 - x)) + (0.083333333333333 / x)) + ((z / x) * ((z * (y + 0.0007936500793651)) - 0.0027777777777778));
}

Python

def code(x, y, z):
	return ((((x - 0.5) * math.log(x)) + (0.91893853320467 - x)) + (0.083333333333333 / x)) + ((z / x) * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))

Julia

function code(x, y, z)
	return Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) + Float64(0.91893853320467 - x)) + Float64(0.083333333333333 / x)) + Float64(Float64(z / x) * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((((x - 0.5) * log(x)) + (0.91893853320467 - x)) + (0.083333333333333 / x)) + ((z / x) * ((z * (y + 0.0007936500793651)) - 0.0027777777777778));
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] + N[(0.91893853320467 - x), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision] + N[(N[(z / x), $MachinePrecision] * N[(N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023271 
(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)))