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

Percentage Accurate: 93.7% → 99.5%

Time: 23.1s

Alternatives: 13

Speedup: 1.0×

• 28.1% 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: 99.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\\ \mathbf{if}\;x \leq 900:\\ \;\;\;\;t_0 + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;t_0 + {\left(\frac{\frac{\frac{x}{z}}{z}}{y + 0.0007936500793651}\right)}^{-1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (- (* (+ x -0.5) (log x)) x) 0.91893853320467)))
   (if (<= x 900.0)
     (+
      t_0
      (/
       (fma
        (fma (+ y 0.0007936500793651) z -0.0027777777777778)
        z
        0.083333333333333)
       x))
     (+ t_0 (pow (/ (/ (/ x z) z) (+ y 0.0007936500793651)) -1.0)))))

C

double code(double x, double y, double z) {
	double t_0 = (((x + -0.5) * log(x)) - x) + 0.91893853320467;
	double tmp;
	if (x <= 900.0) {
		tmp = t_0 + (fma(fma((y + 0.0007936500793651), z, -0.0027777777777778), z, 0.083333333333333) / x);
	} else {
		tmp = t_0 + pow((((x / z) / z) / (y + 0.0007936500793651)), -1.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(x + -0.5) * log(x)) - x) + 0.91893853320467)
	tmp = 0.0
	if (x <= 900.0)
		tmp = Float64(t_0 + Float64(fma(fma(Float64(y + 0.0007936500793651), z, -0.0027777777777778), z, 0.083333333333333) / x));
	else
		tmp = Float64(t_0 + (Float64(Float64(Float64(x / z) / z) / Float64(y + 0.0007936500793651)) ^ -1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision]}, If[LessEqual[x, 900.0], N[(t$95$0 + N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z + -0.0027777777777778), $MachinePrecision] * z + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[Power[N[(N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision] / N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 900

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. metadata-eval 99.7%

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

      3. fma-def 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 900 < x

   1. Initial program 89.3%

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

      1. sub-neg 89.3%

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

      2. metadata-eval 89.3%

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

      3. fma-def 89.3%

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

      4. fma-neg 89.3%

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

      5. metadata-eval 89.3%

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

   3. Simplified 89.3%

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

      1. metadata-eval 89.3%

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

      2. fma-neg 89.3%

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

      3. fma-def 89.3%

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

      4. clear-num 89.3%

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

      5. inv-pow 89.3%

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

      6. *-commutative 89.3%

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

      7. fma-udef 89.3%

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

      8. fma-neg 89.3%

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

      9. metadata-eval 89.3%

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

   5. Applied egg-rr 89.3%

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

   6. Taylor expanded in z around inf 89.3%

      \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + {\color{blue}{\left(\frac{x}{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}\right)}}^{-1} \]
   7. Step-by-step derivation

      1. associate-/r* 92.5%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + {\color{blue}{\left(\frac{\frac{x}{{z}^{2}}}{0.0007936500793651 + y}\right)}}^{-1} \]

      2. unpow2 92.5%

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

      3. associate-/r* 99.6%

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

   8. Simplified 99.6%

      \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + {\color{blue}{\left(\frac{\frac{\frac{x}{z}}{z}}{0.0007936500793651 + y}\right)}}^{-1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 900:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + {\left(\frac{\frac{\frac{x}{z}}{z}}{y + 0.0007936500793651}\right)}^{-1}\\ \end{array} \]

Alternative 2: 99.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 900:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + {\left(\frac{\frac{\frac{x}{z}}{z}}{y + 0.0007936500793651}\right)}^{-1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 900.0)
   (+
    (+ 0.91893853320467 (- (* (log x) (- x 0.5)) x))
    (/
     (+
      0.083333333333333
      (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))
     x))
   (+
    (+ (- (* (+ x -0.5) (log x)) x) 0.91893853320467)
    (pow (/ (/ (/ x z) z) (+ y 0.0007936500793651)) -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 900.0) {
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = ((((x + -0.5) * log(x)) - x) + 0.91893853320467) + pow((((x / z) / z) / (y + 0.0007936500793651)), -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 900.0d0) then
        tmp = (0.91893853320467d0 + ((log(x) * (x - 0.5d0)) - x)) + ((0.083333333333333d0 + (z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0))) / x)
    else
        tmp = ((((x + (-0.5d0)) * log(x)) - x) + 0.91893853320467d0) + ((((x / z) / z) / (y + 0.0007936500793651d0)) ** (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 900.0) {
		tmp = (0.91893853320467 + ((Math.log(x) * (x - 0.5)) - x)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = ((((x + -0.5) * Math.log(x)) - x) + 0.91893853320467) + Math.pow((((x / z) / z) / (y + 0.0007936500793651)), -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 900.0:
		tmp = (0.91893853320467 + ((math.log(x) * (x - 0.5)) - x)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x)
	else:
		tmp = ((((x + -0.5) * math.log(x)) - x) + 0.91893853320467) + math.pow((((x / z) / z) / (y + 0.0007936500793651)), -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 900.0)
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(log(x) * Float64(x - 0.5)) - x)) + Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778))) / x));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(x + -0.5) * log(x)) - x) + 0.91893853320467) + (Float64(Float64(Float64(x / z) / z) / Float64(y + 0.0007936500793651)) ^ -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 900.0)
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	else
		tmp = ((((x + -0.5) * log(x)) - x) + 0.91893853320467) + ((((x / z) / z) / (y + 0.0007936500793651)) ^ -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 900.0], N[(N[(0.91893853320467 + N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(N[(0.083333333333333 + N[(z * N[(N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[Power[N[(N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision] / N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 900

   1. Initial program 99.7%

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

   if 900 < x

   1. Initial program 89.3%

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

      1. sub-neg 89.3%

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

      2. metadata-eval 89.3%

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

      3. fma-def 89.3%

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

      4. fma-neg 89.3%

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

      5. metadata-eval 89.3%

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

   3. Simplified 89.3%

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

      1. metadata-eval 89.3%

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

      2. fma-neg 89.3%

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

      3. fma-def 89.3%

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

      4. clear-num 89.3%

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

      5. inv-pow 89.3%

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

      6. *-commutative 89.3%

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

      7. fma-udef 89.3%

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

      8. fma-neg 89.3%

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

      9. metadata-eval 89.3%

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

   5. Applied egg-rr 89.3%

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

   6. Taylor expanded in z around inf 89.3%

      \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + {\color{blue}{\left(\frac{x}{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}\right)}}^{-1} \]
   7. Step-by-step derivation

      1. associate-/r* 92.5%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + {\color{blue}{\left(\frac{\frac{x}{{z}^{2}}}{0.0007936500793651 + y}\right)}}^{-1} \]

      2. unpow2 92.5%

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

      3. associate-/r* 99.6%

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

   8. Simplified 99.6%

      \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + {\color{blue}{\left(\frac{\frac{\frac{x}{z}}{z}}{0.0007936500793651 + y}\right)}}^{-1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 900:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + {\left(\frac{\frac{\frac{x}{z}}{z}}{y + 0.0007936500793651}\right)}^{-1}\\ \end{array} \]

Alternative 3: 81.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\\ t_1 := t_0 + \left(0.0007936500793651 \cdot z\right) \cdot \frac{z}{x}\\ t_2 := \left(z \cdot z\right) \cdot \frac{y}{x}\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-48}:\\ \;\;\;\;t_0 + t_2\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-23}:\\ \;\;\;\;t_0 + \frac{0.083333333333333}{x}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+114} \lor \neg \left(z \leq 1.95 \cdot 10^{+226}\right) \land z \leq 3.5 \cdot 10^{+250}:\\ \;\;\;\;t_2 + x \cdot \left(\log x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (- (* (+ x -0.5) (log x)) x) 0.91893853320467))
        (t_1 (+ t_0 (* (* 0.0007936500793651 z) (/ z x))))
        (t_2 (* (* z z) (/ y x))))
   (if (<= z -6.5e+138)
     t_1
     (if (<= z -3.6e-48)
       (+ t_0 t_2)
       (if (<= z 1.7e-23)
         (+ t_0 (/ 0.083333333333333 x))
         (if (or (<= z 6.8e+114) (and (not (<= z 1.95e+226)) (<= z 3.5e+250)))
           (+ t_2 (* x (+ (log x) -1.0)))
           t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = (((x + -0.5) * log(x)) - x) + 0.91893853320467;
	double t_1 = t_0 + ((0.0007936500793651 * z) * (z / x));
	double t_2 = (z * z) * (y / x);
	double tmp;
	if (z <= -6.5e+138) {
		tmp = t_1;
	} else if (z <= -3.6e-48) {
		tmp = t_0 + t_2;
	} else if (z <= 1.7e-23) {
		tmp = t_0 + (0.083333333333333 / x);
	} else if ((z <= 6.8e+114) || (!(z <= 1.95e+226) && (z <= 3.5e+250))) {
		tmp = t_2 + (x * (log(x) + -1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (((x + (-0.5d0)) * log(x)) - x) + 0.91893853320467d0
    t_1 = t_0 + ((0.0007936500793651d0 * z) * (z / x))
    t_2 = (z * z) * (y / x)
    if (z <= (-6.5d+138)) then
        tmp = t_1
    else if (z <= (-3.6d-48)) then
        tmp = t_0 + t_2
    else if (z <= 1.7d-23) then
        tmp = t_0 + (0.083333333333333d0 / x)
    else if ((z <= 6.8d+114) .or. (.not. (z <= 1.95d+226)) .and. (z <= 3.5d+250)) then
        tmp = t_2 + (x * (log(x) + (-1.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (((x + -0.5) * Math.log(x)) - x) + 0.91893853320467;
	double t_1 = t_0 + ((0.0007936500793651 * z) * (z / x));
	double t_2 = (z * z) * (y / x);
	double tmp;
	if (z <= -6.5e+138) {
		tmp = t_1;
	} else if (z <= -3.6e-48) {
		tmp = t_0 + t_2;
	} else if (z <= 1.7e-23) {
		tmp = t_0 + (0.083333333333333 / x);
	} else if ((z <= 6.8e+114) || (!(z <= 1.95e+226) && (z <= 3.5e+250))) {
		tmp = t_2 + (x * (Math.log(x) + -1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (((x + -0.5) * math.log(x)) - x) + 0.91893853320467
	t_1 = t_0 + ((0.0007936500793651 * z) * (z / x))
	t_2 = (z * z) * (y / x)
	tmp = 0
	if z <= -6.5e+138:
		tmp = t_1
	elif z <= -3.6e-48:
		tmp = t_0 + t_2
	elif z <= 1.7e-23:
		tmp = t_0 + (0.083333333333333 / x)
	elif (z <= 6.8e+114) or (not (z <= 1.95e+226) and (z <= 3.5e+250)):
		tmp = t_2 + (x * (math.log(x) + -1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(x + -0.5) * log(x)) - x) + 0.91893853320467)
	t_1 = Float64(t_0 + Float64(Float64(0.0007936500793651 * z) * Float64(z / x)))
	t_2 = Float64(Float64(z * z) * Float64(y / x))
	tmp = 0.0
	if (z <= -6.5e+138)
		tmp = t_1;
	elseif (z <= -3.6e-48)
		tmp = Float64(t_0 + t_2);
	elseif (z <= 1.7e-23)
		tmp = Float64(t_0 + Float64(0.083333333333333 / x));
	elseif ((z <= 6.8e+114) || (!(z <= 1.95e+226) && (z <= 3.5e+250)))
		tmp = Float64(t_2 + Float64(x * Float64(log(x) + -1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (((x + -0.5) * log(x)) - x) + 0.91893853320467;
	t_1 = t_0 + ((0.0007936500793651 * z) * (z / x));
	t_2 = (z * z) * (y / x);
	tmp = 0.0;
	if (z <= -6.5e+138)
		tmp = t_1;
	elseif (z <= -3.6e-48)
		tmp = t_0 + t_2;
	elseif (z <= 1.7e-23)
		tmp = t_0 + (0.083333333333333 / x);
	elseif ((z <= 6.8e+114) || (~((z <= 1.95e+226)) && (z <= 3.5e+250)))
		tmp = t_2 + (x * (log(x) + -1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(N[(0.0007936500793651 * z), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * z), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+138], t$95$1, If[LessEqual[z, -3.6e-48], N[(t$95$0 + t$95$2), $MachinePrecision], If[LessEqual[z, 1.7e-23], N[(t$95$0 + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 6.8e+114], And[N[Not[LessEqual[z, 1.95e+226]], $MachinePrecision], LessEqual[z, 3.5e+250]]], N[(t$95$2 + N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.50000000000000054e138 or 6.8000000000000001e114 < z < 1.94999999999999992e226 or 3.5e250 < z

   1. Initial program 88.0%

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

      1. sub-neg 88.0%

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

      2. metadata-eval 88.0%

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

      3. fma-def 88.0%

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

      4. fma-neg 88.0%

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

      5. metadata-eval 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in y around 0 77.1%

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

   5. Taylor expanded in z around inf 77.1%

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

      1. unpow2 77.1%

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

   7. Simplified 77.1%

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

   8. Taylor expanded in z around 0 77.1%

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

      1. *-commutative 77.1%

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

      2. unpow2 77.1%

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

      3. associate-*l/ 81.6%

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

      4. associate-*l* 81.7%

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

   10. Simplified 81.7%

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

   if -6.50000000000000054e138 < z < -3.6000000000000002e-48

   1. Initial program 96.7%

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

      1. sub-neg 96.7%

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

      2. metadata-eval 96.7%

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

      3. fma-def 96.7%

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

      4. fma-neg 96.7%

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

      5. metadata-eval 96.7%

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

   3. Simplified 96.7%

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

      1. metadata-eval 96.7%

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

      2. fma-neg 96.7%

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

      3. fma-def 96.7%

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

      4. clear-num 96.7%

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

      5. inv-pow 96.7%

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

      6. *-commutative 96.7%

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

      7. fma-udef 96.7%

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

      8. fma-neg 96.7%

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

      9. metadata-eval 96.7%

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

   5. Applied egg-rr 96.7%

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

   6. Taylor expanded in y around inf 77.4%

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

      1. associate-/l* 80.4%

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

      2. associate-/r/ 80.5%

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

      3. unpow2 80.5%

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

   8. Simplified 80.5%

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

   if -3.6000000000000002e-48 < z < 1.7e-23

   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%

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

   4. Taylor expanded in z around 0 96.2%

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

   if 1.7e-23 < z < 6.8000000000000001e114 or 1.94999999999999992e226 < z < 3.5e250

   1. Initial program 95.0%

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

      1. sub-neg 95.0%

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

      2. metadata-eval 95.0%

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

      3. fma-def 95.0%

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

      4. fma-neg 95.0%

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

      5. metadata-eval 95.0%

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

   3. Simplified 95.0%

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

      1. metadata-eval 95.0%

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

      2. fma-neg 95.0%

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

      3. fma-def 95.0%

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

      4. clear-num 94.9%

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

      5. inv-pow 94.9%

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

      6. *-commutative 94.9%

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

      7. fma-udef 95.0%

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

      8. fma-neg 95.0%

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

      9. metadata-eval 95.0%

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

   5. Applied egg-rr 95.0%

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

   6. Taylor expanded in y around inf 81.6%

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

      1. associate-/l* 86.3%

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

      2. associate-/r/ 84.1%

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

      3. unpow2 84.1%

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

   8. Simplified 84.1%

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

   9. Taylor expanded in x around inf 84.2%

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

       1. *-commutative 35.4%

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

       2. sub-neg 35.4%

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

       3. mul-1-neg 35.4%

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

       4. log-rec 35.4%

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

       5. remove-double-neg 35.4%

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

       6. metadata-eval 35.4%

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

   11. Simplified 84.2%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+138}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(0.0007936500793651 \cdot z\right) \cdot \frac{z}{x}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-48}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot z\right) \cdot \frac{y}{x}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-23}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+114} \lor \neg \left(z \leq 1.95 \cdot 10^{+226}\right) \land z \leq 3.5 \cdot 10^{+250}:\\ \;\;\;\;\left(z \cdot z\right) \cdot \frac{y}{x} + x \cdot \left(\log x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(0.0007936500793651 \cdot z\right) \cdot \frac{z}{x}\\ \end{array} \]

Alternative 4: 81.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\\ t_1 := t_0 + \left(0.0007936500793651 \cdot z\right) \cdot \frac{z}{x}\\ t_2 := \left(z \cdot z\right) \cdot \frac{y}{x}\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-48}:\\ \;\;\;\;t_0 + t_2\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-24}:\\ \;\;\;\;t_0 + \frac{0.083333333333333}{x}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+113}:\\ \;\;\;\;t_0 + \frac{y}{\frac{x}{z \cdot z}}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+226} \lor \neg \left(z \leq 3.8 \cdot 10^{+251}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2 + x \cdot \left(\log x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (- (* (+ x -0.5) (log x)) x) 0.91893853320467))
        (t_1 (+ t_0 (* (* 0.0007936500793651 z) (/ z x))))
        (t_2 (* (* z z) (/ y x))))
   (if (<= z -7.5e+138)
     t_1
     (if (<= z -3.2e-48)
       (+ t_0 t_2)
       (if (<= z 3.2e-24)
         (+ t_0 (/ 0.083333333333333 x))
         (if (<= z 2e+113)
           (+ t_0 (/ y (/ x (* z z))))
           (if (or (<= z 1.4e+226) (not (<= z 3.8e+251)))
             t_1
             (+ t_2 (* x (+ (log x) -1.0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = (((x + -0.5) * log(x)) - x) + 0.91893853320467;
	double t_1 = t_0 + ((0.0007936500793651 * z) * (z / x));
	double t_2 = (z * z) * (y / x);
	double tmp;
	if (z <= -7.5e+138) {
		tmp = t_1;
	} else if (z <= -3.2e-48) {
		tmp = t_0 + t_2;
	} else if (z <= 3.2e-24) {
		tmp = t_0 + (0.083333333333333 / x);
	} else if (z <= 2e+113) {
		tmp = t_0 + (y / (x / (z * z)));
	} else if ((z <= 1.4e+226) || !(z <= 3.8e+251)) {
		tmp = t_1;
	} else {
		tmp = t_2 + (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) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (((x + (-0.5d0)) * log(x)) - x) + 0.91893853320467d0
    t_1 = t_0 + ((0.0007936500793651d0 * z) * (z / x))
    t_2 = (z * z) * (y / x)
    if (z <= (-7.5d+138)) then
        tmp = t_1
    else if (z <= (-3.2d-48)) then
        tmp = t_0 + t_2
    else if (z <= 3.2d-24) then
        tmp = t_0 + (0.083333333333333d0 / x)
    else if (z <= 2d+113) then
        tmp = t_0 + (y / (x / (z * z)))
    else if ((z <= 1.4d+226) .or. (.not. (z <= 3.8d+251))) then
        tmp = t_1
    else
        tmp = t_2 + (x * (log(x) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (((x + -0.5) * Math.log(x)) - x) + 0.91893853320467;
	double t_1 = t_0 + ((0.0007936500793651 * z) * (z / x));
	double t_2 = (z * z) * (y / x);
	double tmp;
	if (z <= -7.5e+138) {
		tmp = t_1;
	} else if (z <= -3.2e-48) {
		tmp = t_0 + t_2;
	} else if (z <= 3.2e-24) {
		tmp = t_0 + (0.083333333333333 / x);
	} else if (z <= 2e+113) {
		tmp = t_0 + (y / (x / (z * z)));
	} else if ((z <= 1.4e+226) || !(z <= 3.8e+251)) {
		tmp = t_1;
	} else {
		tmp = t_2 + (x * (Math.log(x) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (((x + -0.5) * math.log(x)) - x) + 0.91893853320467
	t_1 = t_0 + ((0.0007936500793651 * z) * (z / x))
	t_2 = (z * z) * (y / x)
	tmp = 0
	if z <= -7.5e+138:
		tmp = t_1
	elif z <= -3.2e-48:
		tmp = t_0 + t_2
	elif z <= 3.2e-24:
		tmp = t_0 + (0.083333333333333 / x)
	elif z <= 2e+113:
		tmp = t_0 + (y / (x / (z * z)))
	elif (z <= 1.4e+226) or not (z <= 3.8e+251):
		tmp = t_1
	else:
		tmp = t_2 + (x * (math.log(x) + -1.0))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(x + -0.5) * log(x)) - x) + 0.91893853320467)
	t_1 = Float64(t_0 + Float64(Float64(0.0007936500793651 * z) * Float64(z / x)))
	t_2 = Float64(Float64(z * z) * Float64(y / x))
	tmp = 0.0
	if (z <= -7.5e+138)
		tmp = t_1;
	elseif (z <= -3.2e-48)
		tmp = Float64(t_0 + t_2);
	elseif (z <= 3.2e-24)
		tmp = Float64(t_0 + Float64(0.083333333333333 / x));
	elseif (z <= 2e+113)
		tmp = Float64(t_0 + Float64(y / Float64(x / Float64(z * z))));
	elseif ((z <= 1.4e+226) || !(z <= 3.8e+251))
		tmp = t_1;
	else
		tmp = Float64(t_2 + Float64(x * Float64(log(x) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (((x + -0.5) * log(x)) - x) + 0.91893853320467;
	t_1 = t_0 + ((0.0007936500793651 * z) * (z / x));
	t_2 = (z * z) * (y / x);
	tmp = 0.0;
	if (z <= -7.5e+138)
		tmp = t_1;
	elseif (z <= -3.2e-48)
		tmp = t_0 + t_2;
	elseif (z <= 3.2e-24)
		tmp = t_0 + (0.083333333333333 / x);
	elseif (z <= 2e+113)
		tmp = t_0 + (y / (x / (z * z)));
	elseif ((z <= 1.4e+226) || ~((z <= 3.8e+251)))
		tmp = t_1;
	else
		tmp = t_2 + (x * (log(x) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(N[(0.0007936500793651 * z), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * z), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e+138], t$95$1, If[LessEqual[z, -3.2e-48], N[(t$95$0 + t$95$2), $MachinePrecision], If[LessEqual[z, 3.2e-24], N[(t$95$0 + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+113], N[(t$95$0 + N[(y / N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.4e+226], N[Not[LessEqual[z, 3.8e+251]], $MachinePrecision]], t$95$1, N[(t$95$2 + N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.4999999999999999e138 or 2e113 < z < 1.4000000000000001e226 or 3.79999999999999983e251 < z

   1. Initial program 88.0%

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

      1. sub-neg 88.0%

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

      2. metadata-eval 88.0%

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

      3. fma-def 88.0%

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

      4. fma-neg 88.0%

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

      5. metadata-eval 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in y around 0 77.1%

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

   5. Taylor expanded in z around inf 77.1%

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

      1. unpow2 77.1%

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

   7. Simplified 77.1%

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

   8. Taylor expanded in z around 0 77.1%

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

      1. *-commutative 77.1%

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

      2. unpow2 77.1%

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

      3. associate-*l/ 81.6%

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

      4. associate-*l* 81.7%

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

   10. Simplified 81.7%

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

   if -7.4999999999999999e138 < z < -3.1999999999999998e-48

   1. Initial program 96.7%

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

      1. sub-neg 96.7%

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

      2. metadata-eval 96.7%

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

      3. fma-def 96.7%

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

      4. fma-neg 96.7%

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

      5. metadata-eval 96.7%

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

   3. Simplified 96.7%

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

      1. metadata-eval 96.7%

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

      2. fma-neg 96.7%

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

      3. fma-def 96.7%

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

      4. clear-num 96.7%

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

      5. inv-pow 96.7%

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

      6. *-commutative 96.7%

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

      7. fma-udef 96.7%

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

      8. fma-neg 96.7%

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

      9. metadata-eval 96.7%

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

   5. Applied egg-rr 96.7%

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

   6. Taylor expanded in y around inf 77.4%

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

      1. associate-/l* 80.4%

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

      2. associate-/r/ 80.5%

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

      3. unpow2 80.5%

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

   8. Simplified 80.5%

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

   if -3.1999999999999998e-48 < z < 3.20000000000000012e-24

   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%

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

   4. Taylor expanded in z around 0 96.2%

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

   if 3.20000000000000012e-24 < z < 2e113

   1. Initial program 94.0%

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

      1. sub-neg 94.0%

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

      2. metadata-eval 94.0%

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

      3. fma-def 94.0%

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

      4. fma-neg 94.0%

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

      5. metadata-eval 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in y around inf 77.8%

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

      1. associate-/l* 83.5%

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

      2. unpow2 83.5%

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

   6. Simplified 83.5%

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

   if 1.4000000000000001e226 < z < 3.79999999999999983e251

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. metadata-eval 100.0%

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

      3. fma-def 100.0%

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

      4. fma-neg 100.0%

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

      5. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. metadata-eval 100.0%

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

      2. fma-neg 100.0%

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

      3. fma-def 100.0%

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

      4. clear-num 100.0%

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

      5. inv-pow 100.0%

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

      6. *-commutative 100.0%

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

      7. fma-udef 100.0%

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

      8. fma-neg 100.0%

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

      9. metadata-eval 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around inf 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate-/r/ 100.0%

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

      3. unpow2 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in x around inf 100.0%

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

       1. *-commutative 1.2%

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

       2. sub-neg 1.2%

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

       3. mul-1-neg 1.2%

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

       4. log-rec 1.2%

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

       5. remove-double-neg 1.2%

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

       6. metadata-eval 1.2%

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

   11. Simplified 100.0%

       \[\leadsto \color{blue}{x \cdot \left(\log x + -1\right)} + \frac{y}{x} \cdot \left(z \cdot z\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+138}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(0.0007936500793651 \cdot z\right) \cdot \frac{z}{x}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-48}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot z\right) \cdot \frac{y}{x}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-24}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+113}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{y}{\frac{x}{z \cdot z}}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+226} \lor \neg \left(z \leq 3.8 \cdot 10^{+251}\right):\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(0.0007936500793651 \cdot z\right) \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot z\right) \cdot \frac{y}{x} + x \cdot \left(\log x + -1\right)\\ \end{array} \]

Alternative 5: 79.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z \cdot z\right) \cdot \frac{y}{x} + x \cdot \left(\log x + -1\right)\\ t_1 := \left(x \cdot \log x - x\right) + 0.0007936500793651 \cdot \frac{z \cdot z}{x}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-22}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-22}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+115} \lor \neg \left(z \leq 1.12 \cdot 10^{+226}\right) \land z \leq 1.4 \cdot 10^{+251}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* (* z z) (/ y x)) (* x (+ (log x) -1.0))))
        (t_1 (+ (- (* x (log x)) x) (* 0.0007936500793651 (/ (* z z) x)))))
   (if (<= z -1.2e+138)
     t_1
     (if (<= z -3.5e-22)
       t_0
       (if (<= z 1.45e-22)
         (+
          (+ (- (* (+ x -0.5) (log x)) x) 0.91893853320467)
          (/ 0.083333333333333 x))
         (if (or (<= z 1.05e+115) (and (not (<= z 1.12e+226)) (<= z 1.4e+251)))
           t_0
           t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = ((z * z) * (y / x)) + (x * (log(x) + -1.0));
	double t_1 = ((x * log(x)) - x) + (0.0007936500793651 * ((z * z) / x));
	double tmp;
	if (z <= -1.2e+138) {
		tmp = t_1;
	} else if (z <= -3.5e-22) {
		tmp = t_0;
	} else if (z <= 1.45e-22) {
		tmp = ((((x + -0.5) * log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	} else if ((z <= 1.05e+115) || (!(z <= 1.12e+226) && (z <= 1.4e+251))) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ((z * z) * (y / x)) + (x * (log(x) + (-1.0d0)))
    t_1 = ((x * log(x)) - x) + (0.0007936500793651d0 * ((z * z) / x))
    if (z <= (-1.2d+138)) then
        tmp = t_1
    else if (z <= (-3.5d-22)) then
        tmp = t_0
    else if (z <= 1.45d-22) then
        tmp = ((((x + (-0.5d0)) * log(x)) - x) + 0.91893853320467d0) + (0.083333333333333d0 / x)
    else if ((z <= 1.05d+115) .or. (.not. (z <= 1.12d+226)) .and. (z <= 1.4d+251)) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((z * z) * (y / x)) + (x * (Math.log(x) + -1.0));
	double t_1 = ((x * Math.log(x)) - x) + (0.0007936500793651 * ((z * z) / x));
	double tmp;
	if (z <= -1.2e+138) {
		tmp = t_1;
	} else if (z <= -3.5e-22) {
		tmp = t_0;
	} else if (z <= 1.45e-22) {
		tmp = ((((x + -0.5) * Math.log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	} else if ((z <= 1.05e+115) || (!(z <= 1.12e+226) && (z <= 1.4e+251))) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((z * z) * (y / x)) + (x * (math.log(x) + -1.0))
	t_1 = ((x * math.log(x)) - x) + (0.0007936500793651 * ((z * z) / x))
	tmp = 0
	if z <= -1.2e+138:
		tmp = t_1
	elif z <= -3.5e-22:
		tmp = t_0
	elif z <= 1.45e-22:
		tmp = ((((x + -0.5) * math.log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x)
	elif (z <= 1.05e+115) or (not (z <= 1.12e+226) and (z <= 1.4e+251)):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(z * z) * Float64(y / x)) + Float64(x * Float64(log(x) + -1.0)))
	t_1 = Float64(Float64(Float64(x * log(x)) - x) + Float64(0.0007936500793651 * Float64(Float64(z * z) / x)))
	tmp = 0.0
	if (z <= -1.2e+138)
		tmp = t_1;
	elseif (z <= -3.5e-22)
		tmp = t_0;
	elseif (z <= 1.45e-22)
		tmp = Float64(Float64(Float64(Float64(Float64(x + -0.5) * log(x)) - x) + 0.91893853320467) + Float64(0.083333333333333 / x));
	elseif ((z <= 1.05e+115) || (!(z <= 1.12e+226) && (z <= 1.4e+251)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((z * z) * (y / x)) + (x * (log(x) + -1.0));
	t_1 = ((x * log(x)) - x) + (0.0007936500793651 * ((z * z) / x));
	tmp = 0.0;
	if (z <= -1.2e+138)
		tmp = t_1;
	elseif (z <= -3.5e-22)
		tmp = t_0;
	elseif (z <= 1.45e-22)
		tmp = ((((x + -0.5) * log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	elseif ((z <= 1.05e+115) || (~((z <= 1.12e+226)) && (z <= 1.4e+251)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(z * z), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + N[(0.0007936500793651 * N[(N[(z * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e+138], t$95$1, If[LessEqual[z, -3.5e-22], t$95$0, If[LessEqual[z, 1.45e-22], N[(N[(N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.05e+115], And[N[Not[LessEqual[z, 1.12e+226]], $MachinePrecision], LessEqual[z, 1.4e+251]]], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2e138 or 1.05000000000000002e115 < z < 1.12e226 or 1.4e251 < z

   1. Initial program 88.0%

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

      1. sub-neg 88.0%

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

      2. metadata-eval 88.0%

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

      3. fma-def 88.0%

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

      4. fma-neg 88.0%

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

      5. metadata-eval 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in y around 0 77.1%

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

   5. Taylor expanded in z around inf 77.1%

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

      1. unpow2 77.1%

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

   7. Simplified 77.1%

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

   8. Taylor expanded in x around inf 77.1%

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

      1. *-commutative 77.1%

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

      2. sub-neg 77.1%

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

      3. mul-1-neg 77.1%

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

      4. log-rec 77.1%

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

      5. remove-double-neg 77.1%

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

      6. metadata-eval 77.1%

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

      7. distribute-rgt-in 77.1%

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

      8. neg-mul-1 77.1%

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

      9. sub-neg 77.1%

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

      10. *-commutative 77.1%

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

   10. Simplified 77.1%

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

   if -1.2e138 < z < -3.50000000000000005e-22 or 1.4500000000000001e-22 < z < 1.05000000000000002e115 or 1.12e226 < z < 1.4e251

   1. Initial program 95.5%

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

      1. sub-neg 95.5%

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

      2. metadata-eval 95.5%

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

      3. fma-def 95.5%

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

      4. fma-neg 95.5%

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

      5. metadata-eval 95.5%

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

   3. Simplified 95.5%

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

      1. metadata-eval 95.5%

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

      2. fma-neg 95.5%

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

      3. fma-def 95.5%

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

      4. clear-num 95.4%

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

      5. inv-pow 95.4%

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

      6. *-commutative 95.4%

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

      7. fma-udef 95.5%

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

      8. fma-neg 95.5%

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

      9. metadata-eval 95.5%

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

   5. Applied egg-rr 95.5%

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

   6. Taylor expanded in y around inf 81.3%

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

      1. associate-/l* 85.5%

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

      2. associate-/r/ 84.2%

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

      3. unpow2 84.2%

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

   8. Simplified 84.2%

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

   9. Taylor expanded in x around inf 84.3%

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

       1. *-commutative 35.0%

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

       2. sub-neg 35.0%

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

       3. mul-1-neg 35.0%

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

       4. log-rec 35.0%

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

       5. remove-double-neg 35.0%

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

       6. metadata-eval 35.0%

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

   11. Simplified 84.3%

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

   if -3.50000000000000005e-22 < z < 1.4500000000000001e-22

   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%

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

   4. Taylor expanded in z around 0 94.6%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+138}:\\ \;\;\;\;\left(x \cdot \log x - x\right) + 0.0007936500793651 \cdot \frac{z \cdot z}{x}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-22}:\\ \;\;\;\;\left(z \cdot z\right) \cdot \frac{y}{x} + x \cdot \left(\log x + -1\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-22}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+115} \lor \neg \left(z \leq 1.12 \cdot 10^{+226}\right) \land z \leq 1.4 \cdot 10^{+251}:\\ \;\;\;\;\left(z \cdot z\right) \cdot \frac{y}{x} + x \cdot \left(\log x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log x - x\right) + 0.0007936500793651 \cdot \frac{z \cdot z}{x}\\ \end{array} \]

Alternative 6: 79.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\\ t_1 := \left(x \cdot \log x - x\right) + 0.0007936500793651 \cdot \frac{z \cdot z}{x}\\ t_2 := \left(z \cdot z\right) \cdot \frac{y}{x}\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-46}:\\ \;\;\;\;t_0 + t_2\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-21}:\\ \;\;\;\;t_0 + \frac{0.083333333333333}{x}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+114} \lor \neg \left(z \leq 2 \cdot 10^{+226}\right) \land z \leq 1.7 \cdot 10^{+250}:\\ \;\;\;\;t_2 + x \cdot \left(\log x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (- (* (+ x -0.5) (log x)) x) 0.91893853320467))
        (t_1 (+ (- (* x (log x)) x) (* 0.0007936500793651 (/ (* z z) x))))
        (t_2 (* (* z z) (/ y x))))
   (if (<= z -5.5e+138)
     t_1
     (if (<= z -6e-46)
       (+ t_0 t_2)
       (if (<= z 1.2e-21)
         (+ t_0 (/ 0.083333333333333 x))
         (if (or (<= z 3.1e+114) (and (not (<= z 2e+226)) (<= z 1.7e+250)))
           (+ t_2 (* x (+ (log x) -1.0)))
           t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = (((x + -0.5) * log(x)) - x) + 0.91893853320467;
	double t_1 = ((x * log(x)) - x) + (0.0007936500793651 * ((z * z) / x));
	double t_2 = (z * z) * (y / x);
	double tmp;
	if (z <= -5.5e+138) {
		tmp = t_1;
	} else if (z <= -6e-46) {
		tmp = t_0 + t_2;
	} else if (z <= 1.2e-21) {
		tmp = t_0 + (0.083333333333333 / x);
	} else if ((z <= 3.1e+114) || (!(z <= 2e+226) && (z <= 1.7e+250))) {
		tmp = t_2 + (x * (log(x) + -1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (((x + (-0.5d0)) * log(x)) - x) + 0.91893853320467d0
    t_1 = ((x * log(x)) - x) + (0.0007936500793651d0 * ((z * z) / x))
    t_2 = (z * z) * (y / x)
    if (z <= (-5.5d+138)) then
        tmp = t_1
    else if (z <= (-6d-46)) then
        tmp = t_0 + t_2
    else if (z <= 1.2d-21) then
        tmp = t_0 + (0.083333333333333d0 / x)
    else if ((z <= 3.1d+114) .or. (.not. (z <= 2d+226)) .and. (z <= 1.7d+250)) then
        tmp = t_2 + (x * (log(x) + (-1.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (((x + -0.5) * Math.log(x)) - x) + 0.91893853320467;
	double t_1 = ((x * Math.log(x)) - x) + (0.0007936500793651 * ((z * z) / x));
	double t_2 = (z * z) * (y / x);
	double tmp;
	if (z <= -5.5e+138) {
		tmp = t_1;
	} else if (z <= -6e-46) {
		tmp = t_0 + t_2;
	} else if (z <= 1.2e-21) {
		tmp = t_0 + (0.083333333333333 / x);
	} else if ((z <= 3.1e+114) || (!(z <= 2e+226) && (z <= 1.7e+250))) {
		tmp = t_2 + (x * (Math.log(x) + -1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (((x + -0.5) * math.log(x)) - x) + 0.91893853320467
	t_1 = ((x * math.log(x)) - x) + (0.0007936500793651 * ((z * z) / x))
	t_2 = (z * z) * (y / x)
	tmp = 0
	if z <= -5.5e+138:
		tmp = t_1
	elif z <= -6e-46:
		tmp = t_0 + t_2
	elif z <= 1.2e-21:
		tmp = t_0 + (0.083333333333333 / x)
	elif (z <= 3.1e+114) or (not (z <= 2e+226) and (z <= 1.7e+250)):
		tmp = t_2 + (x * (math.log(x) + -1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(x + -0.5) * log(x)) - x) + 0.91893853320467)
	t_1 = Float64(Float64(Float64(x * log(x)) - x) + Float64(0.0007936500793651 * Float64(Float64(z * z) / x)))
	t_2 = Float64(Float64(z * z) * Float64(y / x))
	tmp = 0.0
	if (z <= -5.5e+138)
		tmp = t_1;
	elseif (z <= -6e-46)
		tmp = Float64(t_0 + t_2);
	elseif (z <= 1.2e-21)
		tmp = Float64(t_0 + Float64(0.083333333333333 / x));
	elseif ((z <= 3.1e+114) || (!(z <= 2e+226) && (z <= 1.7e+250)))
		tmp = Float64(t_2 + Float64(x * Float64(log(x) + -1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (((x + -0.5) * log(x)) - x) + 0.91893853320467;
	t_1 = ((x * log(x)) - x) + (0.0007936500793651 * ((z * z) / x));
	t_2 = (z * z) * (y / x);
	tmp = 0.0;
	if (z <= -5.5e+138)
		tmp = t_1;
	elseif (z <= -6e-46)
		tmp = t_0 + t_2;
	elseif (z <= 1.2e-21)
		tmp = t_0 + (0.083333333333333 / x);
	elseif ((z <= 3.1e+114) || (~((z <= 2e+226)) && (z <= 1.7e+250)))
		tmp = t_2 + (x * (log(x) + -1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + N[(0.0007936500793651 * N[(N[(z * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * z), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.5e+138], t$95$1, If[LessEqual[z, -6e-46], N[(t$95$0 + t$95$2), $MachinePrecision], If[LessEqual[z, 1.2e-21], N[(t$95$0 + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 3.1e+114], And[N[Not[LessEqual[z, 2e+226]], $MachinePrecision], LessEqual[z, 1.7e+250]]], N[(t$95$2 + N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.4999999999999999e138 or 3.1e114 < z < 1.99999999999999992e226 or 1.69999999999999987e250 < z

   1. Initial program 88.0%

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

      1. sub-neg 88.0%

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

      2. metadata-eval 88.0%

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

      3. fma-def 88.0%

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

      4. fma-neg 88.0%

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

      5. metadata-eval 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in y around 0 77.1%

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

   5. Taylor expanded in z around inf 77.1%

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

      1. unpow2 77.1%

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

   7. Simplified 77.1%

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

   8. Taylor expanded in x around inf 77.1%

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

      1. *-commutative 77.1%

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

      2. sub-neg 77.1%

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

      3. mul-1-neg 77.1%

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

      4. log-rec 77.1%

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

      5. remove-double-neg 77.1%

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

      6. metadata-eval 77.1%

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

      7. distribute-rgt-in 77.1%

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

      8. neg-mul-1 77.1%

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

      9. sub-neg 77.1%

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

      10. *-commutative 77.1%

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

   10. Simplified 77.1%

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

   if -5.4999999999999999e138 < z < -5.99999999999999975e-46

   1. Initial program 96.7%

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

      1. sub-neg 96.7%

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

      2. metadata-eval 96.7%

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

      3. fma-def 96.7%

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

      4. fma-neg 96.7%

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

      5. metadata-eval 96.7%

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

   3. Simplified 96.7%

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

      1. metadata-eval 96.7%

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

      2. fma-neg 96.7%

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

      3. fma-def 96.7%

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

      4. clear-num 96.7%

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

      5. inv-pow 96.7%

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

      6. *-commutative 96.7%

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

      7. fma-udef 96.7%

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

      8. fma-neg 96.7%

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

      9. metadata-eval 96.7%

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

   5. Applied egg-rr 96.7%

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

   6. Taylor expanded in y around inf 77.4%

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

      1. associate-/l* 80.4%

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

      2. associate-/r/ 80.5%

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

      3. unpow2 80.5%

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

   8. Simplified 80.5%

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

   if -5.99999999999999975e-46 < z < 1.2e-21

   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%

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

   4. Taylor expanded in z around 0 96.2%

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

   if 1.2e-21 < z < 3.1e114 or 1.99999999999999992e226 < z < 1.69999999999999987e250

   1. Initial program 95.0%

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

      1. sub-neg 95.0%

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

      2. metadata-eval 95.0%

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

      3. fma-def 95.0%

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

      4. fma-neg 95.0%

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

      5. metadata-eval 95.0%

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

   3. Simplified 95.0%

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

      1. metadata-eval 95.0%

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

      2. fma-neg 95.0%

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

      3. fma-def 95.0%

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

      4. clear-num 94.9%

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

      5. inv-pow 94.9%

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

      6. *-commutative 94.9%

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

      7. fma-udef 95.0%

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

      8. fma-neg 95.0%

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

      9. metadata-eval 95.0%

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

   5. Applied egg-rr 95.0%

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

   6. Taylor expanded in y around inf 81.6%

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

      1. associate-/l* 86.3%

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

      2. associate-/r/ 84.1%

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

      3. unpow2 84.1%

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

   8. Simplified 84.1%

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

   9. Taylor expanded in x around inf 84.2%

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

       1. *-commutative 35.4%

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

       2. sub-neg 35.4%

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

       3. mul-1-neg 35.4%

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

       4. log-rec 35.4%

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

       5. remove-double-neg 35.4%

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

       6. metadata-eval 35.4%

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

   11. Simplified 84.2%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+138}:\\ \;\;\;\;\left(x \cdot \log x - x\right) + 0.0007936500793651 \cdot \frac{z \cdot z}{x}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-46}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot z\right) \cdot \frac{y}{x}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-21}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+114} \lor \neg \left(z \leq 2 \cdot 10^{+226}\right) \land z \leq 1.7 \cdot 10^{+250}:\\ \;\;\;\;\left(z \cdot z\right) \cdot \frac{y}{x} + x \cdot \left(\log x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log x - x\right) + 0.0007936500793651 \cdot \frac{z \cdot z}{x}\\ \end{array} \]

Alternative 7: 94.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{-46} \lor \neg \left(z \leq 6.5 \cdot 10^{-21}\right):\\ \;\;\;\;t_0 + \frac{1}{\frac{\frac{x}{z}}{z \cdot \left(y + 0.0007936500793651\right)}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (- (* (+ x -0.5) (log x)) x) 0.91893853320467)))
   (if (or (<= z -6.2e-46) (not (<= z 6.5e-21)))
     (+ t_0 (/ 1.0 (/ (/ x z) (* z (+ y 0.0007936500793651)))))
     (+ t_0 (/ 0.083333333333333 x)))))

C

double code(double x, double y, double z) {
	double t_0 = (((x + -0.5) * log(x)) - x) + 0.91893853320467;
	double tmp;
	if ((z <= -6.2e-46) || !(z <= 6.5e-21)) {
		tmp = t_0 + (1.0 / ((x / z) / (z * (y + 0.0007936500793651))));
	} else {
		tmp = t_0 + (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 + (-0.5d0)) * log(x)) - x) + 0.91893853320467d0
    if ((z <= (-6.2d-46)) .or. (.not. (z <= 6.5d-21))) then
        tmp = t_0 + (1.0d0 / ((x / z) / (z * (y + 0.0007936500793651d0))))
    else
        tmp = t_0 + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (((x + -0.5) * Math.log(x)) - x) + 0.91893853320467;
	double tmp;
	if ((z <= -6.2e-46) || !(z <= 6.5e-21)) {
		tmp = t_0 + (1.0 / ((x / z) / (z * (y + 0.0007936500793651))));
	} else {
		tmp = t_0 + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (((x + -0.5) * math.log(x)) - x) + 0.91893853320467
	tmp = 0
	if (z <= -6.2e-46) or not (z <= 6.5e-21):
		tmp = t_0 + (1.0 / ((x / z) / (z * (y + 0.0007936500793651))))
	else:
		tmp = t_0 + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(x + -0.5) * log(x)) - x) + 0.91893853320467)
	tmp = 0.0
	if ((z <= -6.2e-46) || !(z <= 6.5e-21))
		tmp = Float64(t_0 + Float64(1.0 / Float64(Float64(x / z) / Float64(z * Float64(y + 0.0007936500793651)))));
	else
		tmp = Float64(t_0 + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (((x + -0.5) * log(x)) - x) + 0.91893853320467;
	tmp = 0.0;
	if ((z <= -6.2e-46) || ~((z <= 6.5e-21)))
		tmp = t_0 + (1.0 / ((x / z) / (z * (y + 0.0007936500793651))));
	else
		tmp = t_0 + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision]}, If[Or[LessEqual[z, -6.2e-46], N[Not[LessEqual[z, 6.5e-21]], $MachinePrecision]], N[(t$95$0 + N[(1.0 / N[(N[(x / z), $MachinePrecision] / N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.2000000000000002e-46 or 6.49999999999999987e-21 < z

   1. Initial program 91.6%

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

      1. sub-neg 91.6%

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

      2. metadata-eval 91.6%

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

      3. fma-def 91.6%

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

      4. fma-neg 91.6%

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

      5. metadata-eval 91.6%

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

   3. Simplified 91.6%

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

      1. metadata-eval 91.6%

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

      2. fma-neg 91.6%

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

      3. fma-def 91.6%

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

      4. clear-num 91.6%

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

      5. inv-pow 91.6%

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

      6. *-commutative 91.6%

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

      7. fma-udef 91.6%

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

      8. fma-neg 91.6%

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

      9. metadata-eval 91.6%

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

   5. Applied egg-rr 91.6%

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

   6. Taylor expanded in z around inf 89.7%

      \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + {\color{blue}{\left(\frac{x}{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}\right)}}^{-1} \]
   7. Step-by-step derivation

      1. associate-/r* 92.3%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + {\color{blue}{\left(\frac{\frac{x}{{z}^{2}}}{0.0007936500793651 + y}\right)}}^{-1} \]

      2. unpow2 92.3%

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

      3. associate-/r* 97.9%

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

   8. Simplified 97.9%

      \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + {\color{blue}{\left(\frac{\frac{\frac{x}{z}}{z}}{0.0007936500793651 + y}\right)}}^{-1} \]
   9. Step-by-step derivation

      1. unpow-1 97.9%

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

      2. associate-/l/ 96.0%

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

      3. +-commutative 96.0%

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

   10. Applied egg-rr 96.0%

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

   if -6.2000000000000002e-46 < z < 6.49999999999999987e-21

   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%

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

   4. Taylor expanded in z around 0 96.2%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-46} \lor \neg \left(z \leq 6.5 \cdot 10^{-21}\right):\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{1}{\frac{\frac{x}{z}}{z \cdot \left(y + 0.0007936500793651\right)}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 8: 98.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(y + 0.0007936500793651\right)\\ \mathbf{if}\;x \leq 900:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333 + z \cdot \left(t_0 - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{1}{\frac{\frac{x}{z}}{t_0}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (+ y 0.0007936500793651))))
   (if (<= x 900.0)
     (+
      (+ 0.91893853320467 (- (* (log x) (- x 0.5)) x))
      (/ (+ 0.083333333333333 (* z (- t_0 0.0027777777777778))) x))
     (+
      (+ (- (* (+ x -0.5) (log x)) x) 0.91893853320467)
      (/ 1.0 (/ (/ x z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (y + 0.0007936500793651);
	double tmp;
	if (x <= 900.0) {
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + ((0.083333333333333 + (z * (t_0 - 0.0027777777777778))) / x);
	} else {
		tmp = ((((x + -0.5) * log(x)) - x) + 0.91893853320467) + (1.0 / ((x / z) / t_0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * (y + 0.0007936500793651d0)
    if (x <= 900.0d0) then
        tmp = (0.91893853320467d0 + ((log(x) * (x - 0.5d0)) - x)) + ((0.083333333333333d0 + (z * (t_0 - 0.0027777777777778d0))) / x)
    else
        tmp = ((((x + (-0.5d0)) * log(x)) - x) + 0.91893853320467d0) + (1.0d0 / ((x / z) / t_0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (y + 0.0007936500793651);
	double tmp;
	if (x <= 900.0) {
		tmp = (0.91893853320467 + ((Math.log(x) * (x - 0.5)) - x)) + ((0.083333333333333 + (z * (t_0 - 0.0027777777777778))) / x);
	} else {
		tmp = ((((x + -0.5) * Math.log(x)) - x) + 0.91893853320467) + (1.0 / ((x / z) / t_0));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (y + 0.0007936500793651)
	tmp = 0
	if x <= 900.0:
		tmp = (0.91893853320467 + ((math.log(x) * (x - 0.5)) - x)) + ((0.083333333333333 + (z * (t_0 - 0.0027777777777778))) / x)
	else:
		tmp = ((((x + -0.5) * math.log(x)) - x) + 0.91893853320467) + (1.0 / ((x / z) / t_0))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(y + 0.0007936500793651))
	tmp = 0.0
	if (x <= 900.0)
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(log(x) * Float64(x - 0.5)) - x)) + Float64(Float64(0.083333333333333 + Float64(z * Float64(t_0 - 0.0027777777777778))) / x));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(x + -0.5) * log(x)) - x) + 0.91893853320467) + Float64(1.0 / Float64(Float64(x / z) / t_0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (y + 0.0007936500793651);
	tmp = 0.0;
	if (x <= 900.0)
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + ((0.083333333333333 + (z * (t_0 - 0.0027777777777778))) / x);
	else
		tmp = ((((x + -0.5) * log(x)) - x) + 0.91893853320467) + (1.0 / ((x / z) / t_0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 900.0], N[(N[(0.91893853320467 + N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(N[(0.083333333333333 + N[(z * N[(t$95$0 - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(1.0 / N[(N[(x / z), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 900

   1. Initial program 99.7%

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

   if 900 < x

   1. Initial program 89.3%

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

      1. sub-neg 89.3%

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

      2. metadata-eval 89.3%

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

      3. fma-def 89.3%

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

      4. fma-neg 89.3%

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

      5. metadata-eval 89.3%

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

   3. Simplified 89.3%

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

      1. metadata-eval 89.3%

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

      2. fma-neg 89.3%

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

      3. fma-def 89.3%

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

      4. clear-num 89.3%

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

      5. inv-pow 89.3%

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

      6. *-commutative 89.3%

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

      7. fma-udef 89.3%

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

      8. fma-neg 89.3%

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

      9. metadata-eval 89.3%

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

   5. Applied egg-rr 89.3%

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

   6. Taylor expanded in z around inf 89.3%

      \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + {\color{blue}{\left(\frac{x}{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}\right)}}^{-1} \]
   7. Step-by-step derivation

      1. associate-/r* 92.5%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + {\color{blue}{\left(\frac{\frac{x}{{z}^{2}}}{0.0007936500793651 + y}\right)}}^{-1} \]

      2. unpow2 92.5%

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

      3. associate-/r* 99.6%

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

   8. Simplified 99.6%

      \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + {\color{blue}{\left(\frac{\frac{\frac{x}{z}}{z}}{0.0007936500793651 + y}\right)}}^{-1} \]
   9. Step-by-step derivation

      1. unpow-1 99.6%

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

      2. associate-/l/ 97.2%

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

      3. +-commutative 97.2%

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

   10. Applied egg-rr 97.2%

       \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{1}{\frac{\frac{x}{z}}{\left(y + 0.0007936500793651\right) \cdot z}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 900:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{1}{\frac{\frac{x}{z}}{z \cdot \left(y + 0.0007936500793651\right)}}\\ \end{array} \]

Alternative 9: 91.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{-46} \lor \neg \left(z \leq 7 \cdot 10^{-28}\right):\\ \;\;\;\;t_0 + \left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (- (* (+ x -0.5) (log x)) x) 0.91893853320467)))
   (if (or (<= z -1.65e-46) (not (<= z 7e-28)))
     (+ t_0 (* (+ y 0.0007936500793651) (/ (* z z) x)))
     (+ t_0 (/ 0.083333333333333 x)))))

C

double code(double x, double y, double z) {
	double t_0 = (((x + -0.5) * log(x)) - x) + 0.91893853320467;
	double tmp;
	if ((z <= -1.65e-46) || !(z <= 7e-28)) {
		tmp = t_0 + ((y + 0.0007936500793651) * ((z * z) / x));
	} else {
		tmp = t_0 + (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 + (-0.5d0)) * log(x)) - x) + 0.91893853320467d0
    if ((z <= (-1.65d-46)) .or. (.not. (z <= 7d-28))) then
        tmp = t_0 + ((y + 0.0007936500793651d0) * ((z * z) / x))
    else
        tmp = t_0 + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (((x + -0.5) * Math.log(x)) - x) + 0.91893853320467;
	double tmp;
	if ((z <= -1.65e-46) || !(z <= 7e-28)) {
		tmp = t_0 + ((y + 0.0007936500793651) * ((z * z) / x));
	} else {
		tmp = t_0 + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (((x + -0.5) * math.log(x)) - x) + 0.91893853320467
	tmp = 0
	if (z <= -1.65e-46) or not (z <= 7e-28):
		tmp = t_0 + ((y + 0.0007936500793651) * ((z * z) / x))
	else:
		tmp = t_0 + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(x + -0.5) * log(x)) - x) + 0.91893853320467)
	tmp = 0.0
	if ((z <= -1.65e-46) || !(z <= 7e-28))
		tmp = Float64(t_0 + Float64(Float64(y + 0.0007936500793651) * Float64(Float64(z * z) / x)));
	else
		tmp = Float64(t_0 + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (((x + -0.5) * log(x)) - x) + 0.91893853320467;
	tmp = 0.0;
	if ((z <= -1.65e-46) || ~((z <= 7e-28)))
		tmp = t_0 + ((y + 0.0007936500793651) * ((z * z) / x));
	else
		tmp = t_0 + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision]}, If[Or[LessEqual[z, -1.65e-46], N[Not[LessEqual[z, 7e-28]], $MachinePrecision]], N[(t$95$0 + N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(N[(z * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.65000000000000007e-46 or 6.9999999999999999e-28 < z

   1. Initial program 91.6%

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

      1. sub-neg 91.6%

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

      2. metadata-eval 91.6%

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

      3. fma-def 91.6%

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

      4. fma-neg 91.6%

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

      5. metadata-eval 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in z around inf 89.7%

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

      1. associate-/l* 91.4%

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

      2. associate-/r/ 92.3%

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

      3. unpow2 92.3%

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

   6. Simplified 92.3%

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

   if -1.65000000000000007e-46 < z < 6.9999999999999999e-28

   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%

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

   4. Taylor expanded in z around 0 96.2%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-46} \lor \neg \left(z \leq 7 \cdot 10^{-28}\right):\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 10: 86.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+29} \lor \neg \left(y \leq 3.75 \cdot 10^{+180}\right):\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{y}{\frac{x}{z \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log x - x\right) + \frac{0.083333333333333 + z \cdot \left(0.0007936500793651 \cdot z - 0.0027777777777778\right)}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.1e+29) (not (<= y 3.75e+180)))
   (+ (+ (- (* (+ x -0.5) (log x)) x) 0.91893853320467) (/ y (/ x (* z z))))
   (+
    (- (* x (log x)) x)
    (/
     (+
      0.083333333333333
      (* z (- (* 0.0007936500793651 z) 0.0027777777777778)))
     x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.1e+29) || !(y <= 3.75e+180)) {
		tmp = ((((x + -0.5) * log(x)) - x) + 0.91893853320467) + (y / (x / (z * z)));
	} else {
		tmp = ((x * log(x)) - x) + ((0.083333333333333 + (z * ((0.0007936500793651 * z) - 0.0027777777777778))) / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-3.1d+29)) .or. (.not. (y <= 3.75d+180))) then
        tmp = ((((x + (-0.5d0)) * log(x)) - x) + 0.91893853320467d0) + (y / (x / (z * z)))
    else
        tmp = ((x * log(x)) - x) + ((0.083333333333333d0 + (z * ((0.0007936500793651d0 * z) - 0.0027777777777778d0))) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.1e+29) || !(y <= 3.75e+180)) {
		tmp = ((((x + -0.5) * Math.log(x)) - x) + 0.91893853320467) + (y / (x / (z * z)));
	} else {
		tmp = ((x * Math.log(x)) - x) + ((0.083333333333333 + (z * ((0.0007936500793651 * z) - 0.0027777777777778))) / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.1e+29) or not (y <= 3.75e+180):
		tmp = ((((x + -0.5) * math.log(x)) - x) + 0.91893853320467) + (y / (x / (z * z)))
	else:
		tmp = ((x * math.log(x)) - x) + ((0.083333333333333 + (z * ((0.0007936500793651 * z) - 0.0027777777777778))) / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.1e+29) || !(y <= 3.75e+180))
		tmp = Float64(Float64(Float64(Float64(Float64(x + -0.5) * log(x)) - x) + 0.91893853320467) + Float64(y / Float64(x / Float64(z * z))));
	else
		tmp = Float64(Float64(Float64(x * log(x)) - x) + Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(0.0007936500793651 * z) - 0.0027777777777778))) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.1e+29) || ~((y <= 3.75e+180)))
		tmp = ((((x + -0.5) * log(x)) - x) + 0.91893853320467) + (y / (x / (z * z)));
	else
		tmp = ((x * log(x)) - x) + ((0.083333333333333 + (z * ((0.0007936500793651 * z) - 0.0027777777777778))) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.1e+29], N[Not[LessEqual[y, 3.75e+180]], $MachinePrecision]], N[(N[(N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(y / N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + N[(N[(0.083333333333333 + N[(z * N[(N[(0.0007936500793651 * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.0999999999999999e29 or 3.75000000000000015e180 < y

   1. Initial program 92.3%

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

      1. sub-neg 92.3%

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

      2. metadata-eval 92.3%

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

      3. fma-def 92.3%

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

      4. fma-neg 92.3%

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

      5. metadata-eval 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in y around inf 78.0%

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

      1. associate-/l* 82.2%

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

      2. unpow2 82.2%

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

   6. Simplified 82.2%

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

   if -3.0999999999999999e29 < y < 3.75000000000000015e180

   1. Initial program 96.2%

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

      1. sub-neg 96.2%

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

      2. metadata-eval 96.2%

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

      3. fma-def 96.2%

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

      4. fma-neg 96.2%

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

      5. metadata-eval 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in y around 0 92.5%

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

   5. Taylor expanded in x around inf 91.7%

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

      1. *-commutative 64.9%

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

      2. sub-neg 64.9%

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

      3. mul-1-neg 64.9%

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

      4. log-rec 64.9%

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

      5. remove-double-neg 64.9%

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

      6. metadata-eval 64.9%

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

      7. distribute-rgt-in 64.8%

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

      8. neg-mul-1 64.8%

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

      9. sub-neg 64.8%

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

      10. *-commutative 64.8%

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

   7. Simplified 91.6%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+29} \lor \neg \left(y \leq 3.75 \cdot 10^{+180}\right):\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{y}{\frac{x}{z \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log x - x\right) + \frac{0.083333333333333 + z \cdot \left(0.0007936500793651 \cdot z - 0.0027777777777778\right)}{x}\\ \end{array} \]

Alternative 11: 78.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(\log x + -1\right)\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{-25} \lor \neg \left(z \leq 4.7 \cdot 10^{-20}\right):\\ \;\;\;\;\left(z \cdot z\right) \cdot \frac{y}{x} + t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x} + t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ (log x) -1.0))))
   (if (or (<= z -5.6e-25) (not (<= z 4.7e-20)))
     (+ (* (* z z) (/ y x)) t_0)
     (+ (/ 0.083333333333333 x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (log(x) + -1.0);
	double tmp;
	if ((z <= -5.6e-25) || !(z <= 4.7e-20)) {
		tmp = ((z * z) * (y / x)) + t_0;
	} else {
		tmp = (0.083333333333333 / x) + t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (log(x) + (-1.0d0))
    if ((z <= (-5.6d-25)) .or. (.not. (z <= 4.7d-20))) then
        tmp = ((z * z) * (y / x)) + t_0
    else
        tmp = (0.083333333333333d0 / x) + t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (Math.log(x) + -1.0);
	double tmp;
	if ((z <= -5.6e-25) || !(z <= 4.7e-20)) {
		tmp = ((z * z) * (y / x)) + t_0;
	} else {
		tmp = (0.083333333333333 / x) + t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (math.log(x) + -1.0)
	tmp = 0
	if (z <= -5.6e-25) or not (z <= 4.7e-20):
		tmp = ((z * z) * (y / x)) + t_0
	else:
		tmp = (0.083333333333333 / x) + t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(log(x) + -1.0))
	tmp = 0.0
	if ((z <= -5.6e-25) || !(z <= 4.7e-20))
		tmp = Float64(Float64(Float64(z * z) * Float64(y / x)) + t_0);
	else
		tmp = Float64(Float64(0.083333333333333 / x) + t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (log(x) + -1.0);
	tmp = 0.0;
	if ((z <= -5.6e-25) || ~((z <= 4.7e-20)))
		tmp = ((z * z) * (y / x)) + t_0;
	else
		tmp = (0.083333333333333 / x) + t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -5.6e-25], N[Not[LessEqual[z, 4.7e-20]], $MachinePrecision]], N[(N[(N[(z * z), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision], N[(N[(0.083333333333333 / x), $MachinePrecision] + t$95$0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.59999999999999976e-25 or 4.70000000000000015e-20 < 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. Step-by-step derivation

      1. metadata-eval 91.4%

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

      2. fma-neg 91.4%

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

      3. fma-def 91.4%

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

      4. clear-num 91.4%

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

      5. inv-pow 91.4%

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

      6. *-commutative 91.4%

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

      7. fma-udef 91.4%

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

      8. fma-neg 91.4%

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

      9. metadata-eval 91.4%

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

   5. Applied egg-rr 91.4%

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

   6. Taylor expanded in y around inf 65.7%

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

      1. associate-/l* 68.9%

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

      2. associate-/r/ 66.3%

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

      3. unpow2 66.3%

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

   8. Simplified 66.3%

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

   9. Taylor expanded in x around inf 66.3%

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

       1. *-commutative 25.1%

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

       2. sub-neg 25.1%

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

       3. mul-1-neg 25.1%

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

       4. log-rec 25.1%

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

       5. remove-double-neg 25.1%

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

       6. metadata-eval 25.1%

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

   11. Simplified 66.3%

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

   if -5.59999999999999976e-25 < z < 4.70000000000000015e-20

   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%

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

   4. Taylor expanded in z around 0 94.6%

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

   5. Taylor expanded in x around inf 92.6%

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

      1. *-commutative 92.6%

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

      2. sub-neg 92.6%

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

      3. mul-1-neg 92.6%

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

      4. log-rec 92.6%

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

      5. remove-double-neg 92.6%

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

      6. metadata-eval 92.6%

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

   7. Simplified 92.6%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-25} \lor \neg \left(z \leq 4.7 \cdot 10^{-20}\right):\\ \;\;\;\;\left(z \cdot z\right) \cdot \frac{y}{x} + x \cdot \left(\log x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x} + x \cdot \left(\log x + -1\right)\\ \end{array} \]

Alternative 12: 79.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-21} \lor \neg \left(z \leq 1.52 \cdot 10^{-24}\right):\\ \;\;\;\;\left(z \cdot z\right) \cdot \frac{y}{x} + x \cdot \left(\log x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3e-21) (not (<= z 1.52e-24)))
   (+ (* (* z z) (/ y x)) (* x (+ (log x) -1.0)))
   (+
    (+ (- (* (+ x -0.5) (log x)) x) 0.91893853320467)
    (/ 0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3e-21) || !(z <= 1.52e-24)) {
		tmp = ((z * z) * (y / x)) + (x * (log(x) + -1.0));
	} else {
		tmp = ((((x + -0.5) * log(x)) - x) + 0.91893853320467) + (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 <= (-3d-21)) .or. (.not. (z <= 1.52d-24))) then
        tmp = ((z * z) * (y / x)) + (x * (log(x) + (-1.0d0)))
    else
        tmp = ((((x + (-0.5d0)) * log(x)) - x) + 0.91893853320467d0) + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3e-21) || !(z <= 1.52e-24)) {
		tmp = ((z * z) * (y / x)) + (x * (Math.log(x) + -1.0));
	} else {
		tmp = ((((x + -0.5) * Math.log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3e-21) or not (z <= 1.52e-24):
		tmp = ((z * z) * (y / x)) + (x * (math.log(x) + -1.0))
	else:
		tmp = ((((x + -0.5) * math.log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3e-21) || !(z <= 1.52e-24))
		tmp = Float64(Float64(Float64(z * z) * Float64(y / x)) + Float64(x * Float64(log(x) + -1.0)));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(x + -0.5) * log(x)) - x) + 0.91893853320467) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3e-21) || ~((z <= 1.52e-24)))
		tmp = ((z * z) * (y / x)) + (x * (log(x) + -1.0));
	else
		tmp = ((((x + -0.5) * log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3e-21], N[Not[LessEqual[z, 1.52e-24]], $MachinePrecision]], N[(N[(N[(z * z), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.99999999999999991e-21 or 1.51999999999999992e-24 < 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. Step-by-step derivation

      1. metadata-eval 91.4%

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

      2. fma-neg 91.4%

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

      3. fma-def 91.4%

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

      4. clear-num 91.4%

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

      5. inv-pow 91.4%

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

      6. *-commutative 91.4%

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

      7. fma-udef 91.4%

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

      8. fma-neg 91.4%

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

      9. metadata-eval 91.4%

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

   5. Applied egg-rr 91.4%

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

   6. Taylor expanded in y around inf 65.7%

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

      1. associate-/l* 68.9%

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

      2. associate-/r/ 66.3%

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

      3. unpow2 66.3%

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

   8. Simplified 66.3%

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

   9. Taylor expanded in x around inf 66.3%

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

       1. *-commutative 25.1%

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

       2. sub-neg 25.1%

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

       3. mul-1-neg 25.1%

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

       4. log-rec 25.1%

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

       5. remove-double-neg 25.1%

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

       6. metadata-eval 25.1%

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

   11. Simplified 66.3%

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

   if -2.99999999999999991e-21 < z < 1.51999999999999992e-24

   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%

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

   4. Taylor expanded in z around 0 94.6%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-21} \lor \neg \left(z \leq 1.52 \cdot 10^{-24}\right):\\ \;\;\;\;\left(z \cdot z\right) \cdot \frac{y}{x} + x \cdot \left(\log x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 13: 56.5% 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 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 94.8%

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

   4. fma-neg 94.8%

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

   5. metadata-eval 94.8%

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

3. Simplified 94.8%

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

4. Taylor expanded in z around 0 54.4%

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

5. Taylor expanded in x around inf 53.6%

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

   1. *-commutative 53.6%

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

   2. sub-neg 53.6%

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

   3. mul-1-neg 53.6%

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

   4. log-rec 53.6%

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

   5. remove-double-neg 53.6%

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

   6. metadata-eval 53.6%

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

7. Simplified 53.6%

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

8. Final simplification 53.6%

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

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 2023279 
(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)))