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

Percentage Accurate: 93.8% → 99.5%

Time: 17.1s

Alternatives: 12

Speedup: 1.1×

• 32.0% 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: 93.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 8.5 \cdot 10^{+55}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(z \cdot \frac{z}{x}\right) \cdot \left(y + 0.0007936500793651\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 8.5e+55)
   (+
    (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
    (/
     (+
      (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778))
      0.083333333333333)
     x))
   (+ (* x (+ (log x) -1.0)) (* (* z (/ z x)) (+ y 0.0007936500793651)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 8.5e+55) {
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x);
	} else {
		tmp = (x * (log(x) + -1.0)) + ((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) :: tmp
    if (x <= 8.5d+55) then
        tmp = ((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + (((z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0)) + 0.083333333333333d0) / x)
    else
        tmp = (x * (log(x) + (-1.0d0))) + ((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 <= 8.5e+55) {
		tmp = ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x);
	} else {
		tmp = (x * (Math.log(x) + -1.0)) + ((z * (z / x)) * (y + 0.0007936500793651));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 8.5e+55:
		tmp = ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x)
	else:
		tmp = (x * (math.log(x) + -1.0)) + ((z * (z / x)) * (y + 0.0007936500793651))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 8.5e+55)
		tmp = Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(Float64(Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x));
	else
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + 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 <= 8.5e+55)
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x);
	else
		tmp = (x * (log(x) + -1.0)) + ((z * (z / x)) * (y + 0.0007936500793651));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 8.5e+55], N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $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[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $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 < 8.50000000000000002e55

   1. Initial program 99.7%

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

   if 8.50000000000000002e55 < x

   1. Initial program 83.6%

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

   2. Taylor expanded in x around inf 83.7%

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

      1. sub-neg 83.7%

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

      2. mul-1-neg 83.7%

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

      3. log-rec 83.7%

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

      4. remove-double-neg 83.7%

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

      5. metadata-eval 83.7%

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

   4. Simplified 83.7%

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

   5. Taylor expanded in z around inf 83.7%

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

      1. associate-/l* 90.1%

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

      2. +-commutative 90.1%

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

      3. associate-/r/ 90.0%

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

      4. +-commutative 90.0%

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

   7. Simplified 90.0%

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

      1. unpow2 90.0%

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

      2. *-un-lft-identity 90.0%

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

      3. times-frac 99.7%

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

   9. Applied egg-rr 99.7%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 8.5 \cdot 10^{+55}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(z \cdot \frac{z}{x}\right) \cdot \left(y + 0.0007936500793651\right)\\ \end{array} \]

Alternative 2: 98.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.00385:\\ \;\;\;\;\frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x} + \left(0.91893853320467 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z}{\frac{x}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 0.00385)
   (+
    (/
     (+
      (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778))
      0.083333333333333)
     x)
    (- 0.91893853320467 x))
   (+ (* x (+ (log x) -1.0)) (* (+ y 0.0007936500793651) (/ z (/ x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 0.00385) {
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + (0.91893853320467 - x);
	} else {
		tmp = (x * (log(x) + -1.0)) + ((y + 0.0007936500793651) * (z / (x / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 0.00385d0) then
        tmp = (((z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0)) + 0.083333333333333d0) / x) + (0.91893853320467d0 - x)
    else
        tmp = (x * (log(x) + (-1.0d0))) + ((y + 0.0007936500793651d0) * (z / (x / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 0.00385) {
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + (0.91893853320467 - x);
	} else {
		tmp = (x * (Math.log(x) + -1.0)) + ((y + 0.0007936500793651) * (z / (x / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 0.00385:
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + (0.91893853320467 - x)
	else:
		tmp = (x * (math.log(x) + -1.0)) + ((y + 0.0007936500793651) * (z / (x / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 0.00385)
		tmp = Float64(Float64(Float64(Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + Float64(0.91893853320467 - x));
	else
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(Float64(y + 0.0007936500793651) * Float64(z / Float64(x / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 0.00385)
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + (0.91893853320467 - x);
	else
		tmp = (x * (log(x) + -1.0)) + ((y + 0.0007936500793651) * (z / (x / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 0.00385], 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 - x), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 0.0038500000000000001

   1. Initial program 99.7%

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

      1. add-cube-cbrt 99.7%

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

      2. pow3 99.7%

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

      3. sub-neg 99.7%

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

      4. metadata-eval 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in x around inf 98.7%

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

      1. neg-mul-1 98.7%

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

      2. unsub-neg 98.7%

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

   6. Simplified 98.7%

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

   if 0.0038500000000000001 < x

   1. Initial program 86.2%

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

   2. Taylor expanded in x around inf 85.1%

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

      1. sub-neg 85.1%

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

      2. mul-1-neg 85.1%

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

      3. log-rec 85.1%

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

      4. remove-double-neg 85.1%

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

      5. metadata-eval 85.1%

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

   4. Simplified 85.1%

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

   5. Taylor expanded in z around inf 85.1%

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

      1. associate-/l* 90.5%

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

      2. +-commutative 90.5%

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

      3. associate-/r/ 90.5%

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

      4. +-commutative 90.5%

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

   7. Simplified 90.5%

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

      1. unpow2 90.5%

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

      2. add-sqr-sqrt 90.4%

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

      3. times-frac 98.5%

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

   9. Applied egg-rr 98.5%

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

       1. unpow2 98.5%

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

   11. Simplified 98.5%

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

       1. unpow2 98.5%

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

       2. frac-times 90.4%

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

       3. add-sqr-sqrt 90.5%

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

       4. associate-/l* 98.5%

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

   13. Applied egg-rr 98.5%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.00385:\\ \;\;\;\;\frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x} + \left(0.91893853320467 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z}{\frac{x}{z}}\\ \end{array} \]

Alternative 3: 98.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.00385:\\ \;\;\;\;\frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x} + \left(0.91893853320467 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(z \cdot \frac{z}{x}\right) \cdot \left(y + 0.0007936500793651\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 0.00385)
   (+
    (/
     (+
      (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778))
      0.083333333333333)
     x)
    (- 0.91893853320467 x))
   (+ (* x (+ (log x) -1.0)) (* (* z (/ z x)) (+ y 0.0007936500793651)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 0.00385) {
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + (0.91893853320467 - x);
	} else {
		tmp = (x * (log(x) + -1.0)) + ((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) :: tmp
    if (x <= 0.00385d0) then
        tmp = (((z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0)) + 0.083333333333333d0) / x) + (0.91893853320467d0 - x)
    else
        tmp = (x * (log(x) + (-1.0d0))) + ((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 <= 0.00385) {
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + (0.91893853320467 - x);
	} else {
		tmp = (x * (Math.log(x) + -1.0)) + ((z * (z / x)) * (y + 0.0007936500793651));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 0.00385:
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + (0.91893853320467 - x)
	else:
		tmp = (x * (math.log(x) + -1.0)) + ((z * (z / x)) * (y + 0.0007936500793651))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 0.00385)
		tmp = Float64(Float64(Float64(Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + Float64(0.91893853320467 - x));
	else
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + 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 <= 0.00385)
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + (0.91893853320467 - x);
	else
		tmp = (x * (log(x) + -1.0)) + ((z * (z / x)) * (y + 0.0007936500793651));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 0.00385], 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 - x), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $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 < 0.0038500000000000001

   1. Initial program 99.7%

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

      1. add-cube-cbrt 99.7%

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

      2. pow3 99.7%

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

      3. sub-neg 99.7%

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

      4. metadata-eval 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in x around inf 98.7%

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

      1. neg-mul-1 98.7%

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

      2. unsub-neg 98.7%

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

   6. Simplified 98.7%

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

   if 0.0038500000000000001 < x

   1. Initial program 86.2%

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

   2. Taylor expanded in x around inf 85.1%

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

      1. sub-neg 85.1%

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

      2. mul-1-neg 85.1%

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

      3. log-rec 85.1%

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

      4. remove-double-neg 85.1%

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

      5. metadata-eval 85.1%

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

   4. Simplified 85.1%

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

   5. Taylor expanded in z around inf 85.1%

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

      1. associate-/l* 90.5%

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

      2. +-commutative 90.5%

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

      3. associate-/r/ 90.5%

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

      4. +-commutative 90.5%

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

   7. Simplified 90.5%

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

      1. unpow2 90.5%

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

      2. *-un-lft-identity 90.5%

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

      3. times-frac 98.5%

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

   9. Applied egg-rr 98.5%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.00385:\\ \;\;\;\;\frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x} + \left(0.91893853320467 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(z \cdot \frac{z}{x}\right) \cdot \left(y + 0.0007936500793651\right)\\ \end{array} \]

Alternative 4: 82.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.26 \cdot 10^{+98}:\\ \;\;\;\;\frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x} + \left(0.91893853320467 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.26e+98)
   (+
    (/
     (+
      (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778))
      0.083333333333333)
     x)
    (- 0.91893853320467 x))
   (* x (+ (log x) -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.26e+98) {
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + (0.91893853320467 - x);
	} else {
		tmp = x * (log(x) + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 1.26d+98) then
        tmp = (((z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0)) + 0.083333333333333d0) / x) + (0.91893853320467d0 - x)
    else
        tmp = x * (log(x) + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.26e+98) {
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + (0.91893853320467 - x);
	} else {
		tmp = x * (Math.log(x) + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1.26e+98:
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + (0.91893853320467 - x)
	else:
		tmp = x * (math.log(x) + -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.26e+98)
		tmp = Float64(Float64(Float64(Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + Float64(0.91893853320467 - x));
	else
		tmp = Float64(x * Float64(log(x) + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1.26e+98)
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + (0.91893853320467 - x);
	else
		tmp = x * (log(x) + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.26e+98], 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 - x), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.25999999999999999e98

   1. Initial program 98.1%

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

      1. add-cube-cbrt 97.9%

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

      2. pow3 97.9%

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

      3. sub-neg 97.9%

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

      4. metadata-eval 97.9%

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

   3. Applied egg-rr 97.9%

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

   4. Taylor expanded in x around inf 86.3%

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

      1. neg-mul-1 86.3%

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

      2. unsub-neg 86.3%

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

   6. Simplified 86.3%

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

   if 1.25999999999999999e98 < x

   1. Initial program 82.1%

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

   2. Taylor expanded in x around inf 82.2%

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

      1. sub-neg 82.2%

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

      2. mul-1-neg 82.2%

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

      3. log-rec 82.2%

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

      4. remove-double-neg 82.2%

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

      5. metadata-eval 82.2%

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

   4. Simplified 82.2%

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

   5. Taylor expanded in z around inf 82.2%

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

      1. associate-/l* 89.3%

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

      2. +-commutative 89.3%

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

      3. associate-/r/ 89.3%

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

      4. +-commutative 89.3%

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

   7. Simplified 89.3%

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

   8. Taylor expanded in z around 0 78.8%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.26 \cdot 10^{+98}:\\ \;\;\;\;\frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x} + \left(0.91893853320467 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right)\\ \end{array} \]

Alternative 5: 54.4% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -16000000000000 \lor \neg \left(y \leq 4.3 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{y}{\frac{x}{z \cdot z}} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(0.0007936500793651 \cdot z - 0.0027777777777778\right)}{x} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -16000000000000.0) (not (<= y 4.3e+19)))
   (- (/ y (/ x (* z z))) x)
   (-
    (/
     (+
      0.083333333333333
      (* z (- (* 0.0007936500793651 z) 0.0027777777777778)))
     x)
    x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -16000000000000.0) || !(y <= 4.3e+19)) {
		tmp = (y / (x / (z * z))) - 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 <= (-16000000000000.0d0)) .or. (.not. (y <= 4.3d+19))) then
        tmp = (y / (x / (z * z))) - 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 <= -16000000000000.0) || !(y <= 4.3e+19)) {
		tmp = (y / (x / (z * z))) - 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 <= -16000000000000.0) or not (y <= 4.3e+19):
		tmp = (y / (x / (z * z))) - 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 <= -16000000000000.0) || !(y <= 4.3e+19))
		tmp = Float64(Float64(y / Float64(x / Float64(z * z))) - 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 <= -16000000000000.0) || ~((y <= 4.3e+19)))
		tmp = (y / (x / (z * z))) - 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, -16000000000000.0], N[Not[LessEqual[y, 4.3e+19]], $MachinePrecision]], N[(N[(y / N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]), $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 < -1.6e13 or 4.3e19 < y

   1. Initial program 94.0%

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

      1. add-cube-cbrt 93.6%

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

      2. pow3 93.6%

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

      3. sub-neg 93.6%

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

      4. metadata-eval 93.6%

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

   3. Applied egg-rr 93.6%

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

   4. Taylor expanded in x around inf 64.0%

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

      1. neg-mul-1 64.0%

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

   6. Simplified 64.0%

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

   7. Taylor expanded in y around inf 48.4%

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

      1. associate-/l* 50.2%

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

   9. Simplified 50.2%

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

       1. unpow2 50.2%

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

   11. Applied egg-rr 50.2%

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

   if -1.6e13 < y < 4.3e19

   1. Initial program 92.3%

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

      1. add-cube-cbrt 91.9%

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

      2. pow3 91.9%

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

      3. sub-neg 91.9%

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

      4. metadata-eval 91.9%

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

   3. Applied egg-rr 91.9%

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

   4. Taylor expanded in x around inf 64.2%

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

      1. neg-mul-1 64.2%

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

   6. Simplified 64.2%

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

   7. Taylor expanded in y around 0 64.2%

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

      1. *-commutative 64.2%

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

   9. Simplified 64.2%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -16000000000000 \lor \neg \left(y \leq 4.3 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{y}{\frac{x}{z \cdot z}} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(0.0007936500793651 \cdot z - 0.0027777777777778\right)}{x} - x\\ \end{array} \]

Alternative 6: 61.9% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -30000000000 \lor \neg \left(y \leq 4.5 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(y \cdot z - 0.0027777777777778\right)}{x} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(0.0007936500793651 \cdot z - 0.0027777777777778\right)}{x} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -30000000000.0) (not (<= y 4.5e-29)))
   (- (/ (+ 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 <= -30000000000.0) || !(y <= 4.5e-29)) {
		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 <= (-30000000000.0d0)) .or. (.not. (y <= 4.5d-29))) 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 <= -30000000000.0) || !(y <= 4.5e-29)) {
		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 <= -30000000000.0) or not (y <= 4.5e-29):
		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 <= -30000000000.0) || !(y <= 4.5e-29))
		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 <= -30000000000.0) || ~((y <= 4.5e-29)))
		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, -30000000000.0], N[Not[LessEqual[y, 4.5e-29]], $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 < -3e10 or 4.4999999999999998e-29 < y

   1. Initial program 92.8%

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

      1. add-cube-cbrt 92.4%

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

      2. pow3 92.4%

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

      3. sub-neg 92.4%

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

      4. metadata-eval 92.4%

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

   3. Applied egg-rr 92.4%

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

   4. Taylor expanded in x around inf 63.5%

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

      1. neg-mul-1 63.5%

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

   6. Simplified 63.5%

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

   7. Taylor expanded in y around inf 63.5%

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

      1. *-commutative 63.5%

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

   9. Simplified 63.5%

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

   if -3e10 < y < 4.4999999999999998e-29

   1. Initial program 93.4%

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

      1. add-cube-cbrt 92.9%

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

      2. pow3 92.9%

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

      3. sub-neg 92.9%

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

      4. metadata-eval 92.9%

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

   3. Applied egg-rr 92.9%

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

   4. Taylor expanded in x around inf 64.7%

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

      1. neg-mul-1 64.7%

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

   6. Simplified 64.7%

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

   7. Taylor expanded in y around 0 64.7%

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

      1. *-commutative 64.7%

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

   9. Simplified 64.7%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -30000000000 \lor \neg \left(y \leq 4.5 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(y \cdot z - 0.0027777777777778\right)}{x} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(0.0007936500793651 \cdot z - 0.0027777777777778\right)}{x} - x\\ \end{array} \]

Alternative 7: 62.5% accurate, 7.2× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + (0.91893853320467 - 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) + (0.91893853320467d0 - 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) + (0.91893853320467 - x);
}

Python

def code(x, y, z):
	return (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + (0.91893853320467 - 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) + Float64(0.91893853320467 - x))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + (0.91893853320467 - 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] + N[(0.91893853320467 - x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 93.1%

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

   1. add-cube-cbrt 92.7%

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

   2. pow3 92.7%

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

   3. sub-neg 92.7%

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

   4. metadata-eval 92.7%

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

3. Applied egg-rr 92.7%

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

4. Taylor expanded in x around inf 64.1%

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

   1. neg-mul-1 64.1%

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

   2. unsub-neg 64.1%

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

6. Simplified 64.1%

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

7. Final simplification 64.1%

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

Alternative 8: 62.5% 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 93.1%

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

   1. add-cube-cbrt 92.7%

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

   2. pow3 92.7%

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

   3. sub-neg 92.7%

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

   4. metadata-eval 92.7%

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

3. Applied egg-rr 92.7%

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

4. Taylor expanded in x around inf 64.1%

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

   1. neg-mul-1 64.1%

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

6. Simplified 64.1%

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

7. Final simplification 64.1%

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

Alternative 9: 46.2% accurate, 9.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-77} \lor \neg \left(z \leq 2 \cdot 10^{-13}\right):\\ \;\;\;\;z \cdot \left(z \cdot \frac{y}{x}\right) - x\\ \mathbf{else}:\\ \;\;\;\;0.91893853320467 + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.2e-77) (not (<= z 2e-13)))
   (- (* z (* z (/ y x))) x)
   (+ 0.91893853320467 (/ 0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.2e-77) || !(z <= 2e-13)) {
		tmp = (z * (z * (y / x))) - x;
	} else {
		tmp = 0.91893853320467 + (0.083333333333333 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-4.2d-77)) .or. (.not. (z <= 2d-13))) then
        tmp = (z * (z * (y / x))) - x
    else
        tmp = 0.91893853320467d0 + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.2e-77) || !(z <= 2e-13)) {
		tmp = (z * (z * (y / x))) - x;
	} else {
		tmp = 0.91893853320467 + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.2e-77) or not (z <= 2e-13):
		tmp = (z * (z * (y / x))) - x
	else:
		tmp = 0.91893853320467 + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.2e-77) || !(z <= 2e-13))
		tmp = Float64(Float64(z * Float64(z * Float64(y / x))) - x);
	else
		tmp = Float64(0.91893853320467 + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.2e-77) || ~((z <= 2e-13)))
		tmp = (z * (z * (y / x))) - x;
	else
		tmp = 0.91893853320467 + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.2e-77], N[Not[LessEqual[z, 2e-13]], $MachinePrecision]], N[(N[(z * N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(0.91893853320467 + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.20000000000000031e-77 or 2.0000000000000001e-13 < z

   1. Initial program 88.5%

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

      1. add-cube-cbrt 88.1%

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

      2. pow3 88.2%

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

      3. sub-neg 88.2%

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

      4. metadata-eval 88.2%

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

   3. Applied egg-rr 88.2%

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

   4. Taylor expanded in x around inf 71.9%

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

      1. neg-mul-1 71.9%

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

   6. Simplified 71.9%

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

   7. Taylor expanded in y around inf 45.7%

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

      1. associate-/l* 49.6%

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

   9. Simplified 49.6%

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

       1. associate-/r/ 43.8%

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

       2. unpow2 43.8%

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

       3. associate-*r* 43.0%

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

   11. Applied egg-rr 43.0%

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

   if -4.20000000000000031e-77 < z < 2.0000000000000001e-13

   1. Initial program 99.5%

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

   2. Taylor expanded in z around 0 96.6%

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

   3. Taylor expanded in x around inf 93.2%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(x \cdot \log \left(\frac{1}{x}\right)\right)} - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]
   4. Step-by-step derivation

      1. mul-1-neg 93.2%

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

      2. distribute-rgt-neg-in 93.2%

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

      3. log-rec 94.1%

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

      4. remove-double-neg 94.1%

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

   5. Simplified 94.1%

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

   6. Taylor expanded in x around 0 51.8%

      \[\leadsto \color{blue}{0.91893853320467 + 0.083333333333333 \cdot \frac{1}{x}} \]
   7. Step-by-step derivation

      1. associate-*r/ 52.7%

         \[\leadsto 0.91893853320467 + \color{blue}{\frac{0.083333333333333 \cdot 1}{x}} \]

      2. metadata-eval 52.7%

         \[\leadsto 0.91893853320467 + \frac{\color{blue}{0.083333333333333}}{x} \]

      3. +-commutative 52.7%

         \[\leadsto \color{blue}{\frac{0.083333333333333}{x} + 0.91893853320467} \]

   8. Simplified 52.7%

      \[\leadsto \color{blue}{\frac{0.083333333333333}{x} + 0.91893853320467} \]
3. Recombined 2 regimes into one program.

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-77} \lor \neg \left(z \leq 2 \cdot 10^{-13}\right):\\ \;\;\;\;z \cdot \left(z \cdot \frac{y}{x}\right) - x\\ \mathbf{else}:\\ \;\;\;\;0.91893853320467 + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 10: 49.1% accurate, 9.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-77} \lor \neg \left(z \leq 1.5 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{y}{\frac{x}{z \cdot z}} - x\\ \mathbf{else}:\\ \;\;\;\;0.91893853320467 + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.8e-77) (not (<= z 1.5e-13)))
   (- (/ y (/ x (* z z))) x)
   (+ 0.91893853320467 (/ 0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.8e-77) || !(z <= 1.5e-13)) {
		tmp = (y / (x / (z * z))) - x;
	} else {
		tmp = 0.91893853320467 + (0.083333333333333 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-3.8d-77)) .or. (.not. (z <= 1.5d-13))) then
        tmp = (y / (x / (z * z))) - x
    else
        tmp = 0.91893853320467d0 + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.8e-77) || !(z <= 1.5e-13)) {
		tmp = (y / (x / (z * z))) - x;
	} else {
		tmp = 0.91893853320467 + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.8e-77) or not (z <= 1.5e-13):
		tmp = (y / (x / (z * z))) - x
	else:
		tmp = 0.91893853320467 + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.8e-77) || !(z <= 1.5e-13))
		tmp = Float64(Float64(y / Float64(x / Float64(z * z))) - x);
	else
		tmp = Float64(0.91893853320467 + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.8e-77) || ~((z <= 1.5e-13)))
		tmp = (y / (x / (z * z))) - x;
	else
		tmp = 0.91893853320467 + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.8e-77], N[Not[LessEqual[z, 1.5e-13]], $MachinePrecision]], N[(N[(y / N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(0.91893853320467 + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7999999999999999e-77 or 1.49999999999999992e-13 < z

   1. Initial program 88.5%

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

      1. add-cube-cbrt 88.1%

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

      2. pow3 88.2%

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

      3. sub-neg 88.2%

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

      4. metadata-eval 88.2%

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

   3. Applied egg-rr 88.2%

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

   4. Taylor expanded in x around inf 71.9%

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

      1. neg-mul-1 71.9%

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

   6. Simplified 71.9%

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

   7. Taylor expanded in y around inf 45.7%

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

      1. associate-/l* 49.6%

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

   9. Simplified 49.6%

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

       1. unpow2 49.6%

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

   11. Applied egg-rr 49.6%

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

   if -3.7999999999999999e-77 < z < 1.49999999999999992e-13

   1. Initial program 99.5%

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

   2. Taylor expanded in z around 0 96.6%

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

   3. Taylor expanded in x around inf 93.2%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(x \cdot \log \left(\frac{1}{x}\right)\right)} - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]
   4. Step-by-step derivation

      1. mul-1-neg 93.2%

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

      2. distribute-rgt-neg-in 93.2%

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

      3. log-rec 94.1%

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

      4. remove-double-neg 94.1%

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

   5. Simplified 94.1%

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

   6. Taylor expanded in x around 0 51.8%

      \[\leadsto \color{blue}{0.91893853320467 + 0.083333333333333 \cdot \frac{1}{x}} \]
   7. Step-by-step derivation

      1. associate-*r/ 52.7%

         \[\leadsto 0.91893853320467 + \color{blue}{\frac{0.083333333333333 \cdot 1}{x}} \]

      2. metadata-eval 52.7%

         \[\leadsto 0.91893853320467 + \frac{\color{blue}{0.083333333333333}}{x} \]

      3. +-commutative 52.7%

         \[\leadsto \color{blue}{\frac{0.083333333333333}{x} + 0.91893853320467} \]

   8. Simplified 52.7%

      \[\leadsto \color{blue}{\frac{0.083333333333333}{x} + 0.91893853320467} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-77} \lor \neg \left(z \leq 1.5 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{y}{\frac{x}{z \cdot z}} - x\\ \mathbf{else}:\\ \;\;\;\;0.91893853320467 + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 11: 23.6% accurate, 24.6× speedup

Math

\[\begin{array}{l} \\ 0.91893853320467 + \frac{0.083333333333333}{x} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 0.91893853320467 (/ 0.083333333333333 x)))

C

double code(double x, double y, double z) {
	return 0.91893853320467 + (0.083333333333333 / x);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 0.91893853320467d0 + (0.083333333333333d0 / x)
end function

Java

public static double code(double x, double y, double z) {
	return 0.91893853320467 + (0.083333333333333 / x);
}

Python

def code(x, y, z):
	return 0.91893853320467 + (0.083333333333333 / x)

Julia

function code(x, y, z)
	return Float64(0.91893853320467 + Float64(0.083333333333333 / x))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 0.91893853320467 + (0.083333333333333 / x);
end

Wolfram

code[x_, y_, z_] := N[(0.91893853320467 + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 93.1%

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

2. Taylor expanded in z around 0 56.2%

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

3. Taylor expanded in x around inf 54.8%

   \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(x \cdot \log \left(\frac{1}{x}\right)\right)} - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]
4. Step-by-step derivation

   1. mul-1-neg 54.8%

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

   2. distribute-rgt-neg-in 54.8%

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

   3. log-rec 55.2%

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

   4. remove-double-neg 55.2%

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

5. Simplified 55.2%

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

6. Taylor expanded in x around 0 25.3%

   \[\leadsto \color{blue}{0.91893853320467 + 0.083333333333333 \cdot \frac{1}{x}} \]
7. Step-by-step derivation

   1. associate-*r/ 25.6%

      \[\leadsto 0.91893853320467 + \color{blue}{\frac{0.083333333333333 \cdot 1}{x}} \]

   2. metadata-eval 25.6%

      \[\leadsto 0.91893853320467 + \frac{\color{blue}{0.083333333333333}}{x} \]

   3. +-commutative 25.6%

      \[\leadsto \color{blue}{\frac{0.083333333333333}{x} + 0.91893853320467} \]

8. Simplified 25.6%

   \[\leadsto \color{blue}{\frac{0.083333333333333}{x} + 0.91893853320467} \]

9. Final simplification 25.6%

   \[\leadsto 0.91893853320467 + \frac{0.083333333333333}{x} \]

Alternative 12: 22.9% accurate, 41.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.1%

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

2. Taylor expanded in z around 0 56.2%

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

3. Taylor expanded in x around inf 54.8%

   \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(x \cdot \log \left(\frac{1}{x}\right)\right)} - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]
4. Step-by-step derivation

   1. mul-1-neg 54.8%

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

   2. distribute-rgt-neg-in 54.8%

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

   3. log-rec 55.2%

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

   4. remove-double-neg 55.2%

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

5. Simplified 55.2%

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

6. Taylor expanded in x around 0 25.0%

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

7. Final simplification 25.0%

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

Developer target: 98.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023336 
(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)))