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

Percentage Accurate: 94.4% → 98.9%

Time: 21.2s

Alternatives: 16

Speedup: 1.0×

• 28.7% 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: 94.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + ((((((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0) * z) + 0.083333333333333d0) / x)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.32 \cdot 10^{+117}:\\ \;\;\;\;\mathsf{fma}\left(x + -0.5, \log x, 0.91893853320467 - x\right) + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + z \cdot \left(z \cdot \frac{y + 0.0007936500793651}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.32e+117)
   (+
    (fma (+ x -0.5) (log x) (- 0.91893853320467 x))
    (/
     (fma
      z
      (fma (+ y 0.0007936500793651) z -0.0027777777777778)
      0.083333333333333)
     x))
   (+
    (+ 0.91893853320467 (- (* (+ x -0.5) (log x)) x))
    (* z (* z (/ (+ y 0.0007936500793651) x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.32e+117) {
		tmp = fma((x + -0.5), log(x), (0.91893853320467 - x)) + (fma(z, fma((y + 0.0007936500793651), z, -0.0027777777777778), 0.083333333333333) / x);
	} else {
		tmp = (0.91893853320467 + (((x + -0.5) * log(x)) - x)) + (z * (z * ((y + 0.0007936500793651) / x)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.32e+117)
		tmp = Float64(fma(Float64(x + -0.5), log(x), Float64(0.91893853320467 - x)) + Float64(fma(z, fma(Float64(y + 0.0007936500793651), z, -0.0027777777777778), 0.083333333333333) / x));
	else
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(Float64(x + -0.5) * log(x)) - x)) + Float64(z * Float64(z * Float64(Float64(y + 0.0007936500793651) / x))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.32e+117], N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision] + N[(0.91893853320467 - x), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(N[(y + 0.0007936500793651), $MachinePrecision] * z + -0.0027777777777778), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(0.91893853320467 + N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(z * N[(z * N[(N[(y + 0.0007936500793651), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.3199999999999999e117

   1. Initial program 99.6%

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

      1. remove-double-neg 99.6%

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

      2. sub-neg 99.6%

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

      3. associate-+l+ 99.6%

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

      4. fma-def 99.7%

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

      5. sub-neg 99.7%

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

      6. metadata-eval 99.7%

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

      7. +-commutative 99.7%

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

      8. unsub-neg 99.7%

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

      9. remove-double-neg 99.7%

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

      10. *-commutative 99.7%

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

      11. fma-def 99.7%

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

      12. fma-neg 99.7%

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

      13. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   if 1.3199999999999999e117 < x

   1. Initial program 81.5%

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

      1. remove-double-neg 81.5%

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

      2. remove-double-neg 81.5%

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

      3. sub-neg 81.5%

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

      4. metadata-eval 81.5%

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

      5. *-commutative 81.5%

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

      6. fma-def 81.5%

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

      7. fma-neg 81.5%

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

      8. metadata-eval 81.5%

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

   3. Simplified 81.5%

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

      1. clear-num 81.5%

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

      2. metadata-eval 81.5%

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

      3. fma-neg 81.5%

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

      4. fma-udef 81.5%

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

      5. *-commutative 81.5%

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

      6. inv-pow 81.5%

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

      7. *-commutative 81.5%

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

      8. fma-udef 81.5%

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

      9. fma-neg 81.5%

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

      10. metadata-eval 81.5%

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

      11. fma-udef 81.5%

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

      12. *-commutative 81.5%

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

      13. fma-def 81.5%

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

   5. Applied egg-rr 81.5%

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

   6. Taylor expanded in z around inf 81.5%

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

      1. unpow2 81.5%

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

      2. associate-/l* 88.4%

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

      3. *-rgt-identity 88.4%

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

      4. +-commutative 88.4%

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

      5. associate-*r/ 88.4%

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

      6. associate-*l* 99.5%

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

      7. associate-/r/ 99.5%

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

      8. *-commutative 99.5%

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

      9. associate-*r/ 99.6%

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

      10. *-rgt-identity 99.6%

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

      11. +-commutative 99.6%

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

   8. Simplified 99.6%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.32 \cdot 10^{+117}:\\ \;\;\;\;\mathsf{fma}\left(x + -0.5, \log x, 0.91893853320467 - x\right) + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + z \cdot \left(z \cdot \frac{y + 0.0007936500793651}{x}\right)\\ \end{array} \]

Alternative 2: 99.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\\ \mathbf{if}\;x \leq 2.15 \cdot 10^{+99}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}{x} + t_0\\ \mathbf{else}:\\ \;\;\;\;t_0 + z \cdot \left(z \cdot \frac{y + 0.0007936500793651}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 0.91893853320467 (- (* (+ x -0.5) (log x)) x))))
   (if (<= x 2.15e+99)
     (+
      (/
       (fma
        z
        (fma (+ y 0.0007936500793651) z -0.0027777777777778)
        0.083333333333333)
       x)
      t_0)
     (+ t_0 (* z (* z (/ (+ y 0.0007936500793651) x)))))))

C

double code(double x, double y, double z) {
	double t_0 = 0.91893853320467 + (((x + -0.5) * log(x)) - x);
	double tmp;
	if (x <= 2.15e+99) {
		tmp = (fma(z, fma((y + 0.0007936500793651), z, -0.0027777777777778), 0.083333333333333) / x) + t_0;
	} else {
		tmp = t_0 + (z * (z * ((y + 0.0007936500793651) / x)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(0.91893853320467 + Float64(Float64(Float64(x + -0.5) * log(x)) - x))
	tmp = 0.0
	if (x <= 2.15e+99)
		tmp = Float64(Float64(fma(z, fma(Float64(y + 0.0007936500793651), z, -0.0027777777777778), 0.083333333333333) / x) + t_0);
	else
		tmp = Float64(t_0 + Float64(z * Float64(z * Float64(Float64(y + 0.0007936500793651) / x))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(0.91893853320467 + N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 2.15e+99], N[(N[(N[(z * N[(N[(y + 0.0007936500793651), $MachinePrecision] * z + -0.0027777777777778), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision] + t$95$0), $MachinePrecision], N[(t$95$0 + N[(z * N[(z * N[(N[(y + 0.0007936500793651), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 2.1500000000000001e99

   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. remove-double-neg 99.7%

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

      2. remove-double-neg 99.7%

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

      3. sub-neg 99.7%

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

      4. metadata-eval 99.7%

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

      5. *-commutative 99.7%

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

      6. fma-def 99.7%

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

      7. fma-neg 99.7%

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

      8. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   if 2.1500000000000001e99 < x

   1. Initial program 82.9%

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

      1. remove-double-neg 82.9%

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

      2. remove-double-neg 82.9%

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

      3. sub-neg 82.9%

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

      4. metadata-eval 82.9%

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

      5. *-commutative 82.9%

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

      6. fma-def 82.9%

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

      7. fma-neg 82.9%

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

      8. metadata-eval 82.9%

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

   3. Simplified 82.9%

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

      1. clear-num 82.9%

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

      2. metadata-eval 82.9%

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

      3. fma-neg 82.9%

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

      4. fma-udef 82.9%

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

      5. *-commutative 82.9%

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

      6. inv-pow 82.9%

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

      7. *-commutative 82.9%

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

      8. fma-udef 82.9%

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

      9. fma-neg 82.9%

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

      10. metadata-eval 82.9%

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

      11. fma-udef 82.9%

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

      12. *-commutative 82.9%

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

      13. fma-def 82.9%

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

   5. Applied egg-rr 82.9%

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

   6. Taylor expanded in z around inf 82.9%

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

      1. unpow2 82.9%

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

      2. associate-/l* 89.2%

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

      3. *-rgt-identity 89.2%

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

      4. +-commutative 89.2%

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

      5. associate-*r/ 89.2%

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

      6. associate-*l* 99.5%

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

      7. associate-/r/ 99.5%

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

      8. *-commutative 99.5%

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

      9. associate-*r/ 99.6%

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

      10. *-rgt-identity 99.6%

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

      11. +-commutative 99.6%

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

   8. Simplified 99.6%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.15 \cdot 10^{+99}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}{x} + \left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + z \cdot \left(z \cdot \frac{y + 0.0007936500793651}{x}\right)\\ \end{array} \]

Alternative 3: 84.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(0.91893853320467 + -0.5 \cdot \log x\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x}\\ t_1 := 0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+113}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{+41}:\\ \;\;\;\;t_1 + \frac{z \cdot \left(z \cdot 0.0007936500793651\right)}{x}\\ \mathbf{elif}\;z \leq -4800000000000 \lor \neg \left(z \leq 5 \cdot 10^{+24}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          (+ 0.91893853320467 (* -0.5 (log x)))
          (* (+ y 0.0007936500793651) (/ (* z z) x))))
        (t_1 (+ 0.91893853320467 (- (* (+ x -0.5) (log x)) x))))
   (if (<= z -1.2e+113)
     t_0
     (if (<= z -6.8e+41)
       (+ t_1 (/ (* z (* z 0.0007936500793651)) x))
       (if (or (<= z -4800000000000.0) (not (<= z 5e+24)))
         t_0
         (+ t_1 (/ (+ 0.083333333333333 (* z -0.0027777777777778)) x)))))))

C

double code(double x, double y, double z) {
	double t_0 = (0.91893853320467 + (-0.5 * log(x))) + ((y + 0.0007936500793651) * ((z * z) / x));
	double t_1 = 0.91893853320467 + (((x + -0.5) * log(x)) - x);
	double tmp;
	if (z <= -1.2e+113) {
		tmp = t_0;
	} else if (z <= -6.8e+41) {
		tmp = t_1 + ((z * (z * 0.0007936500793651)) / x);
	} else if ((z <= -4800000000000.0) || !(z <= 5e+24)) {
		tmp = t_0;
	} else {
		tmp = t_1 + ((0.083333333333333 + (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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (0.91893853320467d0 + ((-0.5d0) * log(x))) + ((y + 0.0007936500793651d0) * ((z * z) / x))
    t_1 = 0.91893853320467d0 + (((x + (-0.5d0)) * log(x)) - x)
    if (z <= (-1.2d+113)) then
        tmp = t_0
    else if (z <= (-6.8d+41)) then
        tmp = t_1 + ((z * (z * 0.0007936500793651d0)) / x)
    else if ((z <= (-4800000000000.0d0)) .or. (.not. (z <= 5d+24))) then
        tmp = t_0
    else
        tmp = t_1 + ((0.083333333333333d0 + (z * (-0.0027777777777778d0))) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (0.91893853320467 + (-0.5 * Math.log(x))) + ((y + 0.0007936500793651) * ((z * z) / x));
	double t_1 = 0.91893853320467 + (((x + -0.5) * Math.log(x)) - x);
	double tmp;
	if (z <= -1.2e+113) {
		tmp = t_0;
	} else if (z <= -6.8e+41) {
		tmp = t_1 + ((z * (z * 0.0007936500793651)) / x);
	} else if ((z <= -4800000000000.0) || !(z <= 5e+24)) {
		tmp = t_0;
	} else {
		tmp = t_1 + ((0.083333333333333 + (z * -0.0027777777777778)) / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (0.91893853320467 + (-0.5 * math.log(x))) + ((y + 0.0007936500793651) * ((z * z) / x))
	t_1 = 0.91893853320467 + (((x + -0.5) * math.log(x)) - x)
	tmp = 0
	if z <= -1.2e+113:
		tmp = t_0
	elif z <= -6.8e+41:
		tmp = t_1 + ((z * (z * 0.0007936500793651)) / x)
	elif (z <= -4800000000000.0) or not (z <= 5e+24):
		tmp = t_0
	else:
		tmp = t_1 + ((0.083333333333333 + (z * -0.0027777777777778)) / x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(0.91893853320467 + Float64(-0.5 * log(x))) + Float64(Float64(y + 0.0007936500793651) * Float64(Float64(z * z) / x)))
	t_1 = Float64(0.91893853320467 + Float64(Float64(Float64(x + -0.5) * log(x)) - x))
	tmp = 0.0
	if (z <= -1.2e+113)
		tmp = t_0;
	elseif (z <= -6.8e+41)
		tmp = Float64(t_1 + Float64(Float64(z * Float64(z * 0.0007936500793651)) / x));
	elseif ((z <= -4800000000000.0) || !(z <= 5e+24))
		tmp = t_0;
	else
		tmp = Float64(t_1 + Float64(Float64(0.083333333333333 + Float64(z * -0.0027777777777778)) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (0.91893853320467 + (-0.5 * log(x))) + ((y + 0.0007936500793651) * ((z * z) / x));
	t_1 = 0.91893853320467 + (((x + -0.5) * log(x)) - x);
	tmp = 0.0;
	if (z <= -1.2e+113)
		tmp = t_0;
	elseif (z <= -6.8e+41)
		tmp = t_1 + ((z * (z * 0.0007936500793651)) / x);
	elseif ((z <= -4800000000000.0) || ~((z <= 5e+24)))
		tmp = t_0;
	else
		tmp = t_1 + ((0.083333333333333 + (z * -0.0027777777777778)) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(0.91893853320467 + N[(-0.5 * N[Log[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(N[(z * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(0.91893853320467 + N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e+113], t$95$0, If[LessEqual[z, -6.8e+41], N[(t$95$1 + N[(N[(z * N[(z * 0.0007936500793651), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -4800000000000.0], N[Not[LessEqual[z, 5e+24]], $MachinePrecision]], t$95$0, N[(t$95$1 + N[(N[(0.083333333333333 + N[(z * -0.0027777777777778), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.19999999999999992e113 or -6.79999999999999996e41 < z < -4.8e12 or 5.00000000000000045e24 < z

   1. Initial program 87.2%

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

      1. remove-double-neg 87.2%

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

      2. remove-double-neg 87.2%

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

      3. sub-neg 87.2%

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

      4. metadata-eval 87.2%

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

      5. *-commutative 87.2%

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

      6. fma-def 87.2%

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

      7. fma-neg 87.2%

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

      8. metadata-eval 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in z around inf 87.2%

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

      1. associate-/l* 91.5%

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

      2. +-commutative 91.5%

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

      3. associate-/r/ 91.5%

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

      4. unpow2 91.5%

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

   6. Simplified 91.5%

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

   7. Taylor expanded in x around 0 86.1%

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

   if -1.19999999999999992e113 < z < -6.79999999999999996e41

   1. Initial program 92.1%

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

      1. remove-double-neg 92.1%

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

      2. remove-double-neg 92.1%

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

      3. sub-neg 92.1%

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

      4. metadata-eval 92.1%

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

      5. *-commutative 92.1%

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

      6. fma-def 92.1%

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

      7. fma-neg 92.1%

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

      8. metadata-eval 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in z around inf 91.9%

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

      1. unpow2 91.9%

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

      2. +-commutative 91.9%

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

   6. Simplified 91.9%

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

   7. Taylor expanded in y around 0 99.7%

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

      1. unpow2 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r* 99.9%

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

   9. Simplified 99.9%

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

   if -4.8e12 < z < 5.00000000000000045e24

   1. Initial program 99.4%

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

      1. remove-double-neg 99.4%

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

      2. remove-double-neg 99.4%

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

      3. sub-neg 99.4%

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

      4. metadata-eval 99.4%

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

      5. *-commutative 99.4%

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

      6. fma-def 99.4%

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

      7. fma-neg 99.4%

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

      8. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 93.4%

      \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{0.083333333333333 + -0.0027777777777778 \cdot z}}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+113}:\\ \;\;\;\;\left(0.91893853320467 + -0.5 \cdot \log x\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{+41}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{z \cdot \left(z \cdot 0.0007936500793651\right)}{x}\\ \mathbf{elif}\;z \leq -4800000000000 \lor \neg \left(z \leq 5 \cdot 10^{+24}\right):\\ \;\;\;\;\left(0.91893853320467 + -0.5 \cdot \log x\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \end{array} \]

Alternative 4: 99.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\\ \mathbf{if}\;z \leq -2800000000000 \lor \neg \left(z \leq 10\right):\\ \;\;\;\;t_0 + z \cdot \left(z \cdot \frac{y + 0.0007936500793651}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(\frac{0.083333333333333}{x} + \frac{y}{\frac{x}{z \cdot z}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 0.91893853320467 (- (* (+ x -0.5) (log x)) x))))
   (if (or (<= z -2800000000000.0) (not (<= z 10.0)))
     (+ t_0 (* z (* z (/ (+ y 0.0007936500793651) x))))
     (+ t_0 (+ (/ 0.083333333333333 x) (/ y (/ x (* z z))))))))

C

double code(double x, double y, double z) {
	double t_0 = 0.91893853320467 + (((x + -0.5) * log(x)) - x);
	double tmp;
	if ((z <= -2800000000000.0) || !(z <= 10.0)) {
		tmp = t_0 + (z * (z * ((y + 0.0007936500793651) / x)));
	} else {
		tmp = t_0 + ((0.083333333333333 / x) + (y / (x / (z * z))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 0.91893853320467d0 + (((x + (-0.5d0)) * log(x)) - x)
    if ((z <= (-2800000000000.0d0)) .or. (.not. (z <= 10.0d0))) then
        tmp = t_0 + (z * (z * ((y + 0.0007936500793651d0) / x)))
    else
        tmp = t_0 + ((0.083333333333333d0 / x) + (y / (x / (z * z))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 0.91893853320467 + (((x + -0.5) * Math.log(x)) - x);
	double tmp;
	if ((z <= -2800000000000.0) || !(z <= 10.0)) {
		tmp = t_0 + (z * (z * ((y + 0.0007936500793651) / x)));
	} else {
		tmp = t_0 + ((0.083333333333333 / x) + (y / (x / (z * z))));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 0.91893853320467 + (((x + -0.5) * math.log(x)) - x)
	tmp = 0
	if (z <= -2800000000000.0) or not (z <= 10.0):
		tmp = t_0 + (z * (z * ((y + 0.0007936500793651) / x)))
	else:
		tmp = t_0 + ((0.083333333333333 / x) + (y / (x / (z * z))))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(0.91893853320467 + Float64(Float64(Float64(x + -0.5) * log(x)) - x))
	tmp = 0.0
	if ((z <= -2800000000000.0) || !(z <= 10.0))
		tmp = Float64(t_0 + Float64(z * Float64(z * Float64(Float64(y + 0.0007936500793651) / x))));
	else
		tmp = Float64(t_0 + Float64(Float64(0.083333333333333 / x) + Float64(y / Float64(x / Float64(z * z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 0.91893853320467 + (((x + -0.5) * log(x)) - x);
	tmp = 0.0;
	if ((z <= -2800000000000.0) || ~((z <= 10.0)))
		tmp = t_0 + (z * (z * ((y + 0.0007936500793651) / x)));
	else
		tmp = t_0 + ((0.083333333333333 / x) + (y / (x / (z * z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(0.91893853320467 + N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -2800000000000.0], N[Not[LessEqual[z, 10.0]], $MachinePrecision]], N[(t$95$0 + N[(z * N[(z * N[(N[(y + 0.0007936500793651), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(N[(0.083333333333333 / x), $MachinePrecision] + N[(y / N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8e12 or 10 < z

   1. Initial program 88.2%

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

      1. remove-double-neg 88.2%

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

      2. remove-double-neg 88.2%

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

      3. sub-neg 88.2%

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

      4. metadata-eval 88.2%

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

      5. *-commutative 88.2%

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

      6. fma-def 88.2%

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

      7. fma-neg 88.2%

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

      8. metadata-eval 88.2%

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

   3. Simplified 88.2%

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

      1. clear-num 88.2%

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

      2. metadata-eval 88.2%

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

      3. fma-neg 88.2%

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

      4. fma-udef 88.2%

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

      5. *-commutative 88.2%

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

      6. inv-pow 88.2%

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

      7. *-commutative 88.2%

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

      8. fma-udef 88.2%

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

      9. fma-neg 88.2%

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

      10. metadata-eval 88.2%

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

      11. fma-udef 88.2%

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

      12. *-commutative 88.2%

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

      13. fma-def 88.2%

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

   5. Applied egg-rr 88.2%

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

   6. Taylor expanded in z around inf 87.9%

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

      1. unpow2 87.9%

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

      2. associate-/l* 92.3%

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

      3. *-rgt-identity 92.3%

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

      4. +-commutative 92.3%

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

      5. associate-*r/ 92.3%

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

      6. associate-*l* 99.5%

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

      7. associate-/r/ 99.5%

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

      8. *-commutative 99.5%

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

      9. associate-*r/ 99.5%

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

      10. *-rgt-identity 99.5%

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

      11. +-commutative 99.5%

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

   8. Simplified 99.5%

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

   if -2.8e12 < z < 10

   1. Initial program 99.3%

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

      1. remove-double-neg 99.3%

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

      2. remove-double-neg 99.3%

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

      3. sub-neg 99.3%

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

      4. metadata-eval 99.3%

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

      5. *-commutative 99.3%

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

      6. fma-def 99.3%

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

      7. fma-neg 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

      1. metadata-eval 99.3%

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

      2. fma-neg 99.3%

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

      3. fma-udef 99.3%

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

      4. *-commutative 99.3%

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

      5. add-log-exp 91.6%

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

      6. *-commutative 91.6%

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

      7. fma-udef 91.6%

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

      8. fma-neg 91.6%

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

      9. metadata-eval 91.6%

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

      10. fma-udef 91.6%

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

      11. *-commutative 91.6%

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

      12. fma-def 91.6%

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

   5. Applied egg-rr 91.6%

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

   6. Taylor expanded in z around inf 99.3%

      \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\left(0.083333333333333 \cdot \frac{1}{x} + \left(\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x} + -0.0027777777777778 \cdot \frac{z}{x}\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r/ 99.3%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\color{blue}{\frac{0.083333333333333 \cdot 1}{x}} + \left(\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x} + -0.0027777777777778 \cdot \frac{z}{x}\right)\right) \]

      2. metadata-eval 99.3%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\frac{\color{blue}{0.083333333333333}}{x} + \left(\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x} + -0.0027777777777778 \cdot \frac{z}{x}\right)\right) \]

      3. +-commutative 99.3%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\frac{0.083333333333333}{x} + \color{blue}{\left(-0.0027777777777778 \cdot \frac{z}{x} + \frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}\right)}\right) \]

      4. unpow2 99.3%

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

      5. associate-/l* 90.3%

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

      6. *-rgt-identity 90.3%

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

      7. +-commutative 90.3%

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

      8. associate-*r/ 89.6%

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

      9. associate-/r/ 89.6%

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

      10. *-commutative 89.6%

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

      11. associate-*r* 99.4%

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

      12. *-commutative 99.4%

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

      13. associate-*r/ 99.3%

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

      14. *-rgt-identity 99.3%

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

      15. associate-*r/ 99.4%

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

      16. +-commutative 99.4%

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

      17. associate-/l* 99.4%

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

   8. Simplified 99.4%

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

   9. Taylor expanded in y around inf 98.4%

      \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\frac{0.083333333333333}{x} + \color{blue}{\frac{y \cdot {z}^{2}}{x}}\right) \]
   10. Step-by-step derivation

       1. unpow2 98.4%

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

       2. associate-/l* 98.4%

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

   11. Simplified 98.4%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2800000000000 \lor \neg \left(z \leq 10\right):\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + z \cdot \left(z \cdot \frac{y + 0.0007936500793651}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \left(\frac{0.083333333333333}{x} + \frac{y}{\frac{x}{z \cdot z}}\right)\\ \end{array} \]

Alternative 5: 99.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.9 \cdot 10^{+99}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + z \cdot \left(z \cdot \frac{y + 0.0007936500793651}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.9e+99)
   (+
    (+ 0.91893853320467 (- (* (log x) (- x 0.5)) x))
    (/
     (+
      0.083333333333333
      (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))
     x))
   (+
    (+ 0.91893853320467 (- (* (+ x -0.5) (log x)) x))
    (* z (* z (/ (+ y 0.0007936500793651) x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.9e+99) {
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = (0.91893853320467 + (((x + -0.5) * log(x)) - x)) + (z * (z * ((y + 0.0007936500793651) / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 1.9d+99) then
        tmp = (0.91893853320467d0 + ((log(x) * (x - 0.5d0)) - x)) + ((0.083333333333333d0 + (z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0))) / x)
    else
        tmp = (0.91893853320467d0 + (((x + (-0.5d0)) * log(x)) - x)) + (z * (z * ((y + 0.0007936500793651d0) / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.9e+99) {
		tmp = (0.91893853320467 + ((Math.log(x) * (x - 0.5)) - x)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = (0.91893853320467 + (((x + -0.5) * Math.log(x)) - x)) + (z * (z * ((y + 0.0007936500793651) / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1.9e+99:
		tmp = (0.91893853320467 + ((math.log(x) * (x - 0.5)) - x)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x)
	else:
		tmp = (0.91893853320467 + (((x + -0.5) * math.log(x)) - x)) + (z * (z * ((y + 0.0007936500793651) / x)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.9e+99)
		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(0.91893853320467 + Float64(Float64(Float64(x + -0.5) * log(x)) - x)) + Float64(z * Float64(z * Float64(Float64(y + 0.0007936500793651) / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1.9e+99)
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	else
		tmp = (0.91893853320467 + (((x + -0.5) * log(x)) - x)) + (z * (z * ((y + 0.0007936500793651) / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.9e+99], 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[(0.91893853320467 + N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(z * N[(z * N[(N[(y + 0.0007936500793651), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.9e99

   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 1.9e99 < x

   1. Initial program 82.9%

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

      1. remove-double-neg 82.9%

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

      2. remove-double-neg 82.9%

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

      3. sub-neg 82.9%

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

      4. metadata-eval 82.9%

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

      5. *-commutative 82.9%

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

      6. fma-def 82.9%

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

      7. fma-neg 82.9%

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

      8. metadata-eval 82.9%

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

   3. Simplified 82.9%

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

      1. clear-num 82.9%

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

      2. metadata-eval 82.9%

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

      3. fma-neg 82.9%

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

      4. fma-udef 82.9%

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

      5. *-commutative 82.9%

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

      6. inv-pow 82.9%

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

      7. *-commutative 82.9%

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

      8. fma-udef 82.9%

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

      9. fma-neg 82.9%

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

      10. metadata-eval 82.9%

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

      11. fma-udef 82.9%

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

      12. *-commutative 82.9%

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

      13. fma-def 82.9%

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

   5. Applied egg-rr 82.9%

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

   6. Taylor expanded in z around inf 82.9%

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

      1. unpow2 82.9%

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

      2. associate-/l* 89.2%

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

      3. *-rgt-identity 89.2%

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

      4. +-commutative 89.2%

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

      5. associate-*r/ 89.2%

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

      6. associate-*l* 99.5%

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

      7. associate-/r/ 99.5%

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

      8. *-commutative 99.5%

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

      9. associate-*r/ 99.6%

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

      10. *-rgt-identity 99.6%

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

      11. +-commutative 99.6%

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

   8. Simplified 99.6%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.9 \cdot 10^{+99}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + z \cdot \left(z \cdot \frac{y + 0.0007936500793651}{x}\right)\\ \end{array} \]

Alternative 6: 84.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(0.91893853320467 + -0.5 \cdot \log x\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x}\\ \mathbf{if}\;z \leq -5 \cdot 10^{+112}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{+41}:\\ \;\;\;\;\frac{z \cdot \left(z \cdot 0.0007936500793651\right)}{x} + x \cdot \left(\log x + -1\right)\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+15} \lor \neg \left(z \leq 5 \cdot 10^{+25}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          (+ 0.91893853320467 (* -0.5 (log x)))
          (* (+ y 0.0007936500793651) (/ (* z z) x)))))
   (if (<= z -5e+112)
     t_0
     (if (<= z -3.4e+41)
       (+ (/ (* z (* z 0.0007936500793651)) x) (* x (+ (log x) -1.0)))
       (if (or (<= z -7.2e+15) (not (<= z 5e+25)))
         t_0
         (+
          (+ 0.91893853320467 (- (* (+ x -0.5) (log x)) x))
          (/ 0.083333333333333 x)))))))

C

double code(double x, double y, double z) {
	double t_0 = (0.91893853320467 + (-0.5 * log(x))) + ((y + 0.0007936500793651) * ((z * z) / x));
	double tmp;
	if (z <= -5e+112) {
		tmp = t_0;
	} else if (z <= -3.4e+41) {
		tmp = ((z * (z * 0.0007936500793651)) / x) + (x * (log(x) + -1.0));
	} else if ((z <= -7.2e+15) || !(z <= 5e+25)) {
		tmp = t_0;
	} else {
		tmp = (0.91893853320467 + (((x + -0.5) * log(x)) - x)) + (0.083333333333333 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (0.91893853320467d0 + ((-0.5d0) * log(x))) + ((y + 0.0007936500793651d0) * ((z * z) / x))
    if (z <= (-5d+112)) then
        tmp = t_0
    else if (z <= (-3.4d+41)) then
        tmp = ((z * (z * 0.0007936500793651d0)) / x) + (x * (log(x) + (-1.0d0)))
    else if ((z <= (-7.2d+15)) .or. (.not. (z <= 5d+25))) then
        tmp = t_0
    else
        tmp = (0.91893853320467d0 + (((x + (-0.5d0)) * log(x)) - x)) + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (0.91893853320467 + (-0.5 * Math.log(x))) + ((y + 0.0007936500793651) * ((z * z) / x));
	double tmp;
	if (z <= -5e+112) {
		tmp = t_0;
	} else if (z <= -3.4e+41) {
		tmp = ((z * (z * 0.0007936500793651)) / x) + (x * (Math.log(x) + -1.0));
	} else if ((z <= -7.2e+15) || !(z <= 5e+25)) {
		tmp = t_0;
	} else {
		tmp = (0.91893853320467 + (((x + -0.5) * Math.log(x)) - x)) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (0.91893853320467 + (-0.5 * math.log(x))) + ((y + 0.0007936500793651) * ((z * z) / x))
	tmp = 0
	if z <= -5e+112:
		tmp = t_0
	elif z <= -3.4e+41:
		tmp = ((z * (z * 0.0007936500793651)) / x) + (x * (math.log(x) + -1.0))
	elif (z <= -7.2e+15) or not (z <= 5e+25):
		tmp = t_0
	else:
		tmp = (0.91893853320467 + (((x + -0.5) * math.log(x)) - x)) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(0.91893853320467 + Float64(-0.5 * log(x))) + Float64(Float64(y + 0.0007936500793651) * Float64(Float64(z * z) / x)))
	tmp = 0.0
	if (z <= -5e+112)
		tmp = t_0;
	elseif (z <= -3.4e+41)
		tmp = Float64(Float64(Float64(z * Float64(z * 0.0007936500793651)) / x) + Float64(x * Float64(log(x) + -1.0)));
	elseif ((z <= -7.2e+15) || !(z <= 5e+25))
		tmp = t_0;
	else
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(Float64(x + -0.5) * log(x)) - x)) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (0.91893853320467 + (-0.5 * log(x))) + ((y + 0.0007936500793651) * ((z * z) / x));
	tmp = 0.0;
	if (z <= -5e+112)
		tmp = t_0;
	elseif (z <= -3.4e+41)
		tmp = ((z * (z * 0.0007936500793651)) / x) + (x * (log(x) + -1.0));
	elseif ((z <= -7.2e+15) || ~((z <= 5e+25)))
		tmp = t_0;
	else
		tmp = (0.91893853320467 + (((x + -0.5) * log(x)) - x)) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(0.91893853320467 + N[(-0.5 * N[Log[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(N[(z * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e+112], t$95$0, If[LessEqual[z, -3.4e+41], N[(N[(N[(z * N[(z * 0.0007936500793651), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] + N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -7.2e+15], N[Not[LessEqual[z, 5e+25]], $MachinePrecision]], t$95$0, N[(N[(0.91893853320467 + N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5e112 or -3.39999999999999998e41 < z < -7.2e15 or 5.00000000000000024e25 < z

   1. Initial program 87.2%

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

      1. remove-double-neg 87.2%

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

      2. remove-double-neg 87.2%

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

      3. sub-neg 87.2%

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

      4. metadata-eval 87.2%

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

      5. *-commutative 87.2%

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

      6. fma-def 87.2%

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

      7. fma-neg 87.2%

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

      8. metadata-eval 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in z around inf 87.2%

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

      1. associate-/l* 91.5%

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

      2. +-commutative 91.5%

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

      3. associate-/r/ 91.5%

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

      4. unpow2 91.5%

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

   6. Simplified 91.5%

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

   7. Taylor expanded in x around 0 86.1%

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

   if -5e112 < z < -3.39999999999999998e41

   1. Initial program 92.1%

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

      1. remove-double-neg 92.1%

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

      2. remove-double-neg 92.1%

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

      3. sub-neg 92.1%

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

      4. metadata-eval 92.1%

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

      5. *-commutative 92.1%

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

      6. fma-def 92.1%

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

      7. fma-neg 92.1%

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

      8. metadata-eval 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in z around inf 91.9%

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

      1. unpow2 91.9%

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

      2. +-commutative 91.9%

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

   6. Simplified 91.9%

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

   7. Taylor expanded in y around 0 99.7%

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

      1. unpow2 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r* 99.9%

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

   9. Simplified 99.9%

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

   10. Taylor expanded in x around inf 99.6%

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

       1. *-commutative 45.8%

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

       2. sub-neg 45.8%

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

       3. mul-1-neg 45.8%

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

       4. log-rec 45.8%

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

       5. remove-double-neg 45.8%

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

       6. metadata-eval 45.8%

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

   12. Simplified 99.6%

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

   if -7.2e15 < z < 5.00000000000000024e25

   1. Initial program 99.4%

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

      1. remove-double-neg 99.4%

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

      2. remove-double-neg 99.4%

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

      3. sub-neg 99.4%

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

      4. metadata-eval 99.4%

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

      5. *-commutative 99.4%

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

      6. fma-def 99.4%

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

      7. fma-neg 99.4%

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

      8. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 92.9%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+112}:\\ \;\;\;\;\left(0.91893853320467 + -0.5 \cdot \log x\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{+41}:\\ \;\;\;\;\frac{z \cdot \left(z \cdot 0.0007936500793651\right)}{x} + x \cdot \left(\log x + -1\right)\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+15} \lor \neg \left(z \leq 5 \cdot 10^{+25}\right):\\ \;\;\;\;\left(0.91893853320467 + -0.5 \cdot \log x\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 7: 84.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(0.91893853320467 + -0.5 \cdot \log x\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x}\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+113}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+41}:\\ \;\;\;\;\frac{z \cdot \left(z \cdot 0.0007936500793651\right)}{x} + x \cdot \left(\log x + -1\right)\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{+14} \lor \neg \left(z \leq 1.2 \cdot 10^{+25}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{1}{x \cdot 12.000000000000048}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          (+ 0.91893853320467 (* -0.5 (log x)))
          (* (+ y 0.0007936500793651) (/ (* z z) x)))))
   (if (<= z -1.1e+113)
     t_0
     (if (<= z -2.8e+41)
       (+ (/ (* z (* z 0.0007936500793651)) x) (* x (+ (log x) -1.0)))
       (if (or (<= z -2.55e+14) (not (<= z 1.2e+25)))
         t_0
         (+
          (+ 0.91893853320467 (- (* (+ x -0.5) (log x)) x))
          (/ 1.0 (* x 12.000000000000048))))))))

C

double code(double x, double y, double z) {
	double t_0 = (0.91893853320467 + (-0.5 * log(x))) + ((y + 0.0007936500793651) * ((z * z) / x));
	double tmp;
	if (z <= -1.1e+113) {
		tmp = t_0;
	} else if (z <= -2.8e+41) {
		tmp = ((z * (z * 0.0007936500793651)) / x) + (x * (log(x) + -1.0));
	} else if ((z <= -2.55e+14) || !(z <= 1.2e+25)) {
		tmp = t_0;
	} else {
		tmp = (0.91893853320467 + (((x + -0.5) * log(x)) - x)) + (1.0 / (x * 12.000000000000048));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (0.91893853320467d0 + ((-0.5d0) * log(x))) + ((y + 0.0007936500793651d0) * ((z * z) / x))
    if (z <= (-1.1d+113)) then
        tmp = t_0
    else if (z <= (-2.8d+41)) then
        tmp = ((z * (z * 0.0007936500793651d0)) / x) + (x * (log(x) + (-1.0d0)))
    else if ((z <= (-2.55d+14)) .or. (.not. (z <= 1.2d+25))) then
        tmp = t_0
    else
        tmp = (0.91893853320467d0 + (((x + (-0.5d0)) * log(x)) - x)) + (1.0d0 / (x * 12.000000000000048d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (0.91893853320467 + (-0.5 * Math.log(x))) + ((y + 0.0007936500793651) * ((z * z) / x));
	double tmp;
	if (z <= -1.1e+113) {
		tmp = t_0;
	} else if (z <= -2.8e+41) {
		tmp = ((z * (z * 0.0007936500793651)) / x) + (x * (Math.log(x) + -1.0));
	} else if ((z <= -2.55e+14) || !(z <= 1.2e+25)) {
		tmp = t_0;
	} else {
		tmp = (0.91893853320467 + (((x + -0.5) * Math.log(x)) - x)) + (1.0 / (x * 12.000000000000048));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (0.91893853320467 + (-0.5 * math.log(x))) + ((y + 0.0007936500793651) * ((z * z) / x))
	tmp = 0
	if z <= -1.1e+113:
		tmp = t_0
	elif z <= -2.8e+41:
		tmp = ((z * (z * 0.0007936500793651)) / x) + (x * (math.log(x) + -1.0))
	elif (z <= -2.55e+14) or not (z <= 1.2e+25):
		tmp = t_0
	else:
		tmp = (0.91893853320467 + (((x + -0.5) * math.log(x)) - x)) + (1.0 / (x * 12.000000000000048))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(0.91893853320467 + Float64(-0.5 * log(x))) + Float64(Float64(y + 0.0007936500793651) * Float64(Float64(z * z) / x)))
	tmp = 0.0
	if (z <= -1.1e+113)
		tmp = t_0;
	elseif (z <= -2.8e+41)
		tmp = Float64(Float64(Float64(z * Float64(z * 0.0007936500793651)) / x) + Float64(x * Float64(log(x) + -1.0)));
	elseif ((z <= -2.55e+14) || !(z <= 1.2e+25))
		tmp = t_0;
	else
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(Float64(x + -0.5) * log(x)) - x)) + Float64(1.0 / Float64(x * 12.000000000000048)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (0.91893853320467 + (-0.5 * log(x))) + ((y + 0.0007936500793651) * ((z * z) / x));
	tmp = 0.0;
	if (z <= -1.1e+113)
		tmp = t_0;
	elseif (z <= -2.8e+41)
		tmp = ((z * (z * 0.0007936500793651)) / x) + (x * (log(x) + -1.0));
	elseif ((z <= -2.55e+14) || ~((z <= 1.2e+25)))
		tmp = t_0;
	else
		tmp = (0.91893853320467 + (((x + -0.5) * log(x)) - x)) + (1.0 / (x * 12.000000000000048));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(0.91893853320467 + N[(-0.5 * N[Log[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(N[(z * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e+113], t$95$0, If[LessEqual[z, -2.8e+41], N[(N[(N[(z * N[(z * 0.0007936500793651), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] + N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -2.55e+14], N[Not[LessEqual[z, 1.2e+25]], $MachinePrecision]], t$95$0, N[(N[(0.91893853320467 + N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(x * 12.000000000000048), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.10000000000000005e113 or -2.7999999999999999e41 < z < -2.55e14 or 1.19999999999999998e25 < z

   1. Initial program 87.2%

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

      1. remove-double-neg 87.2%

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

      2. remove-double-neg 87.2%

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

      3. sub-neg 87.2%

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

      4. metadata-eval 87.2%

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

      5. *-commutative 87.2%

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

      6. fma-def 87.2%

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

      7. fma-neg 87.2%

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

      8. metadata-eval 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in z around inf 87.2%

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

      1. associate-/l* 91.5%

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

      2. +-commutative 91.5%

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

      3. associate-/r/ 91.5%

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

      4. unpow2 91.5%

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

   6. Simplified 91.5%

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

   7. Taylor expanded in x around 0 86.1%

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

   if -1.10000000000000005e113 < z < -2.7999999999999999e41

   1. Initial program 92.1%

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

      1. remove-double-neg 92.1%

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

      2. remove-double-neg 92.1%

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

      3. sub-neg 92.1%

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

      4. metadata-eval 92.1%

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

      5. *-commutative 92.1%

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

      6. fma-def 92.1%

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

      7. fma-neg 92.1%

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

      8. metadata-eval 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in z around inf 91.9%

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

      1. unpow2 91.9%

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

      2. +-commutative 91.9%

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

   6. Simplified 91.9%

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

   7. Taylor expanded in y around 0 99.7%

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

      1. unpow2 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r* 99.9%

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

   9. Simplified 99.9%

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

   10. Taylor expanded in x around inf 99.6%

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

       1. *-commutative 45.8%

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

       2. sub-neg 45.8%

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

       3. mul-1-neg 45.8%

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

       4. log-rec 45.8%

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

       5. remove-double-neg 45.8%

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

       6. metadata-eval 45.8%

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

   12. Simplified 99.6%

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

   if -2.55e14 < z < 1.19999999999999998e25

   1. Initial program 99.4%

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

      1. remove-double-neg 99.4%

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

      2. remove-double-neg 99.4%

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

      3. sub-neg 99.4%

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

      4. metadata-eval 99.4%

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

      5. *-commutative 99.4%

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

      6. fma-def 99.4%

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

      7. fma-neg 99.4%

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

      8. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 92.9%

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

      1. clear-num 93.0%

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

      2. inv-pow 93.0%

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

      3. div-inv 93.0%

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

      4. metadata-eval 93.0%

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

   6. Applied egg-rr 93.0%

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

      1. unpow-1 93.0%

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

   8. Simplified 93.0%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+113}:\\ \;\;\;\;\left(0.91893853320467 + -0.5 \cdot \log x\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+41}:\\ \;\;\;\;\frac{z \cdot \left(z \cdot 0.0007936500793651\right)}{x} + x \cdot \left(\log x + -1\right)\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{+14} \lor \neg \left(z \leq 1.2 \cdot 10^{+25}\right):\\ \;\;\;\;\left(0.91893853320467 + -0.5 \cdot \log x\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{1}{x \cdot 12.000000000000048}\\ \end{array} \]

Alternative 8: 84.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(0.91893853320467 + -0.5 \cdot \log x\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x}\\ t_1 := 0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{+112}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+41}:\\ \;\;\;\;t_1 + z \cdot \left(z \cdot \frac{0.0007936500793651}{x}\right)\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+14} \lor \neg \left(z \leq 9 \cdot 10^{+24}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{1}{x \cdot 12.000000000000048}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          (+ 0.91893853320467 (* -0.5 (log x)))
          (* (+ y 0.0007936500793651) (/ (* z z) x))))
        (t_1 (+ 0.91893853320467 (- (* (+ x -0.5) (log x)) x))))
   (if (<= z -5.4e+112)
     t_0
     (if (<= z -2.4e+41)
       (+ t_1 (* z (* z (/ 0.0007936500793651 x))))
       (if (or (<= z -8.2e+14) (not (<= z 9e+24)))
         t_0
         (+ t_1 (/ 1.0 (* x 12.000000000000048))))))))

C

double code(double x, double y, double z) {
	double t_0 = (0.91893853320467 + (-0.5 * log(x))) + ((y + 0.0007936500793651) * ((z * z) / x));
	double t_1 = 0.91893853320467 + (((x + -0.5) * log(x)) - x);
	double tmp;
	if (z <= -5.4e+112) {
		tmp = t_0;
	} else if (z <= -2.4e+41) {
		tmp = t_1 + (z * (z * (0.0007936500793651 / x)));
	} else if ((z <= -8.2e+14) || !(z <= 9e+24)) {
		tmp = t_0;
	} else {
		tmp = t_1 + (1.0 / (x * 12.000000000000048));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (0.91893853320467d0 + ((-0.5d0) * log(x))) + ((y + 0.0007936500793651d0) * ((z * z) / x))
    t_1 = 0.91893853320467d0 + (((x + (-0.5d0)) * log(x)) - x)
    if (z <= (-5.4d+112)) then
        tmp = t_0
    else if (z <= (-2.4d+41)) then
        tmp = t_1 + (z * (z * (0.0007936500793651d0 / x)))
    else if ((z <= (-8.2d+14)) .or. (.not. (z <= 9d+24))) then
        tmp = t_0
    else
        tmp = t_1 + (1.0d0 / (x * 12.000000000000048d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (0.91893853320467 + (-0.5 * Math.log(x))) + ((y + 0.0007936500793651) * ((z * z) / x));
	double t_1 = 0.91893853320467 + (((x + -0.5) * Math.log(x)) - x);
	double tmp;
	if (z <= -5.4e+112) {
		tmp = t_0;
	} else if (z <= -2.4e+41) {
		tmp = t_1 + (z * (z * (0.0007936500793651 / x)));
	} else if ((z <= -8.2e+14) || !(z <= 9e+24)) {
		tmp = t_0;
	} else {
		tmp = t_1 + (1.0 / (x * 12.000000000000048));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (0.91893853320467 + (-0.5 * math.log(x))) + ((y + 0.0007936500793651) * ((z * z) / x))
	t_1 = 0.91893853320467 + (((x + -0.5) * math.log(x)) - x)
	tmp = 0
	if z <= -5.4e+112:
		tmp = t_0
	elif z <= -2.4e+41:
		tmp = t_1 + (z * (z * (0.0007936500793651 / x)))
	elif (z <= -8.2e+14) or not (z <= 9e+24):
		tmp = t_0
	else:
		tmp = t_1 + (1.0 / (x * 12.000000000000048))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(0.91893853320467 + Float64(-0.5 * log(x))) + Float64(Float64(y + 0.0007936500793651) * Float64(Float64(z * z) / x)))
	t_1 = Float64(0.91893853320467 + Float64(Float64(Float64(x + -0.5) * log(x)) - x))
	tmp = 0.0
	if (z <= -5.4e+112)
		tmp = t_0;
	elseif (z <= -2.4e+41)
		tmp = Float64(t_1 + Float64(z * Float64(z * Float64(0.0007936500793651 / x))));
	elseif ((z <= -8.2e+14) || !(z <= 9e+24))
		tmp = t_0;
	else
		tmp = Float64(t_1 + Float64(1.0 / Float64(x * 12.000000000000048)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (0.91893853320467 + (-0.5 * log(x))) + ((y + 0.0007936500793651) * ((z * z) / x));
	t_1 = 0.91893853320467 + (((x + -0.5) * log(x)) - x);
	tmp = 0.0;
	if (z <= -5.4e+112)
		tmp = t_0;
	elseif (z <= -2.4e+41)
		tmp = t_1 + (z * (z * (0.0007936500793651 / x)));
	elseif ((z <= -8.2e+14) || ~((z <= 9e+24)))
		tmp = t_0;
	else
		tmp = t_1 + (1.0 / (x * 12.000000000000048));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(0.91893853320467 + N[(-0.5 * N[Log[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(N[(z * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(0.91893853320467 + N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.4e+112], t$95$0, If[LessEqual[z, -2.4e+41], N[(t$95$1 + N[(z * N[(z * N[(0.0007936500793651 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -8.2e+14], N[Not[LessEqual[z, 9e+24]], $MachinePrecision]], t$95$0, N[(t$95$1 + N[(1.0 / N[(x * 12.000000000000048), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4000000000000002e112 or -2.4000000000000002e41 < z < -8.2e14 or 9.00000000000000039e24 < z

   1. Initial program 87.2%

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

      1. remove-double-neg 87.2%

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

      2. remove-double-neg 87.2%

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

      3. sub-neg 87.2%

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

      4. metadata-eval 87.2%

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

      5. *-commutative 87.2%

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

      6. fma-def 87.2%

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

      7. fma-neg 87.2%

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

      8. metadata-eval 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in z around inf 87.2%

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

      1. associate-/l* 91.5%

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

      2. +-commutative 91.5%

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

      3. associate-/r/ 91.5%

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

      4. unpow2 91.5%

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

   6. Simplified 91.5%

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

   7. Taylor expanded in x around 0 86.1%

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

   if -5.4000000000000002e112 < z < -2.4000000000000002e41

   1. Initial program 92.1%

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

      1. remove-double-neg 92.1%

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

      2. remove-double-neg 92.1%

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

      3. sub-neg 92.1%

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

      4. metadata-eval 92.1%

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

      5. *-commutative 92.1%

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

      6. fma-def 92.1%

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

      7. fma-neg 92.1%

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

      8. metadata-eval 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in z around inf 91.9%

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

      1. unpow2 91.9%

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

      2. +-commutative 91.9%

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

   6. Simplified 91.9%

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

   7. Taylor expanded in y around 0 99.7%

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

      1. unpow2 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r* 99.9%

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

   9. Simplified 99.9%

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

   10. Taylor expanded in z around 0 99.6%

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

       1. *-commutative 99.6%

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

       2. unpow2 99.6%

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

       3. associate-*l/ 99.7%

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

       4. associate-*r* 99.9%

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

       5. associate-*r/ 99.6%

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

       6. associate-*r/ 99.7%

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

   12. Simplified 99.7%

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

   if -8.2e14 < z < 9.00000000000000039e24

   1. Initial program 99.4%

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

      1. remove-double-neg 99.4%

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

      2. remove-double-neg 99.4%

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

      3. sub-neg 99.4%

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

      4. metadata-eval 99.4%

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

      5. *-commutative 99.4%

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

      6. fma-def 99.4%

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

      7. fma-neg 99.4%

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

      8. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 92.9%

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

      1. clear-num 93.0%

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

      2. inv-pow 93.0%

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

      3. div-inv 93.0%

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

      4. metadata-eval 93.0%

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

   6. Applied egg-rr 93.0%

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

      1. unpow-1 93.0%

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

   8. Simplified 93.0%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+112}:\\ \;\;\;\;\left(0.91893853320467 + -0.5 \cdot \log x\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+41}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + z \cdot \left(z \cdot \frac{0.0007936500793651}{x}\right)\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+14} \lor \neg \left(z \leq 9 \cdot 10^{+24}\right):\\ \;\;\;\;\left(0.91893853320467 + -0.5 \cdot \log x\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{1}{x \cdot 12.000000000000048}\\ \end{array} \]

Alternative 9: 84.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(0.91893853320467 + -0.5 \cdot \log x\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x}\\ t_1 := 0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+112}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+41}:\\ \;\;\;\;t_1 + \frac{z \cdot \left(z \cdot 0.0007936500793651\right)}{x}\\ \mathbf{elif}\;z \leq -85000000000000 \lor \neg \left(z \leq 1.85 \cdot 10^{+25}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{1}{x \cdot 12.000000000000048}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          (+ 0.91893853320467 (* -0.5 (log x)))
          (* (+ y 0.0007936500793651) (/ (* z z) x))))
        (t_1 (+ 0.91893853320467 (- (* (+ x -0.5) (log x)) x))))
   (if (<= z -5.2e+112)
     t_0
     (if (<= z -3.1e+41)
       (+ t_1 (/ (* z (* z 0.0007936500793651)) x))
       (if (or (<= z -85000000000000.0) (not (<= z 1.85e+25)))
         t_0
         (+ t_1 (/ 1.0 (* x 12.000000000000048))))))))

C

double code(double x, double y, double z) {
	double t_0 = (0.91893853320467 + (-0.5 * log(x))) + ((y + 0.0007936500793651) * ((z * z) / x));
	double t_1 = 0.91893853320467 + (((x + -0.5) * log(x)) - x);
	double tmp;
	if (z <= -5.2e+112) {
		tmp = t_0;
	} else if (z <= -3.1e+41) {
		tmp = t_1 + ((z * (z * 0.0007936500793651)) / x);
	} else if ((z <= -85000000000000.0) || !(z <= 1.85e+25)) {
		tmp = t_0;
	} else {
		tmp = t_1 + (1.0 / (x * 12.000000000000048));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (0.91893853320467d0 + ((-0.5d0) * log(x))) + ((y + 0.0007936500793651d0) * ((z * z) / x))
    t_1 = 0.91893853320467d0 + (((x + (-0.5d0)) * log(x)) - x)
    if (z <= (-5.2d+112)) then
        tmp = t_0
    else if (z <= (-3.1d+41)) then
        tmp = t_1 + ((z * (z * 0.0007936500793651d0)) / x)
    else if ((z <= (-85000000000000.0d0)) .or. (.not. (z <= 1.85d+25))) then
        tmp = t_0
    else
        tmp = t_1 + (1.0d0 / (x * 12.000000000000048d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (0.91893853320467 + (-0.5 * Math.log(x))) + ((y + 0.0007936500793651) * ((z * z) / x));
	double t_1 = 0.91893853320467 + (((x + -0.5) * Math.log(x)) - x);
	double tmp;
	if (z <= -5.2e+112) {
		tmp = t_0;
	} else if (z <= -3.1e+41) {
		tmp = t_1 + ((z * (z * 0.0007936500793651)) / x);
	} else if ((z <= -85000000000000.0) || !(z <= 1.85e+25)) {
		tmp = t_0;
	} else {
		tmp = t_1 + (1.0 / (x * 12.000000000000048));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (0.91893853320467 + (-0.5 * math.log(x))) + ((y + 0.0007936500793651) * ((z * z) / x))
	t_1 = 0.91893853320467 + (((x + -0.5) * math.log(x)) - x)
	tmp = 0
	if z <= -5.2e+112:
		tmp = t_0
	elif z <= -3.1e+41:
		tmp = t_1 + ((z * (z * 0.0007936500793651)) / x)
	elif (z <= -85000000000000.0) or not (z <= 1.85e+25):
		tmp = t_0
	else:
		tmp = t_1 + (1.0 / (x * 12.000000000000048))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(0.91893853320467 + Float64(-0.5 * log(x))) + Float64(Float64(y + 0.0007936500793651) * Float64(Float64(z * z) / x)))
	t_1 = Float64(0.91893853320467 + Float64(Float64(Float64(x + -0.5) * log(x)) - x))
	tmp = 0.0
	if (z <= -5.2e+112)
		tmp = t_0;
	elseif (z <= -3.1e+41)
		tmp = Float64(t_1 + Float64(Float64(z * Float64(z * 0.0007936500793651)) / x));
	elseif ((z <= -85000000000000.0) || !(z <= 1.85e+25))
		tmp = t_0;
	else
		tmp = Float64(t_1 + Float64(1.0 / Float64(x * 12.000000000000048)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (0.91893853320467 + (-0.5 * log(x))) + ((y + 0.0007936500793651) * ((z * z) / x));
	t_1 = 0.91893853320467 + (((x + -0.5) * log(x)) - x);
	tmp = 0.0;
	if (z <= -5.2e+112)
		tmp = t_0;
	elseif (z <= -3.1e+41)
		tmp = t_1 + ((z * (z * 0.0007936500793651)) / x);
	elseif ((z <= -85000000000000.0) || ~((z <= 1.85e+25)))
		tmp = t_0;
	else
		tmp = t_1 + (1.0 / (x * 12.000000000000048));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(0.91893853320467 + N[(-0.5 * N[Log[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(N[(z * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(0.91893853320467 + N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e+112], t$95$0, If[LessEqual[z, -3.1e+41], N[(t$95$1 + N[(N[(z * N[(z * 0.0007936500793651), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -85000000000000.0], N[Not[LessEqual[z, 1.85e+25]], $MachinePrecision]], t$95$0, N[(t$95$1 + N[(1.0 / N[(x * 12.000000000000048), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.2000000000000001e112 or -3.1e41 < z < -8.5e13 or 1.8499999999999999e25 < z

   1. Initial program 87.2%

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

      1. remove-double-neg 87.2%

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

      2. remove-double-neg 87.2%

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

      3. sub-neg 87.2%

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

      4. metadata-eval 87.2%

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

      5. *-commutative 87.2%

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

      6. fma-def 87.2%

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

      7. fma-neg 87.2%

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

      8. metadata-eval 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in z around inf 87.2%

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

      1. associate-/l* 91.5%

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

      2. +-commutative 91.5%

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

      3. associate-/r/ 91.5%

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

      4. unpow2 91.5%

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

   6. Simplified 91.5%

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

   7. Taylor expanded in x around 0 86.1%

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

   if -5.2000000000000001e112 < z < -3.1e41

   1. Initial program 92.1%

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

      1. remove-double-neg 92.1%

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

      2. remove-double-neg 92.1%

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

      3. sub-neg 92.1%

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

      4. metadata-eval 92.1%

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

      5. *-commutative 92.1%

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

      6. fma-def 92.1%

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

      7. fma-neg 92.1%

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

      8. metadata-eval 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in z around inf 91.9%

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

      1. unpow2 91.9%

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

      2. +-commutative 91.9%

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

   6. Simplified 91.9%

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

   7. Taylor expanded in y around 0 99.7%

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

      1. unpow2 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r* 99.9%

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

   9. Simplified 99.9%

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

   if -8.5e13 < z < 1.8499999999999999e25

   1. Initial program 99.4%

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

      1. remove-double-neg 99.4%

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

      2. remove-double-neg 99.4%

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

      3. sub-neg 99.4%

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

      4. metadata-eval 99.4%

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

      5. *-commutative 99.4%

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

      6. fma-def 99.4%

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

      7. fma-neg 99.4%

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

      8. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 92.9%

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

      1. clear-num 93.0%

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

      2. inv-pow 93.0%

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

      3. div-inv 93.0%

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

      4. metadata-eval 93.0%

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

   6. Applied egg-rr 93.0%

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

      1. unpow-1 93.0%

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

   8. Simplified 93.0%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+112}:\\ \;\;\;\;\left(0.91893853320467 + -0.5 \cdot \log x\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+41}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{z \cdot \left(z \cdot 0.0007936500793651\right)}{x}\\ \mathbf{elif}\;z \leq -85000000000000 \lor \neg \left(z \leq 1.85 \cdot 10^{+25}\right):\\ \;\;\;\;\left(0.91893853320467 + -0.5 \cdot \log x\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{1}{x \cdot 12.000000000000048}\\ \end{array} \]

Alternative 10: 95.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\\ \mathbf{if}\;z \leq -2800000000000 \lor \neg \left(z \leq 0.0055\right):\\ \;\;\;\;t_0 + z \cdot \left(z \cdot \frac{y + 0.0007936500793651}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 0.91893853320467 (- (* (+ x -0.5) (log x)) x))))
   (if (or (<= z -2800000000000.0) (not (<= z 0.0055)))
     (+ t_0 (* z (* z (/ (+ y 0.0007936500793651) x))))
     (+ t_0 (/ (+ 0.083333333333333 (* z -0.0027777777777778)) x)))))

C

double code(double x, double y, double z) {
	double t_0 = 0.91893853320467 + (((x + -0.5) * log(x)) - x);
	double tmp;
	if ((z <= -2800000000000.0) || !(z <= 0.0055)) {
		tmp = t_0 + (z * (z * ((y + 0.0007936500793651) / x)));
	} else {
		tmp = t_0 + ((0.083333333333333 + (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) :: t_0
    real(8) :: tmp
    t_0 = 0.91893853320467d0 + (((x + (-0.5d0)) * log(x)) - x)
    if ((z <= (-2800000000000.0d0)) .or. (.not. (z <= 0.0055d0))) then
        tmp = t_0 + (z * (z * ((y + 0.0007936500793651d0) / x)))
    else
        tmp = t_0 + ((0.083333333333333d0 + (z * (-0.0027777777777778d0))) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 0.91893853320467 + (((x + -0.5) * Math.log(x)) - x);
	double tmp;
	if ((z <= -2800000000000.0) || !(z <= 0.0055)) {
		tmp = t_0 + (z * (z * ((y + 0.0007936500793651) / x)));
	} else {
		tmp = t_0 + ((0.083333333333333 + (z * -0.0027777777777778)) / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 0.91893853320467 + (((x + -0.5) * math.log(x)) - x)
	tmp = 0
	if (z <= -2800000000000.0) or not (z <= 0.0055):
		tmp = t_0 + (z * (z * ((y + 0.0007936500793651) / x)))
	else:
		tmp = t_0 + ((0.083333333333333 + (z * -0.0027777777777778)) / x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(0.91893853320467 + Float64(Float64(Float64(x + -0.5) * log(x)) - x))
	tmp = 0.0
	if ((z <= -2800000000000.0) || !(z <= 0.0055))
		tmp = Float64(t_0 + Float64(z * Float64(z * Float64(Float64(y + 0.0007936500793651) / x))));
	else
		tmp = Float64(t_0 + Float64(Float64(0.083333333333333 + Float64(z * -0.0027777777777778)) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 0.91893853320467 + (((x + -0.5) * log(x)) - x);
	tmp = 0.0;
	if ((z <= -2800000000000.0) || ~((z <= 0.0055)))
		tmp = t_0 + (z * (z * ((y + 0.0007936500793651) / x)));
	else
		tmp = t_0 + ((0.083333333333333 + (z * -0.0027777777777778)) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(0.91893853320467 + N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -2800000000000.0], N[Not[LessEqual[z, 0.0055]], $MachinePrecision]], N[(t$95$0 + N[(z * N[(z * N[(N[(y + 0.0007936500793651), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(N[(0.083333333333333 + N[(z * -0.0027777777777778), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8e12 or 0.0054999999999999997 < z

   1. Initial program 88.2%

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

      1. remove-double-neg 88.2%

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

      2. remove-double-neg 88.2%

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

      3. sub-neg 88.2%

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

      4. metadata-eval 88.2%

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

      5. *-commutative 88.2%

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

      6. fma-def 88.2%

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

      7. fma-neg 88.2%

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

      8. metadata-eval 88.2%

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

   3. Simplified 88.2%

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

      1. clear-num 88.2%

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

      2. metadata-eval 88.2%

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

      3. fma-neg 88.2%

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

      4. fma-udef 88.2%

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

      5. *-commutative 88.2%

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

      6. inv-pow 88.2%

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

      7. *-commutative 88.2%

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

      8. fma-udef 88.2%

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

      9. fma-neg 88.2%

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

      10. metadata-eval 88.2%

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

      11. fma-udef 88.2%

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

      12. *-commutative 88.2%

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

      13. fma-def 88.2%

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

   5. Applied egg-rr 88.2%

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

   6. Taylor expanded in z around inf 87.9%

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

      1. unpow2 87.9%

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

      2. associate-/l* 92.3%

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

      3. *-rgt-identity 92.3%

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

      4. +-commutative 92.3%

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

      5. associate-*r/ 92.3%

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

      6. associate-*l* 99.5%

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

      7. associate-/r/ 99.5%

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

      8. *-commutative 99.5%

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

      9. associate-*r/ 99.5%

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

      10. *-rgt-identity 99.5%

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

      11. +-commutative 99.5%

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

   8. Simplified 99.5%

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

   if -2.8e12 < z < 0.0054999999999999997

   1. Initial program 99.3%

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

      1. remove-double-neg 99.3%

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

      2. remove-double-neg 99.3%

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

      3. sub-neg 99.3%

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

      4. metadata-eval 99.3%

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

      5. *-commutative 99.3%

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

      6. fma-def 99.3%

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

      7. fma-neg 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in z around 0 94.6%

      \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{0.083333333333333 + -0.0027777777777778 \cdot z}}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2800000000000 \lor \neg \left(z \leq 0.0055\right):\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + z \cdot \left(z \cdot \frac{y + 0.0007936500793651}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \end{array} \]

Alternative 11: 77.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(\log x + -1\right)\\ \mathbf{if}\;z \leq -0.0047 \lor \neg \left(z \leq 10.2\right):\\ \;\;\;\;\frac{z \cdot \left(z \cdot 0.0007936500793651\right)}{x} + t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x} + t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ (log x) -1.0))))
   (if (or (<= z -0.0047) (not (<= z 10.2)))
     (+ (/ (* z (* z 0.0007936500793651)) 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 <= -0.0047) || !(z <= 10.2)) {
		tmp = ((z * (z * 0.0007936500793651)) / 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 <= (-0.0047d0)) .or. (.not. (z <= 10.2d0))) then
        tmp = ((z * (z * 0.0007936500793651d0)) / 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 <= -0.0047) || !(z <= 10.2)) {
		tmp = ((z * (z * 0.0007936500793651)) / 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 <= -0.0047) or not (z <= 10.2):
		tmp = ((z * (z * 0.0007936500793651)) / 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 <= -0.0047) || !(z <= 10.2))
		tmp = Float64(Float64(Float64(z * Float64(z * 0.0007936500793651)) / 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 <= -0.0047) || ~((z <= 10.2)))
		tmp = ((z * (z * 0.0007936500793651)) / 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, -0.0047], N[Not[LessEqual[z, 10.2]], $MachinePrecision]], N[(N[(N[(z * N[(z * 0.0007936500793651), $MachinePrecision]), $MachinePrecision] / x), $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 < -0.00470000000000000018 or 10.199999999999999 < z

   1. Initial program 88.6%

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

      1. remove-double-neg 88.6%

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

      2. remove-double-neg 88.6%

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

      3. sub-neg 88.6%

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

      4. metadata-eval 88.6%

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

      5. *-commutative 88.6%

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

      6. fma-def 88.6%

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

      7. fma-neg 88.6%

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

      8. metadata-eval 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in z around inf 88.2%

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

      1. unpow2 88.2%

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

      2. +-commutative 88.2%

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

   6. Simplified 88.2%

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

   7. Taylor expanded in y around 0 64.6%

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

      1. unpow2 64.6%

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

      2. *-commutative 64.6%

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

      3. associate-*r* 64.6%

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

   9. Simplified 64.6%

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

   10. Taylor expanded in x around inf 64.3%

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

       1. *-commutative 20.7%

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

       2. sub-neg 20.7%

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

       3. mul-1-neg 20.7%

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

       4. log-rec 20.7%

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

       5. remove-double-neg 20.7%

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

       6. metadata-eval 20.7%

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

   12. Simplified 64.3%

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

   if -0.00470000000000000018 < z < 10.199999999999999

   1. Initial program 99.4%

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

      1. remove-double-neg 99.4%

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

      2. remove-double-neg 99.4%

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

      3. sub-neg 99.4%

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

      4. metadata-eval 99.4%

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

      5. *-commutative 99.4%

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

      6. fma-def 99.4%

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

      7. fma-neg 99.4%

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

      8. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 93.9%

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

   5. Taylor expanded in x around inf 92.2%

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

      1. *-commutative 92.2%

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

      2. sub-neg 92.2%

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

      3. mul-1-neg 92.2%

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

      4. log-rec 92.2%

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

      5. remove-double-neg 92.2%

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

      6. metadata-eval 92.2%

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

   7. Simplified 92.2%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0047 \lor \neg \left(z \leq 10.2\right):\\ \;\;\;\;\frac{z \cdot \left(z \cdot 0.0007936500793651\right)}{x} + x \cdot \left(\log x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x} + x \cdot \left(\log x + -1\right)\\ \end{array} \]

Alternative 12: 78.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -11 \lor \neg \left(z \leq 10.2\right):\\ \;\;\;\;\frac{z \cdot \left(z \cdot 0.0007936500793651\right)}{x} + x \cdot \left(\log x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -11.0) (not (<= z 10.2)))
   (+ (/ (* z (* z 0.0007936500793651)) x) (* x (+ (log x) -1.0)))
   (+
    (+ 0.91893853320467 (- (* (+ x -0.5) (log x)) x))
    (/ 0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -11.0) || !(z <= 10.2)) {
		tmp = ((z * (z * 0.0007936500793651)) / x) + (x * (log(x) + -1.0));
	} else {
		tmp = (0.91893853320467 + (((x + -0.5) * log(x)) - x)) + (0.083333333333333 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-11.0d0)) .or. (.not. (z <= 10.2d0))) then
        tmp = ((z * (z * 0.0007936500793651d0)) / x) + (x * (log(x) + (-1.0d0)))
    else
        tmp = (0.91893853320467d0 + (((x + (-0.5d0)) * log(x)) - x)) + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -11.0) || !(z <= 10.2)) {
		tmp = ((z * (z * 0.0007936500793651)) / x) + (x * (Math.log(x) + -1.0));
	} else {
		tmp = (0.91893853320467 + (((x + -0.5) * Math.log(x)) - x)) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -11.0) or not (z <= 10.2):
		tmp = ((z * (z * 0.0007936500793651)) / x) + (x * (math.log(x) + -1.0))
	else:
		tmp = (0.91893853320467 + (((x + -0.5) * math.log(x)) - x)) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -11.0) || !(z <= 10.2))
		tmp = Float64(Float64(Float64(z * Float64(z * 0.0007936500793651)) / x) + Float64(x * Float64(log(x) + -1.0)));
	else
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(Float64(x + -0.5) * log(x)) - x)) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -11.0) || ~((z <= 10.2)))
		tmp = ((z * (z * 0.0007936500793651)) / x) + (x * (log(x) + -1.0));
	else
		tmp = (0.91893853320467 + (((x + -0.5) * log(x)) - x)) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -11.0], N[Not[LessEqual[z, 10.2]], $MachinePrecision]], N[(N[(N[(z * N[(z * 0.0007936500793651), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] + N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.91893853320467 + N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -11 or 10.199999999999999 < z

   1. Initial program 88.4%

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

      1. remove-double-neg 88.4%

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

      2. remove-double-neg 88.4%

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

      3. sub-neg 88.4%

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

      4. metadata-eval 88.4%

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

      5. *-commutative 88.4%

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

      6. fma-def 88.4%

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

      7. fma-neg 88.4%

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

      8. metadata-eval 88.4%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in z around inf 88.0%

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

      1. unpow2 88.0%

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

      2. +-commutative 88.0%

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

   6. Simplified 88.0%

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

   7. Taylor expanded in y around 0 64.1%

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

      1. unpow2 64.1%

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

      2. *-commutative 64.1%

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

      3. associate-*r* 64.1%

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

   9. Simplified 64.1%

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

   10. Taylor expanded in x around inf 64.1%

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

       1. *-commutative 19.8%

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

       2. sub-neg 19.8%

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

       3. mul-1-neg 19.8%

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

       4. log-rec 19.8%

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

       5. remove-double-neg 19.8%

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

       6. metadata-eval 19.8%

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

   12. Simplified 64.1%

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

   if -11 < z < 10.199999999999999

   1. Initial program 99.4%

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

      1. remove-double-neg 99.4%

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

      2. remove-double-neg 99.4%

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

      3. sub-neg 99.4%

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

      4. metadata-eval 99.4%

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

      5. *-commutative 99.4%

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

      6. fma-def 99.4%

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

      7. fma-neg 99.4%

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

      8. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 93.9%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -11 \lor \neg \left(z \leq 10.2\right):\\ \;\;\;\;\frac{z \cdot \left(z \cdot 0.0007936500793651\right)}{x} + x \cdot \left(\log x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 13: 57.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+70} \lor \neg \left(z \leq 1.8 \cdot 10^{+36}\right):\\ \;\;\;\;\sqrt{\frac{0.0069444444444443885}{x \cdot x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x} + x \cdot \left(\log x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6.8e+70) (not (<= z 1.8e+36)))
   (sqrt (/ 0.0069444444444443885 (* x x)))
   (+ (/ 0.083333333333333 x) (* x (+ (log x) -1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.8e+70) || !(z <= 1.8e+36)) {
		tmp = sqrt((0.0069444444444443885 / (x * x)));
	} else {
		tmp = (0.083333333333333 / x) + (x * (log(x) + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-6.8d+70)) .or. (.not. (z <= 1.8d+36))) then
        tmp = sqrt((0.0069444444444443885d0 / (x * x)))
    else
        tmp = (0.083333333333333d0 / x) + (x * (log(x) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.8e+70) || !(z <= 1.8e+36)) {
		tmp = Math.sqrt((0.0069444444444443885 / (x * x)));
	} else {
		tmp = (0.083333333333333 / x) + (x * (Math.log(x) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6.8e+70) or not (z <= 1.8e+36):
		tmp = math.sqrt((0.0069444444444443885 / (x * x)))
	else:
		tmp = (0.083333333333333 / x) + (x * (math.log(x) + -1.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6.8e+70) || !(z <= 1.8e+36))
		tmp = sqrt(Float64(0.0069444444444443885 / Float64(x * x)));
	else
		tmp = Float64(Float64(0.083333333333333 / x) + Float64(x * Float64(log(x) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -6.8e+70) || ~((z <= 1.8e+36)))
		tmp = sqrt((0.0069444444444443885 / (x * x)));
	else
		tmp = (0.083333333333333 / x) + (x * (log(x) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6.8e+70], N[Not[LessEqual[z, 1.8e+36]], $MachinePrecision]], N[Sqrt[N[(0.0069444444444443885 / N[(x * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[(N[(0.083333333333333 / x), $MachinePrecision] + N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.8000000000000002e70 or 1.7999999999999999e36 < z

   1. Initial program 87.6%

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

      1. remove-double-neg 87.6%

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

      2. remove-double-neg 87.6%

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

      3. sub-neg 87.6%

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

      4. metadata-eval 87.6%

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

      5. *-commutative 87.6%

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

      6. fma-def 87.6%

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

      7. fma-neg 87.6%

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

      8. metadata-eval 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in z around 0 14.5%

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

   5. Taylor expanded in x around inf 14.5%

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

      1. *-commutative 14.5%

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

      2. sub-neg 14.5%

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

      3. mul-1-neg 14.5%

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

      4. log-rec 14.5%

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

      5. remove-double-neg 14.5%

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

      6. metadata-eval 14.5%

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

   7. Simplified 14.5%

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

   8. Taylor expanded in x around 0 3.6%

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

      1. add-sqr-sqrt 3.6%

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

      2. sqrt-unprod 30.1%

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

      3. frac-times 30.1%

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

      4. metadata-eval 30.1%

         \[\leadsto \sqrt{\frac{\color{blue}{0.0069444444444443885}}{x \cdot x}} \]

   10. Applied egg-rr 30.1%

       \[\leadsto \color{blue}{\sqrt{\frac{0.0069444444444443885}{x \cdot x}}} \]

   if -6.8000000000000002e70 < z < 1.7999999999999999e36

   1. Initial program 98.7%

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

      1. remove-double-neg 98.7%

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

      2. remove-double-neg 98.7%

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

      3. sub-neg 98.7%

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

      4. metadata-eval 98.7%

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

      5. *-commutative 98.7%

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

      6. fma-def 98.7%

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

      7. fma-neg 98.7%

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

      8. metadata-eval 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in z around 0 89.3%

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

   5. Taylor expanded in x around inf 87.6%

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

      1. *-commutative 87.6%

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

      2. sub-neg 87.6%

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

      3. mul-1-neg 87.6%

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

      4. log-rec 87.6%

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

      5. remove-double-neg 87.6%

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

      6. metadata-eval 87.6%

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

   7. Simplified 87.6%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+70} \lor \neg \left(z \leq 1.8 \cdot 10^{+36}\right):\\ \;\;\;\;\sqrt{\frac{0.0069444444444443885}{x \cdot x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x} + x \cdot \left(\log x + -1\right)\\ \end{array} \]

Alternative 14: 31.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+67} \lor \neg \left(z \leq 5.2 \cdot 10^{+35}\right):\\ \;\;\;\;\sqrt{\frac{0.0069444444444443885}{x \cdot x}}\\ \mathbf{else}:\\ \;\;\;\;0.91893853320467 + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.8e+67) (not (<= z 5.2e+35)))
   (sqrt (/ 0.0069444444444443885 (* x x)))
   (+ 0.91893853320467 (/ 0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.8e+67) || !(z <= 5.2e+35)) {
		tmp = sqrt((0.0069444444444443885 / (x * x)));
	} else {
		tmp = 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 <= (-2.8d+67)) .or. (.not. (z <= 5.2d+35))) then
        tmp = sqrt((0.0069444444444443885d0 / (x * x)))
    else
        tmp = 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 <= -2.8e+67) || !(z <= 5.2e+35)) {
		tmp = Math.sqrt((0.0069444444444443885 / (x * x)));
	} else {
		tmp = 0.91893853320467 + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.8e+67) or not (z <= 5.2e+35):
		tmp = math.sqrt((0.0069444444444443885 / (x * x)))
	else:
		tmp = 0.91893853320467 + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.8e+67) || !(z <= 5.2e+35))
		tmp = sqrt(Float64(0.0069444444444443885 / Float64(x * x)));
	else
		tmp = Float64(0.91893853320467 + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.8e+67) || ~((z <= 5.2e+35)))
		tmp = sqrt((0.0069444444444443885 / (x * x)));
	else
		tmp = 0.91893853320467 + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.8e+67], N[Not[LessEqual[z, 5.2e+35]], $MachinePrecision]], N[Sqrt[N[(0.0069444444444443885 / N[(x * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[(0.91893853320467 + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7999999999999998e67 or 5.20000000000000013e35 < z

   1. Initial program 87.6%

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

      1. remove-double-neg 87.6%

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

      2. remove-double-neg 87.6%

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

      3. sub-neg 87.6%

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

      4. metadata-eval 87.6%

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

      5. *-commutative 87.6%

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

      6. fma-def 87.6%

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

      7. fma-neg 87.6%

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

      8. metadata-eval 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in z around 0 14.5%

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

   5. Taylor expanded in x around inf 14.5%

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

      1. *-commutative 14.5%

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

      2. sub-neg 14.5%

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

      3. mul-1-neg 14.5%

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

      4. log-rec 14.5%

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

      5. remove-double-neg 14.5%

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

      6. metadata-eval 14.5%

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

   7. Simplified 14.5%

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

   8. Taylor expanded in x around 0 3.6%

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

      1. add-sqr-sqrt 3.6%

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

      2. sqrt-unprod 30.1%

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

      3. frac-times 30.1%

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

      4. metadata-eval 30.1%

         \[\leadsto \sqrt{\frac{\color{blue}{0.0069444444444443885}}{x \cdot x}} \]

   10. Applied egg-rr 30.1%

       \[\leadsto \color{blue}{\sqrt{\frac{0.0069444444444443885}{x \cdot x}}} \]

   if -2.7999999999999998e67 < z < 5.20000000000000013e35

   1. Initial program 98.7%

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

      1. remove-double-neg 98.7%

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

      2. remove-double-neg 98.7%

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

      3. sub-neg 98.7%

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

      4. metadata-eval 98.7%

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

      5. *-commutative 98.7%

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

      6. fma-def 98.7%

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

      7. fma-neg 98.7%

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

      8. metadata-eval 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in z around 0 89.3%

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

   5. Taylor expanded in x around inf 87.5%

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

      1. mul-1-neg 87.5%

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

      2. distribute-lft-neg-in 87.5%

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

      3. log-rec 87.5%

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

      4. remove-double-neg 87.5%

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

      5. *-commutative 87.5%

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

   7. Simplified 87.5%

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

   8. Taylor expanded in x around 0 40.5%

      \[\leadsto \color{blue}{0.91893853320467 + 0.083333333333333 \cdot \frac{1}{x}} \]
   9. Step-by-step derivation

      1. associate-*r/ 40.5%

         \[\leadsto 0.91893853320467 + \color{blue}{\frac{0.083333333333333 \cdot 1}{x}} \]

      2. metadata-eval 40.5%

         \[\leadsto 0.91893853320467 + \frac{\color{blue}{0.083333333333333}}{x} \]

      3. +-commutative 40.5%

         \[\leadsto \color{blue}{\frac{0.083333333333333}{x} + 0.91893853320467} \]

   10. Simplified 40.5%

       \[\leadsto \color{blue}{\frac{0.083333333333333}{x} + 0.91893853320467} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+67} \lor \neg \left(z \leq 5.2 \cdot 10^{+35}\right):\\ \;\;\;\;\sqrt{\frac{0.0069444444444443885}{x \cdot x}}\\ \mathbf{else}:\\ \;\;\;\;0.91893853320467 + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 15: 24.4% accurate, 24.6× speedup

Math

\[\begin{array}{l} \\ 0.91893853320467 + \frac{0.083333333333333}{x} \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 0.91893853320467d0 + (0.083333333333333d0 / x)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.8%

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

   1. remove-double-neg 93.8%

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

   2. remove-double-neg 93.8%

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

   3. sub-neg 93.8%

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

   4. metadata-eval 93.8%

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

   5. *-commutative 93.8%

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

   6. fma-def 93.8%

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

   7. fma-neg 93.8%

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

   8. metadata-eval 93.8%

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

3. Simplified 93.8%

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

4. Taylor expanded in z around 0 56.6%

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

5. Taylor expanded in x around inf 55.6%

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

   1. mul-1-neg 55.6%

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

   2. distribute-lft-neg-in 55.6%

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

   3. log-rec 55.6%

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

   4. remove-double-neg 55.6%

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

   5. *-commutative 55.6%

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

7. Simplified 55.6%

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

8. Taylor expanded in x around 0 24.5%

   \[\leadsto \color{blue}{0.91893853320467 + 0.083333333333333 \cdot \frac{1}{x}} \]
9. Step-by-step derivation

   1. associate-*r/ 24.5%

      \[\leadsto 0.91893853320467 + \color{blue}{\frac{0.083333333333333 \cdot 1}{x}} \]

   2. metadata-eval 24.5%

      \[\leadsto 0.91893853320467 + \frac{\color{blue}{0.083333333333333}}{x} \]

   3. +-commutative 24.5%

      \[\leadsto \color{blue}{\frac{0.083333333333333}{x} + 0.91893853320467} \]

10. Simplified 24.5%

    \[\leadsto \color{blue}{\frac{0.083333333333333}{x} + 0.91893853320467} \]

11. Final simplification 24.5%

    \[\leadsto 0.91893853320467 + \frac{0.083333333333333}{x} \]

Alternative 16: 23.8% accurate, 41.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 0.083333333333333d0 / x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.8%

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

   1. remove-double-neg 93.8%

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

   2. remove-double-neg 93.8%

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

   3. sub-neg 93.8%

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

   4. metadata-eval 93.8%

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

   5. *-commutative 93.8%

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

   6. fma-def 93.8%

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

   7. fma-neg 93.8%

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

   8. metadata-eval 93.8%

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

3. Simplified 93.8%

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

4. Taylor expanded in z around 0 56.6%

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

5. Taylor expanded in x around inf 55.6%

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

   1. *-commutative 55.6%

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

   2. sub-neg 55.6%

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

   3. mul-1-neg 55.6%

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

   4. log-rec 55.6%

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

   5. remove-double-neg 55.6%

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

   6. metadata-eval 55.6%

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

7. Simplified 55.6%

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

8. Taylor expanded in x around 0 23.9%

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

9. Final simplification 23.9%

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

Developer target: 98.7% 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 2023192 
(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)))