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

Percentage Accurate: 93.9% → 99.4%

Time: 20.9s

Alternatives: 15

Speedup: 1.0×

• 31.3% 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: 93.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log x \cdot \left(x + -0.5\right)\\ \mathbf{if}\;x \leq 1.35 \cdot 10^{+46}:\\ \;\;\;\;\frac{{t_0}^{3} - {\left(x + -0.91893853320467\right)}^{3}}{{t_0}^{2} + \left(x + -0.91893853320467\right) \cdot \left(t_0 + \left(x + -0.91893853320467\right)\right)} + \frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t_0 + 0.91893853320467\right) - x\right) + \left(z \cdot \frac{z}{x}\right) \cdot \left(y + 0.0007936500793651\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (log x) (+ x -0.5))))
   (if (<= x 1.35e+46)
     (+
      (/
       (- (pow t_0 3.0) (pow (+ x -0.91893853320467) 3.0))
       (+
        (pow t_0 2.0)
        (* (+ x -0.91893853320467) (+ t_0 (+ x -0.91893853320467)))))
      (/
       (+
        (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778))
        0.083333333333333)
       x))
     (+
      (- (+ t_0 0.91893853320467) x)
      (* (* z (/ z x)) (+ y 0.0007936500793651))))))

C

double code(double x, double y, double z) {
	double t_0 = log(x) * (x + -0.5);
	double tmp;
	if (x <= 1.35e+46) {
		tmp = ((pow(t_0, 3.0) - pow((x + -0.91893853320467), 3.0)) / (pow(t_0, 2.0) + ((x + -0.91893853320467) * (t_0 + (x + -0.91893853320467))))) + (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x);
	} else {
		tmp = ((t_0 + 0.91893853320467) - x) + ((z * (z / x)) * (y + 0.0007936500793651));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = log(x) * (x + (-0.5d0))
    if (x <= 1.35d+46) then
        tmp = (((t_0 ** 3.0d0) - ((x + (-0.91893853320467d0)) ** 3.0d0)) / ((t_0 ** 2.0d0) + ((x + (-0.91893853320467d0)) * (t_0 + (x + (-0.91893853320467d0)))))) + (((z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0)) + 0.083333333333333d0) / x)
    else
        tmp = ((t_0 + 0.91893853320467d0) - x) + ((z * (z / x)) * (y + 0.0007936500793651d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.log(x) * (x + -0.5);
	double tmp;
	if (x <= 1.35e+46) {
		tmp = ((Math.pow(t_0, 3.0) - Math.pow((x + -0.91893853320467), 3.0)) / (Math.pow(t_0, 2.0) + ((x + -0.91893853320467) * (t_0 + (x + -0.91893853320467))))) + (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x);
	} else {
		tmp = ((t_0 + 0.91893853320467) - x) + ((z * (z / x)) * (y + 0.0007936500793651));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.log(x) * (x + -0.5)
	tmp = 0
	if x <= 1.35e+46:
		tmp = ((math.pow(t_0, 3.0) - math.pow((x + -0.91893853320467), 3.0)) / (math.pow(t_0, 2.0) + ((x + -0.91893853320467) * (t_0 + (x + -0.91893853320467))))) + (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x)
	else:
		tmp = ((t_0 + 0.91893853320467) - x) + ((z * (z / x)) * (y + 0.0007936500793651))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(log(x) * Float64(x + -0.5))
	tmp = 0.0
	if (x <= 1.35e+46)
		tmp = Float64(Float64(Float64((t_0 ^ 3.0) - (Float64(x + -0.91893853320467) ^ 3.0)) / Float64((t_0 ^ 2.0) + Float64(Float64(x + -0.91893853320467) * Float64(t_0 + Float64(x + -0.91893853320467))))) + Float64(Float64(Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x));
	else
		tmp = Float64(Float64(Float64(t_0 + 0.91893853320467) - x) + Float64(Float64(z * Float64(z / x)) * Float64(y + 0.0007936500793651)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = log(x) * (x + -0.5);
	tmp = 0.0;
	if (x <= 1.35e+46)
		tmp = (((t_0 ^ 3.0) - ((x + -0.91893853320467) ^ 3.0)) / ((t_0 ^ 2.0) + ((x + -0.91893853320467) * (t_0 + (x + -0.91893853320467))))) + (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x);
	else
		tmp = ((t_0 + 0.91893853320467) - x) + ((z * (z / x)) * (y + 0.0007936500793651));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Log[x], $MachinePrecision] * N[(x + -0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 1.35e+46], N[(N[(N[(N[Power[t$95$0, 3.0], $MachinePrecision] - N[Power[N[(x + -0.91893853320467), $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision] / N[(N[Power[t$95$0, 2.0], $MachinePrecision] + N[(N[(x + -0.91893853320467), $MachinePrecision] * N[(t$95$0 + N[(x + -0.91893853320467), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(z * N[(N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t$95$0 + 0.91893853320467), $MachinePrecision] - x), $MachinePrecision] + N[(N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision] * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 1.3500000000000001e46

   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. Add Preprocessing
   3. Step-by-step derivation

      1. associate-+l- 99.7%

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

      2. flip3-- 99.7%

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

      3. sub-neg 99.7%

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

      4. metadata-eval 99.7%

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

      5. *-commutative 99.7%

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

      6. sub-neg 99.7%

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

      7. metadata-eval 99.7%

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

      8. pow2 99.7%

         \[\leadsto \frac{{\left(\log x \cdot \left(x + -0.5\right)\right)}^{3} - {\left(x + -0.91893853320467\right)}^{3}}{\color{blue}{{\left(\left(x - 0.5\right) \cdot \log x\right)}^{2}} + \left(\left(x - 0.91893853320467\right) \cdot \left(x - 0.91893853320467\right) + \left(\left(x - 0.5\right) \cdot \log x\right) \cdot \left(x - 0.91893853320467\right)\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      9. sub-neg 99.7%

         \[\leadsto \frac{{\left(\log x \cdot \left(x + -0.5\right)\right)}^{3} - {\left(x + -0.91893853320467\right)}^{3}}{{\left(\color{blue}{\left(x + \left(-0.5\right)\right)} \cdot \log x\right)}^{2} + \left(\left(x - 0.91893853320467\right) \cdot \left(x - 0.91893853320467\right) + \left(\left(x - 0.5\right) \cdot \log x\right) \cdot \left(x - 0.91893853320467\right)\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      10. metadata-eval 99.7%

          \[\leadsto \frac{{\left(\log x \cdot \left(x + -0.5\right)\right)}^{3} - {\left(x + -0.91893853320467\right)}^{3}}{{\left(\left(x + \color{blue}{-0.5}\right) \cdot \log x\right)}^{2} + \left(\left(x - 0.91893853320467\right) \cdot \left(x - 0.91893853320467\right) + \left(\left(x - 0.5\right) \cdot \log x\right) \cdot \left(x - 0.91893853320467\right)\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

      11. *-commutative 99.7%

          \[\leadsto \frac{{\left(\log x \cdot \left(x + -0.5\right)\right)}^{3} - {\left(x + -0.91893853320467\right)}^{3}}{{\color{blue}{\left(\log x \cdot \left(x + -0.5\right)\right)}}^{2} + \left(\left(x - 0.91893853320467\right) \cdot \left(x - 0.91893853320467\right) + \left(\left(x - 0.5\right) \cdot \log x\right) \cdot \left(x - 0.91893853320467\right)\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{{\left(\log x \cdot \left(x + -0.5\right)\right)}^{3} - {\left(x + -0.91893853320467\right)}^{3}}{{\left(\log x \cdot \left(x + -0.5\right)\right)}^{2} + \left(\left(x + -0.91893853320467\right) \cdot \left(x + -0.91893853320467\right) + \left(\log x \cdot \left(x + -0.5\right)\right) \cdot \left(x + -0.91893853320467\right)\right)}} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   5. Step-by-step derivation

      1. distribute-rgt-out 99.7%

         \[\leadsto \frac{{\left(\log x \cdot \left(x + -0.5\right)\right)}^{3} - {\left(x + -0.91893853320467\right)}^{3}}{{\left(\log x \cdot \left(x + -0.5\right)\right)}^{2} + \color{blue}{\left(x + -0.91893853320467\right) \cdot \left(\left(x + -0.91893853320467\right) + \log x \cdot \left(x + -0.5\right)\right)}} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   6. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{{\left(\log x \cdot \left(x + -0.5\right)\right)}^{3} - {\left(x + -0.91893853320467\right)}^{3}}{{\left(\log x \cdot \left(x + -0.5\right)\right)}^{2} + \left(x + -0.91893853320467\right) \cdot \left(\left(x + -0.91893853320467\right) + \log x \cdot \left(x + -0.5\right)\right)}} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   if 1.3500000000000001e46 < 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. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 89.2%

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

      2. associate-+l+ 89.2%

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

      3. +-commutative 89.2%

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

      4. sub-neg 89.2%

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

      5. associate-+r- 89.2%

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

      6. sub-neg 89.2%

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

      7. metadata-eval 89.2%

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

      8. *-commutative 89.2%

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

   4. Applied egg-rr 89.2%

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

   5. Taylor expanded in z around inf 89.2%

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

      1. associate-/l* 92.0%

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

      2. +-commutative 92.0%

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

      3. associate-/r/ 93.1%

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

      4. +-commutative 93.1%

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

   7. Simplified 93.1%

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

      1. unpow2 93.1%

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

      2. *-un-lft-identity 93.1%

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

      3. times-frac 99.6%

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

   9. Applied egg-rr 99.6%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.35 \cdot 10^{+46}:\\ \;\;\;\;\frac{{\left(\log x \cdot \left(x + -0.5\right)\right)}^{3} - {\left(x + -0.91893853320467\right)}^{3}}{{\left(\log x \cdot \left(x + -0.5\right)\right)}^{2} + \left(x + -0.91893853320467\right) \cdot \left(\log x \cdot \left(x + -0.5\right) + \left(x + -0.91893853320467\right)\right)} + \frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\log x \cdot \left(x + -0.5\right) + 0.91893853320467\right) - x\right) + \left(z \cdot \frac{z}{x}\right) \cdot \left(y + 0.0007936500793651\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\log x \cdot \left(x + -0.5\right) + 0.91893853320467\right) - x\\ \mathbf{if}\;x \leq 100000000:\\ \;\;\;\;\frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x} + t_0\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(y + 0.0007936500793651\right) \cdot {\left(\frac{z}{\sqrt{x}}\right)}^{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (+ (* (log x) (+ x -0.5)) 0.91893853320467) x)))
   (if (<= x 100000000.0)
     (+
      (/
       (+
        (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778))
        0.083333333333333)
       x)
      t_0)
     (+ t_0 (* (+ y 0.0007936500793651) (pow (/ z (sqrt x)) 2.0))))))

C

double code(double x, double y, double z) {
	double t_0 = ((log(x) * (x + -0.5)) + 0.91893853320467) - x;
	double tmp;
	if (x <= 100000000.0) {
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + t_0;
	} else {
		tmp = t_0 + ((y + 0.0007936500793651) * pow((z / sqrt(x)), 2.0));
	}
	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 = ((log(x) * (x + (-0.5d0))) + 0.91893853320467d0) - x
    if (x <= 100000000.0d0) then
        tmp = (((z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0)) + 0.083333333333333d0) / x) + t_0
    else
        tmp = t_0 + ((y + 0.0007936500793651d0) * ((z / sqrt(x)) ** 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((Math.log(x) * (x + -0.5)) + 0.91893853320467) - x;
	double tmp;
	if (x <= 100000000.0) {
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + t_0;
	} else {
		tmp = t_0 + ((y + 0.0007936500793651) * Math.pow((z / Math.sqrt(x)), 2.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((math.log(x) * (x + -0.5)) + 0.91893853320467) - x
	tmp = 0
	if x <= 100000000.0:
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + t_0
	else:
		tmp = t_0 + ((y + 0.0007936500793651) * math.pow((z / math.sqrt(x)), 2.0))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(log(x) * Float64(x + -0.5)) + 0.91893853320467) - x)
	tmp = 0.0
	if (x <= 100000000.0)
		tmp = Float64(Float64(Float64(Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + t_0);
	else
		tmp = Float64(t_0 + Float64(Float64(y + 0.0007936500793651) * (Float64(z / sqrt(x)) ^ 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((log(x) * (x + -0.5)) + 0.91893853320467) - x;
	tmp = 0.0;
	if (x <= 100000000.0)
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + t_0;
	else
		tmp = t_0 + ((y + 0.0007936500793651) * ((z / sqrt(x)) ^ 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[Log[x], $MachinePrecision] * N[(x + -0.5), $MachinePrecision]), $MachinePrecision] + 0.91893853320467), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[x, 100000000.0], N[(N[(N[(N[(z * N[(N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision] + t$95$0), $MachinePrecision], N[(t$95$0 + N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[Power[N[(z / N[Sqrt[x], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 1e8

   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. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 99.7%

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

      2. associate-+l+ 99.7%

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

      3. +-commutative 99.7%

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

      4. sub-neg 99.7%

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

      5. associate-+r- 99.7%

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

      6. sub-neg 99.7%

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

      7. metadata-eval 99.7%

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

      8. *-commutative 99.7%

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

   4. Applied egg-rr 99.7%

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

   if 1e8 < x

   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. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 90.4%

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

      2. associate-+l+ 90.4%

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

      3. +-commutative 90.4%

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

      4. sub-neg 90.4%

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

      5. associate-+r- 90.4%

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

      6. sub-neg 90.4%

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

      7. metadata-eval 90.4%

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

      8. *-commutative 90.4%

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

   4. Applied egg-rr 90.4%

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

   5. Taylor expanded in z around inf 90.4%

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

      1. associate-/l* 92.9%

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

      2. +-commutative 92.9%

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

      3. associate-/r/ 93.8%

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

      4. +-commutative 93.8%

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

   7. Simplified 93.8%

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

      1. unpow2 93.8%

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

      2. add-sqr-sqrt 93.8%

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

      3. times-frac 99.6%

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

   9. Applied egg-rr 99.6%

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

       1. unpow2 99.6%

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

   11. Simplified 99.6%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 100000000:\\ \;\;\;\;\frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x} + \left(\left(\log x \cdot \left(x + -0.5\right) + 0.91893853320467\right) - x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\log x \cdot \left(x + -0.5\right) + 0.91893853320467\right) - x\right) + \left(y + 0.0007936500793651\right) \cdot {\left(\frac{z}{\sqrt{x}}\right)}^{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.5 \cdot 10^{+42}:\\ \;\;\;\;\frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x} + \left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\log x \cdot \left(x + -0.5\right) + 0.91893853320467\right) - x\right) + \left(z \cdot \frac{z}{x}\right) \cdot \left(y + 0.0007936500793651\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 2.5e+42)
   (+
    (/
     (+
      (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778))
      0.083333333333333)
     x)
    (+ 0.91893853320467 (- (* (log x) (- x 0.5)) x)))
   (+
    (- (+ (* (log x) (+ x -0.5)) 0.91893853320467) x)
    (* (* z (/ z x)) (+ y 0.0007936500793651)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 2.5e+42) {
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + (0.91893853320467 + ((log(x) * (x - 0.5)) - x));
	} else {
		tmp = (((log(x) * (x + -0.5)) + 0.91893853320467) - x) + ((z * (z / x)) * (y + 0.0007936500793651));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 2.5d+42) then
        tmp = (((z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0)) + 0.083333333333333d0) / x) + (0.91893853320467d0 + ((log(x) * (x - 0.5d0)) - x))
    else
        tmp = (((log(x) * (x + (-0.5d0))) + 0.91893853320467d0) - x) + ((z * (z / x)) * (y + 0.0007936500793651d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 2.5e+42) {
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + (0.91893853320467 + ((Math.log(x) * (x - 0.5)) - x));
	} else {
		tmp = (((Math.log(x) * (x + -0.5)) + 0.91893853320467) - x) + ((z * (z / x)) * (y + 0.0007936500793651));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 2.5e+42:
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + (0.91893853320467 + ((math.log(x) * (x - 0.5)) - x))
	else:
		tmp = (((math.log(x) * (x + -0.5)) + 0.91893853320467) - x) + ((z * (z / x)) * (y + 0.0007936500793651))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 2.5e+42)
		tmp = Float64(Float64(Float64(Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + Float64(0.91893853320467 + Float64(Float64(log(x) * Float64(x - 0.5)) - x)));
	else
		tmp = Float64(Float64(Float64(Float64(log(x) * Float64(x + -0.5)) + 0.91893853320467) - x) + Float64(Float64(z * Float64(z / x)) * Float64(y + 0.0007936500793651)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 2.5e+42)
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + (0.91893853320467 + ((log(x) * (x - 0.5)) - x));
	else
		tmp = (((log(x) * (x + -0.5)) + 0.91893853320467) - x) + ((z * (z / x)) * (y + 0.0007936500793651));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 2.5e+42], N[(N[(N[(N[(z * N[(N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision] + N[(0.91893853320467 + N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[Log[x], $MachinePrecision] * N[(x + -0.5), $MachinePrecision]), $MachinePrecision] + 0.91893853320467), $MachinePrecision] - x), $MachinePrecision] + N[(N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision] * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.50000000000000003e42

   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. Add Preprocessing

   if 2.50000000000000003e42 < 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. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 89.4%

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

      2. associate-+l+ 89.4%

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

      3. +-commutative 89.4%

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

      4. sub-neg 89.4%

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

      5. associate-+r- 89.4%

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

      6. sub-neg 89.4%

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

      7. metadata-eval 89.4%

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

      8. *-commutative 89.4%

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

   4. Applied egg-rr 89.4%

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

   5. Taylor expanded in z around inf 89.4%

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

      1. associate-/l* 92.2%

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

      2. +-commutative 92.2%

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

      3. associate-/r/ 93.2%

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

      4. +-commutative 93.2%

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

   7. Simplified 93.2%

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

      1. unpow2 93.2%

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

      2. *-un-lft-identity 93.2%

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

      3. times-frac 99.6%

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

   9. Applied egg-rr 99.6%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.5 \cdot 10^{+42}:\\ \;\;\;\;\frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x} + \left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\log x \cdot \left(x + -0.5\right) + 0.91893853320467\right) - x\right) + \left(z \cdot \frac{z}{x}\right) \cdot \left(y + 0.0007936500793651\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\log x \cdot \left(x + -0.5\right) + 0.91893853320467\right) - x\\ \mathbf{if}\;x \leq 2.2 \cdot 10^{+42}:\\ \;\;\;\;\frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x} + t_0\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(z \cdot \frac{z}{x}\right) \cdot \left(y + 0.0007936500793651\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (+ (* (log x) (+ x -0.5)) 0.91893853320467) x)))
   (if (<= x 2.2e+42)
     (+
      (/
       (+
        (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778))
        0.083333333333333)
       x)
      t_0)
     (+ t_0 (* (* z (/ z x)) (+ y 0.0007936500793651))))))

C

double code(double x, double y, double z) {
	double t_0 = ((log(x) * (x + -0.5)) + 0.91893853320467) - x;
	double tmp;
	if (x <= 2.2e+42) {
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + t_0;
	} else {
		tmp = t_0 + ((z * (z / x)) * (y + 0.0007936500793651));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((log(x) * (x + (-0.5d0))) + 0.91893853320467d0) - x
    if (x <= 2.2d+42) then
        tmp = (((z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0)) + 0.083333333333333d0) / x) + t_0
    else
        tmp = t_0 + ((z * (z / x)) * (y + 0.0007936500793651d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((Math.log(x) * (x + -0.5)) + 0.91893853320467) - x;
	double tmp;
	if (x <= 2.2e+42) {
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + t_0;
	} else {
		tmp = t_0 + ((z * (z / x)) * (y + 0.0007936500793651));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((math.log(x) * (x + -0.5)) + 0.91893853320467) - x
	tmp = 0
	if x <= 2.2e+42:
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + t_0
	else:
		tmp = t_0 + ((z * (z / x)) * (y + 0.0007936500793651))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(log(x) * Float64(x + -0.5)) + 0.91893853320467) - x)
	tmp = 0.0
	if (x <= 2.2e+42)
		tmp = Float64(Float64(Float64(Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + t_0);
	else
		tmp = Float64(t_0 + Float64(Float64(z * Float64(z / x)) * Float64(y + 0.0007936500793651)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((log(x) * (x + -0.5)) + 0.91893853320467) - x;
	tmp = 0.0;
	if (x <= 2.2e+42)
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + t_0;
	else
		tmp = t_0 + ((z * (z / x)) * (y + 0.0007936500793651));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[Log[x], $MachinePrecision] * N[(x + -0.5), $MachinePrecision]), $MachinePrecision] + 0.91893853320467), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[x, 2.2e+42], N[(N[(N[(N[(z * N[(N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision] + t$95$0), $MachinePrecision], N[(t$95$0 + N[(N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision] * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 2.2000000000000001e42

   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. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 99.7%

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

      2. associate-+l+ 99.7%

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

      3. +-commutative 99.7%

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

      4. sub-neg 99.7%

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

      5. associate-+r- 99.7%

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

      6. sub-neg 99.7%

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

      7. metadata-eval 99.7%

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

      8. *-commutative 99.7%

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

   4. Applied egg-rr 99.7%

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

   if 2.2000000000000001e42 < 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. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 89.4%

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

      2. associate-+l+ 89.4%

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

      3. +-commutative 89.4%

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

      4. sub-neg 89.4%

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

      5. associate-+r- 89.4%

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

      6. sub-neg 89.4%

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

      7. metadata-eval 89.4%

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

      8. *-commutative 89.4%

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

   4. Applied egg-rr 89.4%

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

   5. Taylor expanded in z around inf 89.4%

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

      1. associate-/l* 92.2%

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

      2. +-commutative 92.2%

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

      3. associate-/r/ 93.2%

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

      4. +-commutative 93.2%

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

   7. Simplified 93.2%

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

      1. unpow2 93.2%

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

      2. *-un-lft-identity 93.2%

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

      3. times-frac 99.6%

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

   9. Applied egg-rr 99.6%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.2 \cdot 10^{+42}:\\ \;\;\;\;\frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x} + \left(\left(\log x \cdot \left(x + -0.5\right) + 0.91893853320467\right) - x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\log x \cdot \left(x + -0.5\right) + 0.91893853320467\right) - x\right) + \left(z \cdot \frac{z}{x}\right) \cdot \left(y + 0.0007936500793651\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.03:\\ \;\;\;\;\frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x} - x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\log x \cdot \left(x + -0.5\right) + 0.91893853320467\right) - x\right) + \left(z \cdot \frac{z}{x}\right) \cdot \left(y + 0.0007936500793651\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 0.03)
   (-
    (/
     (+
      (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778))
      0.083333333333333)
     x)
    x)
   (+
    (- (+ (* (log x) (+ x -0.5)) 0.91893853320467) x)
    (* (* z (/ z x)) (+ y 0.0007936500793651)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 0.03) {
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) - x;
	} else {
		tmp = (((log(x) * (x + -0.5)) + 0.91893853320467) - x) + ((z * (z / x)) * (y + 0.0007936500793651));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 0.03d0) then
        tmp = (((z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0)) + 0.083333333333333d0) / x) - x
    else
        tmp = (((log(x) * (x + (-0.5d0))) + 0.91893853320467d0) - x) + ((z * (z / x)) * (y + 0.0007936500793651d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 0.03) {
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) - x;
	} else {
		tmp = (((Math.log(x) * (x + -0.5)) + 0.91893853320467) - x) + ((z * (z / x)) * (y + 0.0007936500793651));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 0.03:
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) - x
	else:
		tmp = (((math.log(x) * (x + -0.5)) + 0.91893853320467) - x) + ((z * (z / x)) * (y + 0.0007936500793651))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 0.03)
		tmp = Float64(Float64(Float64(Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) - x);
	else
		tmp = Float64(Float64(Float64(Float64(log(x) * Float64(x + -0.5)) + 0.91893853320467) - x) + Float64(Float64(z * Float64(z / x)) * Float64(y + 0.0007936500793651)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 0.03)
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) - x;
	else
		tmp = (((log(x) * (x + -0.5)) + 0.91893853320467) - x) + ((z * (z / x)) * (y + 0.0007936500793651));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 0.03], N[(N[(N[(N[(z * N[(N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision] - x), $MachinePrecision], N[(N[(N[(N[(N[Log[x], $MachinePrecision] * N[(x + -0.5), $MachinePrecision]), $MachinePrecision] + 0.91893853320467), $MachinePrecision] - x), $MachinePrecision] + N[(N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision] * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 0.029999999999999999

   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. Add Preprocessing
   3. Step-by-step derivation

      1. associate-+l- 99.7%

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

      2. add-sqr-sqrt 99.7%

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

      3. fma-neg 99.7%

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

      4. sub-neg 99.7%

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

      5. metadata-eval 99.7%

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

      6. *-commutative 99.7%

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

      7. sub-neg 99.7%

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

      8. metadata-eval 99.7%

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

      9. *-commutative 99.7%

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

      10. sub-neg 99.7%

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

      11. metadata-eval 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around inf 98.8%

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

      1. neg-mul-1 98.8%

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

   7. Simplified 98.8%

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

   if 0.029999999999999999 < x

   1. Initial program 90.6%

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

      1. sub-neg 90.6%

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

      2. associate-+l+ 90.7%

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

      3. +-commutative 90.7%

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

      4. sub-neg 90.7%

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

      5. associate-+r- 90.7%

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

      6. sub-neg 90.7%

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

      7. metadata-eval 90.7%

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

      8. *-commutative 90.7%

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

   4. Applied egg-rr 90.7%

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

   5. Taylor expanded in z around inf 89.3%

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

      1. associate-/l* 91.8%

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

      2. +-commutative 91.8%

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

      3. associate-/r/ 92.7%

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

      4. +-commutative 92.7%

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

   7. Simplified 92.7%

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

      1. unpow2 92.7%

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

      2. *-un-lft-identity 92.7%

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

      3. times-frac 98.2%

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

   9. Applied egg-rr 98.2%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.03:\\ \;\;\;\;\frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x} - x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\log x \cdot \left(x + -0.5\right) + 0.91893853320467\right) - x\right) + \left(z \cdot \frac{z}{x}\right) \cdot \left(y + 0.0007936500793651\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.45:\\ \;\;\;\;\frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x} - x\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + z \cdot \left(z \cdot \frac{y}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 0.45)
   (-
    (/
     (+
      (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778))
      0.083333333333333)
     x)
    x)
   (+ (+ 0.91893853320467 (- (* (log x) (- x 0.5)) x)) (* z (* z (/ y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 0.45) {
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) - x;
	} else {
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + (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 <= 0.45d0) then
        tmp = (((z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0)) + 0.083333333333333d0) / x) - x
    else
        tmp = (0.91893853320467d0 + ((log(x) * (x - 0.5d0)) - x)) + (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 <= 0.45) {
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) - x;
	} else {
		tmp = (0.91893853320467 + ((Math.log(x) * (x - 0.5)) - x)) + (z * (z * (y / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 0.45:
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) - x
	else:
		tmp = (0.91893853320467 + ((math.log(x) * (x - 0.5)) - x)) + (z * (z * (y / x)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 0.45)
		tmp = Float64(Float64(Float64(Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) - x);
	else
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(log(x) * Float64(x - 0.5)) - x)) + Float64(z * Float64(z * Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 0.45)
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) - x;
	else
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + (z * (z * (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 0.45], N[(N[(N[(N[(z * N[(N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision] - x), $MachinePrecision], N[(N[(0.91893853320467 + N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(z * N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 0.450000000000000011

   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. Add Preprocessing
   3. Step-by-step derivation

      1. associate-+l- 99.7%

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

      2. add-sqr-sqrt 99.7%

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

      3. fma-neg 99.7%

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

      4. sub-neg 99.7%

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

      5. metadata-eval 99.7%

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

      6. *-commutative 99.7%

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

      7. sub-neg 99.7%

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

      8. metadata-eval 99.7%

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

      9. *-commutative 99.7%

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

      10. sub-neg 99.7%

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

      11. metadata-eval 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around inf 98.8%

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

      1. neg-mul-1 98.8%

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

   7. Simplified 98.8%

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

   if 0.450000000000000011 < x

   1. Initial program 90.6%

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

   3. Taylor expanded in y around inf 77.9%

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

      1. associate-/l* 81.2%

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

   5. Simplified 81.2%

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

      1. associate-/r/ 80.3%

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

      2. unpow2 80.3%

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

      3. associate-*r* 84.7%

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

   7. Applied egg-rr 84.7%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.45:\\ \;\;\;\;\frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x} - x\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + z \cdot \left(z \cdot \frac{y}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 92.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x} + x \cdot \left(\log x + -1\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+
  (/
   (+
    (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778))
    0.083333333333333)
   x)
  (* x (+ (log x) -1.0))))

C

double code(double x, double y, double z) {
	return (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + (x * (log(x) + -1.0));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (((z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0)) + 0.083333333333333d0) / x) + (x * (log(x) + (-1.0d0)))
end function

Java

public static double code(double x, double y, double z) {
	return (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + (x * (Math.log(x) + -1.0));
}

Python

def code(x, y, z):
	return (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + (x * (math.log(x) + -1.0))

Julia

function code(x, y, z)
	return Float64(Float64(Float64(Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + Float64(x * Float64(log(x) + -1.0)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + (x * (log(x) + -1.0));
end

Wolfram

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

Derivation

1. Initial program 95.6%

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

3. Taylor expanded in x around inf 94.3%

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

   1. sub-neg 59.3%

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

   2. mul-1-neg 59.3%

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

   3. log-rec 59.3%

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

   4. remove-double-neg 59.3%

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

   5. metadata-eval 59.3%

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

5. Simplified 94.3%

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

6. Final simplification 94.3%

   \[\leadsto \frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x} + x \cdot \left(\log x + -1\right) \]
7. Add Preprocessing

Alternative 8: 83.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.95 \cdot 10^{-16}:\\ \;\;\;\;\frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x} - x\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.95e-16)
   (-
    (/
     (+
      (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778))
      0.083333333333333)
     x)
    x)
   (+
    (+ 0.91893853320467 (- (* (log x) (- x 0.5)) x))
    (/ 0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.95e-16) {
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) - x;
	} else {
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + (0.083333333333333 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 1.95d-16) then
        tmp = (((z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0)) + 0.083333333333333d0) / x) - x
    else
        tmp = (0.91893853320467d0 + ((log(x) * (x - 0.5d0)) - x)) + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.95e-16) {
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) - x;
	} else {
		tmp = (0.91893853320467 + ((Math.log(x) * (x - 0.5)) - x)) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1.95e-16:
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) - x
	else:
		tmp = (0.91893853320467 + ((math.log(x) * (x - 0.5)) - x)) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.95e-16)
		tmp = Float64(Float64(Float64(Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) - x);
	else
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(log(x) * Float64(x - 0.5)) - x)) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1.95e-16)
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) - x;
	else
		tmp = (0.91893853320467 + ((log(x) * (x - 0.5)) - x)) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.95e-16], N[(N[(N[(N[(z * N[(N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision] - x), $MachinePrecision], N[(N[(0.91893853320467 + N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.94999999999999989e-16

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. add-sqr-sqrt 99.8%

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

      3. fma-neg 99.8%

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

      4. sub-neg 99.8%

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

      5. metadata-eval 99.8%

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

      6. *-commutative 99.8%

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

      7. sub-neg 99.8%

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

      8. metadata-eval 99.8%

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

      9. *-commutative 99.8%

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

      10. sub-neg 99.8%

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

      11. metadata-eval 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in x around inf 99.8%

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

      1. neg-mul-1 99.8%

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

   7. Simplified 99.8%

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

   if 1.94999999999999989e-16 < x

   1. Initial program 90.9%

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

   3. Taylor expanded in z around 0 78.3%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.95 \cdot 10^{-16}:\\ \;\;\;\;\frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x} - x\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \left(\log x \cdot \left(x - 0.5\right) - x\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.95 \cdot 10^{-16}:\\ \;\;\;\;\frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x} - x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\log x \cdot \left(x + -0.5\right) + 0.91893853320467\right) - x\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.95e-16)
   (-
    (/
     (+
      (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778))
      0.083333333333333)
     x)
    x)
   (+
    (- (+ (* (log x) (+ x -0.5)) 0.91893853320467) x)
    (/ 0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.95e-16) {
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) - x;
	} else {
		tmp = (((log(x) * (x + -0.5)) + 0.91893853320467) - x) + (0.083333333333333 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 1.95d-16) then
        tmp = (((z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0)) + 0.083333333333333d0) / x) - x
    else
        tmp = (((log(x) * (x + (-0.5d0))) + 0.91893853320467d0) - x) + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.95e-16) {
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) - x;
	} else {
		tmp = (((Math.log(x) * (x + -0.5)) + 0.91893853320467) - x) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1.95e-16:
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) - x
	else:
		tmp = (((math.log(x) * (x + -0.5)) + 0.91893853320467) - x) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.95e-16)
		tmp = Float64(Float64(Float64(Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) - x);
	else
		tmp = Float64(Float64(Float64(Float64(log(x) * Float64(x + -0.5)) + 0.91893853320467) - x) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1.95e-16)
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) - x;
	else
		tmp = (((log(x) * (x + -0.5)) + 0.91893853320467) - x) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.95e-16], N[(N[(N[(N[(z * N[(N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision] - x), $MachinePrecision], N[(N[(N[(N[(N[Log[x], $MachinePrecision] * N[(x + -0.5), $MachinePrecision]), $MachinePrecision] + 0.91893853320467), $MachinePrecision] - x), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.94999999999999989e-16

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. add-sqr-sqrt 99.8%

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

      3. fma-neg 99.8%

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

      4. sub-neg 99.8%

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

      5. metadata-eval 99.8%

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

      6. *-commutative 99.8%

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

      7. sub-neg 99.8%

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

      8. metadata-eval 99.8%

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

      9. *-commutative 99.8%

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

      10. sub-neg 99.8%

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

      11. metadata-eval 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in x around inf 99.8%

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

      1. neg-mul-1 99.8%

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

   7. Simplified 99.8%

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

   if 1.94999999999999989e-16 < x

   1. Initial program 90.9%

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

      1. sub-neg 90.9%

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

      2. associate-+l+ 90.9%

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

      3. +-commutative 90.9%

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

      4. sub-neg 90.9%

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

      5. associate-+r- 90.9%

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

      6. sub-neg 90.9%

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

      7. metadata-eval 90.9%

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

      8. *-commutative 90.9%

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

   4. Applied egg-rr 90.9%

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

   5. Taylor expanded in z around 0 78.3%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.95 \cdot 10^{-16}:\\ \;\;\;\;\frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x} - x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\log x \cdot \left(x + -0.5\right) + 0.91893853320467\right) - x\right) + \frac{0.083333333333333}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 84.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 28000000000000:\\ \;\;\;\;\frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x} - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 28000000000000.0)
   (-
    (/
     (+
      (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778))
      0.083333333333333)
     x)
    x)
   (+ (* x (+ (log x) -1.0)) (/ 0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 28000000000000.0) {
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) - x;
	} else {
		tmp = (x * (log(x) + -1.0)) + (0.083333333333333 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 28000000000000.0d0) then
        tmp = (((z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0)) + 0.083333333333333d0) / x) - x
    else
        tmp = (x * (log(x) + (-1.0d0))) + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 28000000000000.0) {
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) - x;
	} else {
		tmp = (x * (Math.log(x) + -1.0)) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 28000000000000.0:
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) - x
	else:
		tmp = (x * (math.log(x) + -1.0)) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 28000000000000.0)
		tmp = Float64(Float64(Float64(Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) - x);
	else
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 28000000000000.0)
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) - x;
	else
		tmp = (x * (log(x) + -1.0)) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 28000000000000.0], N[(N[(N[(N[(z * N[(N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision] - x), $MachinePrecision], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.8e13

   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. Add Preprocessing
   3. Step-by-step derivation

      1. associate-+l- 99.7%

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

      2. add-sqr-sqrt 99.0%

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

      3. fma-neg 99.0%

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

      4. sub-neg 99.0%

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

      5. metadata-eval 99.0%

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

      6. *-commutative 99.0%

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

      7. sub-neg 99.0%

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

      8. metadata-eval 99.0%

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

      9. *-commutative 99.0%

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

      10. sub-neg 99.0%

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

      11. metadata-eval 99.0%

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

   4. Applied egg-rr 99.0%

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

   5. Taylor expanded in x around inf 96.7%

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

      1. neg-mul-1 96.7%

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

   7. Simplified 96.7%

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

   if 2.8e13 < x

   1. Initial program 90.3%

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

   3. Taylor expanded in z around 0 77.8%

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

   4. Taylor expanded in x around inf 77.9%

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

      1. sub-neg 77.9%

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

      2. mul-1-neg 77.9%

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

      3. log-rec 77.9%

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

      4. remove-double-neg 77.9%

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

      5. metadata-eval 77.9%

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

   6. Simplified 77.9%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 28000000000000:\\ \;\;\;\;\frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x} - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.7% accurate, 5.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+31} \lor \neg \left(y \leq 6.4 \cdot 10^{-35}\right):\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(y \cdot z - 0.0027777777777778\right)}{x} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(0.0007936500793651 \cdot z - 0.0027777777777778\right)}{x} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.4e+31) (not (<= y 6.4e-35)))
   (- (/ (+ 0.083333333333333 (* z (- (* y z) 0.0027777777777778))) x) x)
   (-
    (/
     (+
      0.083333333333333
      (* z (- (* 0.0007936500793651 z) 0.0027777777777778)))
     x)
    x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.4e+31) || !(y <= 6.4e-35)) {
		tmp = ((0.083333333333333 + (z * ((y * z) - 0.0027777777777778))) / x) - x;
	} else {
		tmp = ((0.083333333333333 + (z * ((0.0007936500793651 * 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 ((y <= (-1.4d+31)) .or. (.not. (y <= 6.4d-35))) then
        tmp = ((0.083333333333333d0 + (z * ((y * z) - 0.0027777777777778d0))) / x) - x
    else
        tmp = ((0.083333333333333d0 + (z * ((0.0007936500793651d0 * 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 ((y <= -1.4e+31) || !(y <= 6.4e-35)) {
		tmp = ((0.083333333333333 + (z * ((y * z) - 0.0027777777777778))) / x) - x;
	} else {
		tmp = ((0.083333333333333 + (z * ((0.0007936500793651 * z) - 0.0027777777777778))) / x) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.4e+31) or not (y <= 6.4e-35):
		tmp = ((0.083333333333333 + (z * ((y * z) - 0.0027777777777778))) / x) - x
	else:
		tmp = ((0.083333333333333 + (z * ((0.0007936500793651 * z) - 0.0027777777777778))) / x) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.4e+31) || !(y <= 6.4e-35))
		tmp = Float64(Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(y * z) - 0.0027777777777778))) / x) - x);
	else
		tmp = Float64(Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(0.0007936500793651 * z) - 0.0027777777777778))) / x) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.4e+31) || ~((y <= 6.4e-35)))
		tmp = ((0.083333333333333 + (z * ((y * z) - 0.0027777777777778))) / x) - x;
	else
		tmp = ((0.083333333333333 + (z * ((0.0007936500793651 * z) - 0.0027777777777778))) / x) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.4e+31], N[Not[LessEqual[y, 6.4e-35]], $MachinePrecision]], N[(N[(N[(0.083333333333333 + N[(z * N[(N[(y * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - x), $MachinePrecision], N[(N[(N[(0.083333333333333 + N[(z * N[(N[(0.0007936500793651 * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.40000000000000008e31 or 6.3999999999999996e-35 < y

   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. Add Preprocessing
   3. Step-by-step derivation

      1. associate-+l- 95.5%

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

      2. add-sqr-sqrt 94.4%

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

      3. fma-neg 94.4%

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

      4. sub-neg 94.4%

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

      5. metadata-eval 94.4%

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

      6. *-commutative 94.4%

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

      7. sub-neg 94.4%

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

      8. metadata-eval 94.4%

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

      9. *-commutative 94.4%

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

      10. sub-neg 94.4%

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

      11. metadata-eval 94.4%

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

   4. Applied egg-rr 94.4%

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

   5. Taylor expanded in x around inf 61.4%

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

      1. neg-mul-1 61.4%

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

   7. Simplified 61.4%

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

   8. Taylor expanded in y around inf 61.4%

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

      1. *-commutative 61.4%

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

   10. Simplified 61.4%

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

   if -1.40000000000000008e31 < y < 6.3999999999999996e-35

   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. Add Preprocessing
   3. Step-by-step derivation

      1. associate-+l- 95.8%

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

      2. add-sqr-sqrt 95.6%

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

      3. fma-neg 95.7%

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

      4. sub-neg 95.7%

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

      5. metadata-eval 95.7%

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

      6. *-commutative 95.7%

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

      7. sub-neg 95.7%

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

      8. metadata-eval 95.7%

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

      9. *-commutative 95.7%

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

      10. sub-neg 95.7%

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

      11. metadata-eval 95.7%

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

   4. Applied egg-rr 95.7%

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

   5. Taylor expanded in x around inf 65.0%

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

      1. neg-mul-1 65.0%

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

   7. Simplified 65.0%

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

   8. Taylor expanded in y around 0 65.0%

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

      1. *-commutative 65.0%

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

   10. Simplified 65.0%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+31} \lor \neg \left(y \leq 6.4 \cdot 10^{-35}\right):\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(y \cdot z - 0.0027777777777778\right)}{x} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(0.0007936500793651 \cdot z - 0.0027777777777778\right)}{x} - x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 47.3% accurate, 6.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+31}:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot -0.0027777777777778}{x} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(0.0007936500793651 \cdot z - 0.0027777777777778\right)}{x} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.4e+31)
   (- (/ (+ 0.083333333333333 (* z -0.0027777777777778)) x) x)
   (-
    (/
     (+
      0.083333333333333
      (* z (- (* 0.0007936500793651 z) 0.0027777777777778)))
     x)
    x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.4e+31) {
		tmp = ((0.083333333333333 + (z * -0.0027777777777778)) / x) - x;
	} else {
		tmp = ((0.083333333333333 + (z * ((0.0007936500793651 * 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 (y <= (-1.4d+31)) then
        tmp = ((0.083333333333333d0 + (z * (-0.0027777777777778d0))) / x) - x
    else
        tmp = ((0.083333333333333d0 + (z * ((0.0007936500793651d0 * 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 (y <= -1.4e+31) {
		tmp = ((0.083333333333333 + (z * -0.0027777777777778)) / x) - x;
	} else {
		tmp = ((0.083333333333333 + (z * ((0.0007936500793651 * z) - 0.0027777777777778))) / x) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.4e+31:
		tmp = ((0.083333333333333 + (z * -0.0027777777777778)) / x) - x
	else:
		tmp = ((0.083333333333333 + (z * ((0.0007936500793651 * z) - 0.0027777777777778))) / x) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.4e+31)
		tmp = Float64(Float64(Float64(0.083333333333333 + Float64(z * -0.0027777777777778)) / x) - x);
	else
		tmp = Float64(Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(0.0007936500793651 * z) - 0.0027777777777778))) / x) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.4e+31)
		tmp = ((0.083333333333333 + (z * -0.0027777777777778)) / x) - x;
	else
		tmp = ((0.083333333333333 + (z * ((0.0007936500793651 * z) - 0.0027777777777778))) / x) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.4e+31], N[(N[(N[(0.083333333333333 + N[(z * -0.0027777777777778), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - x), $MachinePrecision], N[(N[(N[(0.083333333333333 + N[(z * N[(N[(0.0007936500793651 * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.40000000000000008e31

   1. Initial program 92.0%

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

      1. associate-+l- 92.0%

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

      2. add-sqr-sqrt 91.8%

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

      3. fma-neg 91.8%

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

      4. sub-neg 91.8%

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

      5. metadata-eval 91.8%

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

      6. *-commutative 91.8%

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

      7. sub-neg 91.8%

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

      8. metadata-eval 91.8%

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

      9. *-commutative 91.8%

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

      10. sub-neg 91.8%

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

      11. metadata-eval 91.8%

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

   4. Applied egg-rr 91.8%

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

   5. Taylor expanded in x around inf 57.3%

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

      1. neg-mul-1 57.3%

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

   7. Simplified 57.3%

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

   8. Taylor expanded in z around 0 33.8%

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

   if -1.40000000000000008e31 < y

   1. Initial program 96.5%

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

      1. associate-+l- 96.5%

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

      2. add-sqr-sqrt 95.9%

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

      3. fma-neg 96.0%

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

      4. sub-neg 96.0%

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

      5. metadata-eval 96.0%

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

      6. *-commutative 96.0%

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

      7. sub-neg 96.0%

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

      8. metadata-eval 96.0%

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

      9. *-commutative 96.0%

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

      10. sub-neg 96.0%

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

      11. metadata-eval 96.0%

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

   4. Applied egg-rr 96.0%

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

   5. Taylor expanded in x around inf 64.9%

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

      1. neg-mul-1 64.9%

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

   7. Simplified 64.9%

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

   8. Taylor expanded in y around 0 60.4%

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

      1. *-commutative 60.4%

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

   10. Simplified 60.4%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+31}:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot -0.0027777777777778}{x} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(0.0007936500793651 \cdot z - 0.0027777777777778\right)}{x} - x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 61.9% accurate, 8.2× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 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 = (((z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0)) + 0.083333333333333d0) / x) - x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.6%

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

   1. associate-+l- 95.7%

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

   2. add-sqr-sqrt 95.1%

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

   3. fma-neg 95.1%

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

   4. sub-neg 95.1%

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

   5. metadata-eval 95.1%

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

   6. *-commutative 95.1%

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

   7. sub-neg 95.1%

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

   8. metadata-eval 95.1%

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

   9. *-commutative 95.1%

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

   10. sub-neg 95.1%

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

   11. metadata-eval 95.1%

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

4. Applied egg-rr 95.1%

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

5. Taylor expanded in x around inf 63.4%

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

   1. neg-mul-1 63.4%

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

7. Simplified 63.4%

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

8. Final simplification 63.4%

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

Alternative 14: 28.3% accurate, 13.7× speedup

Math

\[\begin{array}{l} \\ \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x} - x \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return ((0.083333333333333 + (z * -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 * (-0.0027777777777778d0))) / x) - x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.6%

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

   1. associate-+l- 95.7%

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

   2. add-sqr-sqrt 95.1%

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

   3. fma-neg 95.1%

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

   4. sub-neg 95.1%

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

   5. metadata-eval 95.1%

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

   6. *-commutative 95.1%

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

   7. sub-neg 95.1%

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

   8. metadata-eval 95.1%

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

   9. *-commutative 95.1%

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

   10. sub-neg 95.1%

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

   11. metadata-eval 95.1%

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

4. Applied egg-rr 95.1%

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

5. Taylor expanded in x around inf 63.4%

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

   1. neg-mul-1 63.4%

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

7. Simplified 63.4%

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

8. Taylor expanded in z around 0 31.5%

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

9. Final simplification 31.5%

   \[\leadsto \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x} - x \]
10. Add Preprocessing

Alternative 15: 23.6% accurate, 41.0× speedup

Math

\[\begin{array}{l} \\ \frac{0.083333333333333}{x} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ 0.083333333333333 x))

C

double code(double x, double y, double z) {
	return 0.083333333333333 / x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 0.083333333333333d0 / x
end function

Java

public static double code(double x, double y, double z) {
	return 0.083333333333333 / x;
}

Python

def code(x, y, z):
	return 0.083333333333333 / x

Julia

function code(x, y, z)
	return Float64(0.083333333333333 / x)
end

MATLAB

function tmp = code(x, y, z)
	tmp = 0.083333333333333 / x;
end

Wolfram

code[x_, y_, z_] := N[(0.083333333333333 / x), $MachinePrecision]

Derivation

1. Initial program 95.6%

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

3. Taylor expanded in z around 0 60.6%

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

4. Taylor expanded in x around 0 26.0%

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

5. Taylor expanded in x around 0 26.6%

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

6. Final simplification 26.6%

   \[\leadsto \frac{0.083333333333333}{x} \]
7. Add Preprocessing

Developer target: 98.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024019 
(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)))