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

Percentage Accurate: 93.7% → 96.7%

Time: 26.8s

Alternatives: 19

Speedup: 1.0×

• 28.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.05 \cdot 10^{+149}:\\ \;\;\;\;\left(\mathsf{fma}\left(x + -0.5, \log x, -x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + z \cdot \left(z \cdot \frac{y}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.05e+149)
   (+
    (+ (fma (+ x -0.5) (log x) (- x)) 0.91893853320467)
    (/
     (fma
      z
      (fma (+ y 0.0007936500793651) z -0.0027777777777778)
      0.083333333333333)
     x))
   (+ (* x (+ (log x) -1.0)) (* z (* z (/ y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.05e+149) {
		tmp = (fma((x + -0.5), log(x), -x) + 0.91893853320467) + (fma(z, fma((y + 0.0007936500793651), z, -0.0027777777777778), 0.083333333333333) / x);
	} else {
		tmp = (x * (log(x) + -1.0)) + (z * (z * (y / x)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.05e+149)
		tmp = Float64(Float64(fma(Float64(x + -0.5), log(x), Float64(-x)) + 0.91893853320467) + Float64(fma(z, fma(Float64(y + 0.0007936500793651), z, -0.0027777777777778), 0.083333333333333) / x));
	else
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(z * Float64(z * Float64(y / x))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.05e+149], N[(N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision] + (-x)), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(N[(z * N[(N[(y + 0.0007936500793651), $MachinePrecision] * z + -0.0027777777777778), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(z * N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.0500000000000001e149

   1. Initial program 98.7%

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

      1. fma-neg 98.7%

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

      2. sub-neg 98.7%

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

      3. metadata-eval 98.7%

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

      4. *-commutative 98.7%

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

      5. fma-def 98.7%

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

      6. fma-neg 98.7%

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

      7. metadata-eval 98.7%

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

   3. Simplified 98.7%

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

   if 1.0500000000000001e149 < x

   1. Initial program 83.1%

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

      1. sub-neg 83.1%

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

      2. metadata-eval 83.1%

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

      3. fma-def 83.1%

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

      4. fma-neg 83.1%

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

      5. metadata-eval 83.1%

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

   3. Simplified 83.1%

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

      1. metadata-eval 83.1%

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

      2. fma-neg 83.1%

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

      3. fma-def 83.1%

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

      4. clear-num 83.1%

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

      5. inv-pow 83.1%

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

      6. *-commutative 83.1%

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

      7. fma-udef 83.1%

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

      8. fma-neg 83.1%

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

      9. metadata-eval 83.1%

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

   5. Applied egg-rr 83.1%

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

   6. Taylor expanded in y around inf 79.9%

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

      1. associate-*l/ 85.9%

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

      2. *-commutative 85.9%

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

      3. unpow2 85.9%

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

      4. associate-*l* 95.4%

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

   8. Simplified 95.4%

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

   9. Taylor expanded in x around inf 95.4%

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

       1. sub-neg 95.4%

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

       2. mul-1-neg 95.4%

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

       3. log-rec 95.4%

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

       4. remove-double-neg 95.4%

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

       5. metadata-eval 95.4%

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

   11. Simplified 95.4%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.05 \cdot 10^{+149}:\\ \;\;\;\;\left(\mathsf{fma}\left(x + -0.5, \log x, -x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + z \cdot \left(z \cdot \frac{y}{x}\right)\\ \end{array} \]

Alternative 2: 96.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.25 \cdot 10^{+148}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + z \cdot \left(z \cdot \frac{y}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 2.25e+148)
   (+
    (+ 0.91893853320467 (- (* (+ x -0.5) (log x)) x))
    (/
     (fma
      (fma (+ y 0.0007936500793651) z -0.0027777777777778)
      z
      0.083333333333333)
     x))
   (+ (* x (+ (log x) -1.0)) (* z (* z (/ y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 2.25e+148) {
		tmp = (0.91893853320467 + (((x + -0.5) * log(x)) - x)) + (fma(fma((y + 0.0007936500793651), z, -0.0027777777777778), z, 0.083333333333333) / x);
	} else {
		tmp = (x * (log(x) + -1.0)) + (z * (z * (y / x)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 2.25e+148)
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(Float64(x + -0.5) * log(x)) - x)) + Float64(fma(fma(Float64(y + 0.0007936500793651), z, -0.0027777777777778), z, 0.083333333333333) / x));
	else
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(z * Float64(z * Float64(y / x))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 2.25e+148], N[(N[(0.91893853320467 + N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z + -0.0027777777777778), $MachinePrecision] * z + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(z * N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.24999999999999997e148

   1. Initial program 98.7%

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

      1. sub-neg 98.7%

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

      2. metadata-eval 98.7%

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

      3. fma-def 98.7%

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

      4. fma-neg 98.7%

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

      5. metadata-eval 98.7%

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

   3. Simplified 98.7%

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

   if 2.24999999999999997e148 < x

   1. Initial program 83.1%

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

      1. sub-neg 83.1%

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

      2. metadata-eval 83.1%

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

      3. fma-def 83.1%

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

      4. fma-neg 83.1%

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

      5. metadata-eval 83.1%

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

   3. Simplified 83.1%

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

      1. metadata-eval 83.1%

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

      2. fma-neg 83.1%

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

      3. fma-def 83.1%

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

      4. clear-num 83.1%

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

      5. inv-pow 83.1%

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

      6. *-commutative 83.1%

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

      7. fma-udef 83.1%

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

      8. fma-neg 83.1%

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

      9. metadata-eval 83.1%

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

   5. Applied egg-rr 83.1%

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

   6. Taylor expanded in y around inf 79.9%

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

      1. associate-*l/ 85.9%

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

      2. *-commutative 85.9%

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

      3. unpow2 85.9%

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

      4. associate-*l* 95.4%

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

   8. Simplified 95.4%

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

   9. Taylor expanded in x around inf 95.4%

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

       1. sub-neg 95.4%

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

       2. mul-1-neg 95.4%

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

       3. log-rec 95.4%

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

       4. remove-double-neg 95.4%

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

       5. metadata-eval 95.4%

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

   11. Simplified 95.4%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.25 \cdot 10^{+148}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + z \cdot \left(z \cdot \frac{y}{x}\right)\\ \end{array} \]

Alternative 3: 96.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 8.8 \cdot 10^{+146}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + z \cdot \left(z \cdot \frac{y}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 8.8e+146)
   (+
    (+ 0.91893853320467 (- (* (log x) (- x 0.5)) x))
    (/
     (+
      0.083333333333333
      (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))
     x))
   (+ (* x (+ (log x) -1.0)) (* z (* z (/ y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 8.8e+146) {
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = (x * (log(x) + -1.0)) + (z * (z * (y / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 8.8d+146) then
        tmp = (0.91893853320467d0 + ((log(x) * (x - 0.5d0)) - x)) + ((0.083333333333333d0 + (z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0))) / x)
    else
        tmp = (x * (log(x) + (-1.0d0))) + (z * (z * (y / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 8.8e+146) {
		tmp = (0.91893853320467 + ((Math.log(x) * (x - 0.5)) - x)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = (x * (Math.log(x) + -1.0)) + (z * (z * (y / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 8.8e+146:
		tmp = (0.91893853320467 + ((math.log(x) * (x - 0.5)) - x)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x)
	else:
		tmp = (x * (math.log(x) + -1.0)) + (z * (z * (y / x)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 8.8e+146)
		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(x * Float64(log(x) + -1.0)) + Float64(z * Float64(z * Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 8.8e+146)
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	else
		tmp = (x * (log(x) + -1.0)) + (z * (z * (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 8.8e+146], 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[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(z * N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 8.7999999999999992e146

   1. Initial program 98.7%

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

   if 8.7999999999999992e146 < x

   1. Initial program 83.1%

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

      1. sub-neg 83.1%

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

      2. metadata-eval 83.1%

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

      3. fma-def 83.1%

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

      4. fma-neg 83.1%

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

      5. metadata-eval 83.1%

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

   3. Simplified 83.1%

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

      1. metadata-eval 83.1%

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

      2. fma-neg 83.1%

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

      3. fma-def 83.1%

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

      4. clear-num 83.1%

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

      5. inv-pow 83.1%

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

      6. *-commutative 83.1%

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

      7. fma-udef 83.1%

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

      8. fma-neg 83.1%

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

      9. metadata-eval 83.1%

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

   5. Applied egg-rr 83.1%

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

   6. Taylor expanded in y around inf 79.9%

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

      1. associate-*l/ 85.9%

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

      2. *-commutative 85.9%

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

      3. unpow2 85.9%

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

      4. associate-*l* 95.4%

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

   8. Simplified 95.4%

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

   9. Taylor expanded in x around inf 95.4%

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

       1. sub-neg 95.4%

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

       2. mul-1-neg 95.4%

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

       3. log-rec 95.4%

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

       4. remove-double-neg 95.4%

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

       5. metadata-eval 95.4%

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

   11. Simplified 95.4%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 8.8 \cdot 10^{+146}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + z \cdot \left(z \cdot \frac{y}{x}\right)\\ \end{array} \]

Alternative 4: 95.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.15 \cdot 10^{-21}:\\ \;\;\;\;\frac{z}{x} \cdot \mathsf{fma}\left(z, y + 0.0007936500793651, -0.0027777777777778\right) + \left(\frac{0.083333333333333}{x} - x\right)\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{+161}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + z \cdot \left(z \cdot \frac{y}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.15e-21)
   (+
    (* (/ z x) (fma z (+ y 0.0007936500793651) -0.0027777777777778))
    (- (/ 0.083333333333333 x) x))
   (if (<= x 8.6e+161)
     (+
      (+ 0.91893853320467 (- (* (+ x -0.5) (log x)) x))
      (* (+ y 0.0007936500793651) (/ (* z z) x)))
     (+ (* x (+ (log x) -1.0)) (* z (* z (/ y x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.15e-21) {
		tmp = ((z / x) * fma(z, (y + 0.0007936500793651), -0.0027777777777778)) + ((0.083333333333333 / x) - x);
	} else if (x <= 8.6e+161) {
		tmp = (0.91893853320467 + (((x + -0.5) * log(x)) - x)) + ((y + 0.0007936500793651) * ((z * z) / x));
	} else {
		tmp = (x * (log(x) + -1.0)) + (z * (z * (y / x)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.15e-21)
		tmp = Float64(Float64(Float64(z / x) * fma(z, Float64(y + 0.0007936500793651), -0.0027777777777778)) + Float64(Float64(0.083333333333333 / x) - x));
	elseif (x <= 8.6e+161)
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(Float64(x + -0.5) * log(x)) - x)) + Float64(Float64(y + 0.0007936500793651) * Float64(Float64(z * z) / x)));
	else
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(z * Float64(z * Float64(y / x))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.15e-21], N[(N[(N[(z / x), $MachinePrecision] * N[(z * N[(y + 0.0007936500793651), $MachinePrecision] + -0.0027777777777778), $MachinePrecision]), $MachinePrecision] + N[(N[(0.083333333333333 / x), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.6e+161], N[(N[(0.91893853320467 + N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(N[(z * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(z * N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < 1.15e-21

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. metadata-eval 99.7%

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

      3. fma-def 99.7%

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

      4. fma-neg 99.7%

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

      5. metadata-eval 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}} \]
   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-sqr-sqrt 99.7%

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

      4. pow2 99.7%

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

      5. *-commutative 99.7%

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

      6. sub-neg 99.7%

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

      7. metadata-eval 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around inf 99.7%

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

      1. neg-mul-1 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in x around 0 99.7%

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

       1. mul-1-neg 99.7%

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

       2. +-commutative 99.7%

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

       3. associate-*r/ 99.7%

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

       4. metadata-eval 99.7%

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

       5. +-commutative 99.7%

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

       6. associate-+l+ 99.7%

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

       7. associate-/l* 98.2%

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

       8. *-commutative 98.2%

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

       9. fma-neg 98.2%

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

       10. metadata-eval 98.2%

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

       11. associate-/r/ 99.7%

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

       12. fma-def 99.7%

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

       13. *-commutative 99.7%

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

       14. fma-udef 99.7%

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

       15. sub-neg 99.7%

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

   11. Simplified 99.7%

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

   if 1.15e-21 < x < 8.6e161

   1. Initial program 95.7%

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

      1. sub-neg 95.7%

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

      2. metadata-eval 95.7%

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

      3. fma-def 95.7%

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

      4. fma-neg 95.7%

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

      5. metadata-eval 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in z around inf 93.1%

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

      1. associate-/l* 94.4%

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

      2. associate-/r/ 94.5%

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

      3. unpow2 94.5%

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

   6. Simplified 94.5%

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

   if 8.6e161 < x

   1. Initial program 82.7%

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

      1. sub-neg 82.7%

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

      2. metadata-eval 82.7%

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

      3. fma-def 82.7%

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

      4. fma-neg 82.7%

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

      5. metadata-eval 82.7%

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

   3. Simplified 82.7%

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

      1. metadata-eval 82.7%

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

      2. fma-neg 82.7%

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

      3. fma-def 82.7%

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

      4. clear-num 82.7%

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

      5. inv-pow 82.7%

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

      6. *-commutative 82.7%

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

      7. fma-udef 82.7%

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

      8. fma-neg 82.7%

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

      9. metadata-eval 82.7%

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

   5. Applied egg-rr 82.7%

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

   6. Taylor expanded in y around inf 79.0%

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

      1. associate-*l/ 84.2%

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

      2. *-commutative 84.2%

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

      3. unpow2 84.2%

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

      4. associate-*l* 96.4%

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

   8. Simplified 96.4%

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

   9. Taylor expanded in x around inf 96.4%

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

       1. sub-neg 96.4%

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

       2. mul-1-neg 96.4%

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

       3. log-rec 96.4%

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

       4. remove-double-neg 96.4%

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

       5. metadata-eval 96.4%

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

   11. Simplified 96.4%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.15 \cdot 10^{-21}:\\ \;\;\;\;\frac{z}{x} \cdot \mathsf{fma}\left(z, y + 0.0007936500793651, -0.0027777777777778\right) + \left(\frac{0.083333333333333}{x} - x\right)\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{+161}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + z \cdot \left(z \cdot \frac{y}{x}\right)\\ \end{array} \]

Alternative 5: 95.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.2 \cdot 10^{-28}:\\ \;\;\;\;\frac{z}{x} \cdot \mathsf{fma}\left(z, y + 0.0007936500793651, -0.0027777777777778\right) + \left(\frac{0.083333333333333}{x} - x\right)\\ \mathbf{elif}\;x \leq 3.85 \cdot 10^{+161}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{y + 0.0007936500793651}{\frac{x}{z \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + z \cdot \left(z \cdot \frac{y}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 2.2e-28)
   (+
    (* (/ z x) (fma z (+ y 0.0007936500793651) -0.0027777777777778))
    (- (/ 0.083333333333333 x) x))
   (if (<= x 3.85e+161)
     (+
      (+ 0.91893853320467 (- (* (+ x -0.5) (log x)) x))
      (/ (+ y 0.0007936500793651) (/ x (* z z))))
     (+ (* x (+ (log x) -1.0)) (* z (* z (/ y x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 2.2e-28) {
		tmp = ((z / x) * fma(z, (y + 0.0007936500793651), -0.0027777777777778)) + ((0.083333333333333 / x) - x);
	} else if (x <= 3.85e+161) {
		tmp = (0.91893853320467 + (((x + -0.5) * log(x)) - x)) + ((y + 0.0007936500793651) / (x / (z * z)));
	} else {
		tmp = (x * (log(x) + -1.0)) + (z * (z * (y / x)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 2.2e-28)
		tmp = Float64(Float64(Float64(z / x) * fma(z, Float64(y + 0.0007936500793651), -0.0027777777777778)) + Float64(Float64(0.083333333333333 / x) - x));
	elseif (x <= 3.85e+161)
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(Float64(x + -0.5) * log(x)) - x)) + Float64(Float64(y + 0.0007936500793651) / Float64(x / Float64(z * z))));
	else
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(z * Float64(z * Float64(y / x))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 2.2e-28], N[(N[(N[(z / x), $MachinePrecision] * N[(z * N[(y + 0.0007936500793651), $MachinePrecision] + -0.0027777777777778), $MachinePrecision]), $MachinePrecision] + N[(N[(0.083333333333333 / x), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.85e+161], N[(N[(0.91893853320467 + N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(N[(y + 0.0007936500793651), $MachinePrecision] / N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(z * N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < 2.19999999999999996e-28

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. metadata-eval 99.7%

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

      3. fma-def 99.7%

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

      4. fma-neg 99.7%

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

      5. metadata-eval 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}} \]
   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-sqr-sqrt 99.7%

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

      4. pow2 99.7%

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

      5. *-commutative 99.7%

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

      6. sub-neg 99.7%

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

      7. metadata-eval 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around inf 99.7%

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

      1. neg-mul-1 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in x around 0 99.7%

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

       1. mul-1-neg 99.7%

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

       2. +-commutative 99.7%

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

       3. associate-*r/ 99.7%

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

       4. metadata-eval 99.7%

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

       5. +-commutative 99.7%

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

       6. associate-+l+ 99.7%

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

       7. associate-/l* 98.2%

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

       8. *-commutative 98.2%

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

       9. fma-neg 98.2%

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

       10. metadata-eval 98.2%

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

       11. associate-/r/ 99.7%

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

       12. fma-def 99.7%

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

       13. *-commutative 99.7%

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

       14. fma-udef 99.7%

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

       15. sub-neg 99.7%

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

   11. Simplified 99.7%

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

   if 2.19999999999999996e-28 < x < 3.85000000000000022e161

   1. Initial program 95.8%

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

      1. sub-neg 95.8%

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

      2. metadata-eval 95.8%

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

      3. fma-def 95.8%

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

      4. fma-neg 95.8%

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

      5. metadata-eval 95.8%

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

   3. Simplified 95.8%

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

      1. metadata-eval 95.8%

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

      2. fma-neg 95.8%

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

      3. fma-def 95.8%

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

      4. clear-num 95.8%

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

      5. inv-pow 95.8%

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

      6. *-commutative 95.8%

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

      7. fma-udef 95.8%

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

      8. fma-neg 95.8%

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

      9. metadata-eval 95.8%

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

   5. Applied egg-rr 95.8%

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

   6. Taylor expanded in z around inf 93.2%

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

      1. *-commutative 93.2%

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

      2. associate-/l* 94.6%

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

      3. unpow2 94.6%

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

   8. Simplified 94.6%

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

   if 3.85000000000000022e161 < x

   1. Initial program 82.7%

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

      1. sub-neg 82.7%

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

      2. metadata-eval 82.7%

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

      3. fma-def 82.7%

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

      4. fma-neg 82.7%

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

      5. metadata-eval 82.7%

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

   3. Simplified 82.7%

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

      1. metadata-eval 82.7%

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

      2. fma-neg 82.7%

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

      3. fma-def 82.7%

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

      4. clear-num 82.7%

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

      5. inv-pow 82.7%

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

      6. *-commutative 82.7%

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

      7. fma-udef 82.7%

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

      8. fma-neg 82.7%

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

      9. metadata-eval 82.7%

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

   5. Applied egg-rr 82.7%

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

   6. Taylor expanded in y around inf 79.0%

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

      1. associate-*l/ 84.2%

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

      2. *-commutative 84.2%

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

      3. unpow2 84.2%

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

      4. associate-*l* 96.4%

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

   8. Simplified 96.4%

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

   9. Taylor expanded in x around inf 96.4%

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

       1. sub-neg 96.4%

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

       2. mul-1-neg 96.4%

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

       3. log-rec 96.4%

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

       4. remove-double-neg 96.4%

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

       5. metadata-eval 96.4%

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

   11. Simplified 96.4%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.2 \cdot 10^{-28}:\\ \;\;\;\;\frac{z}{x} \cdot \mathsf{fma}\left(z, y + 0.0007936500793651, -0.0027777777777778\right) + \left(\frac{0.083333333333333}{x} - x\right)\\ \mathbf{elif}\;x \leq 3.85 \cdot 10^{+161}:\\ \;\;\;\;\left(0.91893853320467 + \left(\left(x + -0.5\right) \cdot \log x - x\right)\right) + \frac{y + 0.0007936500793651}{\frac{x}{z \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + z \cdot \left(z \cdot \frac{y}{x}\right)\\ \end{array} \]

Alternative 6: 90.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.3 \cdot 10^{+36}:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} - x\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+128} \lor \neg \left(x \leq 4.8 \cdot 10^{+145}\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + z \cdot \left(z \cdot \frac{y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot z, \frac{1}{\frac{x}{y + 0.0007936500793651}}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.3e+36)
   (-
    (/
     (+
      0.083333333333333
      (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))
     x)
    x)
   (if (or (<= x 1.55e+128) (not (<= x 4.8e+145)))
     (+ (* x (+ (log x) -1.0)) (* z (* z (/ y x))))
     (fma (* z z) (/ 1.0 (/ x (+ y 0.0007936500793651))) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.3e+36) {
		tmp = ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) - x;
	} else if ((x <= 1.55e+128) || !(x <= 4.8e+145)) {
		tmp = (x * (log(x) + -1.0)) + (z * (z * (y / x)));
	} else {
		tmp = fma((z * z), (1.0 / (x / (y + 0.0007936500793651))), x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.3e+36)
		tmp = Float64(Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778))) / x) - x);
	elseif ((x <= 1.55e+128) || !(x <= 4.8e+145))
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(z * Float64(z * Float64(y / x))));
	else
		tmp = fma(Float64(z * z), Float64(1.0 / Float64(x / Float64(y + 0.0007936500793651))), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.3e+36], 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], If[Or[LessEqual[x, 1.55e+128], N[Not[LessEqual[x, 4.8e+145]], $MachinePrecision]], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(z * N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * z), $MachinePrecision] * N[(1.0 / N[(x / N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < 1.3000000000000001e36

   1. Initial program 99.1%

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

      1. sub-neg 99.1%

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

      2. metadata-eval 99.1%

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

      3. fma-def 99.1%

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

      4. fma-neg 99.1%

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

      5. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

      1. metadata-eval 99.1%

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

      2. sub-neg 99.1%

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

      3. add-sqr-sqrt 99.1%

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

      4. pow2 99.1%

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

      5. *-commutative 99.1%

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

      6. sub-neg 99.1%

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

      7. metadata-eval 99.1%

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

   5. Applied egg-rr 99.1%

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

   6. Taylor expanded in x around inf 96.5%

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

      1. neg-mul-1 96.5%

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

   8. Simplified 96.5%

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

   9. Taylor expanded in x around 0 96.5%

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

   if 1.3000000000000001e36 < x < 1.55000000000000002e128 or 4.79999999999999984e145 < x

   1. Initial program 89.4%

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

      1. sub-neg 89.4%

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

      2. metadata-eval 89.4%

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

      3. fma-def 89.4%

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

      4. fma-neg 89.4%

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

      5. metadata-eval 89.4%

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

   3. Simplified 89.4%

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

      1. metadata-eval 89.4%

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

      2. fma-neg 89.4%

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

      3. fma-def 89.4%

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

      4. clear-num 89.4%

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

      5. inv-pow 89.4%

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

      6. *-commutative 89.4%

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

      7. fma-udef 89.4%

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

      8. fma-neg 89.4%

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

      9. metadata-eval 89.4%

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

   5. Applied egg-rr 89.4%

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

   6. Taylor expanded in y around inf 83.5%

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

      1. associate-*l/ 87.3%

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

      2. *-commutative 87.3%

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

      3. unpow2 87.3%

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

      4. associate-*l* 92.3%

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

   8. Simplified 92.3%

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

   9. Taylor expanded in x around inf 92.3%

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

       1. sub-neg 92.3%

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

       2. mul-1-neg 92.3%

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

       3. log-rec 92.3%

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

       4. remove-double-neg 92.3%

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

       5. metadata-eval 92.3%

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

   11. Simplified 92.3%

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

   if 1.55000000000000002e128 < x < 4.79999999999999984e145

   1. Initial program 86.3%

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

      1. sub-neg 86.3%

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

      2. metadata-eval 86.3%

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

      3. fma-def 86.3%

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

      4. fma-neg 86.3%

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

      5. metadata-eval 86.3%

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

   3. Simplified 86.3%

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

      1. metadata-eval 86.3%

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

      2. sub-neg 86.3%

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

      3. add-sqr-sqrt 86.3%

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

      4. pow2 86.3%

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

      5. *-commutative 86.3%

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

      6. sub-neg 86.3%

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

      7. metadata-eval 86.3%

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

   5. Applied egg-rr 86.3%

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

   6. Taylor expanded in x around inf 81.9%

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

      1. neg-mul-1 81.9%

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

   8. Simplified 81.9%

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

   9. Taylor expanded in z around inf 81.9%

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

       1. associate-/l* 81.9%

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

       2. unpow2 81.9%

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

   11. Simplified 81.9%

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

       1. +-commutative 81.9%

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

       2. div-inv 81.9%

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

       3. fma-def 81.9%

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

       4. add-sqr-sqrt 0.0%

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

       5. sqrt-unprod 81.9%

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

       6. sqr-neg 81.9%

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

       7. sqrt-unprod 81.9%

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

       8. add-sqr-sqrt 81.9%

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

   13. Applied egg-rr 81.9%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.3 \cdot 10^{+36}:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} - x\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+128} \lor \neg \left(x \leq 4.8 \cdot 10^{+145}\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + z \cdot \left(z \cdot \frac{y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot z, \frac{1}{\frac{x}{y + 0.0007936500793651}}, x\right)\\ \end{array} \]

Alternative 7: 91.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.15 \cdot 10^{+36}:\\ \;\;\;\;\frac{z}{x} \cdot \mathsf{fma}\left(z, y + 0.0007936500793651, -0.0027777777777778\right) + \left(\frac{0.083333333333333}{x} - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + z \cdot \left(z \cdot \frac{y}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.15e+36)
   (+
    (* (/ z x) (fma z (+ y 0.0007936500793651) -0.0027777777777778))
    (- (/ 0.083333333333333 x) x))
   (+ (* x (+ (log x) -1.0)) (* z (* z (/ y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.15e+36) {
		tmp = ((z / x) * fma(z, (y + 0.0007936500793651), -0.0027777777777778)) + ((0.083333333333333 / x) - x);
	} else {
		tmp = (x * (log(x) + -1.0)) + (z * (z * (y / x)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.15e+36)
		tmp = Float64(Float64(Float64(z / x) * fma(z, Float64(y + 0.0007936500793651), -0.0027777777777778)) + Float64(Float64(0.083333333333333 / x) - x));
	else
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(z * Float64(z * Float64(y / x))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.15e+36], N[(N[(N[(z / x), $MachinePrecision] * N[(z * N[(y + 0.0007936500793651), $MachinePrecision] + -0.0027777777777778), $MachinePrecision]), $MachinePrecision] + N[(N[(0.083333333333333 / x), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(z * N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.14999999999999998e36

   1. Initial program 99.1%

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

      1. sub-neg 99.1%

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

      2. metadata-eval 99.1%

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

      3. fma-def 99.1%

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

      4. fma-neg 99.1%

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

      5. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

      1. metadata-eval 99.1%

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

      2. sub-neg 99.1%

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

      3. add-sqr-sqrt 99.1%

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

      4. pow2 99.1%

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

      5. *-commutative 99.1%

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

      6. sub-neg 99.1%

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

      7. metadata-eval 99.1%

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

   5. Applied egg-rr 99.1%

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

   6. Taylor expanded in x around inf 96.5%

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

      1. neg-mul-1 96.5%

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

   8. Simplified 96.5%

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

   9. Taylor expanded in x around 0 96.4%

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

       1. mul-1-neg 96.4%

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

       2. +-commutative 96.4%

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

       3. associate-*r/ 96.5%

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

       4. metadata-eval 96.5%

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

       5. +-commutative 96.5%

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

       6. associate-+l+ 96.5%

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

       7. associate-/l* 95.8%

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

       8. *-commutative 95.8%

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

       9. fma-neg 95.8%

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

       10. metadata-eval 95.8%

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

       11. associate-/r/ 97.1%

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

       12. fma-def 97.1%

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

       13. *-commutative 97.1%

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

       14. fma-udef 97.1%

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

       15. sub-neg 97.1%

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

   11. Simplified 97.1%

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

   if 1.14999999999999998e36 < x

   1. Initial program 89.2%

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

      1. sub-neg 89.2%

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

      2. metadata-eval 89.2%

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

      3. fma-def 89.2%

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

      4. fma-neg 89.2%

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

      5. metadata-eval 89.2%

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

   3. Simplified 89.2%

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

      1. metadata-eval 89.2%

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

      2. fma-neg 89.2%

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

      3. fma-def 89.2%

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

      4. clear-num 89.2%

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

      5. inv-pow 89.2%

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

      6. *-commutative 89.2%

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

      7. fma-udef 89.2%

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

      8. fma-neg 89.2%

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

      9. metadata-eval 89.2%

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

   5. Applied egg-rr 89.2%

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

   6. Taylor expanded in y around inf 81.2%

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

      1. associate-*l/ 83.7%

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

      2. *-commutative 83.7%

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

      3. unpow2 83.7%

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

      4. associate-*l* 87.7%

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

   8. Simplified 87.7%

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

   9. Taylor expanded in x around inf 87.8%

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

       1. sub-neg 87.8%

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

       2. mul-1-neg 87.8%

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

       3. log-rec 87.8%

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

       4. remove-double-neg 87.8%

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

       5. metadata-eval 87.8%

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

   11. Simplified 87.8%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.15 \cdot 10^{+36}:\\ \;\;\;\;\frac{z}{x} \cdot \mathsf{fma}\left(z, y + 0.0007936500793651, -0.0027777777777778\right) + \left(\frac{0.083333333333333}{x} - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + z \cdot \left(z \cdot \frac{y}{x}\right)\\ \end{array} \]

Alternative 8: 80.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 7.5 \cdot 10^{+72}:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} - x\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+128} \lor \neg \left(x \leq 1.5 \cdot 10^{+165}\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot z\right) \cdot \left(\frac{y}{x} + \frac{0.0007936500793651}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 7.5e+72)
   (-
    (/
     (+
      0.083333333333333
      (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))
     x)
    x)
   (if (or (<= x 1.55e+128) (not (<= x 1.5e+165)))
     (+ (* x (+ (log x) -1.0)) (/ 0.083333333333333 x))
     (* (* z z) (+ (/ y x) (/ 0.0007936500793651 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 7.5e+72) {
		tmp = ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) - x;
	} else if ((x <= 1.55e+128) || !(x <= 1.5e+165)) {
		tmp = (x * (log(x) + -1.0)) + (0.083333333333333 / x);
	} else {
		tmp = (z * z) * ((y / x) + (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 <= 7.5d+72) then
        tmp = ((0.083333333333333d0 + (z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0))) / x) - x
    else if ((x <= 1.55d+128) .or. (.not. (x <= 1.5d+165))) then
        tmp = (x * (log(x) + (-1.0d0))) + (0.083333333333333d0 / x)
    else
        tmp = (z * z) * ((y / x) + (0.0007936500793651d0 / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 7.5e+72) {
		tmp = ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) - x;
	} else if ((x <= 1.55e+128) || !(x <= 1.5e+165)) {
		tmp = (x * (Math.log(x) + -1.0)) + (0.083333333333333 / x);
	} else {
		tmp = (z * z) * ((y / x) + (0.0007936500793651 / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 7.5e+72:
		tmp = ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) - x
	elif (x <= 1.55e+128) or not (x <= 1.5e+165):
		tmp = (x * (math.log(x) + -1.0)) + (0.083333333333333 / x)
	else:
		tmp = (z * z) * ((y / x) + (0.0007936500793651 / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 7.5e+72)
		tmp = Float64(Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778))) / x) - x);
	elseif ((x <= 1.55e+128) || !(x <= 1.5e+165))
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(0.083333333333333 / x));
	else
		tmp = Float64(Float64(z * z) * Float64(Float64(y / x) + Float64(0.0007936500793651 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 7.5e+72)
		tmp = ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) - x;
	elseif ((x <= 1.55e+128) || ~((x <= 1.5e+165)))
		tmp = (x * (log(x) + -1.0)) + (0.083333333333333 / x);
	else
		tmp = (z * z) * ((y / x) + (0.0007936500793651 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 7.5e+72], 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], If[Or[LessEqual[x, 1.55e+128], N[Not[LessEqual[x, 1.5e+165]], $MachinePrecision]], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision], N[(N[(z * z), $MachinePrecision] * N[(N[(y / x), $MachinePrecision] + N[(0.0007936500793651 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < 7.50000000000000027e72

   1. Initial program 99.1%

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

      1. sub-neg 99.1%

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

      2. metadata-eval 99.1%

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

      3. fma-def 99.1%

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

      4. fma-neg 99.1%

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

      5. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

      1. metadata-eval 99.1%

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

      2. sub-neg 99.1%

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

      3. add-sqr-sqrt 99.1%

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

      4. pow2 99.1%

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

      5. *-commutative 99.1%

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

      6. sub-neg 99.1%

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

      7. metadata-eval 99.1%

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

   5. Applied egg-rr 99.1%

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

   6. Taylor expanded in x around inf 93.7%

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

      1. neg-mul-1 93.7%

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

   8. Simplified 93.7%

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

   9. Taylor expanded in x around 0 93.7%

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

   if 7.50000000000000027e72 < x < 1.55000000000000002e128 or 1.49999999999999995e165 < x

   1. Initial program 87.1%

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

      1. sub-neg 87.1%

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

      2. metadata-eval 87.1%

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

      3. fma-def 87.1%

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

      4. fma-neg 87.1%

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

      5. metadata-eval 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in z around 0 83.1%

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

   5. Taylor expanded in x around inf 83.1%

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

      1. sub-neg 94.7%

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

      2. mul-1-neg 94.7%

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

      3. log-rec 94.7%

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

      4. remove-double-neg 94.7%

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

      5. metadata-eval 94.7%

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

   7. Simplified 83.1%

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

   if 1.55000000000000002e128 < x < 1.49999999999999995e165

   1. Initial program 89.5%

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

      1. sub-neg 89.5%

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

      2. metadata-eval 89.5%

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

      3. fma-def 89.5%

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

      4. fma-neg 89.5%

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

      5. metadata-eval 89.5%

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

   3. Simplified 89.5%

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

      1. metadata-eval 89.5%

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

      2. sub-neg 89.5%

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

      3. add-sqr-sqrt 89.3%

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

      4. pow2 89.3%

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

      5. *-commutative 89.3%

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

      6. sub-neg 89.3%

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

      7. metadata-eval 89.3%

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

   5. Applied egg-rr 89.3%

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

   6. Taylor expanded in x around inf 60.2%

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

      1. neg-mul-1 60.2%

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

   8. Simplified 60.2%

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

   9. Taylor expanded in z around inf 66.3%

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

       1. unpow2 66.3%

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

       2. associate-*r/ 66.3%

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

       3. metadata-eval 66.3%

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

   11. Simplified 66.3%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 7.5 \cdot 10^{+72}:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} - x\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+128} \lor \neg \left(x \leq 1.5 \cdot 10^{+165}\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot z\right) \cdot \left(\frac{y}{x} + \frac{0.0007936500793651}{x}\right)\\ \end{array} \]

Alternative 9: 80.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.9 \cdot 10^{+73}:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} - x\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+128} \lor \neg \left(x \leq 9.6 \cdot 10^{+164}\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z \cdot z}{x}, y + 0.0007936500793651, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.9e+73)
   (-
    (/
     (+
      0.083333333333333
      (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))
     x)
    x)
   (if (or (<= x 1.55e+128) (not (<= x 9.6e+164)))
     (+ (* x (+ (log x) -1.0)) (/ 0.083333333333333 x))
     (fma (/ (* z z) x) (+ y 0.0007936500793651) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.9e+73) {
		tmp = ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) - x;
	} else if ((x <= 1.55e+128) || !(x <= 9.6e+164)) {
		tmp = (x * (log(x) + -1.0)) + (0.083333333333333 / x);
	} else {
		tmp = fma(((z * z) / x), (y + 0.0007936500793651), x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.9e+73)
		tmp = Float64(Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778))) / x) - x);
	elseif ((x <= 1.55e+128) || !(x <= 9.6e+164))
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(0.083333333333333 / x));
	else
		tmp = fma(Float64(Float64(z * z) / x), Float64(y + 0.0007936500793651), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.9e+73], 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], If[Or[LessEqual[x, 1.55e+128], N[Not[LessEqual[x, 9.6e+164]], $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] / x), $MachinePrecision] * N[(y + 0.0007936500793651), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < 1.90000000000000011e73

   1. Initial program 99.1%

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

      1. sub-neg 99.1%

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

      2. metadata-eval 99.1%

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

      3. fma-def 99.1%

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

      4. fma-neg 99.1%

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

      5. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

      1. metadata-eval 99.1%

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

      2. sub-neg 99.1%

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

      3. add-sqr-sqrt 99.1%

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

      4. pow2 99.1%

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

      5. *-commutative 99.1%

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

      6. sub-neg 99.1%

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

      7. metadata-eval 99.1%

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

   5. Applied egg-rr 99.1%

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

   6. Taylor expanded in x around inf 93.7%

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

      1. neg-mul-1 93.7%

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

   8. Simplified 93.7%

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

   9. Taylor expanded in x around 0 93.7%

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

   if 1.90000000000000011e73 < x < 1.55000000000000002e128 or 9.60000000000000043e164 < x

   1. Initial program 87.1%

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

      1. sub-neg 87.1%

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

      2. metadata-eval 87.1%

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

      3. fma-def 87.1%

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

      4. fma-neg 87.1%

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

      5. metadata-eval 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in z around 0 83.1%

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

   5. Taylor expanded in x around inf 83.1%

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

      1. sub-neg 94.7%

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

      2. mul-1-neg 94.7%

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

      3. log-rec 94.7%

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

      4. remove-double-neg 94.7%

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

      5. metadata-eval 94.7%

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

   7. Simplified 83.1%

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

   if 1.55000000000000002e128 < x < 9.60000000000000043e164

   1. Initial program 89.5%

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

      1. sub-neg 89.5%

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

      2. metadata-eval 89.5%

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

      3. fma-def 89.5%

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

      4. fma-neg 89.5%

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

      5. metadata-eval 89.5%

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

   3. Simplified 89.5%

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

      1. metadata-eval 89.5%

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

      2. sub-neg 89.5%

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

      3. add-sqr-sqrt 89.3%

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

      4. pow2 89.3%

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

      5. *-commutative 89.3%

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

      6. sub-neg 89.3%

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

      7. metadata-eval 89.3%

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

   5. Applied egg-rr 89.3%

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

   6. Taylor expanded in x around inf 60.2%

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

      1. neg-mul-1 60.2%

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

   8. Simplified 60.2%

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

   9. Taylor expanded in z around inf 60.2%

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

       1. associate-/l* 65.3%

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

       2. unpow2 65.3%

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

   11. Simplified 65.3%

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

       1. +-commutative 65.3%

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

       2. associate-/r/ 65.4%

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

       3. fma-def 65.4%

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

       4. add-sqr-sqrt 0.0%

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

       5. sqrt-unprod 56.4%

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

       6. sqr-neg 56.4%

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

       7. sqrt-unprod 69.1%

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

       8. add-sqr-sqrt 69.1%

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

   13. Applied egg-rr 69.1%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.9 \cdot 10^{+73}:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} - x\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+128} \lor \neg \left(x \leq 9.6 \cdot 10^{+164}\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z \cdot z}{x}, y + 0.0007936500793651, x\right)\\ \end{array} \]

Alternative 10: 46.7% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{x} \cdot \left(z \cdot z\right) - x\\ t_1 := \frac{z \cdot z}{x \cdot 1260.0011340009878} - x\\ \mathbf{if}\;z \leq -1.22 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{-23}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-20}:\\ \;\;\;\;\frac{0.083333333333333}{x} - x\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+114}:\\ \;\;\;\;\frac{y}{\frac{x}{z \cdot z}} - x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+226} \lor \neg \left(z \leq 7.5 \cdot 10^{+251}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* (/ y x) (* z z)) x))
        (t_1 (- (/ (* z z) (* x 1260.0011340009878)) x)))
   (if (<= z -1.22e+138)
     t_1
     (if (<= z -1.18e-23)
       t_0
       (if (<= z 1.45e-20)
         (- (/ 0.083333333333333 x) x)
         (if (<= z 8.2e+114)
           (- (/ y (/ x (* z z))) x)
           (if (or (<= z 1.7e+226) (not (<= z 7.5e+251))) t_1 t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = ((y / x) * (z * z)) - x;
	double t_1 = ((z * z) / (x * 1260.0011340009878)) - x;
	double tmp;
	if (z <= -1.22e+138) {
		tmp = t_1;
	} else if (z <= -1.18e-23) {
		tmp = t_0;
	} else if (z <= 1.45e-20) {
		tmp = (0.083333333333333 / x) - x;
	} else if (z <= 8.2e+114) {
		tmp = (y / (x / (z * z))) - x;
	} else if ((z <= 1.7e+226) || !(z <= 7.5e+251)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ((y / x) * (z * z)) - x
    t_1 = ((z * z) / (x * 1260.0011340009878d0)) - x
    if (z <= (-1.22d+138)) then
        tmp = t_1
    else if (z <= (-1.18d-23)) then
        tmp = t_0
    else if (z <= 1.45d-20) then
        tmp = (0.083333333333333d0 / x) - x
    else if (z <= 8.2d+114) then
        tmp = (y / (x / (z * z))) - x
    else if ((z <= 1.7d+226) .or. (.not. (z <= 7.5d+251))) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((y / x) * (z * z)) - x;
	double t_1 = ((z * z) / (x * 1260.0011340009878)) - x;
	double tmp;
	if (z <= -1.22e+138) {
		tmp = t_1;
	} else if (z <= -1.18e-23) {
		tmp = t_0;
	} else if (z <= 1.45e-20) {
		tmp = (0.083333333333333 / x) - x;
	} else if (z <= 8.2e+114) {
		tmp = (y / (x / (z * z))) - x;
	} else if ((z <= 1.7e+226) || !(z <= 7.5e+251)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((y / x) * (z * z)) - x
	t_1 = ((z * z) / (x * 1260.0011340009878)) - x
	tmp = 0
	if z <= -1.22e+138:
		tmp = t_1
	elif z <= -1.18e-23:
		tmp = t_0
	elif z <= 1.45e-20:
		tmp = (0.083333333333333 / x) - x
	elif z <= 8.2e+114:
		tmp = (y / (x / (z * z))) - x
	elif (z <= 1.7e+226) or not (z <= 7.5e+251):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y / x) * Float64(z * z)) - x)
	t_1 = Float64(Float64(Float64(z * z) / Float64(x * 1260.0011340009878)) - x)
	tmp = 0.0
	if (z <= -1.22e+138)
		tmp = t_1;
	elseif (z <= -1.18e-23)
		tmp = t_0;
	elseif (z <= 1.45e-20)
		tmp = Float64(Float64(0.083333333333333 / x) - x);
	elseif (z <= 8.2e+114)
		tmp = Float64(Float64(y / Float64(x / Float64(z * z))) - x);
	elseif ((z <= 1.7e+226) || !(z <= 7.5e+251))
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((y / x) * (z * z)) - x;
	t_1 = ((z * z) / (x * 1260.0011340009878)) - x;
	tmp = 0.0;
	if (z <= -1.22e+138)
		tmp = t_1;
	elseif (z <= -1.18e-23)
		tmp = t_0;
	elseif (z <= 1.45e-20)
		tmp = (0.083333333333333 / x) - x;
	elseif (z <= 8.2e+114)
		tmp = (y / (x / (z * z))) - x;
	elseif ((z <= 1.7e+226) || ~((z <= 7.5e+251)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y / x), $MachinePrecision] * N[(z * z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(z * z), $MachinePrecision] / N[(x * 1260.0011340009878), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[z, -1.22e+138], t$95$1, If[LessEqual[z, -1.18e-23], t$95$0, If[LessEqual[z, 1.45e-20], N[(N[(0.083333333333333 / x), $MachinePrecision] - x), $MachinePrecision], If[LessEqual[z, 8.2e+114], N[(N[(y / N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], If[Or[LessEqual[z, 1.7e+226], N[Not[LessEqual[z, 7.5e+251]], $MachinePrecision]], t$95$1, t$95$0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.22000000000000001e138 or 8.2000000000000001e114 < z < 1.69999999999999989e226 or 7.49999999999999973e251 < z

   1. Initial program 88.0%

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

      1. sub-neg 88.0%

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

      2. metadata-eval 88.0%

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

      3. fma-def 88.0%

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

      4. fma-neg 88.0%

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

      5. metadata-eval 88.0%

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

   3. Simplified 88.0%

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

      1. metadata-eval 88.0%

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

      2. sub-neg 88.0%

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

      3. add-sqr-sqrt 88.0%

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

      4. pow2 88.0%

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

      5. *-commutative 88.0%

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

      6. sub-neg 88.0%

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

      7. metadata-eval 88.0%

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

   5. Applied egg-rr 88.0%

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

   6. Taylor expanded in x around inf 83.9%

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

      1. neg-mul-1 83.9%

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

   8. Simplified 83.9%

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

   9. Taylor expanded in z around inf 83.9%

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

       1. associate-/l* 82.6%

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

       2. unpow2 82.6%

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

   11. Simplified 82.6%

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

   12. Taylor expanded in y around 0 69.3%

       \[\leadsto \left(-x\right) + \frac{z \cdot z}{\color{blue}{1260.0011340009878 \cdot x}} \]
   13. Step-by-step derivation

       1. *-commutative 69.3%

          \[\leadsto \left(-x\right) + \frac{z \cdot z}{\color{blue}{x \cdot 1260.0011340009878}} \]

   14. Simplified 69.3%

       \[\leadsto \left(-x\right) + \frac{z \cdot z}{\color{blue}{x \cdot 1260.0011340009878}} \]

   if -1.22000000000000001e138 < z < -1.18e-23 or 1.69999999999999989e226 < z < 7.49999999999999973e251

   1. Initial program 97.0%

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

      1. sub-neg 97.0%

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

      2. metadata-eval 97.0%

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

      3. fma-def 97.0%

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

      4. fma-neg 97.0%

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

      5. metadata-eval 97.0%

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

   3. Simplified 97.0%

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

      1. metadata-eval 97.0%

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

      2. sub-neg 97.0%

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

      3. add-sqr-sqrt 96.8%

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

      4. pow2 96.8%

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

      5. *-commutative 96.8%

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

      6. sub-neg 96.8%

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

      7. metadata-eval 96.8%

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

   5. Applied egg-rr 96.8%

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

   6. Taylor expanded in x around inf 70.7%

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

      1. neg-mul-1 70.7%

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

   8. Simplified 70.7%

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

   9. Taylor expanded in y around inf 59.2%

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

       1. *-commutative 59.2%

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

       2. associate-*r/ 62.0%

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

       3. unpow2 62.0%

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

   11. Simplified 62.0%

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

   if -1.18e-23 < z < 1.45e-20

   1. Initial program 99.5%

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

      1. sub-neg 99.5%

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

      2. metadata-eval 99.5%

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

      3. fma-def 99.5%

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

      4. fma-neg 99.5%

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

      5. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

      1. metadata-eval 99.5%

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

      2. sub-neg 99.5%

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

      3. add-sqr-sqrt 99.3%

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

      4. pow2 99.3%

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

      5. *-commutative 99.3%

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

      6. sub-neg 99.3%

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

      7. metadata-eval 99.3%

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

   5. Applied egg-rr 99.3%

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

   6. Taylor expanded in x around inf 58.4%

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

      1. neg-mul-1 58.4%

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

   8. Simplified 58.4%

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

   9. Taylor expanded in z around 0 53.5%

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

       1. associate-*r/ 53.6%

          \[\leadsto \color{blue}{\frac{0.083333333333333 \cdot 1}{x}} - x \]

       2. metadata-eval 53.6%

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

   11. Simplified 53.6%

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

   if 1.45e-20 < z < 8.2000000000000001e114

   1. Initial program 94.0%

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

      1. sub-neg 94.0%

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

      2. metadata-eval 94.0%

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

      3. fma-def 94.0%

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

      4. fma-neg 94.0%

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

      5. metadata-eval 94.0%

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

   3. Simplified 94.0%

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

      1. metadata-eval 94.0%

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

      2. sub-neg 94.0%

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

      3. add-sqr-sqrt 93.8%

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

      4. pow2 93.8%

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

      5. *-commutative 93.8%

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

      6. sub-neg 93.8%

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

      7. metadata-eval 93.8%

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

   5. Applied egg-rr 93.8%

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

   6. Taylor expanded in x around inf 56.2%

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

      1. neg-mul-1 56.2%

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

   8. Simplified 56.2%

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

   9. Taylor expanded in y around inf 40.0%

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

       1. associate-/l* 42.7%

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

       2. unpow2 42.7%

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

   11. Simplified 42.7%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+138}:\\ \;\;\;\;\frac{z \cdot z}{x \cdot 1260.0011340009878} - x\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{-23}:\\ \;\;\;\;\frac{y}{x} \cdot \left(z \cdot z\right) - x\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-20}:\\ \;\;\;\;\frac{0.083333333333333}{x} - x\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+114}:\\ \;\;\;\;\frac{y}{\frac{x}{z \cdot z}} - x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+226} \lor \neg \left(z \leq 7.5 \cdot 10^{+251}\right):\\ \;\;\;\;\frac{z \cdot z}{x \cdot 1260.0011340009878} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} \cdot \left(z \cdot z\right) - x\\ \end{array} \]

Alternative 11: 46.7% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{x} \cdot \left(z \cdot z\right) - x\\ t_1 := \frac{z \cdot z}{x \cdot 1260.0011340009878} - x\\ \mathbf{if}\;z \leq -6 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-19}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-20}:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot -0.0027777777777778}{x} - x\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+113}:\\ \;\;\;\;\frac{y}{\frac{x}{z \cdot z}} - x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+226} \lor \neg \left(z \leq 1.15 \cdot 10^{+251}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* (/ y x) (* z z)) x))
        (t_1 (- (/ (* z z) (* x 1260.0011340009878)) x)))
   (if (<= z -6e+138)
     t_1
     (if (<= z -8.5e-19)
       t_0
       (if (<= z 1.95e-20)
         (- (/ (+ 0.083333333333333 (* z -0.0027777777777778)) x) x)
         (if (<= z 2e+113)
           (- (/ y (/ x (* z z))) x)
           (if (or (<= z 2.4e+226) (not (<= z 1.15e+251))) t_1 t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = ((y / x) * (z * z)) - x;
	double t_1 = ((z * z) / (x * 1260.0011340009878)) - x;
	double tmp;
	if (z <= -6e+138) {
		tmp = t_1;
	} else if (z <= -8.5e-19) {
		tmp = t_0;
	} else if (z <= 1.95e-20) {
		tmp = ((0.083333333333333 + (z * -0.0027777777777778)) / x) - x;
	} else if (z <= 2e+113) {
		tmp = (y / (x / (z * z))) - x;
	} else if ((z <= 2.4e+226) || !(z <= 1.15e+251)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ((y / x) * (z * z)) - x
    t_1 = ((z * z) / (x * 1260.0011340009878d0)) - x
    if (z <= (-6d+138)) then
        tmp = t_1
    else if (z <= (-8.5d-19)) then
        tmp = t_0
    else if (z <= 1.95d-20) then
        tmp = ((0.083333333333333d0 + (z * (-0.0027777777777778d0))) / x) - x
    else if (z <= 2d+113) then
        tmp = (y / (x / (z * z))) - x
    else if ((z <= 2.4d+226) .or. (.not. (z <= 1.15d+251))) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((y / x) * (z * z)) - x;
	double t_1 = ((z * z) / (x * 1260.0011340009878)) - x;
	double tmp;
	if (z <= -6e+138) {
		tmp = t_1;
	} else if (z <= -8.5e-19) {
		tmp = t_0;
	} else if (z <= 1.95e-20) {
		tmp = ((0.083333333333333 + (z * -0.0027777777777778)) / x) - x;
	} else if (z <= 2e+113) {
		tmp = (y / (x / (z * z))) - x;
	} else if ((z <= 2.4e+226) || !(z <= 1.15e+251)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((y / x) * (z * z)) - x
	t_1 = ((z * z) / (x * 1260.0011340009878)) - x
	tmp = 0
	if z <= -6e+138:
		tmp = t_1
	elif z <= -8.5e-19:
		tmp = t_0
	elif z <= 1.95e-20:
		tmp = ((0.083333333333333 + (z * -0.0027777777777778)) / x) - x
	elif z <= 2e+113:
		tmp = (y / (x / (z * z))) - x
	elif (z <= 2.4e+226) or not (z <= 1.15e+251):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y / x) * Float64(z * z)) - x)
	t_1 = Float64(Float64(Float64(z * z) / Float64(x * 1260.0011340009878)) - x)
	tmp = 0.0
	if (z <= -6e+138)
		tmp = t_1;
	elseif (z <= -8.5e-19)
		tmp = t_0;
	elseif (z <= 1.95e-20)
		tmp = Float64(Float64(Float64(0.083333333333333 + Float64(z * -0.0027777777777778)) / x) - x);
	elseif (z <= 2e+113)
		tmp = Float64(Float64(y / Float64(x / Float64(z * z))) - x);
	elseif ((z <= 2.4e+226) || !(z <= 1.15e+251))
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((y / x) * (z * z)) - x;
	t_1 = ((z * z) / (x * 1260.0011340009878)) - x;
	tmp = 0.0;
	if (z <= -6e+138)
		tmp = t_1;
	elseif (z <= -8.5e-19)
		tmp = t_0;
	elseif (z <= 1.95e-20)
		tmp = ((0.083333333333333 + (z * -0.0027777777777778)) / x) - x;
	elseif (z <= 2e+113)
		tmp = (y / (x / (z * z))) - x;
	elseif ((z <= 2.4e+226) || ~((z <= 1.15e+251)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y / x), $MachinePrecision] * N[(z * z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(z * z), $MachinePrecision] / N[(x * 1260.0011340009878), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[z, -6e+138], t$95$1, If[LessEqual[z, -8.5e-19], t$95$0, If[LessEqual[z, 1.95e-20], N[(N[(N[(0.083333333333333 + N[(z * -0.0027777777777778), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - x), $MachinePrecision], If[LessEqual[z, 2e+113], N[(N[(y / N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], If[Or[LessEqual[z, 2.4e+226], N[Not[LessEqual[z, 1.15e+251]], $MachinePrecision]], t$95$1, t$95$0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.0000000000000002e138 or 2e113 < z < 2.4e226 or 1.14999999999999994e251 < z

   1. Initial program 88.0%

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

      1. sub-neg 88.0%

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

      2. metadata-eval 88.0%

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

      3. fma-def 88.0%

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

      4. fma-neg 88.0%

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

      5. metadata-eval 88.0%

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

   3. Simplified 88.0%

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

      1. metadata-eval 88.0%

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

      2. sub-neg 88.0%

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

      3. add-sqr-sqrt 88.0%

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

      4. pow2 88.0%

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

      5. *-commutative 88.0%

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

      6. sub-neg 88.0%

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

      7. metadata-eval 88.0%

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

   5. Applied egg-rr 88.0%

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

   6. Taylor expanded in x around inf 83.9%

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

      1. neg-mul-1 83.9%

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

   8. Simplified 83.9%

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

   9. Taylor expanded in z around inf 83.9%

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

       1. associate-/l* 82.6%

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

       2. unpow2 82.6%

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

   11. Simplified 82.6%

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

   12. Taylor expanded in y around 0 69.3%

       \[\leadsto \left(-x\right) + \frac{z \cdot z}{\color{blue}{1260.0011340009878 \cdot x}} \]
   13. Step-by-step derivation

       1. *-commutative 69.3%

          \[\leadsto \left(-x\right) + \frac{z \cdot z}{\color{blue}{x \cdot 1260.0011340009878}} \]

   14. Simplified 69.3%

       \[\leadsto \left(-x\right) + \frac{z \cdot z}{\color{blue}{x \cdot 1260.0011340009878}} \]

   if -6.0000000000000002e138 < z < -8.50000000000000003e-19 or 2.4e226 < z < 1.14999999999999994e251

   1. Initial program 97.0%

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

      1. sub-neg 97.0%

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

      2. metadata-eval 97.0%

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

      3. fma-def 97.0%

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

      4. fma-neg 97.0%

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

      5. metadata-eval 97.0%

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

   3. Simplified 97.0%

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

      1. metadata-eval 97.0%

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

      2. sub-neg 97.0%

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

      3. add-sqr-sqrt 96.8%

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

      4. pow2 96.8%

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

      5. *-commutative 96.8%

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

      6. sub-neg 96.8%

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

      7. metadata-eval 96.8%

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

   5. Applied egg-rr 96.8%

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

   6. Taylor expanded in x around inf 70.7%

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

      1. neg-mul-1 70.7%

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

   8. Simplified 70.7%

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

   9. Taylor expanded in y around inf 59.2%

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

       1. *-commutative 59.2%

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

       2. associate-*r/ 62.0%

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

       3. unpow2 62.0%

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

   11. Simplified 62.0%

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

   if -8.50000000000000003e-19 < z < 1.95000000000000004e-20

   1. Initial program 99.5%

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

      1. sub-neg 99.5%

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

      2. metadata-eval 99.5%

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

      3. fma-def 99.5%

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

      4. fma-neg 99.5%

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

      5. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

      1. metadata-eval 99.5%

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

      2. sub-neg 99.5%

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

      3. add-sqr-sqrt 99.3%

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

      4. pow2 99.3%

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

      5. *-commutative 99.3%

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

      6. sub-neg 99.3%

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

      7. metadata-eval 99.3%

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

   5. Applied egg-rr 99.3%

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

   6. Taylor expanded in x around inf 58.4%

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

      1. neg-mul-1 58.4%

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

   8. Simplified 58.4%

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

   9. Taylor expanded in z around 0 53.6%

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

   if 1.95000000000000004e-20 < z < 2e113

   1. Initial program 94.0%

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

      1. sub-neg 94.0%

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

      2. metadata-eval 94.0%

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

      3. fma-def 94.0%

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

      4. fma-neg 94.0%

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

      5. metadata-eval 94.0%

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

   3. Simplified 94.0%

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

      1. metadata-eval 94.0%

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

      2. sub-neg 94.0%

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

      3. add-sqr-sqrt 93.8%

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

      4. pow2 93.8%

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

      5. *-commutative 93.8%

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

      6. sub-neg 93.8%

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

      7. metadata-eval 93.8%

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

   5. Applied egg-rr 93.8%

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

   6. Taylor expanded in x around inf 56.2%

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

      1. neg-mul-1 56.2%

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

   8. Simplified 56.2%

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

   9. Taylor expanded in y around inf 40.0%

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

       1. associate-/l* 42.7%

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

       2. unpow2 42.7%

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

   11. Simplified 42.7%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+138}:\\ \;\;\;\;\frac{z \cdot z}{x \cdot 1260.0011340009878} - x\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-19}:\\ \;\;\;\;\frac{y}{x} \cdot \left(z \cdot z\right) - x\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-20}:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot -0.0027777777777778}{x} - x\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+113}:\\ \;\;\;\;\frac{y}{\frac{x}{z \cdot z}} - x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+226} \lor \neg \left(z \leq 1.15 \cdot 10^{+251}\right):\\ \;\;\;\;\frac{z \cdot z}{x \cdot 1260.0011340009878} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} \cdot \left(z \cdot z\right) - x\\ \end{array} \]

Alternative 12: 46.8% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{x} \cdot \left(z \cdot z\right) - x\\ t_1 := z \cdot \left(z \cdot \frac{0.0007936500793651}{x}\right) - x\\ \mathbf{if}\;z \leq -9 \cdot 10^{+137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-16}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-20}:\\ \;\;\;\;\frac{0.083333333333333}{x} - x\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+114}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+251}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;0.0007936500793651 \cdot \frac{z}{\frac{x}{z}} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* (/ y x) (* z z)) x))
        (t_1 (- (* z (* z (/ 0.0007936500793651 x))) x)))
   (if (<= z -9e+137)
     t_1
     (if (<= z -7.8e-16)
       t_0
       (if (<= z 3.2e-20)
         (- (/ 0.083333333333333 x) x)
         (if (<= z 8.6e+114)
           t_0
           (if (<= z 1.1e+226)
             t_1
             (if (<= z 1.5e+251)
               t_0
               (- (* 0.0007936500793651 (/ z (/ x z))) x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = ((y / x) * (z * z)) - x;
	double t_1 = (z * (z * (0.0007936500793651 / x))) - x;
	double tmp;
	if (z <= -9e+137) {
		tmp = t_1;
	} else if (z <= -7.8e-16) {
		tmp = t_0;
	} else if (z <= 3.2e-20) {
		tmp = (0.083333333333333 / x) - x;
	} else if (z <= 8.6e+114) {
		tmp = t_0;
	} else if (z <= 1.1e+226) {
		tmp = t_1;
	} else if (z <= 1.5e+251) {
		tmp = t_0;
	} else {
		tmp = (0.0007936500793651 * (z / (x / z))) - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ((y / x) * (z * z)) - x
    t_1 = (z * (z * (0.0007936500793651d0 / x))) - x
    if (z <= (-9d+137)) then
        tmp = t_1
    else if (z <= (-7.8d-16)) then
        tmp = t_0
    else if (z <= 3.2d-20) then
        tmp = (0.083333333333333d0 / x) - x
    else if (z <= 8.6d+114) then
        tmp = t_0
    else if (z <= 1.1d+226) then
        tmp = t_1
    else if (z <= 1.5d+251) then
        tmp = t_0
    else
        tmp = (0.0007936500793651d0 * (z / (x / z))) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((y / x) * (z * z)) - x;
	double t_1 = (z * (z * (0.0007936500793651 / x))) - x;
	double tmp;
	if (z <= -9e+137) {
		tmp = t_1;
	} else if (z <= -7.8e-16) {
		tmp = t_0;
	} else if (z <= 3.2e-20) {
		tmp = (0.083333333333333 / x) - x;
	} else if (z <= 8.6e+114) {
		tmp = t_0;
	} else if (z <= 1.1e+226) {
		tmp = t_1;
	} else if (z <= 1.5e+251) {
		tmp = t_0;
	} else {
		tmp = (0.0007936500793651 * (z / (x / z))) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((y / x) * (z * z)) - x
	t_1 = (z * (z * (0.0007936500793651 / x))) - x
	tmp = 0
	if z <= -9e+137:
		tmp = t_1
	elif z <= -7.8e-16:
		tmp = t_0
	elif z <= 3.2e-20:
		tmp = (0.083333333333333 / x) - x
	elif z <= 8.6e+114:
		tmp = t_0
	elif z <= 1.1e+226:
		tmp = t_1
	elif z <= 1.5e+251:
		tmp = t_0
	else:
		tmp = (0.0007936500793651 * (z / (x / z))) - x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y / x) * Float64(z * z)) - x)
	t_1 = Float64(Float64(z * Float64(z * Float64(0.0007936500793651 / x))) - x)
	tmp = 0.0
	if (z <= -9e+137)
		tmp = t_1;
	elseif (z <= -7.8e-16)
		tmp = t_0;
	elseif (z <= 3.2e-20)
		tmp = Float64(Float64(0.083333333333333 / x) - x);
	elseif (z <= 8.6e+114)
		tmp = t_0;
	elseif (z <= 1.1e+226)
		tmp = t_1;
	elseif (z <= 1.5e+251)
		tmp = t_0;
	else
		tmp = Float64(Float64(0.0007936500793651 * Float64(z / Float64(x / z))) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((y / x) * (z * z)) - x;
	t_1 = (z * (z * (0.0007936500793651 / x))) - x;
	tmp = 0.0;
	if (z <= -9e+137)
		tmp = t_1;
	elseif (z <= -7.8e-16)
		tmp = t_0;
	elseif (z <= 3.2e-20)
		tmp = (0.083333333333333 / x) - x;
	elseif (z <= 8.6e+114)
		tmp = t_0;
	elseif (z <= 1.1e+226)
		tmp = t_1;
	elseif (z <= 1.5e+251)
		tmp = t_0;
	else
		tmp = (0.0007936500793651 * (z / (x / z))) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y / x), $MachinePrecision] * N[(z * z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$1 = N[(N[(z * N[(z * N[(0.0007936500793651 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[z, -9e+137], t$95$1, If[LessEqual[z, -7.8e-16], t$95$0, If[LessEqual[z, 3.2e-20], N[(N[(0.083333333333333 / x), $MachinePrecision] - x), $MachinePrecision], If[LessEqual[z, 8.6e+114], t$95$0, If[LessEqual[z, 1.1e+226], t$95$1, If[LessEqual[z, 1.5e+251], t$95$0, N[(N[(0.0007936500793651 * N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.0000000000000003e137 or 8.6000000000000001e114 < z < 1.09999999999999997e226

   1. Initial program 87.1%

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

      1. sub-neg 87.1%

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

      2. metadata-eval 87.1%

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

      3. fma-def 87.1%

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

      4. fma-neg 87.1%

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

      5. metadata-eval 87.1%

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

   3. Simplified 87.1%

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

      1. metadata-eval 87.1%

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

      2. sub-neg 87.1%

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

      3. add-sqr-sqrt 87.1%

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

      4. pow2 87.1%

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

      5. *-commutative 87.1%

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

      6. sub-neg 87.1%

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

      7. metadata-eval 87.1%

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

   5. Applied egg-rr 87.1%

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

   6. Taylor expanded in x around inf 81.7%

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

      1. neg-mul-1 81.7%

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

   8. Simplified 81.7%

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

   9. Taylor expanded in z around inf 81.7%

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

       1. associate-/l* 80.0%

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

       2. unpow2 80.0%

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

   11. Simplified 80.0%

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

   12. Taylor expanded in y around 0 67.2%

       \[\leadsto \color{blue}{0.0007936500793651 \cdot \frac{{z}^{2}}{x} - x} \]
   13. Step-by-step derivation

       1. associate-*r/ 67.2%

          \[\leadsto \color{blue}{\frac{0.0007936500793651 \cdot {z}^{2}}{x}} - x \]

       2. *-commutative 67.2%

          \[\leadsto \frac{\color{blue}{{z}^{2} \cdot 0.0007936500793651}}{x} - x \]

       3. associate-*r/ 67.2%

          \[\leadsto \color{blue}{{z}^{2} \cdot \frac{0.0007936500793651}{x}} - x \]

       4. metadata-eval 67.2%

          \[\leadsto {z}^{2} \cdot \frac{\color{blue}{0.0007936500793651 \cdot 1}}{x} - x \]

       5. associate-*r/ 67.2%

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

       6. unpow2 67.2%

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

       7. associate-*l* 63.1%

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

       8. associate-*r/ 63.2%

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

       9. metadata-eval 63.2%

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

   14. Simplified 63.2%

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

   if -9.0000000000000003e137 < z < -7.79999999999999954e-16 or 3.1999999999999997e-20 < z < 8.6000000000000001e114 or 1.09999999999999997e226 < z < 1.4999999999999999e251

   1. Initial program 95.5%

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

      1. sub-neg 95.5%

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

      2. metadata-eval 95.5%

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

      3. fma-def 95.5%

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

      4. fma-neg 95.5%

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

      5. metadata-eval 95.5%

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

   3. Simplified 95.5%

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

      1. metadata-eval 95.5%

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

      2. sub-neg 95.5%

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

      3. add-sqr-sqrt 95.3%

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

      4. pow2 95.3%

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

      5. *-commutative 95.3%

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

      6. sub-neg 95.3%

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

      7. metadata-eval 95.3%

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

   5. Applied egg-rr 95.3%

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

   6. Taylor expanded in x around inf 63.5%

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

      1. neg-mul-1 63.5%

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

   8. Simplified 63.5%

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

   9. Taylor expanded in y around inf 49.6%

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

       1. *-commutative 49.6%

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

       2. associate-*r/ 51.0%

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

       3. unpow2 51.0%

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

   11. Simplified 51.0%

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

   if -7.79999999999999954e-16 < z < 3.1999999999999997e-20

   1. Initial program 99.5%

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

      1. sub-neg 99.5%

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

      2. metadata-eval 99.5%

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

      3. fma-def 99.5%

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

      4. fma-neg 99.5%

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

      5. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

      1. metadata-eval 99.5%

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

      2. sub-neg 99.5%

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

      3. add-sqr-sqrt 99.3%

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

      4. pow2 99.3%

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

      5. *-commutative 99.3%

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

      6. sub-neg 99.3%

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

      7. metadata-eval 99.3%

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

   5. Applied egg-rr 99.3%

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

   6. Taylor expanded in x around inf 58.4%

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

      1. neg-mul-1 58.4%

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

   8. Simplified 58.4%

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

   9. Taylor expanded in z around 0 53.5%

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

       1. associate-*r/ 53.6%

          \[\leadsto \color{blue}{\frac{0.083333333333333 \cdot 1}{x}} - x \]

       2. metadata-eval 53.6%

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

   11. Simplified 53.6%

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

   if 1.4999999999999999e251 < z

   1. Initial program 90.4%

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

      1. sub-neg 90.4%

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

      2. metadata-eval 90.4%

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

      3. fma-def 90.4%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\mathsf{fma}\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778, z, 0.083333333333333\right)}}{x} \]

      4. fma-neg 90.4%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right)}, z, 0.083333333333333\right)}{x} \]

      5. metadata-eval 90.4%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, \color{blue}{-0.0027777777777778}\right), z, 0.083333333333333\right)}{x} \]

   3. Simplified 90.4%

      \[\leadsto \color{blue}{\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}} \]
   4. Step-by-step derivation

      1. metadata-eval 90.4%

         \[\leadsto \left(\left(\left(x + \color{blue}{\left(-0.5\right)}\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      2. sub-neg 90.4%

         \[\leadsto \left(\left(\color{blue}{\left(x - 0.5\right)} \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      3. add-sqr-sqrt 90.4%

         \[\leadsto \left(\left(\color{blue}{\sqrt{\left(x - 0.5\right) \cdot \log x} \cdot \sqrt{\left(x - 0.5\right) \cdot \log x}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      4. pow2 90.4%

         \[\leadsto \left(\left(\color{blue}{{\left(\sqrt{\left(x - 0.5\right) \cdot \log x}\right)}^{2}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      5. *-commutative 90.4%

         \[\leadsto \left(\left({\left(\sqrt{\color{blue}{\log x \cdot \left(x - 0.5\right)}}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      6. sub-neg 90.4%

         \[\leadsto \left(\left({\left(\sqrt{\log x \cdot \color{blue}{\left(x + \left(-0.5\right)\right)}}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      7. metadata-eval 90.4%

         \[\leadsto \left(\left({\left(\sqrt{\log x \cdot \left(x + \color{blue}{-0.5}\right)}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   5. Applied egg-rr 90.4%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt{\log x \cdot \left(x + -0.5\right)}\right)}^{2}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   6. Taylor expanded in x around inf 90.4%

      \[\leadsto \color{blue}{-1 \cdot x} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]
   7. Step-by-step derivation

      1. neg-mul-1 90.4%

         \[\leadsto \color{blue}{\left(-x\right)} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   8. Simplified 90.4%

      \[\leadsto \color{blue}{\left(-x\right)} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   9. Taylor expanded in z around inf 90.4%

      \[\leadsto \left(-x\right) + \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   10. Step-by-step derivation

       1. associate-/l* 90.4%

          \[\leadsto \left(-x\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

       2. unpow2 90.4%

          \[\leadsto \left(-x\right) + \frac{\color{blue}{z \cdot z}}{\frac{x}{0.0007936500793651 + y}} \]

   11. Simplified 90.4%

       \[\leadsto \left(-x\right) + \color{blue}{\frac{z \cdot z}{\frac{x}{0.0007936500793651 + y}}} \]

   12. Taylor expanded in y around 0 85.4%

       \[\leadsto \color{blue}{0.0007936500793651 \cdot \frac{{z}^{2}}{x} - x} \]
   13. Step-by-step derivation

       1. unpow2 85.4%

          \[\leadsto 0.0007936500793651 \cdot \frac{\color{blue}{z \cdot z}}{x} - x \]

       2. associate-/l* 79.9%

          \[\leadsto 0.0007936500793651 \cdot \color{blue}{\frac{z}{\frac{x}{z}}} - x \]

   14. Simplified 79.9%

       \[\leadsto \color{blue}{0.0007936500793651 \cdot \frac{z}{\frac{x}{z}} - x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+137}:\\ \;\;\;\;z \cdot \left(z \cdot \frac{0.0007936500793651}{x}\right) - x\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-16}:\\ \;\;\;\;\frac{y}{x} \cdot \left(z \cdot z\right) - x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-20}:\\ \;\;\;\;\frac{0.083333333333333}{x} - x\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+114}:\\ \;\;\;\;\frac{y}{x} \cdot \left(z \cdot z\right) - x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+226}:\\ \;\;\;\;z \cdot \left(z \cdot \frac{0.0007936500793651}{x}\right) - x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+251}:\\ \;\;\;\;\frac{y}{x} \cdot \left(z \cdot z\right) - x\\ \mathbf{else}:\\ \;\;\;\;0.0007936500793651 \cdot \frac{z}{\frac{x}{z}} - x\\ \end{array} \]

Alternative 13: 47.5% accurate, 6.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(z \cdot \frac{0.0007936500793651}{x}\right) - x\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+138}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-16}:\\ \;\;\;\;\frac{y}{x} \cdot \left(z \cdot z\right) - x\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-22}:\\ \;\;\;\;\frac{0.083333333333333}{x} - x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+115} \lor \neg \left(z \leq 9.5 \cdot 10^{+225}\right):\\ \;\;\;\;\frac{y}{\frac{x}{z \cdot z}} - x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* z (* z (/ 0.0007936500793651 x))) x)))
   (if (<= z -1.45e+138)
     t_0
     (if (<= z -1.7e-16)
       (- (* (/ y x) (* z z)) x)
       (if (<= z 2.95e-22)
         (- (/ 0.083333333333333 x) x)
         (if (or (<= z 1.25e+115) (not (<= z 9.5e+225)))
           (- (/ y (/ x (* z z))) x)
           t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (z * (z * (0.0007936500793651 / x))) - x;
	double tmp;
	if (z <= -1.45e+138) {
		tmp = t_0;
	} else if (z <= -1.7e-16) {
		tmp = ((y / x) * (z * z)) - x;
	} else if (z <= 2.95e-22) {
		tmp = (0.083333333333333 / x) - x;
	} else if ((z <= 1.25e+115) || !(z <= 9.5e+225)) {
		tmp = (y / (x / (z * z))) - x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (z * (z * (0.0007936500793651d0 / x))) - x
    if (z <= (-1.45d+138)) then
        tmp = t_0
    else if (z <= (-1.7d-16)) then
        tmp = ((y / x) * (z * z)) - x
    else if (z <= 2.95d-22) then
        tmp = (0.083333333333333d0 / x) - x
    else if ((z <= 1.25d+115) .or. (.not. (z <= 9.5d+225))) then
        tmp = (y / (x / (z * z))) - x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z * (z * (0.0007936500793651 / x))) - x;
	double tmp;
	if (z <= -1.45e+138) {
		tmp = t_0;
	} else if (z <= -1.7e-16) {
		tmp = ((y / x) * (z * z)) - x;
	} else if (z <= 2.95e-22) {
		tmp = (0.083333333333333 / x) - x;
	} else if ((z <= 1.25e+115) || !(z <= 9.5e+225)) {
		tmp = (y / (x / (z * z))) - x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z * (z * (0.0007936500793651 / x))) - x
	tmp = 0
	if z <= -1.45e+138:
		tmp = t_0
	elif z <= -1.7e-16:
		tmp = ((y / x) * (z * z)) - x
	elif z <= 2.95e-22:
		tmp = (0.083333333333333 / x) - x
	elif (z <= 1.25e+115) or not (z <= 9.5e+225):
		tmp = (y / (x / (z * z))) - x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * Float64(z * Float64(0.0007936500793651 / x))) - x)
	tmp = 0.0
	if (z <= -1.45e+138)
		tmp = t_0;
	elseif (z <= -1.7e-16)
		tmp = Float64(Float64(Float64(y / x) * Float64(z * z)) - x);
	elseif (z <= 2.95e-22)
		tmp = Float64(Float64(0.083333333333333 / x) - x);
	elseif ((z <= 1.25e+115) || !(z <= 9.5e+225))
		tmp = Float64(Float64(y / Float64(x / Float64(z * z))) - x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z * (z * (0.0007936500793651 / x))) - x;
	tmp = 0.0;
	if (z <= -1.45e+138)
		tmp = t_0;
	elseif (z <= -1.7e-16)
		tmp = ((y / x) * (z * z)) - x;
	elseif (z <= 2.95e-22)
		tmp = (0.083333333333333 / x) - x;
	elseif ((z <= 1.25e+115) || ~((z <= 9.5e+225)))
		tmp = (y / (x / (z * z))) - x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * N[(z * N[(0.0007936500793651 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[z, -1.45e+138], t$95$0, If[LessEqual[z, -1.7e-16], N[(N[(N[(y / x), $MachinePrecision] * N[(z * z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], If[LessEqual[z, 2.95e-22], N[(N[(0.083333333333333 / x), $MachinePrecision] - x), $MachinePrecision], If[Or[LessEqual[z, 1.25e+115], N[Not[LessEqual[z, 9.5e+225]], $MachinePrecision]], N[(N[(y / N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.45000000000000005e138 or 1.25000000000000002e115 < z < 9.49999999999999957e225

   1. Initial program 87.1%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

      1. sub-neg 87.1%

         \[\leadsto \left(\left(\color{blue}{\left(x + \left(-0.5\right)\right)} \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      2. metadata-eval 87.1%

         \[\leadsto \left(\left(\left(x + \color{blue}{-0.5}\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      3. fma-def 87.1%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\mathsf{fma}\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778, z, 0.083333333333333\right)}}{x} \]

      4. fma-neg 87.1%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right)}, z, 0.083333333333333\right)}{x} \]

      5. metadata-eval 87.1%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, \color{blue}{-0.0027777777777778}\right), z, 0.083333333333333\right)}{x} \]

   3. Simplified 87.1%

      \[\leadsto \color{blue}{\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}} \]
   4. Step-by-step derivation

      1. metadata-eval 87.1%

         \[\leadsto \left(\left(\left(x + \color{blue}{\left(-0.5\right)}\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      2. sub-neg 87.1%

         \[\leadsto \left(\left(\color{blue}{\left(x - 0.5\right)} \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      3. add-sqr-sqrt 87.1%

         \[\leadsto \left(\left(\color{blue}{\sqrt{\left(x - 0.5\right) \cdot \log x} \cdot \sqrt{\left(x - 0.5\right) \cdot \log x}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      4. pow2 87.1%

         \[\leadsto \left(\left(\color{blue}{{\left(\sqrt{\left(x - 0.5\right) \cdot \log x}\right)}^{2}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      5. *-commutative 87.1%

         \[\leadsto \left(\left({\left(\sqrt{\color{blue}{\log x \cdot \left(x - 0.5\right)}}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      6. sub-neg 87.1%

         \[\leadsto \left(\left({\left(\sqrt{\log x \cdot \color{blue}{\left(x + \left(-0.5\right)\right)}}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      7. metadata-eval 87.1%

         \[\leadsto \left(\left({\left(\sqrt{\log x \cdot \left(x + \color{blue}{-0.5}\right)}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   5. Applied egg-rr 87.1%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt{\log x \cdot \left(x + -0.5\right)}\right)}^{2}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   6. Taylor expanded in x around inf 81.7%

      \[\leadsto \color{blue}{-1 \cdot x} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]
   7. Step-by-step derivation

      1. neg-mul-1 81.7%

         \[\leadsto \color{blue}{\left(-x\right)} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   8. Simplified 81.7%

      \[\leadsto \color{blue}{\left(-x\right)} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   9. Taylor expanded in z around inf 81.7%

      \[\leadsto \left(-x\right) + \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   10. Step-by-step derivation

       1. associate-/l* 80.0%

          \[\leadsto \left(-x\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

       2. unpow2 80.0%

          \[\leadsto \left(-x\right) + \frac{\color{blue}{z \cdot z}}{\frac{x}{0.0007936500793651 + y}} \]

   11. Simplified 80.0%

       \[\leadsto \left(-x\right) + \color{blue}{\frac{z \cdot z}{\frac{x}{0.0007936500793651 + y}}} \]

   12. Taylor expanded in y around 0 67.2%

       \[\leadsto \color{blue}{0.0007936500793651 \cdot \frac{{z}^{2}}{x} - x} \]
   13. Step-by-step derivation

       1. associate-*r/ 67.2%

          \[\leadsto \color{blue}{\frac{0.0007936500793651 \cdot {z}^{2}}{x}} - x \]

       2. *-commutative 67.2%

          \[\leadsto \frac{\color{blue}{{z}^{2} \cdot 0.0007936500793651}}{x} - x \]

       3. associate-*r/ 67.2%

          \[\leadsto \color{blue}{{z}^{2} \cdot \frac{0.0007936500793651}{x}} - x \]

       4. metadata-eval 67.2%

          \[\leadsto {z}^{2} \cdot \frac{\color{blue}{0.0007936500793651 \cdot 1}}{x} - x \]

       5. associate-*r/ 67.2%

          \[\leadsto {z}^{2} \cdot \color{blue}{\left(0.0007936500793651 \cdot \frac{1}{x}\right)} - x \]

       6. unpow2 67.2%

          \[\leadsto \color{blue}{\left(z \cdot z\right)} \cdot \left(0.0007936500793651 \cdot \frac{1}{x}\right) - x \]

       7. associate-*l* 63.1%

          \[\leadsto \color{blue}{z \cdot \left(z \cdot \left(0.0007936500793651 \cdot \frac{1}{x}\right)\right)} - x \]

       8. associate-*r/ 63.2%

          \[\leadsto z \cdot \left(z \cdot \color{blue}{\frac{0.0007936500793651 \cdot 1}{x}}\right) - x \]

       9. metadata-eval 63.2%

          \[\leadsto z \cdot \left(z \cdot \frac{\color{blue}{0.0007936500793651}}{x}\right) - x \]

   14. Simplified 63.2%

       \[\leadsto \color{blue}{z \cdot \left(z \cdot \frac{0.0007936500793651}{x}\right) - x} \]

   if -1.45000000000000005e138 < z < -1.7e-16

   1. Initial program 96.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

      1. sub-neg 96.2%

         \[\leadsto \left(\left(\color{blue}{\left(x + \left(-0.5\right)\right)} \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      2. metadata-eval 96.2%

         \[\leadsto \left(\left(\left(x + \color{blue}{-0.5}\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      3. fma-def 96.2%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\mathsf{fma}\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778, z, 0.083333333333333\right)}}{x} \]

      4. fma-neg 96.2%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right)}, z, 0.083333333333333\right)}{x} \]

      5. metadata-eval 96.2%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, \color{blue}{-0.0027777777777778}\right), z, 0.083333333333333\right)}{x} \]

   3. Simplified 96.2%

      \[\leadsto \color{blue}{\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}} \]
   4. Step-by-step derivation

      1. metadata-eval 96.2%

         \[\leadsto \left(\left(\left(x + \color{blue}{\left(-0.5\right)}\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      2. sub-neg 96.2%

         \[\leadsto \left(\left(\color{blue}{\left(x - 0.5\right)} \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      3. add-sqr-sqrt 96.0%

         \[\leadsto \left(\left(\color{blue}{\sqrt{\left(x - 0.5\right) \cdot \log x} \cdot \sqrt{\left(x - 0.5\right) \cdot \log x}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      4. pow2 96.0%

         \[\leadsto \left(\left(\color{blue}{{\left(\sqrt{\left(x - 0.5\right) \cdot \log x}\right)}^{2}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      5. *-commutative 96.0%

         \[\leadsto \left(\left({\left(\sqrt{\color{blue}{\log x \cdot \left(x - 0.5\right)}}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      6. sub-neg 96.0%

         \[\leadsto \left(\left({\left(\sqrt{\log x \cdot \color{blue}{\left(x + \left(-0.5\right)\right)}}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      7. metadata-eval 96.0%

         \[\leadsto \left(\left({\left(\sqrt{\log x \cdot \left(x + \color{blue}{-0.5}\right)}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   5. Applied egg-rr 96.0%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt{\log x \cdot \left(x + -0.5\right)}\right)}^{2}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   6. Taylor expanded in x around inf 63.2%

      \[\leadsto \color{blue}{-1 \cdot x} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]
   7. Step-by-step derivation

      1. neg-mul-1 63.2%

         \[\leadsto \color{blue}{\left(-x\right)} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   8. Simplified 63.2%

      \[\leadsto \color{blue}{\left(-x\right)} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   9. Taylor expanded in y around inf 48.7%

      \[\leadsto \left(-x\right) + \color{blue}{\frac{y \cdot {z}^{2}}{x}} \]
   10. Step-by-step derivation

       1. *-commutative 48.7%

          \[\leadsto \left(-x\right) + \frac{\color{blue}{{z}^{2} \cdot y}}{x} \]

       2. associate-*r/ 52.1%

          \[\leadsto \left(-x\right) + \color{blue}{{z}^{2} \cdot \frac{y}{x}} \]

       3. unpow2 52.1%

          \[\leadsto \left(-x\right) + \color{blue}{\left(z \cdot z\right)} \cdot \frac{y}{x} \]

   11. Simplified 52.1%

       \[\leadsto \left(-x\right) + \color{blue}{\left(z \cdot z\right) \cdot \frac{y}{x}} \]

   if -1.7e-16 < z < 2.95000000000000004e-22

   1. Initial program 99.5%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

      1. sub-neg 99.5%

         \[\leadsto \left(\left(\color{blue}{\left(x + \left(-0.5\right)\right)} \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      2. metadata-eval 99.5%

         \[\leadsto \left(\left(\left(x + \color{blue}{-0.5}\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      3. fma-def 99.5%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\mathsf{fma}\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778, z, 0.083333333333333\right)}}{x} \]

      4. fma-neg 99.5%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right)}, z, 0.083333333333333\right)}{x} \]

      5. metadata-eval 99.5%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, \color{blue}{-0.0027777777777778}\right), z, 0.083333333333333\right)}{x} \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}} \]
   4. Step-by-step derivation

      1. metadata-eval 99.5%

         \[\leadsto \left(\left(\left(x + \color{blue}{\left(-0.5\right)}\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      2. sub-neg 99.5%

         \[\leadsto \left(\left(\color{blue}{\left(x - 0.5\right)} \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      3. add-sqr-sqrt 99.3%

         \[\leadsto \left(\left(\color{blue}{\sqrt{\left(x - 0.5\right) \cdot \log x} \cdot \sqrt{\left(x - 0.5\right) \cdot \log x}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      4. pow2 99.3%

         \[\leadsto \left(\left(\color{blue}{{\left(\sqrt{\left(x - 0.5\right) \cdot \log x}\right)}^{2}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      5. *-commutative 99.3%

         \[\leadsto \left(\left({\left(\sqrt{\color{blue}{\log x \cdot \left(x - 0.5\right)}}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      6. sub-neg 99.3%

         \[\leadsto \left(\left({\left(\sqrt{\log x \cdot \color{blue}{\left(x + \left(-0.5\right)\right)}}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      7. metadata-eval 99.3%

         \[\leadsto \left(\left({\left(\sqrt{\log x \cdot \left(x + \color{blue}{-0.5}\right)}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   5. Applied egg-rr 99.3%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt{\log x \cdot \left(x + -0.5\right)}\right)}^{2}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   6. Taylor expanded in x around inf 58.4%

      \[\leadsto \color{blue}{-1 \cdot x} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]
   7. Step-by-step derivation

      1. neg-mul-1 58.4%

         \[\leadsto \color{blue}{\left(-x\right)} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   8. Simplified 58.4%

      \[\leadsto \color{blue}{\left(-x\right)} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   9. Taylor expanded in z around 0 53.5%

      \[\leadsto \color{blue}{0.083333333333333 \cdot \frac{1}{x} - x} \]
   10. Step-by-step derivation

       1. associate-*r/ 53.6%

          \[\leadsto \color{blue}{\frac{0.083333333333333 \cdot 1}{x}} - x \]

       2. metadata-eval 53.6%

          \[\leadsto \frac{\color{blue}{0.083333333333333}}{x} - x \]

   11. Simplified 53.6%

       \[\leadsto \color{blue}{\frac{0.083333333333333}{x} - x} \]

   if 2.95000000000000004e-22 < z < 1.25000000000000002e115 or 9.49999999999999957e225 < z

   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 93.5%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right)}, z, 0.083333333333333\right)}{x} \]

      5. metadata-eval 93.5%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, \color{blue}{-0.0027777777777778}\right), z, 0.083333333333333\right)}{x} \]

   3. Simplified 93.5%

      \[\leadsto \color{blue}{\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}} \]
   4. Step-by-step derivation

      1. metadata-eval 93.5%

         \[\leadsto \left(\left(\left(x + \color{blue}{\left(-0.5\right)}\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      2. sub-neg 93.5%

         \[\leadsto \left(\left(\color{blue}{\left(x - 0.5\right)} \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      3. add-sqr-sqrt 93.4%

         \[\leadsto \left(\left(\color{blue}{\sqrt{\left(x - 0.5\right) \cdot \log x} \cdot \sqrt{\left(x - 0.5\right) \cdot \log x}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      4. pow2 93.4%

         \[\leadsto \left(\left(\color{blue}{{\left(\sqrt{\left(x - 0.5\right) \cdot \log x}\right)}^{2}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      5. *-commutative 93.4%

         \[\leadsto \left(\left({\left(\sqrt{\color{blue}{\log x \cdot \left(x - 0.5\right)}}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      6. sub-neg 93.4%

         \[\leadsto \left(\left({\left(\sqrt{\log x \cdot \color{blue}{\left(x + \left(-0.5\right)\right)}}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      7. metadata-eval 93.4%

         \[\leadsto \left(\left({\left(\sqrt{\log x \cdot \left(x + \color{blue}{-0.5}\right)}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   5. Applied egg-rr 93.4%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt{\log x \cdot \left(x + -0.5\right)}\right)}^{2}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   6. Taylor expanded in x around inf 72.5%

      \[\leadsto \color{blue}{-1 \cdot x} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]
   7. Step-by-step derivation

      1. neg-mul-1 72.5%

         \[\leadsto \color{blue}{\left(-x\right)} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   8. Simplified 72.5%

      \[\leadsto \color{blue}{\left(-x\right)} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   9. Taylor expanded in y around inf 55.2%

      \[\leadsto \left(-x\right) + \color{blue}{\frac{y \cdot {z}^{2}}{x}} \]
   10. Step-by-step derivation

       1. associate-/l* 56.7%

          \[\leadsto \left(-x\right) + \color{blue}{\frac{y}{\frac{x}{{z}^{2}}}} \]

       2. unpow2 56.7%

          \[\leadsto \left(-x\right) + \frac{y}{\frac{x}{\color{blue}{z \cdot z}}} \]

   11. Simplified 56.7%

       \[\leadsto \left(-x\right) + \color{blue}{\frac{y}{\frac{x}{z \cdot z}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+138}:\\ \;\;\;\;z \cdot \left(z \cdot \frac{0.0007936500793651}{x}\right) - x\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-16}:\\ \;\;\;\;\frac{y}{x} \cdot \left(z \cdot z\right) - x\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-22}:\\ \;\;\;\;\frac{0.083333333333333}{x} - x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+115} \lor \neg \left(z \leq 9.5 \cdot 10^{+225}\right):\\ \;\;\;\;\frac{y}{\frac{x}{z \cdot z}} - x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(z \cdot \frac{0.0007936500793651}{x}\right) - x\\ \end{array} \]

Alternative 14: 58.8% accurate, 8.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-46} \lor \neg \left(z \leq 5.8 \cdot 10^{-27}\right):\\ \;\;\;\;\left(z \cdot z\right) \cdot \left(\frac{y}{x} + \frac{0.0007936500793651}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot -0.0027777777777778}{x} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.8e-46) (not (<= z 5.8e-27)))
   (* (* z z) (+ (/ y x) (/ 0.0007936500793651 x)))
   (- (/ (+ 0.083333333333333 (* z -0.0027777777777778)) x) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.8e-46) || !(z <= 5.8e-27)) {
		tmp = (z * z) * ((y / x) + (0.0007936500793651 / x));
	} else {
		tmp = ((0.083333333333333 + (z * -0.0027777777777778)) / 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 ((z <= (-1.8d-46)) .or. (.not. (z <= 5.8d-27))) then
        tmp = (z * z) * ((y / x) + (0.0007936500793651d0 / x))
    else
        tmp = ((0.083333333333333d0 + (z * (-0.0027777777777778d0))) / x) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.8e-46) || !(z <= 5.8e-27)) {
		tmp = (z * z) * ((y / x) + (0.0007936500793651 / x));
	} else {
		tmp = ((0.083333333333333 + (z * -0.0027777777777778)) / x) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.8e-46) or not (z <= 5.8e-27):
		tmp = (z * z) * ((y / x) + (0.0007936500793651 / x))
	else:
		tmp = ((0.083333333333333 + (z * -0.0027777777777778)) / x) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.8e-46) || !(z <= 5.8e-27))
		tmp = Float64(Float64(z * z) * Float64(Float64(y / x) + Float64(0.0007936500793651 / x)));
	else
		tmp = Float64(Float64(Float64(0.083333333333333 + Float64(z * -0.0027777777777778)) / x) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.8e-46) || ~((z <= 5.8e-27)))
		tmp = (z * z) * ((y / x) + (0.0007936500793651 / x));
	else
		tmp = ((0.083333333333333 + (z * -0.0027777777777778)) / x) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.8e-46], N[Not[LessEqual[z, 5.8e-27]], $MachinePrecision]], N[(N[(z * z), $MachinePrecision] * N[(N[(y / x), $MachinePrecision] + N[(0.0007936500793651 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(0.083333333333333 + N[(z * -0.0027777777777778), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e-46 or 5.80000000000000008e-27 < z

   1. Initial program 91.6%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

      1. sub-neg 91.6%

         \[\leadsto \left(\left(\color{blue}{\left(x + \left(-0.5\right)\right)} \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      2. metadata-eval 91.6%

         \[\leadsto \left(\left(\left(x + \color{blue}{-0.5}\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      3. fma-def 91.6%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\mathsf{fma}\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778, z, 0.083333333333333\right)}}{x} \]

      4. fma-neg 91.6%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right)}, z, 0.083333333333333\right)}{x} \]

      5. metadata-eval 91.6%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, \color{blue}{-0.0027777777777778}\right), z, 0.083333333333333\right)}{x} \]

   3. Simplified 91.6%

      \[\leadsto \color{blue}{\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}} \]
   4. Step-by-step derivation

      1. metadata-eval 91.6%

         \[\leadsto \left(\left(\left(x + \color{blue}{\left(-0.5\right)}\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      2. sub-neg 91.6%

         \[\leadsto \left(\left(\color{blue}{\left(x - 0.5\right)} \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      3. add-sqr-sqrt 91.6%

         \[\leadsto \left(\left(\color{blue}{\sqrt{\left(x - 0.5\right) \cdot \log x} \cdot \sqrt{\left(x - 0.5\right) \cdot \log x}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      4. pow2 91.6%

         \[\leadsto \left(\left(\color{blue}{{\left(\sqrt{\left(x - 0.5\right) \cdot \log x}\right)}^{2}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      5. *-commutative 91.6%

         \[\leadsto \left(\left({\left(\sqrt{\color{blue}{\log x \cdot \left(x - 0.5\right)}}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      6. sub-neg 91.6%

         \[\leadsto \left(\left({\left(\sqrt{\log x \cdot \color{blue}{\left(x + \left(-0.5\right)\right)}}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      7. metadata-eval 91.6%

         \[\leadsto \left(\left({\left(\sqrt{\log x \cdot \left(x + \color{blue}{-0.5}\right)}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   5. Applied egg-rr 91.6%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt{\log x \cdot \left(x + -0.5\right)}\right)}^{2}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   6. Taylor expanded in x around inf 75.2%

      \[\leadsto \color{blue}{-1 \cdot x} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]
   7. Step-by-step derivation

      1. neg-mul-1 75.2%

         \[\leadsto \color{blue}{\left(-x\right)} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   8. Simplified 75.2%

      \[\leadsto \color{blue}{\left(-x\right)} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   9. Taylor expanded in z around inf 74.4%

      \[\leadsto \color{blue}{{z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right)} \]
   10. Step-by-step derivation

       1. unpow2 74.4%

          \[\leadsto \color{blue}{\left(z \cdot z\right)} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) \]

       2. associate-*r/ 74.4%

          \[\leadsto \left(z \cdot z\right) \cdot \left(\color{blue}{\frac{0.0007936500793651 \cdot 1}{x}} + \frac{y}{x}\right) \]

       3. metadata-eval 74.4%

          \[\leadsto \left(z \cdot z\right) \cdot \left(\frac{\color{blue}{0.0007936500793651}}{x} + \frac{y}{x}\right) \]

   11. Simplified 74.4%

       \[\leadsto \color{blue}{\left(z \cdot z\right) \cdot \left(\frac{0.0007936500793651}{x} + \frac{y}{x}\right)} \]

   if -1.8e-46 < z < 5.80000000000000008e-27

   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. Step-by-step derivation

      1. metadata-eval 99.5%

         \[\leadsto \left(\left(\left(x + \color{blue}{\left(-0.5\right)}\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      2. sub-neg 99.5%

         \[\leadsto \left(\left(\color{blue}{\left(x - 0.5\right)} \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      3. add-sqr-sqrt 99.3%

         \[\leadsto \left(\left(\color{blue}{\sqrt{\left(x - 0.5\right) \cdot \log x} \cdot \sqrt{\left(x - 0.5\right) \cdot \log x}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      4. pow2 99.3%

         \[\leadsto \left(\left(\color{blue}{{\left(\sqrt{\left(x - 0.5\right) \cdot \log x}\right)}^{2}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      5. *-commutative 99.3%

         \[\leadsto \left(\left({\left(\sqrt{\color{blue}{\log x \cdot \left(x - 0.5\right)}}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      6. sub-neg 99.3%

         \[\leadsto \left(\left({\left(\sqrt{\log x \cdot \color{blue}{\left(x + \left(-0.5\right)\right)}}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      7. metadata-eval 99.3%

         \[\leadsto \left(\left({\left(\sqrt{\log x \cdot \left(x + \color{blue}{-0.5}\right)}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   5. Applied egg-rr 99.3%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt{\log x \cdot \left(x + -0.5\right)}\right)}^{2}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   6. Taylor expanded in x around inf 56.9%

      \[\leadsto \color{blue}{-1 \cdot x} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]
   7. Step-by-step derivation

      1. neg-mul-1 56.9%

         \[\leadsto \color{blue}{\left(-x\right)} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   8. Simplified 56.9%

      \[\leadsto \color{blue}{\left(-x\right)} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   9. Taylor expanded in z around 0 53.6%

      \[\leadsto \left(-x\right) + \frac{\color{blue}{0.083333333333333 + -0.0027777777777778 \cdot z}}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-46} \lor \neg \left(z \leq 5.8 \cdot 10^{-27}\right):\\ \;\;\;\;\left(z \cdot z\right) \cdot \left(\frac{y}{x} + \frac{0.0007936500793651}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot -0.0027777777777778}{x} - x\\ \end{array} \]

Alternative 15: 61.7% 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 94.8%

   \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
2. Step-by-step derivation

   1. sub-neg 94.8%

      \[\leadsto \left(\left(\color{blue}{\left(x + \left(-0.5\right)\right)} \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. metadata-eval 94.8%

      \[\leadsto \left(\left(\left(x + \color{blue}{-0.5}\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   3. fma-def 94.8%

      \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\mathsf{fma}\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778, z, 0.083333333333333\right)}}{x} \]

   4. fma-neg 94.8%

      \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right)}, z, 0.083333333333333\right)}{x} \]

   5. metadata-eval 94.8%

      \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, \color{blue}{-0.0027777777777778}\right), z, 0.083333333333333\right)}{x} \]

3. Simplified 94.8%

   \[\leadsto \color{blue}{\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}} \]
4. Step-by-step derivation

   1. metadata-eval 94.8%

      \[\leadsto \left(\left(\left(x + \color{blue}{\left(-0.5\right)}\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   2. sub-neg 94.8%

      \[\leadsto \left(\left(\color{blue}{\left(x - 0.5\right)} \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   3. add-sqr-sqrt 94.7%

      \[\leadsto \left(\left(\color{blue}{\sqrt{\left(x - 0.5\right) \cdot \log x} \cdot \sqrt{\left(x - 0.5\right) \cdot \log x}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   4. pow2 94.7%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt{\left(x - 0.5\right) \cdot \log x}\right)}^{2}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   5. *-commutative 94.7%

      \[\leadsto \left(\left({\left(\sqrt{\color{blue}{\log x \cdot \left(x - 0.5\right)}}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   6. sub-neg 94.7%

      \[\leadsto \left(\left({\left(\sqrt{\log x \cdot \color{blue}{\left(x + \left(-0.5\right)\right)}}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   7. metadata-eval 94.7%

      \[\leadsto \left(\left({\left(\sqrt{\log x \cdot \left(x + \color{blue}{-0.5}\right)}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

5. Applied egg-rr 94.7%

   \[\leadsto \left(\left(\color{blue}{{\left(\sqrt{\log x \cdot \left(x + -0.5\right)}\right)}^{2}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

6. Taylor expanded in x around inf 67.7%

   \[\leadsto \color{blue}{-1 \cdot x} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]
7. Step-by-step derivation

   1. neg-mul-1 67.7%

      \[\leadsto \color{blue}{\left(-x\right)} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

8. Simplified 67.7%

   \[\leadsto \color{blue}{\left(-x\right)} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

9. Taylor expanded in x around 0 67.7%

   \[\leadsto \left(-x\right) + \color{blue}{\frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x}} \]

10. Final simplification 67.7%

    \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} - x \]

Alternative 16: 44.6% accurate, 9.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5500000 \lor \neg \left(z \leq 4.8 \cdot 10^{-20}\right):\\ \;\;\;\;0.0007936500793651 \cdot \frac{z}{\frac{x}{z}} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5500000.0) (not (<= z 4.8e-20)))
   (- (* 0.0007936500793651 (/ z (/ x z))) x)
   (- (/ 0.083333333333333 x) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5500000.0) || !(z <= 4.8e-20)) {
		tmp = (0.0007936500793651 * (z / (x / z))) - x;
	} else {
		tmp = (0.083333333333333 / 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 ((z <= (-5500000.0d0)) .or. (.not. (z <= 4.8d-20))) then
        tmp = (0.0007936500793651d0 * (z / (x / z))) - x
    else
        tmp = (0.083333333333333d0 / x) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5500000.0) || !(z <= 4.8e-20)) {
		tmp = (0.0007936500793651 * (z / (x / z))) - x;
	} else {
		tmp = (0.083333333333333 / x) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5500000.0) or not (z <= 4.8e-20):
		tmp = (0.0007936500793651 * (z / (x / z))) - x
	else:
		tmp = (0.083333333333333 / x) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5500000.0) || !(z <= 4.8e-20))
		tmp = Float64(Float64(0.0007936500793651 * Float64(z / Float64(x / z))) - x);
	else
		tmp = Float64(Float64(0.083333333333333 / x) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5500000.0) || ~((z <= 4.8e-20)))
		tmp = (0.0007936500793651 * (z / (x / z))) - x;
	else
		tmp = (0.083333333333333 / x) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5500000.0], N[Not[LessEqual[z, 4.8e-20]], $MachinePrecision]], N[(N[(0.0007936500793651 * N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(N[(0.083333333333333 / x), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5e6 or 4.79999999999999986e-20 < z

   1. Initial program 91.1%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

      1. sub-neg 91.1%

         \[\leadsto \left(\left(\color{blue}{\left(x + \left(-0.5\right)\right)} \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      2. metadata-eval 91.1%

         \[\leadsto \left(\left(\left(x + \color{blue}{-0.5}\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      3. fma-def 91.1%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\mathsf{fma}\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778, z, 0.083333333333333\right)}}{x} \]

      4. fma-neg 91.1%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right)}, z, 0.083333333333333\right)}{x} \]

      5. metadata-eval 91.1%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, \color{blue}{-0.0027777777777778}\right), z, 0.083333333333333\right)}{x} \]

   3. Simplified 91.1%

      \[\leadsto \color{blue}{\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}} \]
   4. Step-by-step derivation

      1. metadata-eval 91.1%

         \[\leadsto \left(\left(\left(x + \color{blue}{\left(-0.5\right)}\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      2. sub-neg 91.1%

         \[\leadsto \left(\left(\color{blue}{\left(x - 0.5\right)} \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      3. add-sqr-sqrt 91.1%

         \[\leadsto \left(\left(\color{blue}{\sqrt{\left(x - 0.5\right) \cdot \log x} \cdot \sqrt{\left(x - 0.5\right) \cdot \log x}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      4. pow2 91.1%

         \[\leadsto \left(\left(\color{blue}{{\left(\sqrt{\left(x - 0.5\right) \cdot \log x}\right)}^{2}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      5. *-commutative 91.1%

         \[\leadsto \left(\left({\left(\sqrt{\color{blue}{\log x \cdot \left(x - 0.5\right)}}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      6. sub-neg 91.1%

         \[\leadsto \left(\left({\left(\sqrt{\log x \cdot \color{blue}{\left(x + \left(-0.5\right)\right)}}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      7. metadata-eval 91.1%

         \[\leadsto \left(\left({\left(\sqrt{\log x \cdot \left(x + \color{blue}{-0.5}\right)}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   5. Applied egg-rr 91.1%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt{\log x \cdot \left(x + -0.5\right)}\right)}^{2}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   6. Taylor expanded in x around inf 75.7%

      \[\leadsto \color{blue}{-1 \cdot x} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]
   7. Step-by-step derivation

      1. neg-mul-1 75.7%

         \[\leadsto \color{blue}{\left(-x\right)} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   8. Simplified 75.7%

      \[\leadsto \color{blue}{\left(-x\right)} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   9. Taylor expanded in z around inf 74.9%

      \[\leadsto \left(-x\right) + \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   10. Step-by-step derivation

       1. associate-/l* 75.3%

          \[\leadsto \left(-x\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

       2. unpow2 75.3%

          \[\leadsto \left(-x\right) + \frac{\color{blue}{z \cdot z}}{\frac{x}{0.0007936500793651 + y}} \]

   11. Simplified 75.3%

       \[\leadsto \left(-x\right) + \color{blue}{\frac{z \cdot z}{\frac{x}{0.0007936500793651 + y}}} \]

   12. Taylor expanded in y around 0 48.2%

       \[\leadsto \color{blue}{0.0007936500793651 \cdot \frac{{z}^{2}}{x} - x} \]
   13. Step-by-step derivation

       1. unpow2 48.2%

          \[\leadsto 0.0007936500793651 \cdot \frac{\color{blue}{z \cdot z}}{x} - x \]

       2. associate-/l* 45.8%

          \[\leadsto 0.0007936500793651 \cdot \color{blue}{\frac{z}{\frac{x}{z}}} - x \]

   14. Simplified 45.8%

       \[\leadsto \color{blue}{0.0007936500793651 \cdot \frac{z}{\frac{x}{z}} - x} \]

   if -5.5e6 < z < 4.79999999999999986e-20

   1. Initial program 99.5%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

      1. sub-neg 99.5%

         \[\leadsto \left(\left(\color{blue}{\left(x + \left(-0.5\right)\right)} \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      2. metadata-eval 99.5%

         \[\leadsto \left(\left(\left(x + \color{blue}{-0.5}\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      3. fma-def 99.5%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\mathsf{fma}\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778, z, 0.083333333333333\right)}}{x} \]

      4. fma-neg 99.5%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right)}, z, 0.083333333333333\right)}{x} \]

      5. metadata-eval 99.5%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, \color{blue}{-0.0027777777777778}\right), z, 0.083333333333333\right)}{x} \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}} \]
   4. Step-by-step derivation

      1. metadata-eval 99.5%

         \[\leadsto \left(\left(\left(x + \color{blue}{\left(-0.5\right)}\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      2. sub-neg 99.5%

         \[\leadsto \left(\left(\color{blue}{\left(x - 0.5\right)} \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      3. add-sqr-sqrt 99.3%

         \[\leadsto \left(\left(\color{blue}{\sqrt{\left(x - 0.5\right) \cdot \log x} \cdot \sqrt{\left(x - 0.5\right) \cdot \log x}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      4. pow2 99.3%

         \[\leadsto \left(\left(\color{blue}{{\left(\sqrt{\left(x - 0.5\right) \cdot \log x}\right)}^{2}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      5. *-commutative 99.3%

         \[\leadsto \left(\left({\left(\sqrt{\color{blue}{\log x \cdot \left(x - 0.5\right)}}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      6. sub-neg 99.3%

         \[\leadsto \left(\left({\left(\sqrt{\log x \cdot \color{blue}{\left(x + \left(-0.5\right)\right)}}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      7. metadata-eval 99.3%

         \[\leadsto \left(\left({\left(\sqrt{\log x \cdot \left(x + \color{blue}{-0.5}\right)}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   5. Applied egg-rr 99.3%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt{\log x \cdot \left(x + -0.5\right)}\right)}^{2}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   6. Taylor expanded in x around inf 57.6%

      \[\leadsto \color{blue}{-1 \cdot x} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]
   7. Step-by-step derivation

      1. neg-mul-1 57.6%

         \[\leadsto \color{blue}{\left(-x\right)} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   8. Simplified 57.6%

      \[\leadsto \color{blue}{\left(-x\right)} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   9. Taylor expanded in z around 0 51.2%

      \[\leadsto \color{blue}{0.083333333333333 \cdot \frac{1}{x} - x} \]
   10. Step-by-step derivation

       1. associate-*r/ 51.3%

          \[\leadsto \color{blue}{\frac{0.083333333333333 \cdot 1}{x}} - x \]

       2. metadata-eval 51.3%

          \[\leadsto \frac{\color{blue}{0.083333333333333}}{x} - x \]

   11. Simplified 51.3%

       \[\leadsto \color{blue}{\frac{0.083333333333333}{x} - x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5500000 \lor \neg \left(z \leq 4.8 \cdot 10^{-20}\right):\\ \;\;\;\;0.0007936500793651 \cdot \frac{z}{\frac{x}{z}} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x} - x\\ \end{array} \]

Alternative 17: 44.6% accurate, 9.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5500000 \lor \neg \left(z \leq 4.8 \cdot 10^{-20}\right):\\ \;\;\;\;z \cdot \left(z \cdot \frac{0.0007936500793651}{x}\right) - x\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5500000.0) (not (<= z 4.8e-20)))
   (- (* z (* z (/ 0.0007936500793651 x))) x)
   (- (/ 0.083333333333333 x) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5500000.0) || !(z <= 4.8e-20)) {
		tmp = (z * (z * (0.0007936500793651 / x))) - x;
	} else {
		tmp = (0.083333333333333 / 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 ((z <= (-5500000.0d0)) .or. (.not. (z <= 4.8d-20))) then
        tmp = (z * (z * (0.0007936500793651d0 / x))) - x
    else
        tmp = (0.083333333333333d0 / x) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5500000.0) || !(z <= 4.8e-20)) {
		tmp = (z * (z * (0.0007936500793651 / x))) - x;
	} else {
		tmp = (0.083333333333333 / x) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5500000.0) or not (z <= 4.8e-20):
		tmp = (z * (z * (0.0007936500793651 / x))) - x
	else:
		tmp = (0.083333333333333 / x) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5500000.0) || !(z <= 4.8e-20))
		tmp = Float64(Float64(z * Float64(z * Float64(0.0007936500793651 / x))) - x);
	else
		tmp = Float64(Float64(0.083333333333333 / x) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5500000.0) || ~((z <= 4.8e-20)))
		tmp = (z * (z * (0.0007936500793651 / x))) - x;
	else
		tmp = (0.083333333333333 / x) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5500000.0], N[Not[LessEqual[z, 4.8e-20]], $MachinePrecision]], N[(N[(z * N[(z * N[(0.0007936500793651 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(N[(0.083333333333333 / x), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5e6 or 4.79999999999999986e-20 < z

   1. Initial program 91.1%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

      1. sub-neg 91.1%

         \[\leadsto \left(\left(\color{blue}{\left(x + \left(-0.5\right)\right)} \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      2. metadata-eval 91.1%

         \[\leadsto \left(\left(\left(x + \color{blue}{-0.5}\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      3. fma-def 91.1%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\mathsf{fma}\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778, z, 0.083333333333333\right)}}{x} \]

      4. fma-neg 91.1%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right)}, z, 0.083333333333333\right)}{x} \]

      5. metadata-eval 91.1%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, \color{blue}{-0.0027777777777778}\right), z, 0.083333333333333\right)}{x} \]

   3. Simplified 91.1%

      \[\leadsto \color{blue}{\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}} \]
   4. Step-by-step derivation

      1. metadata-eval 91.1%

         \[\leadsto \left(\left(\left(x + \color{blue}{\left(-0.5\right)}\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      2. sub-neg 91.1%

         \[\leadsto \left(\left(\color{blue}{\left(x - 0.5\right)} \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      3. add-sqr-sqrt 91.1%

         \[\leadsto \left(\left(\color{blue}{\sqrt{\left(x - 0.5\right) \cdot \log x} \cdot \sqrt{\left(x - 0.5\right) \cdot \log x}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      4. pow2 91.1%

         \[\leadsto \left(\left(\color{blue}{{\left(\sqrt{\left(x - 0.5\right) \cdot \log x}\right)}^{2}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      5. *-commutative 91.1%

         \[\leadsto \left(\left({\left(\sqrt{\color{blue}{\log x \cdot \left(x - 0.5\right)}}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      6. sub-neg 91.1%

         \[\leadsto \left(\left({\left(\sqrt{\log x \cdot \color{blue}{\left(x + \left(-0.5\right)\right)}}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      7. metadata-eval 91.1%

         \[\leadsto \left(\left({\left(\sqrt{\log x \cdot \left(x + \color{blue}{-0.5}\right)}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   5. Applied egg-rr 91.1%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt{\log x \cdot \left(x + -0.5\right)}\right)}^{2}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   6. Taylor expanded in x around inf 75.7%

      \[\leadsto \color{blue}{-1 \cdot x} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]
   7. Step-by-step derivation

      1. neg-mul-1 75.7%

         \[\leadsto \color{blue}{\left(-x\right)} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   8. Simplified 75.7%

      \[\leadsto \color{blue}{\left(-x\right)} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   9. Taylor expanded in z around inf 74.9%

      \[\leadsto \left(-x\right) + \color{blue}{\frac{{z}^{2} \cdot \left(0.0007936500793651 + y\right)}{x}} \]
   10. Step-by-step derivation

       1. associate-/l* 75.3%

          \[\leadsto \left(-x\right) + \color{blue}{\frac{{z}^{2}}{\frac{x}{0.0007936500793651 + y}}} \]

       2. unpow2 75.3%

          \[\leadsto \left(-x\right) + \frac{\color{blue}{z \cdot z}}{\frac{x}{0.0007936500793651 + y}} \]

   11. Simplified 75.3%

       \[\leadsto \left(-x\right) + \color{blue}{\frac{z \cdot z}{\frac{x}{0.0007936500793651 + y}}} \]

   12. Taylor expanded in y around 0 48.2%

       \[\leadsto \color{blue}{0.0007936500793651 \cdot \frac{{z}^{2}}{x} - x} \]
   13. Step-by-step derivation

       1. associate-*r/ 48.2%

          \[\leadsto \color{blue}{\frac{0.0007936500793651 \cdot {z}^{2}}{x}} - x \]

       2. *-commutative 48.2%

          \[\leadsto \frac{\color{blue}{{z}^{2} \cdot 0.0007936500793651}}{x} - x \]

       3. associate-*r/ 48.2%

          \[\leadsto \color{blue}{{z}^{2} \cdot \frac{0.0007936500793651}{x}} - x \]

       4. metadata-eval 48.2%

          \[\leadsto {z}^{2} \cdot \frac{\color{blue}{0.0007936500793651 \cdot 1}}{x} - x \]

       5. associate-*r/ 48.2%

          \[\leadsto {z}^{2} \cdot \color{blue}{\left(0.0007936500793651 \cdot \frac{1}{x}\right)} - x \]

       6. unpow2 48.2%

          \[\leadsto \color{blue}{\left(z \cdot z\right)} \cdot \left(0.0007936500793651 \cdot \frac{1}{x}\right) - x \]

       7. associate-*l* 45.8%

          \[\leadsto \color{blue}{z \cdot \left(z \cdot \left(0.0007936500793651 \cdot \frac{1}{x}\right)\right)} - x \]

       8. associate-*r/ 45.8%

          \[\leadsto z \cdot \left(z \cdot \color{blue}{\frac{0.0007936500793651 \cdot 1}{x}}\right) - x \]

       9. metadata-eval 45.8%

          \[\leadsto z \cdot \left(z \cdot \frac{\color{blue}{0.0007936500793651}}{x}\right) - x \]

   14. Simplified 45.8%

       \[\leadsto \color{blue}{z \cdot \left(z \cdot \frac{0.0007936500793651}{x}\right) - x} \]

   if -5.5e6 < z < 4.79999999999999986e-20

   1. Initial program 99.5%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

      1. sub-neg 99.5%

         \[\leadsto \left(\left(\color{blue}{\left(x + \left(-0.5\right)\right)} \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      2. metadata-eval 99.5%

         \[\leadsto \left(\left(\left(x + \color{blue}{-0.5}\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      3. fma-def 99.5%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\mathsf{fma}\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778, z, 0.083333333333333\right)}}{x} \]

      4. fma-neg 99.5%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right)}, z, 0.083333333333333\right)}{x} \]

      5. metadata-eval 99.5%

         \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, \color{blue}{-0.0027777777777778}\right), z, 0.083333333333333\right)}{x} \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}} \]
   4. Step-by-step derivation

      1. metadata-eval 99.5%

         \[\leadsto \left(\left(\left(x + \color{blue}{\left(-0.5\right)}\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      2. sub-neg 99.5%

         \[\leadsto \left(\left(\color{blue}{\left(x - 0.5\right)} \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      3. add-sqr-sqrt 99.3%

         \[\leadsto \left(\left(\color{blue}{\sqrt{\left(x - 0.5\right) \cdot \log x} \cdot \sqrt{\left(x - 0.5\right) \cdot \log x}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      4. pow2 99.3%

         \[\leadsto \left(\left(\color{blue}{{\left(\sqrt{\left(x - 0.5\right) \cdot \log x}\right)}^{2}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      5. *-commutative 99.3%

         \[\leadsto \left(\left({\left(\sqrt{\color{blue}{\log x \cdot \left(x - 0.5\right)}}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      6. sub-neg 99.3%

         \[\leadsto \left(\left({\left(\sqrt{\log x \cdot \color{blue}{\left(x + \left(-0.5\right)\right)}}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

      7. metadata-eval 99.3%

         \[\leadsto \left(\left({\left(\sqrt{\log x \cdot \left(x + \color{blue}{-0.5}\right)}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   5. Applied egg-rr 99.3%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt{\log x \cdot \left(x + -0.5\right)}\right)}^{2}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   6. Taylor expanded in x around inf 57.6%

      \[\leadsto \color{blue}{-1 \cdot x} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]
   7. Step-by-step derivation

      1. neg-mul-1 57.6%

         \[\leadsto \color{blue}{\left(-x\right)} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   8. Simplified 57.6%

      \[\leadsto \color{blue}{\left(-x\right)} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   9. Taylor expanded in z around 0 51.2%

      \[\leadsto \color{blue}{0.083333333333333 \cdot \frac{1}{x} - x} \]
   10. Step-by-step derivation

       1. associate-*r/ 51.3%

          \[\leadsto \color{blue}{\frac{0.083333333333333 \cdot 1}{x}} - x \]

       2. metadata-eval 51.3%

          \[\leadsto \frac{\color{blue}{0.083333333333333}}{x} - x \]

   11. Simplified 51.3%

       \[\leadsto \color{blue}{\frac{0.083333333333333}{x} - x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5500000 \lor \neg \left(z \leq 4.8 \cdot 10^{-20}\right):\\ \;\;\;\;z \cdot \left(z \cdot \frac{0.0007936500793651}{x}\right) - x\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x} - x\\ \end{array} \]

Alternative 18: 22.3% accurate, 24.6× speedup

Math

\[\begin{array}{l} \\ \frac{0.083333333333333}{x} - x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (/ 0.083333333333333 x) x))

C

double code(double x, double y, double z) {
	return (0.083333333333333 / x) - x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (0.083333333333333d0 / x) - x
end function

Java

public static double code(double x, double y, double z) {
	return (0.083333333333333 / x) - x;
}

Python

def code(x, y, z):
	return (0.083333333333333 / x) - x

Julia

function code(x, y, z)
	return Float64(Float64(0.083333333333333 / x) - x)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (0.083333333333333 / x) - x;
end

Wolfram

code[x_, y_, z_] := N[(N[(0.083333333333333 / x), $MachinePrecision] - x), $MachinePrecision]

Derivation

1. Initial program 94.8%

   \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
2. Step-by-step derivation

   1. sub-neg 94.8%

      \[\leadsto \left(\left(\color{blue}{\left(x + \left(-0.5\right)\right)} \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. metadata-eval 94.8%

      \[\leadsto \left(\left(\left(x + \color{blue}{-0.5}\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   3. fma-def 94.8%

      \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\mathsf{fma}\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778, z, 0.083333333333333\right)}}{x} \]

   4. fma-neg 94.8%

      \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right)}, z, 0.083333333333333\right)}{x} \]

   5. metadata-eval 94.8%

      \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, \color{blue}{-0.0027777777777778}\right), z, 0.083333333333333\right)}{x} \]

3. Simplified 94.8%

   \[\leadsto \color{blue}{\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}} \]
4. Step-by-step derivation

   1. metadata-eval 94.8%

      \[\leadsto \left(\left(\left(x + \color{blue}{\left(-0.5\right)}\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   2. sub-neg 94.8%

      \[\leadsto \left(\left(\color{blue}{\left(x - 0.5\right)} \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   3. add-sqr-sqrt 94.7%

      \[\leadsto \left(\left(\color{blue}{\sqrt{\left(x - 0.5\right) \cdot \log x} \cdot \sqrt{\left(x - 0.5\right) \cdot \log x}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   4. pow2 94.7%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt{\left(x - 0.5\right) \cdot \log x}\right)}^{2}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   5. *-commutative 94.7%

      \[\leadsto \left(\left({\left(\sqrt{\color{blue}{\log x \cdot \left(x - 0.5\right)}}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   6. sub-neg 94.7%

      \[\leadsto \left(\left({\left(\sqrt{\log x \cdot \color{blue}{\left(x + \left(-0.5\right)\right)}}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   7. metadata-eval 94.7%

      \[\leadsto \left(\left({\left(\sqrt{\log x \cdot \left(x + \color{blue}{-0.5}\right)}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

5. Applied egg-rr 94.7%

   \[\leadsto \left(\left(\color{blue}{{\left(\sqrt{\log x \cdot \left(x + -0.5\right)}\right)}^{2}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

6. Taylor expanded in x around inf 67.7%

   \[\leadsto \color{blue}{-1 \cdot x} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]
7. Step-by-step derivation

   1. neg-mul-1 67.7%

      \[\leadsto \color{blue}{\left(-x\right)} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

8. Simplified 67.7%

   \[\leadsto \color{blue}{\left(-x\right)} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

9. Taylor expanded in z around 0 23.9%

   \[\leadsto \color{blue}{0.083333333333333 \cdot \frac{1}{x} - x} \]
10. Step-by-step derivation

    1. associate-*r/ 23.9%

       \[\leadsto \color{blue}{\frac{0.083333333333333 \cdot 1}{x}} - x \]

    2. metadata-eval 23.9%

       \[\leadsto \frac{\color{blue}{0.083333333333333}}{x} - x \]

11. Simplified 23.9%

    \[\leadsto \color{blue}{\frac{0.083333333333333}{x} - x} \]

12. Final simplification 23.9%

    \[\leadsto \frac{0.083333333333333}{x} - x \]

Alternative 19: 1.3% accurate, 61.5× speedup

Math

\[\begin{array}{l} \\ -x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- x))

C

double code(double x, double y, double z) {
	return -x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = -x
end function

Java

public static double code(double x, double y, double z) {
	return -x;
}

Python

def code(x, y, z):
	return -x

Julia

function code(x, y, z)
	return Float64(-x)
end

MATLAB

function tmp = code(x, y, z)
	tmp = -x;
end

Wolfram

code[x_, y_, z_] := (-x)

Derivation

1. Initial program 94.8%

   \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
2. Step-by-step derivation

   1. sub-neg 94.8%

      \[\leadsto \left(\left(\color{blue}{\left(x + \left(-0.5\right)\right)} \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. metadata-eval 94.8%

      \[\leadsto \left(\left(\left(x + \color{blue}{-0.5}\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   3. fma-def 94.8%

      \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\mathsf{fma}\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778, z, 0.083333333333333\right)}}{x} \]

   4. fma-neg 94.8%

      \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right)}, z, 0.083333333333333\right)}{x} \]

   5. metadata-eval 94.8%

      \[\leadsto \left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, \color{blue}{-0.0027777777777778}\right), z, 0.083333333333333\right)}{x} \]

3. Simplified 94.8%

   \[\leadsto \color{blue}{\left(\left(\left(x + -0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}} \]
4. Step-by-step derivation

   1. metadata-eval 94.8%

      \[\leadsto \left(\left(\left(x + \color{blue}{\left(-0.5\right)}\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   2. sub-neg 94.8%

      \[\leadsto \left(\left(\color{blue}{\left(x - 0.5\right)} \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   3. add-sqr-sqrt 94.7%

      \[\leadsto \left(\left(\color{blue}{\sqrt{\left(x - 0.5\right) \cdot \log x} \cdot \sqrt{\left(x - 0.5\right) \cdot \log x}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   4. pow2 94.7%

      \[\leadsto \left(\left(\color{blue}{{\left(\sqrt{\left(x - 0.5\right) \cdot \log x}\right)}^{2}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   5. *-commutative 94.7%

      \[\leadsto \left(\left({\left(\sqrt{\color{blue}{\log x \cdot \left(x - 0.5\right)}}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   6. sub-neg 94.7%

      \[\leadsto \left(\left({\left(\sqrt{\log x \cdot \color{blue}{\left(x + \left(-0.5\right)\right)}}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   7. metadata-eval 94.7%

      \[\leadsto \left(\left({\left(\sqrt{\log x \cdot \left(x + \color{blue}{-0.5}\right)}\right)}^{2} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

5. Applied egg-rr 94.7%

   \[\leadsto \left(\left(\color{blue}{{\left(\sqrt{\log x \cdot \left(x + -0.5\right)}\right)}^{2}} - x\right) + 0.91893853320467\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

6. Taylor expanded in x around inf 67.7%

   \[\leadsto \color{blue}{-1 \cdot x} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]
7. Step-by-step derivation

   1. neg-mul-1 67.7%

      \[\leadsto \color{blue}{\left(-x\right)} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

8. Simplified 67.7%

   \[\leadsto \color{blue}{\left(-x\right)} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

9. Taylor expanded in x around inf 1.3%

   \[\leadsto \color{blue}{-1 \cdot x} \]
10. Step-by-step derivation

    1. mul-1-neg 1.3%

       \[\leadsto \color{blue}{-x} \]

11. Simplified 1.3%

    \[\leadsto \color{blue}{-x} \]

12. Final simplification 1.3%

    \[\leadsto -x \]

Developer target: 98.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(x - 0.5\right) \cdot \log x + \left(0.91893853320467 - x\right)\right) + \frac{0.083333333333333}{x}\right) + \frac{z}{x} \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+
  (+ (+ (* (- x 0.5) (log x)) (- 0.91893853320467 x)) (/ 0.083333333333333 x))
  (* (/ z x) (- (* z (+ y 0.0007936500793651)) 0.0027777777777778))))

C

double code(double x, double y, double z) {
	return ((((x - 0.5) * log(x)) + (0.91893853320467 - x)) + (0.083333333333333 / x)) + ((z / x) * ((z * (y + 0.0007936500793651)) - 0.0027777777777778));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((((x - 0.5d0) * log(x)) + (0.91893853320467d0 - x)) + (0.083333333333333d0 / x)) + ((z / x) * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0))
end function

Java

public static double code(double x, double y, double z) {
	return ((((x - 0.5) * Math.log(x)) + (0.91893853320467 - x)) + (0.083333333333333 / x)) + ((z / x) * ((z * (y + 0.0007936500793651)) - 0.0027777777777778));
}

Python

def code(x, y, z):
	return ((((x - 0.5) * math.log(x)) + (0.91893853320467 - x)) + (0.083333333333333 / x)) + ((z / x) * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))

Julia

function code(x, y, z)
	return Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) + Float64(0.91893853320467 - x)) + Float64(0.083333333333333 / x)) + Float64(Float64(z / x) * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((((x - 0.5) * log(x)) + (0.91893853320467 - x)) + (0.083333333333333 / x)) + ((z / x) * ((z * (y + 0.0007936500793651)) - 0.0027777777777778));
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] + N[(0.91893853320467 - x), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision] + N[(N[(z / x), $MachinePrecision] * N[(N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023279 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (+ (+ (+ (* (- x 0.5) (log x)) (- 0.91893853320467 x)) (/ 0.083333333333333 x)) (* (/ z x) (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))

  (+ (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467) (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)))