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

Percentage Accurate: 93.5% → 99.3%

Time: 16.1s

Alternatives: 17

Speedup: 1.1×

• 27.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\\ \mathbf{if}\;x \leq 0.0026:\\ \;\;\;\;t_0 + {\left(\frac{x}{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;t_0 + z \cdot \left(z \cdot \left(\frac{0.0007936500793651}{x} + \frac{y}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (- (* (+ x -0.5) (log x)) x) 0.91893853320467)))
   (if (<= x 0.0026)
     (+
      t_0
      (pow
       (/
        x
        (fma
         z
         (fma (+ y 0.0007936500793651) z -0.0027777777777778)
         0.083333333333333))
       -1.0))
     (+ t_0 (* z (* z (+ (/ 0.0007936500793651 x) (/ y x))))))))

C

double code(double x, double y, double z) {
	double t_0 = (((x + -0.5) * log(x)) - x) + 0.91893853320467;
	double tmp;
	if (x <= 0.0026) {
		tmp = t_0 + pow((x / fma(z, fma((y + 0.0007936500793651), z, -0.0027777777777778), 0.083333333333333)), -1.0);
	} else {
		tmp = t_0 + (z * (z * ((0.0007936500793651 / x) + (y / x))));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(x + -0.5) * log(x)) - x) + 0.91893853320467)
	tmp = 0.0
	if (x <= 0.0026)
		tmp = Float64(t_0 + (Float64(x / fma(z, fma(Float64(y + 0.0007936500793651), z, -0.0027777777777778), 0.083333333333333)) ^ -1.0));
	else
		tmp = Float64(t_0 + Float64(z * Float64(z * Float64(Float64(0.0007936500793651 / x) + Float64(y / x)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision]}, If[LessEqual[x, 0.0026], N[(t$95$0 + N[Power[N[(x / N[(z * N[(N[(y + 0.0007936500793651), $MachinePrecision] * z + -0.0027777777777778), $MachinePrecision] + 0.083333333333333), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(z * N[(z * N[(N[(0.0007936500793651 / x), $MachinePrecision] + N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 0.0025999999999999999

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. metadata-eval 99.6%

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

      3. fma-def 99.6%

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

      4. fma-neg 99.7%

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

      5. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. metadata-eval 99.7%

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

      2. fma-neg 99.6%

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

      3. fma-def 99.6%

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

      4. clear-num 99.7%

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

      5. inv-pow 99.7%

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

      6. *-commutative 99.7%

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

      7. fma-udef 99.7%

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

      8. fma-neg 99.7%

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

      9. metadata-eval 99.7%

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

   5. Applied egg-rr 99.7%

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

   if 0.0025999999999999999 < x

   1. Initial program 87.3%

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

      1. sub-neg 87.3%

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

      2. metadata-eval 87.3%

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

      3. fma-def 87.3%

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

      4. fma-neg 87.3%

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

      5. metadata-eval 87.3%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in z around inf 87.3%

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

      1. associate-+r+ 87.3%

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

      2. fma-def 87.3%

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

      3. associate-*r/ 87.3%

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

      4. metadata-eval 87.3%

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

      5. associate-/l* 89.5%

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

      6. unpow2 89.5%

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

   6. Simplified 89.5%

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

   7. Taylor expanded in z around inf 89.5%

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

      1. unpow2 89.5%

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

      2. associate-*l* 99.6%

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

      3. associate-*r/ 99.6%

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

      4. metadata-eval 99.6%

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

   9. Simplified 99.6%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.0026:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + {\left(\frac{x}{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + z \cdot \left(z \cdot \left(\frac{0.0007936500793651}{x} + \frac{y}{x}\right)\right)\\ \end{array} \]

Alternative 2: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4 \cdot 10^{+22}:\\ \;\;\;\;\left(0.91893853320467 + \mathsf{fma}\left(x + -0.5, \log x, -x\right)\right) + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + z \cdot \left(z \cdot \left(\frac{0.0007936500793651}{x} + \frac{y}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 4e+22)
   (+
    (+ 0.91893853320467 (fma (+ x -0.5) (log x) (- x)))
    (/
     (fma
      z
      (fma (+ y 0.0007936500793651) z -0.0027777777777778)
      0.083333333333333)
     x))
   (+
    (+ (- (* (+ x -0.5) (log x)) x) 0.91893853320467)
    (* z (* z (+ (/ 0.0007936500793651 x) (/ y x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 4e+22) {
		tmp = (0.91893853320467 + fma((x + -0.5), log(x), -x)) + (fma(z, fma((y + 0.0007936500793651), z, -0.0027777777777778), 0.083333333333333) / x);
	} else {
		tmp = ((((x + -0.5) * log(x)) - x) + 0.91893853320467) + (z * (z * ((0.0007936500793651 / x) + (y / x))));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 4e+22)
		tmp = Float64(Float64(0.91893853320467 + fma(Float64(x + -0.5), log(x), Float64(-x))) + Float64(fma(z, fma(Float64(y + 0.0007936500793651), z, -0.0027777777777778), 0.083333333333333) / x));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(x + -0.5) * log(x)) - x) + 0.91893853320467) + Float64(z * Float64(z * Float64(Float64(0.0007936500793651 / x) + Float64(y / x)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 4e+22], N[(N[(0.91893853320467 + N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision] + (-x)), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(N[(y + 0.0007936500793651), $MachinePrecision] * z + -0.0027777777777778), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(z * N[(z * N[(N[(0.0007936500793651 / x), $MachinePrecision] + N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4e22

   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. fma-neg 99.6%

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

      2. sub-neg 99.6%

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

      3. metadata-eval 99.6%

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

      4. *-commutative 99.6%

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

      5. fma-def 99.6%

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

      6. fma-neg 99.7%

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

      7. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   if 4e22 < x

   1. Initial program 86.1%

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

      1. sub-neg 86.1%

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

      2. metadata-eval 86.1%

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

      3. fma-def 86.1%

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

      4. fma-neg 86.1%

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

      5. metadata-eval 86.1%

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

   3. Simplified 86.1%

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

   4. Taylor expanded in z around inf 86.1%

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

      1. associate-+r+ 86.1%

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

      2. fma-def 86.1%

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

      3. associate-*r/ 86.1%

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

      4. metadata-eval 86.1%

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

      5. associate-/l* 88.6%

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

      6. unpow2 88.6%

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

   6. Simplified 88.6%

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

   7. Taylor expanded in z around inf 88.5%

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

      1. unpow2 88.5%

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

      2. associate-*l* 99.6%

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

      3. associate-*r/ 99.6%

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

      4. metadata-eval 99.6%

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

   9. Simplified 99.6%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4 \cdot 10^{+22}:\\ \;\;\;\;\left(0.91893853320467 + \mathsf{fma}\left(x + -0.5, \log x, -x\right)\right) + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + z \cdot \left(z \cdot \left(\frac{0.0007936500793651}{x} + \frac{y}{x}\right)\right)\\ \end{array} \]

Alternative 3: 99.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\\ \mathbf{if}\;x \leq 0.0026:\\ \;\;\;\;t_0 + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;t_0 + z \cdot \left(z \cdot \left(\frac{0.0007936500793651}{x} + \frac{y}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (- (* (+ x -0.5) (log x)) x) 0.91893853320467)))
   (if (<= x 0.0026)
     (+
      t_0
      (/
       (fma
        (fma (+ y 0.0007936500793651) z -0.0027777777777778)
        z
        0.083333333333333)
       x))
     (+ t_0 (* z (* z (+ (/ 0.0007936500793651 x) (/ y x))))))))

C

double code(double x, double y, double z) {
	double t_0 = (((x + -0.5) * log(x)) - x) + 0.91893853320467;
	double tmp;
	if (x <= 0.0026) {
		tmp = t_0 + (fma(fma((y + 0.0007936500793651), z, -0.0027777777777778), z, 0.083333333333333) / x);
	} else {
		tmp = t_0 + (z * (z * ((0.0007936500793651 / x) + (y / x))));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(x + -0.5) * log(x)) - x) + 0.91893853320467)
	tmp = 0.0
	if (x <= 0.0026)
		tmp = Float64(t_0 + Float64(fma(fma(Float64(y + 0.0007936500793651), z, -0.0027777777777778), z, 0.083333333333333) / x));
	else
		tmp = Float64(t_0 + Float64(z * Float64(z * Float64(Float64(0.0007936500793651 / x) + Float64(y / x)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision]}, If[LessEqual[x, 0.0026], N[(t$95$0 + N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z + -0.0027777777777778), $MachinePrecision] * z + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(z * N[(z * N[(N[(0.0007936500793651 / x), $MachinePrecision] + N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 0.0025999999999999999

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. metadata-eval 99.6%

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

      3. fma-def 99.6%

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

      4. fma-neg 99.7%

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

      5. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   if 0.0025999999999999999 < x

   1. Initial program 87.3%

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

      1. sub-neg 87.3%

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

      2. metadata-eval 87.3%

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

      3. fma-def 87.3%

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

      4. fma-neg 87.3%

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

      5. metadata-eval 87.3%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in z around inf 87.3%

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

      1. associate-+r+ 87.3%

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

      2. fma-def 87.3%

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

      3. associate-*r/ 87.3%

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

      4. metadata-eval 87.3%

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

      5. associate-/l* 89.5%

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

      6. unpow2 89.5%

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

   6. Simplified 89.5%

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

   7. Taylor expanded in z around inf 89.5%

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

      1. unpow2 89.5%

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

      2. associate-*l* 99.6%

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

      3. associate-*r/ 99.6%

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

      4. metadata-eval 99.6%

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

   9. Simplified 99.6%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.0026:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + z \cdot \left(z \cdot \left(\frac{0.0007936500793651}{x} + \frac{y}{x}\right)\right)\\ \end{array} \]

Alternative 4: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.0026:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + z \cdot \left(z \cdot \left(\frac{0.0007936500793651}{x} + \frac{y}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 0.0026)
   (+
    (+ 0.91893853320467 (- (* (log x) (- x 0.5)) x))
    (/
     (+
      0.083333333333333
      (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))
     x))
   (+
    (+ (- (* (+ x -0.5) (log x)) x) 0.91893853320467)
    (* z (* z (+ (/ 0.0007936500793651 x) (/ y x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 0.0026) {
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = ((((x + -0.5) * log(x)) - x) + 0.91893853320467) + (z * (z * ((0.0007936500793651 / x) + (y / x))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 0.0026d0) then
        tmp = (0.91893853320467d0 + ((log(x) * (x - 0.5d0)) - x)) + ((0.083333333333333d0 + (z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0))) / x)
    else
        tmp = ((((x + (-0.5d0)) * log(x)) - x) + 0.91893853320467d0) + (z * (z * ((0.0007936500793651d0 / x) + (y / x))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 0.0026) {
		tmp = (0.91893853320467 + ((Math.log(x) * (x - 0.5)) - x)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = ((((x + -0.5) * Math.log(x)) - x) + 0.91893853320467) + (z * (z * ((0.0007936500793651 / x) + (y / x))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 0.0026:
		tmp = (0.91893853320467 + ((math.log(x) * (x - 0.5)) - x)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x)
	else:
		tmp = ((((x + -0.5) * math.log(x)) - x) + 0.91893853320467) + (z * (z * ((0.0007936500793651 / x) + (y / x))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 0.0026)
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(log(x) * Float64(x - 0.5)) - x)) + Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778))) / x));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(x + -0.5) * log(x)) - x) + 0.91893853320467) + Float64(z * Float64(z * Float64(Float64(0.0007936500793651 / x) + Float64(y / x)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 0.0026)
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	else
		tmp = ((((x + -0.5) * log(x)) - x) + 0.91893853320467) + (z * (z * ((0.0007936500793651 / x) + (y / x))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 0.0026], N[(N[(0.91893853320467 + N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(N[(0.083333333333333 + N[(z * N[(N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(z * N[(z * N[(N[(0.0007936500793651 / x), $MachinePrecision] + N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 0.0025999999999999999

   1. Initial program 99.6%

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

   if 0.0025999999999999999 < x

   1. Initial program 87.3%

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

      1. sub-neg 87.3%

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

      2. metadata-eval 87.3%

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

      3. fma-def 87.3%

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

      4. fma-neg 87.3%

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

      5. metadata-eval 87.3%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in z around inf 87.3%

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

      1. associate-+r+ 87.3%

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

      2. fma-def 87.3%

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

      3. associate-*r/ 87.3%

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

      4. metadata-eval 87.3%

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

      5. associate-/l* 89.5%

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

      6. unpow2 89.5%

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

   6. Simplified 89.5%

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

   7. Taylor expanded in z around inf 89.5%

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

      1. unpow2 89.5%

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

      2. associate-*l* 99.6%

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

      3. associate-*r/ 99.6%

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

      4. metadata-eval 99.6%

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

   9. Simplified 99.6%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.0026:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + z \cdot \left(z \cdot \left(\frac{0.0007936500793651}{x} + \frac{y}{x}\right)\right)\\ \end{array} \]

Alternative 5: 98.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.0026:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(z \cdot 0.0007936500793651 + z \cdot y\right) - 0.0027777777777778, z, 0.083333333333333\right)}{x} - x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + z \cdot \left(z \cdot \left(\frac{0.0007936500793651}{x} + \frac{y}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 0.0026)
   (-
    (/
     (fma
      (- (+ (* z 0.0007936500793651) (* z y)) 0.0027777777777778)
      z
      0.083333333333333)
     x)
    x)
   (+
    (+ (- (* (+ x -0.5) (log x)) x) 0.91893853320467)
    (* z (* z (+ (/ 0.0007936500793651 x) (/ y x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 0.0026) {
		tmp = (fma((((z * 0.0007936500793651) + (z * y)) - 0.0027777777777778), z, 0.083333333333333) / x) - x;
	} else {
		tmp = ((((x + -0.5) * log(x)) - x) + 0.91893853320467) + (z * (z * ((0.0007936500793651 / x) + (y / x))));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 0.0026)
		tmp = Float64(Float64(fma(Float64(Float64(Float64(z * 0.0007936500793651) + Float64(z * y)) - 0.0027777777777778), z, 0.083333333333333) / x) - x);
	else
		tmp = Float64(Float64(Float64(Float64(Float64(x + -0.5) * log(x)) - x) + 0.91893853320467) + Float64(z * Float64(z * Float64(Float64(0.0007936500793651 / x) + Float64(y / x)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 0.0026], N[(N[(N[(N[(N[(N[(z * 0.0007936500793651), $MachinePrecision] + N[(z * y), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision] - x), $MachinePrecision], N[(N[(N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(z * N[(z * N[(N[(0.0007936500793651 / x), $MachinePrecision] + N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 0.0025999999999999999

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. metadata-eval 99.6%

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

      3. fma-def 99.6%

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

      4. fma-neg 99.7%

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

      5. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. metadata-eval 99.7%

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

      2. sub-neg 99.7%

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

      3. add-cube-cbrt 99.7%

         \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x} \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right) \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      4. pow3 99.7%

         \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      5. *-commutative 99.7%

         \[\leadsto \left(\left({\left(\sqrt[3]{\color{blue}{\log x \cdot \left(x - 0.5\right)}}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      6. sub-neg 99.7%

         \[\leadsto \left(\left({\left(\sqrt[3]{\log x \cdot \color{blue}{\left(x + \left(-0.5\right)\right)}}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      7. metadata-eval 99.7%

         \[\leadsto \left(\left({\left(\sqrt[3]{\log x \cdot \left(x + \color{blue}{-0.5}\right)}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   5. Applied egg-rr 99.7%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\log x \cdot \left(x + -0.5\right)}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   6. Taylor expanded in x around inf 98.9%

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

      1. neg-mul-1 98.9%

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

   8. Simplified 98.9%

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

   9. Taylor expanded in y around 0 98.9%

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

   if 0.0025999999999999999 < x

   1. Initial program 87.3%

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

      1. sub-neg 87.3%

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

      2. metadata-eval 87.3%

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

      3. fma-def 87.3%

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

      4. fma-neg 87.3%

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

      5. metadata-eval 87.3%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in z around inf 87.3%

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

      1. associate-+r+ 87.3%

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

      2. fma-def 87.3%

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

      3. associate-*r/ 87.3%

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

      4. metadata-eval 87.3%

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

      5. associate-/l* 89.5%

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

      6. unpow2 89.5%

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

   6. Simplified 89.5%

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

   7. Taylor expanded in z around inf 89.5%

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

      1. unpow2 89.5%

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

      2. associate-*l* 99.6%

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

      3. associate-*r/ 99.6%

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

      4. metadata-eval 99.6%

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

   9. Simplified 99.6%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.0026:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(z \cdot 0.0007936500793651 + z \cdot y\right) - 0.0027777777777778, z, 0.083333333333333\right)}{x} - x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + z \cdot \left(z \cdot \left(\frac{0.0007936500793651}{x} + \frac{y}{x}\right)\right)\\ \end{array} \]

Alternative 6: 98.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.0026:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(z \cdot 0.0007936500793651 + z \cdot y\right) - 0.0027777777777778, z, 0.083333333333333\right)}{x} - x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z}{\frac{x}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 0.0026)
   (-
    (/
     (fma
      (- (+ (* z 0.0007936500793651) (* z y)) 0.0027777777777778)
      z
      0.083333333333333)
     x)
    x)
   (+
    (+ (- (* (+ x -0.5) (log x)) x) 0.91893853320467)
    (* (+ y 0.0007936500793651) (/ z (/ x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 0.0026) {
		tmp = (fma((((z * 0.0007936500793651) + (z * y)) - 0.0027777777777778), z, 0.083333333333333) / x) - x;
	} else {
		tmp = ((((x + -0.5) * log(x)) - x) + 0.91893853320467) + ((y + 0.0007936500793651) * (z / (x / z)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 0.0026)
		tmp = Float64(Float64(fma(Float64(Float64(Float64(z * 0.0007936500793651) + Float64(z * y)) - 0.0027777777777778), z, 0.083333333333333) / x) - x);
	else
		tmp = Float64(Float64(Float64(Float64(Float64(x + -0.5) * log(x)) - x) + 0.91893853320467) + Float64(Float64(y + 0.0007936500793651) * Float64(z / Float64(x / z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 0.0026], N[(N[(N[(N[(N[(N[(z * 0.0007936500793651), $MachinePrecision] + N[(z * y), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision] - x), $MachinePrecision], N[(N[(N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 0.0025999999999999999

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. metadata-eval 99.6%

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

      3. fma-def 99.6%

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

      4. fma-neg 99.7%

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

      5. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. metadata-eval 99.7%

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

      2. sub-neg 99.7%

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

      3. add-cube-cbrt 99.7%

         \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x} \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right) \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      4. pow3 99.7%

         \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      5. *-commutative 99.7%

         \[\leadsto \left(\left({\left(\sqrt[3]{\color{blue}{\log x \cdot \left(x - 0.5\right)}}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      6. sub-neg 99.7%

         \[\leadsto \left(\left({\left(\sqrt[3]{\log x \cdot \color{blue}{\left(x + \left(-0.5\right)\right)}}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      7. metadata-eval 99.7%

         \[\leadsto \left(\left({\left(\sqrt[3]{\log x \cdot \left(x + \color{blue}{-0.5}\right)}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   5. Applied egg-rr 99.7%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\log x \cdot \left(x + -0.5\right)}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   6. Taylor expanded in x around inf 98.9%

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

      1. neg-mul-1 98.9%

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

   8. Simplified 98.9%

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

   9. Taylor expanded in y around 0 98.9%

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

   if 0.0025999999999999999 < x

   1. Initial program 87.3%

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

      1. sub-neg 87.3%

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

      2. metadata-eval 87.3%

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

      3. fma-def 87.3%

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

      4. fma-neg 87.3%

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

      5. metadata-eval 87.3%

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

   3. Simplified 87.3%

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

      1. metadata-eval 87.3%

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

      2. fma-neg 87.3%

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

      3. fma-def 87.3%

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

      4. clear-num 87.3%

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

      5. inv-pow 87.3%

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

      6. *-commutative 87.3%

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

      7. fma-udef 87.3%

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

      8. fma-neg 87.3%

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

      9. metadata-eval 87.3%

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

   5. Applied egg-rr 87.3%

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

   6. Taylor expanded in z around inf 87.3%

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

      1. *-commutative 87.3%

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

      2. associate-*r/ 89.5%

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

      3. unpow2 89.5%

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

      4. associate-/l* 98.9%

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

   8. Simplified 98.9%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.0026:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(z \cdot 0.0007936500793651 + z \cdot y\right) - 0.0027777777777778, z, 0.083333333333333\right)}{x} - x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z}{\frac{x}{z}}\\ \end{array} \]

Alternative 7: 92.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 18500:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(\left(z \cdot 0.0007936500793651 + z \cdot y\right) - 0.0027777777777778\right)}{x} - x\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+236} \lor \neg \left(x \leq 5 \cdot 10^{+301}\right):\\ \;\;\;\;\left(x \cdot \log x - x\right) + \frac{y}{\frac{x}{z \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 18500.0)
   (-
    (/
     (+
      0.083333333333333
      (* z (- (+ (* z 0.0007936500793651) (* z y)) 0.0027777777777778)))
     x)
    x)
   (if (or (<= x 2.5e+236) (not (<= x 5e+301)))
     (+ (- (* x (log x)) x) (/ y (/ x (* z z))))
     (+ (* x (+ (log x) -1.0)) (/ 0.083333333333333 x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 18500.0) {
		tmp = ((0.083333333333333 + (z * (((z * 0.0007936500793651) + (z * y)) - 0.0027777777777778))) / x) - x;
	} else if ((x <= 2.5e+236) || !(x <= 5e+301)) {
		tmp = ((x * log(x)) - x) + (y / (x / (z * z)));
	} else {
		tmp = (x * (log(x) + -1.0)) + (0.083333333333333 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 18500.0d0) then
        tmp = ((0.083333333333333d0 + (z * (((z * 0.0007936500793651d0) + (z * y)) - 0.0027777777777778d0))) / x) - x
    else if ((x <= 2.5d+236) .or. (.not. (x <= 5d+301))) then
        tmp = ((x * log(x)) - x) + (y / (x / (z * z)))
    else
        tmp = (x * (log(x) + (-1.0d0))) + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 18500.0) {
		tmp = ((0.083333333333333 + (z * (((z * 0.0007936500793651) + (z * y)) - 0.0027777777777778))) / x) - x;
	} else if ((x <= 2.5e+236) || !(x <= 5e+301)) {
		tmp = ((x * Math.log(x)) - x) + (y / (x / (z * z)));
	} else {
		tmp = (x * (Math.log(x) + -1.0)) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 18500.0:
		tmp = ((0.083333333333333 + (z * (((z * 0.0007936500793651) + (z * y)) - 0.0027777777777778))) / x) - x
	elif (x <= 2.5e+236) or not (x <= 5e+301):
		tmp = ((x * math.log(x)) - x) + (y / (x / (z * z)))
	else:
		tmp = (x * (math.log(x) + -1.0)) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 18500.0)
		tmp = Float64(Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(Float64(z * 0.0007936500793651) + Float64(z * y)) - 0.0027777777777778))) / x) - x);
	elseif ((x <= 2.5e+236) || !(x <= 5e+301))
		tmp = Float64(Float64(Float64(x * log(x)) - x) + Float64(y / Float64(x / Float64(z * z))));
	else
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 18500.0)
		tmp = ((0.083333333333333 + (z * (((z * 0.0007936500793651) + (z * y)) - 0.0027777777777778))) / x) - x;
	elseif ((x <= 2.5e+236) || ~((x <= 5e+301)))
		tmp = ((x * log(x)) - x) + (y / (x / (z * z)));
	else
		tmp = (x * (log(x) + -1.0)) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 18500.0], N[(N[(N[(0.083333333333333 + N[(z * N[(N[(N[(z * 0.0007936500793651), $MachinePrecision] + N[(z * y), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - x), $MachinePrecision], If[Or[LessEqual[x, 2.5e+236], N[Not[LessEqual[x, 5e+301]], $MachinePrecision]], N[(N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + N[(y / N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < 18500

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. metadata-eval 99.6%

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

      3. fma-def 99.6%

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

      4. fma-neg 99.7%

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

      5. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. metadata-eval 99.7%

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

      2. sub-neg 99.7%

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

      3. add-cube-cbrt 99.7%

         \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x} \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right) \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      4. pow3 99.7%

         \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      5. *-commutative 99.7%

         \[\leadsto \left(\left({\left(\sqrt[3]{\color{blue}{\log x \cdot \left(x - 0.5\right)}}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      6. sub-neg 99.7%

         \[\leadsto \left(\left({\left(\sqrt[3]{\log x \cdot \color{blue}{\left(x + \left(-0.5\right)\right)}}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      7. metadata-eval 99.7%

         \[\leadsto \left(\left({\left(\sqrt[3]{\log x \cdot \left(x + \color{blue}{-0.5}\right)}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   5. Applied egg-rr 99.7%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\log x \cdot \left(x + -0.5\right)}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   6. Taylor expanded in x around inf 98.9%

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

      1. neg-mul-1 98.9%

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

   8. Simplified 98.9%

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

   9. Taylor expanded in y around 0 98.9%

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

   10. Taylor expanded in x around 0 98.9%

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

   if 18500 < x < 2.49999999999999985e236 or 5.0000000000000004e301 < x

   1. Initial program 91.2%

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

      1. sub-neg 91.2%

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

      2. metadata-eval 91.2%

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

      3. fma-def 91.2%

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

      4. fma-neg 91.2%

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

      5. metadata-eval 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in y around inf 86.9%

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

      1. associate-/l* 31.1%

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

      2. unpow2 31.1%

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

   6. Simplified 88.8%

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

   7. Taylor expanded in x around inf 88.2%

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

      1. sub-neg 88.2%

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

      2. mul-1-neg 88.2%

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

      3. log-rec 88.2%

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

      4. remove-double-neg 88.2%

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

      5. metadata-eval 88.2%

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

      6. distribute-rgt-in 88.2%

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

      7. *-rgt-identity 88.2%

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

      8. neg-mul-1 88.2%

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

      9. *-rgt-identity 88.2%

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

      10. sub-neg 88.2%

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

      11. *-commutative 88.2%

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

   9. Simplified 88.2%

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

   if 2.49999999999999985e236 < x < 5.0000000000000004e301

   1. Initial program 70.2%

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

      1. sub-neg 70.2%

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

      2. metadata-eval 70.2%

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

      3. fma-def 70.2%

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

      4. fma-neg 70.2%

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

      5. metadata-eval 70.2%

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

   3. Simplified 70.2%

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

   4. Taylor expanded in z around 0 90.2%

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

   5. Taylor expanded in x around inf 90.2%

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

      1. sub-neg 90.2%

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

      2. mul-1-neg 90.2%

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

      3. log-rec 90.2%

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

      4. remove-double-neg 90.2%

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

      5. metadata-eval 90.2%

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

   7. Simplified 90.2%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 18500:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(\left(z \cdot 0.0007936500793651 + z \cdot y\right) - 0.0027777777777778\right)}{x} - x\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+236} \lor \neg \left(x \leq 5 \cdot 10^{+301}\right):\\ \;\;\;\;\left(x \cdot \log x - x\right) + \frac{y}{\frac{x}{z \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 8: 84.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 54000000:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(\left(z \cdot 0.0007936500793651 + z \cdot y\right) - 0.0027777777777778\right)}{x} - x\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+77}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+90}:\\ \;\;\;\;\frac{z \cdot z}{\frac{x}{y + 0.0007936500793651}} - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 54000000.0)
   (-
    (/
     (+
      0.083333333333333
      (* z (- (+ (* z 0.0007936500793651) (* z y)) 0.0027777777777778)))
     x)
    x)
   (if (<= x 4.2e+77)
     (+
      (+ (- (* (+ x -0.5) (log x)) x) 0.91893853320467)
      (/ 0.083333333333333 x))
     (if (<= x 2.3e+90)
       (- (/ (* z z) (/ x (+ y 0.0007936500793651))) x)
       (+ (* x (+ (log x) -1.0)) (/ 0.083333333333333 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 54000000.0) {
		tmp = ((0.083333333333333 + (z * (((z * 0.0007936500793651) + (z * y)) - 0.0027777777777778))) / x) - x;
	} else if (x <= 4.2e+77) {
		tmp = ((((x + -0.5) * log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	} else if (x <= 2.3e+90) {
		tmp = ((z * z) / (x / (y + 0.0007936500793651))) - x;
	} else {
		tmp = (x * (log(x) + -1.0)) + (0.083333333333333 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 54000000.0d0) then
        tmp = ((0.083333333333333d0 + (z * (((z * 0.0007936500793651d0) + (z * y)) - 0.0027777777777778d0))) / x) - x
    else if (x <= 4.2d+77) then
        tmp = ((((x + (-0.5d0)) * log(x)) - x) + 0.91893853320467d0) + (0.083333333333333d0 / x)
    else if (x <= 2.3d+90) then
        tmp = ((z * z) / (x / (y + 0.0007936500793651d0))) - x
    else
        tmp = (x * (log(x) + (-1.0d0))) + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 54000000.0) {
		tmp = ((0.083333333333333 + (z * (((z * 0.0007936500793651) + (z * y)) - 0.0027777777777778))) / x) - x;
	} else if (x <= 4.2e+77) {
		tmp = ((((x + -0.5) * Math.log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	} else if (x <= 2.3e+90) {
		tmp = ((z * z) / (x / (y + 0.0007936500793651))) - x;
	} else {
		tmp = (x * (Math.log(x) + -1.0)) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 54000000.0:
		tmp = ((0.083333333333333 + (z * (((z * 0.0007936500793651) + (z * y)) - 0.0027777777777778))) / x) - x
	elif x <= 4.2e+77:
		tmp = ((((x + -0.5) * math.log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x)
	elif x <= 2.3e+90:
		tmp = ((z * z) / (x / (y + 0.0007936500793651))) - x
	else:
		tmp = (x * (math.log(x) + -1.0)) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 54000000.0)
		tmp = Float64(Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(Float64(z * 0.0007936500793651) + Float64(z * y)) - 0.0027777777777778))) / x) - x);
	elseif (x <= 4.2e+77)
		tmp = Float64(Float64(Float64(Float64(Float64(x + -0.5) * log(x)) - x) + 0.91893853320467) + Float64(0.083333333333333 / x));
	elseif (x <= 2.3e+90)
		tmp = Float64(Float64(Float64(z * z) / Float64(x / Float64(y + 0.0007936500793651))) - x);
	else
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 54000000.0)
		tmp = ((0.083333333333333 + (z * (((z * 0.0007936500793651) + (z * y)) - 0.0027777777777778))) / x) - x;
	elseif (x <= 4.2e+77)
		tmp = ((((x + -0.5) * log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	elseif (x <= 2.3e+90)
		tmp = ((z * z) / (x / (y + 0.0007936500793651))) - x;
	else
		tmp = (x * (log(x) + -1.0)) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 54000000.0], N[(N[(N[(0.083333333333333 + N[(z * N[(N[(N[(z * 0.0007936500793651), $MachinePrecision] + N[(z * y), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - x), $MachinePrecision], If[LessEqual[x, 4.2e+77], N[(N[(N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e+90], N[(N[(N[(z * z), $MachinePrecision] / N[(x / N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < 5.4e7

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. metadata-eval 99.6%

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

      3. fma-def 99.6%

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

      4. fma-neg 99.7%

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

      5. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. metadata-eval 99.7%

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

      2. sub-neg 99.7%

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

      3. add-cube-cbrt 99.7%

         \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x} \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right) \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      4. pow3 99.7%

         \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      5. *-commutative 99.7%

         \[\leadsto \left(\left({\left(\sqrt[3]{\color{blue}{\log x \cdot \left(x - 0.5\right)}}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      6. sub-neg 99.7%

         \[\leadsto \left(\left({\left(\sqrt[3]{\log x \cdot \color{blue}{\left(x + \left(-0.5\right)\right)}}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      7. metadata-eval 99.7%

         \[\leadsto \left(\left({\left(\sqrt[3]{\log x \cdot \left(x + \color{blue}{-0.5}\right)}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   5. Applied egg-rr 99.7%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\log x \cdot \left(x + -0.5\right)}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   6. Taylor expanded in x around inf 98.9%

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

      1. neg-mul-1 98.9%

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

   8. Simplified 98.9%

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

   9. Taylor expanded in y around 0 98.9%

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

   10. Taylor expanded in x around 0 98.9%

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

   if 5.4e7 < x < 4.1999999999999997e77

   1. Initial program 96.4%

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

      1. sub-neg 96.4%

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

      2. metadata-eval 96.4%

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

      3. fma-def 96.4%

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

      4. fma-neg 96.4%

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

      5. metadata-eval 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in z around 0 64.9%

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

   if 4.1999999999999997e77 < x < 2.3e90

   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. sub-neg 88.2%

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

      2. metadata-eval 88.2%

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

      3. fma-def 88.2%

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

      4. fma-neg 88.2%

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

      5. metadata-eval 88.2%

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

   3. Simplified 88.2%

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

      1. metadata-eval 88.2%

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

      2. sub-neg 88.2%

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

      3. add-cube-cbrt 88.2%

         \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x} \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right) \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      4. pow3 88.2%

         \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      5. *-commutative 88.2%

         \[\leadsto \left(\left({\left(\sqrt[3]{\color{blue}{\log x \cdot \left(x - 0.5\right)}}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      6. sub-neg 88.2%

         \[\leadsto \left(\left({\left(\sqrt[3]{\log x \cdot \color{blue}{\left(x + \left(-0.5\right)\right)}}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      7. metadata-eval 88.2%

         \[\leadsto \left(\left({\left(\sqrt[3]{\log x \cdot \left(x + \color{blue}{-0.5}\right)}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   5. Applied egg-rr 88.2%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\log x \cdot \left(x + -0.5\right)}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   6. Taylor expanded in x around inf 88.2%

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

      1. neg-mul-1 88.2%

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

   8. Simplified 88.2%

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

   9. Taylor expanded in z around inf 88.2%

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

       1. associate-/l* 100.0%

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

       2. unpow2 100.0%

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

   11. Simplified 100.0%

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

   if 2.3e90 < x

   1. Initial program 83.6%

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

      1. sub-neg 83.6%

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

      2. metadata-eval 83.6%

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

      3. fma-def 83.6%

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

      4. fma-neg 83.6%

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

      5. metadata-eval 83.6%

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

   3. Simplified 83.6%

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

   4. Taylor expanded in z around 0 75.8%

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

   5. Taylor expanded in x around inf 75.8%

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

      1. sub-neg 75.8%

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

      2. mul-1-neg 75.8%

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

      3. log-rec 75.8%

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

      4. remove-double-neg 75.8%

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

      5. metadata-eval 75.8%

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

   7. Simplified 75.8%

      \[\leadsto \color{blue}{x \cdot \left(\log x + -1\right)} + \frac{0.083333333333333}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 54000000:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(\left(z \cdot 0.0007936500793651 + z \cdot y\right) - 0.0027777777777778\right)}{x} - x\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+77}:\\ \;\;\;\;\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+90}:\\ \;\;\;\;\frac{z \cdot z}{\frac{x}{y + 0.0007936500793651}} - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 9: 98.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.0026:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(\left(z \cdot 0.0007936500793651 + z \cdot y\right) - 0.0027777777777778\right)}{x} - x\\ \mathbf{else}:\\ \;\;\;\;\left(y + 0.0007936500793651\right) \cdot \frac{z}{\frac{x}{z}} + \left(x \cdot \log x - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 0.0026)
   (-
    (/
     (+
      0.083333333333333
      (* z (- (+ (* z 0.0007936500793651) (* z y)) 0.0027777777777778)))
     x)
    x)
   (+ (* (+ y 0.0007936500793651) (/ z (/ x z))) (- (* x (log x)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 0.0026) {
		tmp = ((0.083333333333333 + (z * (((z * 0.0007936500793651) + (z * y)) - 0.0027777777777778))) / x) - x;
	} else {
		tmp = ((y + 0.0007936500793651) * (z / (x / z))) + ((x * log(x)) - 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 <= 0.0026d0) then
        tmp = ((0.083333333333333d0 + (z * (((z * 0.0007936500793651d0) + (z * y)) - 0.0027777777777778d0))) / x) - x
    else
        tmp = ((y + 0.0007936500793651d0) * (z / (x / z))) + ((x * log(x)) - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 0.0026) {
		tmp = ((0.083333333333333 + (z * (((z * 0.0007936500793651) + (z * y)) - 0.0027777777777778))) / x) - x;
	} else {
		tmp = ((y + 0.0007936500793651) * (z / (x / z))) + ((x * Math.log(x)) - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 0.0026:
		tmp = ((0.083333333333333 + (z * (((z * 0.0007936500793651) + (z * y)) - 0.0027777777777778))) / x) - x
	else:
		tmp = ((y + 0.0007936500793651) * (z / (x / z))) + ((x * math.log(x)) - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 0.0026)
		tmp = Float64(Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(Float64(z * 0.0007936500793651) + Float64(z * y)) - 0.0027777777777778))) / x) - x);
	else
		tmp = Float64(Float64(Float64(y + 0.0007936500793651) * Float64(z / Float64(x / z))) + Float64(Float64(x * log(x)) - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 0.0026)
		tmp = ((0.083333333333333 + (z * (((z * 0.0007936500793651) + (z * y)) - 0.0027777777777778))) / x) - x;
	else
		tmp = ((y + 0.0007936500793651) * (z / (x / z))) + ((x * log(x)) - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 0.0026], N[(N[(N[(0.083333333333333 + N[(z * N[(N[(N[(z * 0.0007936500793651), $MachinePrecision] + N[(z * y), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - x), $MachinePrecision], N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 0.0025999999999999999

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. metadata-eval 99.6%

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

      3. fma-def 99.6%

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

      4. fma-neg 99.7%

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

      5. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. metadata-eval 99.7%

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

      2. sub-neg 99.7%

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

      3. add-cube-cbrt 99.7%

         \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x} \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right) \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      4. pow3 99.7%

         \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      5. *-commutative 99.7%

         \[\leadsto \left(\left({\left(\sqrt[3]{\color{blue}{\log x \cdot \left(x - 0.5\right)}}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      6. sub-neg 99.7%

         \[\leadsto \left(\left({\left(\sqrt[3]{\log x \cdot \color{blue}{\left(x + \left(-0.5\right)\right)}}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      7. metadata-eval 99.7%

         \[\leadsto \left(\left({\left(\sqrt[3]{\log x \cdot \left(x + \color{blue}{-0.5}\right)}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   5. Applied egg-rr 99.7%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\log x \cdot \left(x + -0.5\right)}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   6. Taylor expanded in x around inf 98.9%

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

      1. neg-mul-1 98.9%

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

   8. Simplified 98.9%

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

   9. Taylor expanded in y around 0 98.9%

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

   10. Taylor expanded in x around 0 98.9%

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

   if 0.0025999999999999999 < x

   1. Initial program 87.3%

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

      1. sub-neg 87.3%

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

      2. metadata-eval 87.3%

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

      3. fma-def 87.3%

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

      4. fma-neg 87.3%

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

      5. metadata-eval 87.3%

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

   3. Simplified 87.3%

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

      1. metadata-eval 87.3%

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

      2. fma-neg 87.3%

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

      3. fma-def 87.3%

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

      4. clear-num 87.3%

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

      5. inv-pow 87.3%

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

      6. *-commutative 87.3%

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

      7. fma-udef 87.3%

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

      8. fma-neg 87.3%

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

      9. metadata-eval 87.3%

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

   5. Applied egg-rr 87.3%

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

   6. Taylor expanded in z around inf 87.3%

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

      1. *-commutative 87.3%

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

      2. associate-*r/ 89.5%

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

      3. unpow2 89.5%

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

      4. associate-/l* 98.9%

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

   8. Simplified 98.9%

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

   9. Taylor expanded in x around inf 98.5%

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

       1. sub-neg 83.9%

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

       2. mul-1-neg 83.9%

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

       3. log-rec 83.9%

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

       4. remove-double-neg 83.9%

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

       5. metadata-eval 83.9%

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

       6. distribute-rgt-in 83.9%

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

       7. *-rgt-identity 83.9%

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

       8. neg-mul-1 83.9%

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

       9. *-rgt-identity 83.9%

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

       10. sub-neg 83.9%

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

       11. *-commutative 83.9%

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

   11. Simplified 98.5%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.0026:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(\left(z \cdot 0.0007936500793651 + z \cdot y\right) - 0.0027777777777778\right)}{x} - x\\ \mathbf{else}:\\ \;\;\;\;\left(y + 0.0007936500793651\right) \cdot \frac{z}{\frac{x}{z}} + \left(x \cdot \log x - x\right)\\ \end{array} \]

Alternative 10: 98.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.0026:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(z \cdot 0.0007936500793651 + z \cdot y\right) - 0.0027777777777778, z, 0.083333333333333\right)}{x} - x\\ \mathbf{else}:\\ \;\;\;\;\left(y + 0.0007936500793651\right) \cdot \frac{z}{\frac{x}{z}} + \left(x \cdot \log x - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 0.0026)
   (-
    (/
     (fma
      (- (+ (* z 0.0007936500793651) (* z y)) 0.0027777777777778)
      z
      0.083333333333333)
     x)
    x)
   (+ (* (+ y 0.0007936500793651) (/ z (/ x z))) (- (* x (log x)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 0.0026) {
		tmp = (fma((((z * 0.0007936500793651) + (z * y)) - 0.0027777777777778), z, 0.083333333333333) / x) - x;
	} else {
		tmp = ((y + 0.0007936500793651) * (z / (x / z))) + ((x * log(x)) - x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 0.0026)
		tmp = Float64(Float64(fma(Float64(Float64(Float64(z * 0.0007936500793651) + Float64(z * y)) - 0.0027777777777778), z, 0.083333333333333) / x) - x);
	else
		tmp = Float64(Float64(Float64(y + 0.0007936500793651) * Float64(z / Float64(x / z))) + Float64(Float64(x * log(x)) - x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 0.0026], N[(N[(N[(N[(N[(N[(z * 0.0007936500793651), $MachinePrecision] + N[(z * y), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision] - x), $MachinePrecision], N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 0.0025999999999999999

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. metadata-eval 99.6%

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

      3. fma-def 99.6%

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

      4. fma-neg 99.7%

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

      5. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. metadata-eval 99.7%

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

      2. sub-neg 99.7%

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

      3. add-cube-cbrt 99.7%

         \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x} \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right) \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      4. pow3 99.7%

         \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      5. *-commutative 99.7%

         \[\leadsto \left(\left({\left(\sqrt[3]{\color{blue}{\log x \cdot \left(x - 0.5\right)}}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      6. sub-neg 99.7%

         \[\leadsto \left(\left({\left(\sqrt[3]{\log x \cdot \color{blue}{\left(x + \left(-0.5\right)\right)}}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      7. metadata-eval 99.7%

         \[\leadsto \left(\left({\left(\sqrt[3]{\log x \cdot \left(x + \color{blue}{-0.5}\right)}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   5. Applied egg-rr 99.7%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\log x \cdot \left(x + -0.5\right)}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   6. Taylor expanded in x around inf 98.9%

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

      1. neg-mul-1 98.9%

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

   8. Simplified 98.9%

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

   9. Taylor expanded in y around 0 98.9%

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

   if 0.0025999999999999999 < x

   1. Initial program 87.3%

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

      1. sub-neg 87.3%

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

      2. metadata-eval 87.3%

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

      3. fma-def 87.3%

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

      4. fma-neg 87.3%

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

      5. metadata-eval 87.3%

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

   3. Simplified 87.3%

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

      1. metadata-eval 87.3%

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

      2. fma-neg 87.3%

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

      3. fma-def 87.3%

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

      4. clear-num 87.3%

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

      5. inv-pow 87.3%

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

      6. *-commutative 87.3%

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

      7. fma-udef 87.3%

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

      8. fma-neg 87.3%

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

      9. metadata-eval 87.3%

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

   5. Applied egg-rr 87.3%

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

   6. Taylor expanded in z around inf 87.3%

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

      1. *-commutative 87.3%

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

      2. associate-*r/ 89.5%

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

      3. unpow2 89.5%

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

      4. associate-/l* 98.9%

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

   8. Simplified 98.9%

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

   9. Taylor expanded in x around inf 98.5%

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

       1. sub-neg 83.9%

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

       2. mul-1-neg 83.9%

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

       3. log-rec 83.9%

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

       4. remove-double-neg 83.9%

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

       5. metadata-eval 83.9%

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

       6. distribute-rgt-in 83.9%

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

       7. *-rgt-identity 83.9%

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

       8. neg-mul-1 83.9%

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

       9. *-rgt-identity 83.9%

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

       10. sub-neg 83.9%

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

       11. *-commutative 83.9%

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

   11. Simplified 98.5%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.0026:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(z \cdot 0.0007936500793651 + z \cdot y\right) - 0.0027777777777778, z, 0.083333333333333\right)}{x} - x\\ \mathbf{else}:\\ \;\;\;\;\left(y + 0.0007936500793651\right) \cdot \frac{z}{\frac{x}{z}} + \left(x \cdot \log x - x\right)\\ \end{array} \]

Alternative 11: 84.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2800000000:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(\left(z \cdot 0.0007936500793651 + z \cdot y\right) - 0.0027777777777778\right)}{x} - x\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+76} \lor \neg \left(x \leq 2.8 \cdot 10^{+90}\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot z}{\frac{x}{y + 0.0007936500793651}} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 2800000000.0)
   (-
    (/
     (+
      0.083333333333333
      (* z (- (+ (* z 0.0007936500793651) (* z y)) 0.0027777777777778)))
     x)
    x)
   (if (or (<= x 1.35e+76) (not (<= x 2.8e+90)))
     (+ (* x (+ (log x) -1.0)) (/ 0.083333333333333 x))
     (- (/ (* z z) (/ x (+ y 0.0007936500793651))) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 2800000000.0) {
		tmp = ((0.083333333333333 + (z * (((z * 0.0007936500793651) + (z * y)) - 0.0027777777777778))) / x) - x;
	} else if ((x <= 1.35e+76) || !(x <= 2.8e+90)) {
		tmp = (x * (log(x) + -1.0)) + (0.083333333333333 / x);
	} else {
		tmp = ((z * z) / (x / (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 <= 2800000000.0d0) then
        tmp = ((0.083333333333333d0 + (z * (((z * 0.0007936500793651d0) + (z * y)) - 0.0027777777777778d0))) / x) - x
    else if ((x <= 1.35d+76) .or. (.not. (x <= 2.8d+90))) then
        tmp = (x * (log(x) + (-1.0d0))) + (0.083333333333333d0 / x)
    else
        tmp = ((z * z) / (x / (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 <= 2800000000.0) {
		tmp = ((0.083333333333333 + (z * (((z * 0.0007936500793651) + (z * y)) - 0.0027777777777778))) / x) - x;
	} else if ((x <= 1.35e+76) || !(x <= 2.8e+90)) {
		tmp = (x * (Math.log(x) + -1.0)) + (0.083333333333333 / x);
	} else {
		tmp = ((z * z) / (x / (y + 0.0007936500793651))) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 2800000000.0:
		tmp = ((0.083333333333333 + (z * (((z * 0.0007936500793651) + (z * y)) - 0.0027777777777778))) / x) - x
	elif (x <= 1.35e+76) or not (x <= 2.8e+90):
		tmp = (x * (math.log(x) + -1.0)) + (0.083333333333333 / x)
	else:
		tmp = ((z * z) / (x / (y + 0.0007936500793651))) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 2800000000.0)
		tmp = Float64(Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(Float64(z * 0.0007936500793651) + Float64(z * y)) - 0.0027777777777778))) / x) - x);
	elseif ((x <= 1.35e+76) || !(x <= 2.8e+90))
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(0.083333333333333 / x));
	else
		tmp = Float64(Float64(Float64(z * z) / Float64(x / Float64(y + 0.0007936500793651))) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 2800000000.0)
		tmp = ((0.083333333333333 + (z * (((z * 0.0007936500793651) + (z * y)) - 0.0027777777777778))) / x) - x;
	elseif ((x <= 1.35e+76) || ~((x <= 2.8e+90)))
		tmp = (x * (log(x) + -1.0)) + (0.083333333333333 / x);
	else
		tmp = ((z * z) / (x / (y + 0.0007936500793651))) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 2800000000.0], N[(N[(N[(0.083333333333333 + N[(z * N[(N[(N[(z * 0.0007936500793651), $MachinePrecision] + N[(z * y), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - x), $MachinePrecision], If[Or[LessEqual[x, 1.35e+76], N[Not[LessEqual[x, 2.8e+90]], $MachinePrecision]], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * z), $MachinePrecision] / N[(x / N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < 2.8e9

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. metadata-eval 99.6%

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

      3. fma-def 99.6%

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

      4. fma-neg 99.7%

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

      5. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. metadata-eval 99.7%

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

      2. sub-neg 99.7%

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

      3. add-cube-cbrt 99.7%

         \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x} \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right) \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      4. pow3 99.7%

         \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      5. *-commutative 99.7%

         \[\leadsto \left(\left({\left(\sqrt[3]{\color{blue}{\log x \cdot \left(x - 0.5\right)}}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      6. sub-neg 99.7%

         \[\leadsto \left(\left({\left(\sqrt[3]{\log x \cdot \color{blue}{\left(x + \left(-0.5\right)\right)}}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      7. metadata-eval 99.7%

         \[\leadsto \left(\left({\left(\sqrt[3]{\log x \cdot \left(x + \color{blue}{-0.5}\right)}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   5. Applied egg-rr 99.7%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\log x \cdot \left(x + -0.5\right)}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   6. Taylor expanded in x around inf 98.9%

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

      1. neg-mul-1 98.9%

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

   8. Simplified 98.9%

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

   9. Taylor expanded in y around 0 98.9%

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

   10. Taylor expanded in x around 0 98.9%

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

   if 2.8e9 < x < 1.34999999999999995e76 or 2.8e90 < x

   1. Initial program 86.8%

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

      1. sub-neg 86.8%

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

      2. metadata-eval 86.8%

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

      3. fma-def 86.8%

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

      4. fma-neg 86.8%

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

      5. metadata-eval 86.8%

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

   3. Simplified 86.8%

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

   4. Taylor expanded in z around 0 73.1%

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

   5. Taylor expanded in x around inf 72.6%

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

      1. sub-neg 72.6%

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

      2. mul-1-neg 72.6%

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

      3. log-rec 72.6%

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

      4. remove-double-neg 72.6%

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

      5. metadata-eval 72.6%

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

   7. Simplified 72.6%

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

   if 1.34999999999999995e76 < x < 2.8e90

   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. sub-neg 88.2%

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

      2. metadata-eval 88.2%

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

      3. fma-def 88.2%

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

      4. fma-neg 88.2%

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

      5. metadata-eval 88.2%

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

   3. Simplified 88.2%

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

      1. metadata-eval 88.2%

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

      2. sub-neg 88.2%

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

      3. add-cube-cbrt 88.2%

         \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x} \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right) \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      4. pow3 88.2%

         \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      5. *-commutative 88.2%

         \[\leadsto \left(\left({\left(\sqrt[3]{\color{blue}{\log x \cdot \left(x - 0.5\right)}}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      6. sub-neg 88.2%

         \[\leadsto \left(\left({\left(\sqrt[3]{\log x \cdot \color{blue}{\left(x + \left(-0.5\right)\right)}}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      7. metadata-eval 88.2%

         \[\leadsto \left(\left({\left(\sqrt[3]{\log x \cdot \left(x + \color{blue}{-0.5}\right)}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   5. Applied egg-rr 88.2%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\log x \cdot \left(x + -0.5\right)}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   6. Taylor expanded in x around inf 88.2%

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

      1. neg-mul-1 88.2%

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

   8. Simplified 88.2%

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

   9. Taylor expanded in z around inf 88.2%

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

       1. associate-/l* 100.0%

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

       2. unpow2 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2800000000:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(\left(z \cdot 0.0007936500793651 + z \cdot y\right) - 0.0027777777777778\right)}{x} - x\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+76} \lor \neg \left(x \leq 2.8 \cdot 10^{+90}\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot z}{\frac{x}{y + 0.0007936500793651}} - x\\ \end{array} \]

Alternative 12: 61.4% accurate, 7.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.5%

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

   1. sub-neg 93.5%

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

   2. metadata-eval 93.5%

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

   3. fma-def 93.5%

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

   4. fma-neg 93.6%

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

   5. metadata-eval 93.6%

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

3. Simplified 93.6%

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

   1. metadata-eval 93.6%

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

   2. sub-neg 93.6%

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

   3. add-cube-cbrt 93.1%

      \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x} \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right) \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   4. pow3 93.1%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   5. *-commutative 93.1%

      \[\leadsto \left(\left({\left(\sqrt[3]{\color{blue}{\log x \cdot \left(x - 0.5\right)}}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   6. sub-neg 93.1%

      \[\leadsto \left(\left({\left(\sqrt[3]{\log x \cdot \color{blue}{\left(x + \left(-0.5\right)\right)}}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   7. metadata-eval 93.1%

      \[\leadsto \left(\left({\left(\sqrt[3]{\log x \cdot \left(x + \color{blue}{-0.5}\right)}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

5. Applied egg-rr 93.1%

   \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\log x \cdot \left(x + -0.5\right)}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

6. Taylor expanded in x around inf 64.5%

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

   1. neg-mul-1 64.5%

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

8. Simplified 64.5%

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

9. Taylor expanded in y around 0 64.5%

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

10. Taylor expanded in x around 0 64.5%

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

11. Final simplification 64.5%

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

Alternative 13: 58.5% accurate, 8.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-33} \lor \neg \left(z \leq 3.5 \cdot 10^{-79}\right):\\ \;\;\;\;\left(z \cdot z\right) \cdot \frac{y + 0.0007936500793651}{x} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -7e-33) (not (<= z 3.5e-79)))
   (- (* (* z z) (/ (+ y 0.0007936500793651) x)) x)
   (/ 0.083333333333333 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7e-33) || !(z <= 3.5e-79)) {
		tmp = ((z * z) * ((y + 0.0007936500793651) / x)) - x;
	} else {
		tmp = 0.083333333333333 / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-7d-33)) .or. (.not. (z <= 3.5d-79))) then
        tmp = ((z * z) * ((y + 0.0007936500793651d0) / x)) - x
    else
        tmp = 0.083333333333333d0 / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7e-33) || !(z <= 3.5e-79)) {
		tmp = ((z * z) * ((y + 0.0007936500793651) / x)) - x;
	} else {
		tmp = 0.083333333333333 / x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -7e-33) or not (z <= 3.5e-79):
		tmp = ((z * z) * ((y + 0.0007936500793651) / x)) - x
	else:
		tmp = 0.083333333333333 / x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -7e-33) || !(z <= 3.5e-79))
		tmp = Float64(Float64(Float64(z * z) * Float64(Float64(y + 0.0007936500793651) / x)) - x);
	else
		tmp = Float64(0.083333333333333 / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -7e-33) || ~((z <= 3.5e-79)))
		tmp = ((z * z) * ((y + 0.0007936500793651) / x)) - x;
	else
		tmp = 0.083333333333333 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -7e-33], N[Not[LessEqual[z, 3.5e-79]], $MachinePrecision]], N[(N[(N[(z * z), $MachinePrecision] * N[(N[(y + 0.0007936500793651), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(0.083333333333333 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.9999999999999997e-33 or 3.5000000000000003e-79 < z

   1. Initial program 89.7%

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

      1. sub-neg 89.7%

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

      2. metadata-eval 89.7%

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

      3. fma-def 89.7%

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

      4. fma-neg 89.7%

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

      5. metadata-eval 89.7%

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

   3. Simplified 89.7%

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

      1. metadata-eval 89.7%

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

      2. sub-neg 89.7%

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

      3. add-cube-cbrt 89.4%

         \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x} \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right) \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      4. pow3 89.4%

         \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      5. *-commutative 89.4%

         \[\leadsto \left(\left({\left(\sqrt[3]{\color{blue}{\log x \cdot \left(x - 0.5\right)}}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      6. sub-neg 89.4%

         \[\leadsto \left(\left({\left(\sqrt[3]{\log x \cdot \color{blue}{\left(x + \left(-0.5\right)\right)}}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      7. metadata-eval 89.4%

         \[\leadsto \left(\left({\left(\sqrt[3]{\log x \cdot \left(x + \color{blue}{-0.5}\right)}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   5. Applied egg-rr 89.4%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\log x \cdot \left(x + -0.5\right)}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   6. Taylor expanded in x around inf 72.9%

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

      1. neg-mul-1 72.9%

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

   8. Simplified 72.9%

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

   9. Taylor expanded in z around inf 70.3%

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

       1. *-lft-identity 70.3%

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

       2. times-frac 70.9%

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

       3. /-rgt-identity 70.9%

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

       4. unpow2 70.9%

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

   11. Simplified 70.9%

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

   if -6.9999999999999997e-33 < z < 3.5000000000000003e-79

   1. Initial program 99.5%

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

      1. sub-neg 99.5%

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

      2. metadata-eval 99.5%

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

      3. fma-def 99.5%

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

      4. fma-neg 99.5%

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

      5. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in z around 0 93.7%

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

   5. Taylor expanded in x around inf 92.2%

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

      1. sub-neg 92.2%

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

      2. mul-1-neg 92.2%

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

      3. log-rec 92.2%

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

      4. remove-double-neg 92.2%

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

      5. metadata-eval 92.2%

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

   7. Simplified 92.2%

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

   8. Taylor expanded in x around 0 47.2%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-33} \lor \neg \left(z \leq 3.5 \cdot 10^{-79}\right):\\ \;\;\;\;\left(z \cdot z\right) \cdot \frac{y + 0.0007936500793651}{x} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 14: 58.6% accurate, 8.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{-50} \lor \neg \left(z \leq 3.4 \cdot 10^{-79}\right):\\ \;\;\;\;\left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8.4e-50) (not (<= z 3.4e-79)))
   (- (* (+ y 0.0007936500793651) (/ (* z z) x)) x)
   (/ 0.083333333333333 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.4e-50) || !(z <= 3.4e-79)) {
		tmp = ((y + 0.0007936500793651) * ((z * z) / x)) - x;
	} else {
		tmp = 0.083333333333333 / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-8.4d-50)) .or. (.not. (z <= 3.4d-79))) then
        tmp = ((y + 0.0007936500793651d0) * ((z * z) / x)) - x
    else
        tmp = 0.083333333333333d0 / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.4e-50) || !(z <= 3.4e-79)) {
		tmp = ((y + 0.0007936500793651) * ((z * z) / x)) - x;
	} else {
		tmp = 0.083333333333333 / x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8.4e-50) or not (z <= 3.4e-79):
		tmp = ((y + 0.0007936500793651) * ((z * z) / x)) - x
	else:
		tmp = 0.083333333333333 / x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8.4e-50) || !(z <= 3.4e-79))
		tmp = Float64(Float64(Float64(y + 0.0007936500793651) * Float64(Float64(z * z) / x)) - x);
	else
		tmp = Float64(0.083333333333333 / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -8.4e-50) || ~((z <= 3.4e-79)))
		tmp = ((y + 0.0007936500793651) * ((z * z) / x)) - x;
	else
		tmp = 0.083333333333333 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8.4e-50], N[Not[LessEqual[z, 3.4e-79]], $MachinePrecision]], N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(N[(z * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(0.083333333333333 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.4000000000000003e-50 or 3.39999999999999976e-79 < z

   1. Initial program 89.9%

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

      1. sub-neg 89.9%

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

      2. metadata-eval 89.9%

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

      3. fma-def 89.9%

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

      4. fma-neg 89.9%

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

      5. metadata-eval 89.9%

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

   3. Simplified 89.9%

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

      1. metadata-eval 89.9%

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

      2. sub-neg 89.9%

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

      3. add-cube-cbrt 89.6%

         \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x} \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right) \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      4. pow3 89.6%

         \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      5. *-commutative 89.6%

         \[\leadsto \left(\left({\left(\sqrt[3]{\color{blue}{\log x \cdot \left(x - 0.5\right)}}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      6. sub-neg 89.6%

         \[\leadsto \left(\left({\left(\sqrt[3]{\log x \cdot \color{blue}{\left(x + \left(-0.5\right)\right)}}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      7. metadata-eval 89.6%

         \[\leadsto \left(\left({\left(\sqrt[3]{\log x \cdot \left(x + \color{blue}{-0.5}\right)}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   5. Applied egg-rr 89.6%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\log x \cdot \left(x + -0.5\right)}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   6. Taylor expanded in x around inf 72.2%

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

      1. neg-mul-1 72.2%

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

   8. Simplified 72.2%

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

   9. Taylor expanded in z around inf 69.6%

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

       1. associate-/l* 69.6%

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

       2. associate-/r/ 70.8%

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

       3. unpow2 70.8%

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

   11. Simplified 70.8%

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

   if -8.4000000000000003e-50 < z < 3.39999999999999976e-79

   1. Initial program 99.5%

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

      1. sub-neg 99.5%

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

      2. metadata-eval 99.5%

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

      3. fma-def 99.5%

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

      4. fma-neg 99.5%

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

      5. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in z around 0 94.5%

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

   5. Taylor expanded in x around inf 93.0%

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

      1. sub-neg 93.0%

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

      2. mul-1-neg 93.0%

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

      3. log-rec 93.0%

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

      4. remove-double-neg 93.0%

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

      5. metadata-eval 93.0%

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

   7. Simplified 93.0%

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

   8. Taylor expanded in x around 0 48.6%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{-50} \lor \neg \left(z \leq 3.4 \cdot 10^{-79}\right):\\ \;\;\;\;\left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 15: 61.4% accurate, 8.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.5%

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

   1. sub-neg 93.5%

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

   2. metadata-eval 93.5%

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

   3. fma-def 93.5%

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

   4. fma-neg 93.6%

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

   5. metadata-eval 93.6%

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

3. Simplified 93.6%

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

   1. metadata-eval 93.6%

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

   2. sub-neg 93.6%

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

   3. add-cube-cbrt 93.1%

      \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x} \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right) \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   4. pow3 93.1%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   5. *-commutative 93.1%

      \[\leadsto \left(\left({\left(\sqrt[3]{\color{blue}{\log x \cdot \left(x - 0.5\right)}}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   6. sub-neg 93.1%

      \[\leadsto \left(\left({\left(\sqrt[3]{\log x \cdot \color{blue}{\left(x + \left(-0.5\right)\right)}}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   7. metadata-eval 93.1%

      \[\leadsto \left(\left({\left(\sqrt[3]{\log x \cdot \left(x + \color{blue}{-0.5}\right)}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

5. Applied egg-rr 93.1%

   \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\log x \cdot \left(x + -0.5\right)}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

6. Taylor expanded in x around inf 64.5%

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

   1. neg-mul-1 64.5%

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

8. Simplified 64.5%

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

9. Taylor expanded in x around 0 64.5%

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

10. Final simplification 64.5%

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

Alternative 16: 47.7% accurate, 9.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-50} \lor \neg \left(z \leq 3.5 \cdot 10^{-79}\right):\\ \;\;\;\;\frac{y}{\frac{x}{z \cdot z}} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5e-50) (not (<= z 3.5e-79)))
   (- (/ y (/ x (* z z))) x)
   (/ 0.083333333333333 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5e-50) || !(z <= 3.5e-79)) {
		tmp = (y / (x / (z * z))) - x;
	} else {
		tmp = 0.083333333333333 / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-5d-50)) .or. (.not. (z <= 3.5d-79))) then
        tmp = (y / (x / (z * z))) - x
    else
        tmp = 0.083333333333333d0 / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5e-50) || !(z <= 3.5e-79)) {
		tmp = (y / (x / (z * z))) - x;
	} else {
		tmp = 0.083333333333333 / x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5e-50) or not (z <= 3.5e-79):
		tmp = (y / (x / (z * z))) - x
	else:
		tmp = 0.083333333333333 / x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5e-50) || !(z <= 3.5e-79))
		tmp = Float64(Float64(y / Float64(x / Float64(z * z))) - x);
	else
		tmp = Float64(0.083333333333333 / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5e-50) || ~((z <= 3.5e-79)))
		tmp = (y / (x / (z * z))) - x;
	else
		tmp = 0.083333333333333 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5e-50], N[Not[LessEqual[z, 3.5e-79]], $MachinePrecision]], N[(N[(y / N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(0.083333333333333 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.99999999999999968e-50 or 3.5000000000000003e-79 < z

   1. Initial program 89.9%

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

      1. sub-neg 89.9%

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

      2. metadata-eval 89.9%

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

      3. fma-def 89.9%

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

      4. fma-neg 89.9%

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

      5. metadata-eval 89.9%

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

   3. Simplified 89.9%

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

      1. metadata-eval 89.9%

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

      2. sub-neg 89.9%

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

      3. add-cube-cbrt 89.6%

         \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x} \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right) \cdot \sqrt[3]{\left(x - 0.5\right) \cdot \log x}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      4. pow3 89.6%

         \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\left(x - 0.5\right) \cdot \log x}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      5. *-commutative 89.6%

         \[\leadsto \left(\left({\left(\sqrt[3]{\color{blue}{\log x \cdot \left(x - 0.5\right)}}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      6. sub-neg 89.6%

         \[\leadsto \left(\left({\left(\sqrt[3]{\log x \cdot \color{blue}{\left(x + \left(-0.5\right)\right)}}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      7. metadata-eval 89.6%

         \[\leadsto \left(\left({\left(\sqrt[3]{\log x \cdot \left(x + \color{blue}{-0.5}\right)}\right)}^{3} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   5. Applied egg-rr 89.6%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt[3]{\log x \cdot \left(x + -0.5\right)}\right)}^{3}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   6. Taylor expanded in x around inf 72.2%

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

      1. neg-mul-1 72.2%

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

   8. Simplified 72.2%

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

   9. Taylor expanded in y around inf 48.4%

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

       1. associate-/l* 50.7%

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

       2. unpow2 50.7%

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

   11. Simplified 50.7%

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

   if -4.99999999999999968e-50 < z < 3.5000000000000003e-79

   1. Initial program 99.5%

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

      1. sub-neg 99.5%

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

      2. metadata-eval 99.5%

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

      3. fma-def 99.5%

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

      4. fma-neg 99.5%

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

      5. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in z around 0 94.5%

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

   5. Taylor expanded in x around inf 93.0%

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

      1. sub-neg 93.0%

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

      2. mul-1-neg 93.0%

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

      3. log-rec 93.0%

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

      4. remove-double-neg 93.0%

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

      5. metadata-eval 93.0%

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

   7. Simplified 93.0%

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

   8. Taylor expanded in x around 0 48.6%

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

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-50} \lor \neg \left(z \leq 3.5 \cdot 10^{-79}\right):\\ \;\;\;\;\frac{y}{\frac{x}{z \cdot z}} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 17: 23.2% 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 93.5%

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

   1. sub-neg 93.5%

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

   2. metadata-eval 93.5%

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

   3. fma-def 93.5%

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

   4. fma-neg 93.6%

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

   5. metadata-eval 93.6%

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

3. Simplified 93.6%

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

4. Taylor expanded in z around 0 52.8%

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

5. Taylor expanded in x around inf 52.2%

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

   1. sub-neg 52.2%

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

   2. mul-1-neg 52.2%

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

   3. log-rec 52.2%

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

   4. remove-double-neg 52.2%

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

   5. metadata-eval 52.2%

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

7. Simplified 52.2%

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

8. Taylor expanded in x around 0 21.2%

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

9. Final simplification 21.2%

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

Developer target: 98.5% 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 2023293 
(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)))