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

Percentage Accurate: 94.2% → 99.4%

Time: 14.9s

Alternatives: 20

Speedup: 1.0×

• 27.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 94.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 8 \cdot 10^{+65}:\\ \;\;\;\;\left(\left(x + -0.5\right) \cdot \log x - \left(x + -0.91893853320467\right)\right) + \frac{z \cdot \left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) + 0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(0.083333333333333 \cdot \frac{1}{x} + z \cdot \left(z \cdot \left(\frac{y}{x} + \frac{0.0007936500793651}{x}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 8e+65)
   (+
    (- (* (+ x -0.5) (log x)) (+ x -0.91893853320467))
    (/
     (+
      (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778))
      0.083333333333333)
     x))
   (+
    (* x (+ (log x) -1.0))
    (+
     (* 0.083333333333333 (/ 1.0 x))
     (* z (* z (+ (/ y x) (/ 0.0007936500793651 x))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 8e+65) {
		tmp = (((x + -0.5) * log(x)) - (x + -0.91893853320467)) + (((z * (((y + 0.0007936500793651) * z) - 0.0027777777777778)) + 0.083333333333333) / x);
	} else {
		tmp = (x * (log(x) + -1.0)) + ((0.083333333333333 * (1.0 / x)) + (z * (z * ((y / x) + (0.0007936500793651 / x)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 8d+65) then
        tmp = (((x + (-0.5d0)) * log(x)) - (x + (-0.91893853320467d0))) + (((z * (((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0)) + 0.083333333333333d0) / x)
    else
        tmp = (x * (log(x) + (-1.0d0))) + ((0.083333333333333d0 * (1.0d0 / x)) + (z * (z * ((y / x) + (0.0007936500793651d0 / x)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 8e+65) {
		tmp = (((x + -0.5) * Math.log(x)) - (x + -0.91893853320467)) + (((z * (((y + 0.0007936500793651) * z) - 0.0027777777777778)) + 0.083333333333333) / x);
	} else {
		tmp = (x * (Math.log(x) + -1.0)) + ((0.083333333333333 * (1.0 / x)) + (z * (z * ((y / x) + (0.0007936500793651 / x)))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 8e+65:
		tmp = (((x + -0.5) * math.log(x)) - (x + -0.91893853320467)) + (((z * (((y + 0.0007936500793651) * z) - 0.0027777777777778)) + 0.083333333333333) / x)
	else:
		tmp = (x * (math.log(x) + -1.0)) + ((0.083333333333333 * (1.0 / x)) + (z * (z * ((y / x) + (0.0007936500793651 / x)))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 8e+65)
		tmp = Float64(Float64(Float64(Float64(x + -0.5) * log(x)) - Float64(x + -0.91893853320467)) + Float64(Float64(Float64(z * Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778)) + 0.083333333333333) / x));
	else
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(Float64(0.083333333333333 * Float64(1.0 / x)) + Float64(z * Float64(z * Float64(Float64(y / x) + Float64(0.0007936500793651 / x))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 8e+65)
		tmp = (((x + -0.5) * log(x)) - (x + -0.91893853320467)) + (((z * (((y + 0.0007936500793651) * z) - 0.0027777777777778)) + 0.083333333333333) / x);
	else
		tmp = (x * (log(x) + -1.0)) + ((0.083333333333333 * (1.0 / x)) + (z * (z * ((y / x) + (0.0007936500793651 / x)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 8e+65], N[(N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - N[(x + -0.91893853320467), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(z * N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $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[(0.083333333333333 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision] + N[(z * N[(z * N[(N[(y / x), $MachinePrecision] + N[(0.0007936500793651 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 7.9999999999999999e65

   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. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. metadata-eval 99.8%

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

      4. sub-neg 99.8%

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

      5. metadata-eval 99.8%

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

   3. Applied egg-rr 99.8%

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

   if 7.9999999999999999e65 < 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 z around 0 89.0%

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

   3. Taylor expanded in z around inf 89.0%

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

      1. *-commutative 89.0%

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

      2. unpow2 89.0%

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

      3. associate-*r/ 89.0%

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

      4. metadata-eval 89.0%

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

      5. associate-*l* 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in x around inf 99.7%

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

      1. *-commutative 99.7%

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

      2. sub-neg 99.7%

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

      3. mul-1-neg 99.7%

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

      4. log-rec 99.7%

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

      5. remove-double-neg 99.7%

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

      6. metadata-eval 99.7%

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

   8. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \left(\log x + -1\right)} + \left(0.083333333333333 \cdot \frac{1}{x} + z \cdot \left(z \cdot \left(\frac{y}{x} + \frac{0.0007936500793651}{x}\right)\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 8 \cdot 10^{+65}:\\ \;\;\;\;\left(\left(x + -0.5\right) \cdot \log x - \left(x + -0.91893853320467\right)\right) + \frac{z \cdot \left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) + 0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(0.083333333333333 \cdot \frac{1}{x} + z \cdot \left(z \cdot \left(\frac{y}{x} + \frac{0.0007936500793651}{x}\right)\right)\right)\\ \end{array} \]

Alternative 2: 98.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.8 \cdot 10^{+65}:\\ \;\;\;\;\frac{z \cdot \left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) + 0.083333333333333}{x} + \left(x \cdot \log x - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(0.083333333333333 \cdot \frac{1}{x} + z \cdot \left(z \cdot \left(\frac{y}{x} + \frac{0.0007936500793651}{x}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.8e+65)
   (+
    (/
     (+
      (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778))
      0.083333333333333)
     x)
    (- (* x (log x)) x))
   (+
    (* x (+ (log x) -1.0))
    (+
     (* 0.083333333333333 (/ 1.0 x))
     (* z (* z (+ (/ y x) (/ 0.0007936500793651 x))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.8e+65) {
		tmp = (((z * (((y + 0.0007936500793651) * z) - 0.0027777777777778)) + 0.083333333333333) / x) + ((x * log(x)) - x);
	} else {
		tmp = (x * (log(x) + -1.0)) + ((0.083333333333333 * (1.0 / x)) + (z * (z * ((y / x) + (0.0007936500793651 / x)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 1.8d+65) then
        tmp = (((z * (((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0)) + 0.083333333333333d0) / x) + ((x * log(x)) - x)
    else
        tmp = (x * (log(x) + (-1.0d0))) + ((0.083333333333333d0 * (1.0d0 / x)) + (z * (z * ((y / x) + (0.0007936500793651d0 / x)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.8e+65) {
		tmp = (((z * (((y + 0.0007936500793651) * z) - 0.0027777777777778)) + 0.083333333333333) / x) + ((x * Math.log(x)) - x);
	} else {
		tmp = (x * (Math.log(x) + -1.0)) + ((0.083333333333333 * (1.0 / x)) + (z * (z * ((y / x) + (0.0007936500793651 / x)))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1.8e+65:
		tmp = (((z * (((y + 0.0007936500793651) * z) - 0.0027777777777778)) + 0.083333333333333) / x) + ((x * math.log(x)) - x)
	else:
		tmp = (x * (math.log(x) + -1.0)) + ((0.083333333333333 * (1.0 / x)) + (z * (z * ((y / x) + (0.0007936500793651 / x)))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.8e+65)
		tmp = Float64(Float64(Float64(Float64(z * Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778)) + 0.083333333333333) / x) + Float64(Float64(x * log(x)) - x));
	else
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(Float64(0.083333333333333 * Float64(1.0 / x)) + Float64(z * Float64(z * Float64(Float64(y / x) + Float64(0.0007936500793651 / x))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1.8e+65)
		tmp = (((z * (((y + 0.0007936500793651) * z) - 0.0027777777777778)) + 0.083333333333333) / x) + ((x * log(x)) - x);
	else
		tmp = (x * (log(x) + -1.0)) + ((0.083333333333333 * (1.0 / x)) + (z * (z * ((y / x) + (0.0007936500793651 / x)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.8e+65], N[(N[(N[(N[(z * N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision] + N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(0.083333333333333 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision] + N[(z * N[(z * N[(N[(y / x), $MachinePrecision] + N[(0.0007936500793651 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.79999999999999989e65

   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. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. metadata-eval 99.8%

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

      4. sub-neg 99.8%

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

      5. metadata-eval 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in x around inf 98.1%

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

      1. *-commutative 50.1%

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

      2. sub-neg 50.1%

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

      3. mul-1-neg 50.1%

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

      4. log-rec 50.1%

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

      5. remove-double-neg 50.1%

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

      6. metadata-eval 50.1%

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

      7. distribute-rgt-in 50.1%

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

      8. remove-double-neg 50.1%

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

      9. log-rec 50.1%

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

      10. distribute-lft-neg-in 50.1%

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

      11. mul-1-neg 50.1%

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

      12. neg-mul-1 50.1%

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

      13. unsub-neg 50.1%

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

      14. mul-1-neg 50.1%

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

      15. distribute-lft-neg-in 50.1%

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

      16. log-rec 50.1%

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

      17. remove-double-neg 50.1%

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

      18. *-commutative 50.1%

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

   6. Simplified 98.1%

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

   if 1.79999999999999989e65 < 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 z around 0 89.0%

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

   3. Taylor expanded in z around inf 89.0%

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

      1. *-commutative 89.0%

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

      2. unpow2 89.0%

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

      3. associate-*r/ 89.0%

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

      4. metadata-eval 89.0%

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

      5. associate-*l* 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in x around inf 99.7%

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

      1. *-commutative 99.7%

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

      2. sub-neg 99.7%

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

      3. mul-1-neg 99.7%

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

      4. log-rec 99.7%

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

      5. remove-double-neg 99.7%

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

      6. metadata-eval 99.7%

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

   8. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \left(\log x + -1\right)} + \left(0.083333333333333 \cdot \frac{1}{x} + z \cdot \left(z \cdot \left(\frac{y}{x} + \frac{0.0007936500793651}{x}\right)\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.8 \cdot 10^{+65}:\\ \;\;\;\;\frac{z \cdot \left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) + 0.083333333333333}{x} + \left(x \cdot \log x - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(0.083333333333333 \cdot \frac{1}{x} + z \cdot \left(z \cdot \left(\frac{y}{x} + \frac{0.0007936500793651}{x}\right)\right)\right)\\ \end{array} \]

Alternative 3: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.5 \cdot 10^{+65}:\\ \;\;\;\;\frac{z \cdot \left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) + 0.083333333333333}{x} + \left(\left(\log x \cdot \left(x - 0.5\right) - x\right) + 0.91893853320467\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(0.083333333333333 \cdot \frac{1}{x} + z \cdot \left(z \cdot \left(\frac{y}{x} + \frac{0.0007936500793651}{x}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.5e+65)
   (+
    (/
     (+
      (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778))
      0.083333333333333)
     x)
    (+ (- (* (log x) (- x 0.5)) x) 0.91893853320467))
   (+
    (* x (+ (log x) -1.0))
    (+
     (* 0.083333333333333 (/ 1.0 x))
     (* z (* z (+ (/ y x) (/ 0.0007936500793651 x))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.5e+65) {
		tmp = (((z * (((y + 0.0007936500793651) * z) - 0.0027777777777778)) + 0.083333333333333) / x) + (((log(x) * (x - 0.5)) - x) + 0.91893853320467);
	} else {
		tmp = (x * (log(x) + -1.0)) + ((0.083333333333333 * (1.0 / x)) + (z * (z * ((y / x) + (0.0007936500793651 / x)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 1.5d+65) then
        tmp = (((z * (((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0)) + 0.083333333333333d0) / x) + (((log(x) * (x - 0.5d0)) - x) + 0.91893853320467d0)
    else
        tmp = (x * (log(x) + (-1.0d0))) + ((0.083333333333333d0 * (1.0d0 / x)) + (z * (z * ((y / x) + (0.0007936500793651d0 / x)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.5e+65) {
		tmp = (((z * (((y + 0.0007936500793651) * z) - 0.0027777777777778)) + 0.083333333333333) / x) + (((Math.log(x) * (x - 0.5)) - x) + 0.91893853320467);
	} else {
		tmp = (x * (Math.log(x) + -1.0)) + ((0.083333333333333 * (1.0 / x)) + (z * (z * ((y / x) + (0.0007936500793651 / x)))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1.5e+65:
		tmp = (((z * (((y + 0.0007936500793651) * z) - 0.0027777777777778)) + 0.083333333333333) / x) + (((math.log(x) * (x - 0.5)) - x) + 0.91893853320467)
	else:
		tmp = (x * (math.log(x) + -1.0)) + ((0.083333333333333 * (1.0 / x)) + (z * (z * ((y / x) + (0.0007936500793651 / x)))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.5e+65)
		tmp = Float64(Float64(Float64(Float64(z * Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778)) + 0.083333333333333) / x) + Float64(Float64(Float64(log(x) * Float64(x - 0.5)) - x) + 0.91893853320467));
	else
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(Float64(0.083333333333333 * Float64(1.0 / x)) + Float64(z * Float64(z * Float64(Float64(y / x) + Float64(0.0007936500793651 / x))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1.5e+65)
		tmp = (((z * (((y + 0.0007936500793651) * z) - 0.0027777777777778)) + 0.083333333333333) / x) + (((log(x) * (x - 0.5)) - x) + 0.91893853320467);
	else
		tmp = (x * (log(x) + -1.0)) + ((0.083333333333333 * (1.0 / x)) + (z * (z * ((y / x) + (0.0007936500793651 / x)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.5e+65], N[(N[(N[(N[(z * N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision] + N[(N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(0.083333333333333 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision] + N[(z * N[(z * N[(N[(y / x), $MachinePrecision] + N[(0.0007936500793651 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.5000000000000001e65

   1. Initial program 99.7%

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

   if 1.5000000000000001e65 < 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 z around 0 89.0%

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

   3. Taylor expanded in z around inf 89.0%

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

      1. *-commutative 89.0%

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

      2. unpow2 89.0%

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

      3. associate-*r/ 89.0%

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

      4. metadata-eval 89.0%

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

      5. associate-*l* 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in x around inf 99.7%

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

      1. *-commutative 99.7%

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

      2. sub-neg 99.7%

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

      3. mul-1-neg 99.7%

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

      4. log-rec 99.7%

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

      5. remove-double-neg 99.7%

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

      6. metadata-eval 99.7%

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

   8. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \left(\log x + -1\right)} + \left(0.083333333333333 \cdot \frac{1}{x} + z \cdot \left(z \cdot \left(\frac{y}{x} + \frac{0.0007936500793651}{x}\right)\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.5 \cdot 10^{+65}:\\ \;\;\;\;\frac{z \cdot \left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) + 0.083333333333333}{x} + \left(\left(\log x \cdot \left(x - 0.5\right) - x\right) + 0.91893853320467\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(0.083333333333333 \cdot \frac{1}{x} + z \cdot \left(z \cdot \left(\frac{y}{x} + \frac{0.0007936500793651}{x}\right)\right)\right)\\ \end{array} \]

Alternative 4: 90.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.051:\\ \;\;\;\;\left(\left(\log x \cdot \left(x - 0.5\right) - x\right) + 0.91893853320467\right) + \frac{y}{\frac{\frac{x}{z}}{z}}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(0.083333333333333 \cdot \frac{1}{x} + z \cdot \left(z \cdot \frac{0.0007936500793651}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + -0.5\right) \cdot \log x - \left(x + -0.91893853320467\right)\right) + y \cdot \frac{z}{\frac{x}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -0.051)
   (+ (+ (- (* (log x) (- x 0.5)) x) 0.91893853320467) (/ y (/ (/ x z) z)))
   (if (<= y 3.5e+97)
     (+
      (* x (+ (log x) -1.0))
      (+ (* 0.083333333333333 (/ 1.0 x)) (* z (* z (/ 0.0007936500793651 x)))))
     (+
      (- (* (+ x -0.5) (log x)) (+ x -0.91893853320467))
      (* y (/ z (/ x z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.051) {
		tmp = (((log(x) * (x - 0.5)) - x) + 0.91893853320467) + (y / ((x / z) / z));
	} else if (y <= 3.5e+97) {
		tmp = (x * (log(x) + -1.0)) + ((0.083333333333333 * (1.0 / x)) + (z * (z * (0.0007936500793651 / x))));
	} else {
		tmp = (((x + -0.5) * log(x)) - (x + -0.91893853320467)) + (y * (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 (y <= (-0.051d0)) then
        tmp = (((log(x) * (x - 0.5d0)) - x) + 0.91893853320467d0) + (y / ((x / z) / z))
    else if (y <= 3.5d+97) then
        tmp = (x * (log(x) + (-1.0d0))) + ((0.083333333333333d0 * (1.0d0 / x)) + (z * (z * (0.0007936500793651d0 / x))))
    else
        tmp = (((x + (-0.5d0)) * log(x)) - (x + (-0.91893853320467d0))) + (y * (z / (x / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.051) {
		tmp = (((Math.log(x) * (x - 0.5)) - x) + 0.91893853320467) + (y / ((x / z) / z));
	} else if (y <= 3.5e+97) {
		tmp = (x * (Math.log(x) + -1.0)) + ((0.083333333333333 * (1.0 / x)) + (z * (z * (0.0007936500793651 / x))));
	} else {
		tmp = (((x + -0.5) * Math.log(x)) - (x + -0.91893853320467)) + (y * (z / (x / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -0.051:
		tmp = (((math.log(x) * (x - 0.5)) - x) + 0.91893853320467) + (y / ((x / z) / z))
	elif y <= 3.5e+97:
		tmp = (x * (math.log(x) + -1.0)) + ((0.083333333333333 * (1.0 / x)) + (z * (z * (0.0007936500793651 / x))))
	else:
		tmp = (((x + -0.5) * math.log(x)) - (x + -0.91893853320467)) + (y * (z / (x / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -0.051)
		tmp = Float64(Float64(Float64(Float64(log(x) * Float64(x - 0.5)) - x) + 0.91893853320467) + Float64(y / Float64(Float64(x / z) / z)));
	elseif (y <= 3.5e+97)
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(Float64(0.083333333333333 * Float64(1.0 / x)) + Float64(z * Float64(z * Float64(0.0007936500793651 / x)))));
	else
		tmp = Float64(Float64(Float64(Float64(x + -0.5) * log(x)) - Float64(x + -0.91893853320467)) + Float64(y * Float64(z / Float64(x / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -0.051)
		tmp = (((log(x) * (x - 0.5)) - x) + 0.91893853320467) + (y / ((x / z) / z));
	elseif (y <= 3.5e+97)
		tmp = (x * (log(x) + -1.0)) + ((0.083333333333333 * (1.0 / x)) + (z * (z * (0.0007936500793651 / x))));
	else
		tmp = (((x + -0.5) * log(x)) - (x + -0.91893853320467)) + (y * (z / (x / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -0.051], N[(N[(N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(y / N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+97], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(0.083333333333333 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision] + N[(z * N[(z * N[(0.0007936500793651 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - N[(x + -0.91893853320467), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.0509999999999999967

   1. Initial program 95.3%

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

   2. Taylor expanded in y around inf 74.4%

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

      1. associate-/l* 77.5%

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

      2. unpow2 77.5%

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

      3. associate-/r* 78.9%

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

   4. Simplified 78.9%

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

   if -0.0509999999999999967 < y < 3.5000000000000001e97

   1. Initial program 93.3%

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

   2. Taylor expanded in z around 0 87.8%

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

   3. Taylor expanded in z around inf 92.9%

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

      1. *-commutative 92.9%

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

      2. unpow2 92.9%

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

      3. associate-*r/ 92.8%

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

      4. metadata-eval 92.8%

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

      5. associate-*l* 99.2%

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

   5. Simplified 99.2%

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

   6. Taylor expanded in x around inf 97.9%

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

      1. *-commutative 97.9%

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

      2. sub-neg 97.9%

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

      3. mul-1-neg 97.9%

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

      4. log-rec 97.9%

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

      5. remove-double-neg 97.9%

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

      6. metadata-eval 97.9%

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

   8. Simplified 97.9%

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

   9. Taylor expanded in y around 0 96.5%

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

       1. associate-*r/ 96.5%

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

       2. associate-*l/ 96.6%

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

       3. *-commutative 96.6%

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

   11. Simplified 96.6%

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

   if 3.5000000000000001e97 < y

   1. Initial program 90.1%

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

      1. associate-+l- 90.1%

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

      2. sub-neg 90.1%

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

      3. metadata-eval 90.1%

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

      4. sub-neg 90.1%

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

      5. metadata-eval 90.1%

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

   3. Applied egg-rr 90.1%

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

   4. Taylor expanded in y around inf 82.3%

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

      1. associate-/l* 91.9%

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

      2. unpow2 91.9%

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

   6. Simplified 91.9%

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

      1. clear-num 91.9%

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

      2. associate-/r/ 91.9%

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

      3. clear-num 91.9%

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

      4. associate-/l* 91.9%

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

   8. Applied egg-rr 91.9%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.051:\\ \;\;\;\;\left(\left(\log x \cdot \left(x - 0.5\right) - x\right) + 0.91893853320467\right) + \frac{y}{\frac{\frac{x}{z}}{z}}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(0.083333333333333 \cdot \frac{1}{x} + z \cdot \left(z \cdot \frac{0.0007936500793651}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + -0.5\right) \cdot \log x - \left(x + -0.91893853320467\right)\right) + y \cdot \frac{z}{\frac{x}{z}}\\ \end{array} \]

Alternative 5: 82.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-10} \lor \neg \left(z \leq 3.7 \cdot 10^{-9}\right):\\ \;\;\;\;\left(\left(\log x \cdot \left(x - 0.5\right) - x\right) + 0.91893853320467\right) + \frac{y}{\frac{x}{z \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + -0.5\right) \cdot \log x - \left(x + -0.91893853320467\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.8e-10) (not (<= z 3.7e-9)))
   (+ (+ (- (* (log x) (- x 0.5)) x) 0.91893853320467) (/ y (/ x (* z z))))
   (+
    (- (* (+ x -0.5) (log x)) (+ x -0.91893853320467))
    (/ 0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.8e-10) || !(z <= 3.7e-9)) {
		tmp = (((log(x) * (x - 0.5)) - x) + 0.91893853320467) + (y / (x / (z * z)));
	} else {
		tmp = (((x + -0.5) * log(x)) - (x + -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 <= (-4.8d-10)) .or. (.not. (z <= 3.7d-9))) then
        tmp = (((log(x) * (x - 0.5d0)) - x) + 0.91893853320467d0) + (y / (x / (z * z)))
    else
        tmp = (((x + (-0.5d0)) * log(x)) - (x + (-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 <= -4.8e-10) || !(z <= 3.7e-9)) {
		tmp = (((Math.log(x) * (x - 0.5)) - x) + 0.91893853320467) + (y / (x / (z * z)));
	} else {
		tmp = (((x + -0.5) * Math.log(x)) - (x + -0.91893853320467)) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.8e-10) or not (z <= 3.7e-9):
		tmp = (((math.log(x) * (x - 0.5)) - x) + 0.91893853320467) + (y / (x / (z * z)))
	else:
		tmp = (((x + -0.5) * math.log(x)) - (x + -0.91893853320467)) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.8e-10) || !(z <= 3.7e-9))
		tmp = Float64(Float64(Float64(Float64(log(x) * Float64(x - 0.5)) - x) + 0.91893853320467) + Float64(y / Float64(x / Float64(z * z))));
	else
		tmp = Float64(Float64(Float64(Float64(x + -0.5) * log(x)) - Float64(x + -0.91893853320467)) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.8e-10) || ~((z <= 3.7e-9)))
		tmp = (((log(x) * (x - 0.5)) - x) + 0.91893853320467) + (y / (x / (z * z)));
	else
		tmp = (((x + -0.5) * log(x)) - (x + -0.91893853320467)) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.8e-10], N[Not[LessEqual[z, 3.7e-9]], $MachinePrecision]], N[(N[(N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(y / N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - N[(x + -0.91893853320467), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8e-10 or 3.7e-9 < z

   1. Initial program 88.1%

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

   2. Taylor expanded in y around inf 66.5%

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

      1. associate-/l* 73.8%

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

      2. unpow2 73.8%

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

   4. Simplified 73.8%

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

   if -4.8e-10 < z < 3.7e-9

   1. Initial program 99.6%

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

      1. associate-+l- 99.6%

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

      2. sub-neg 99.6%

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

      3. metadata-eval 99.6%

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

      4. sub-neg 99.6%

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

      5. metadata-eval 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in z around 0 95.9%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-10} \lor \neg \left(z \leq 3.7 \cdot 10^{-9}\right):\\ \;\;\;\;\left(\left(\log x \cdot \left(x - 0.5\right) - x\right) + 0.91893853320467\right) + \frac{y}{\frac{x}{z \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + -0.5\right) \cdot \log x - \left(x + -0.91893853320467\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 6: 84.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-10} \lor \neg \left(z \leq 7.8 \cdot 10^{-8}\right):\\ \;\;\;\;\left(\left(\log x \cdot \left(x - 0.5\right) - x\right) + 0.91893853320467\right) + \frac{y}{\frac{\frac{x}{z}}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + -0.5\right) \cdot \log x - \left(x + -0.91893853320467\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.3e-10) (not (<= z 7.8e-8)))
   (+ (+ (- (* (log x) (- x 0.5)) x) 0.91893853320467) (/ y (/ (/ x z) z)))
   (+
    (- (* (+ x -0.5) (log x)) (+ x -0.91893853320467))
    (/ 0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.3e-10) || !(z <= 7.8e-8)) {
		tmp = (((log(x) * (x - 0.5)) - x) + 0.91893853320467) + (y / ((x / z) / z));
	} else {
		tmp = (((x + -0.5) * log(x)) - (x + -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 <= (-1.3d-10)) .or. (.not. (z <= 7.8d-8))) then
        tmp = (((log(x) * (x - 0.5d0)) - x) + 0.91893853320467d0) + (y / ((x / z) / z))
    else
        tmp = (((x + (-0.5d0)) * log(x)) - (x + (-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 <= -1.3e-10) || !(z <= 7.8e-8)) {
		tmp = (((Math.log(x) * (x - 0.5)) - x) + 0.91893853320467) + (y / ((x / z) / z));
	} else {
		tmp = (((x + -0.5) * Math.log(x)) - (x + -0.91893853320467)) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.3e-10) or not (z <= 7.8e-8):
		tmp = (((math.log(x) * (x - 0.5)) - x) + 0.91893853320467) + (y / ((x / z) / z))
	else:
		tmp = (((x + -0.5) * math.log(x)) - (x + -0.91893853320467)) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.3e-10) || !(z <= 7.8e-8))
		tmp = Float64(Float64(Float64(Float64(log(x) * Float64(x - 0.5)) - x) + 0.91893853320467) + Float64(y / Float64(Float64(x / z) / z)));
	else
		tmp = Float64(Float64(Float64(Float64(x + -0.5) * log(x)) - Float64(x + -0.91893853320467)) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.3e-10) || ~((z <= 7.8e-8)))
		tmp = (((log(x) * (x - 0.5)) - x) + 0.91893853320467) + (y / ((x / z) / z));
	else
		tmp = (((x + -0.5) * log(x)) - (x + -0.91893853320467)) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.3e-10], N[Not[LessEqual[z, 7.8e-8]], $MachinePrecision]], N[(N[(N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(y / N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - N[(x + -0.91893853320467), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.29999999999999991e-10 or 7.7999999999999997e-8 < z

   1. Initial program 88.1%

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

   2. Taylor expanded in y around inf 66.5%

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

      1. associate-/l* 73.8%

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

      2. unpow2 73.8%

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

      3. associate-/r* 79.8%

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

   4. Simplified 79.8%

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

   if -1.29999999999999991e-10 < z < 7.7999999999999997e-8

   1. Initial program 99.6%

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

      1. associate-+l- 99.6%

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

      2. sub-neg 99.6%

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

      3. metadata-eval 99.6%

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

      4. sub-neg 99.6%

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

      5. metadata-eval 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in z around 0 95.9%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-10} \lor \neg \left(z \leq 7.8 \cdot 10^{-8}\right):\\ \;\;\;\;\left(\left(\log x \cdot \left(x - 0.5\right) - x\right) + 0.91893853320467\right) + \frac{y}{\frac{\frac{x}{z}}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + -0.5\right) \cdot \log x - \left(x + -0.91893853320467\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 7: 84.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + -0.5\right) \cdot \log x - \left(x + -0.91893853320467\right)\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{-9}:\\ \;\;\;\;\left(\left(\log x \cdot \left(x - 0.5\right) - x\right) + 0.91893853320467\right) + \frac{y}{\frac{\frac{x}{z}}{z}}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-8}:\\ \;\;\;\;t_0 + \frac{0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;t_0 + y \cdot \frac{z}{\frac{x}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* (+ x -0.5) (log x)) (+ x -0.91893853320467))))
   (if (<= z -1.05e-9)
     (+ (+ (- (* (log x) (- x 0.5)) x) 0.91893853320467) (/ y (/ (/ x z) z)))
     (if (<= z 1.75e-8)
       (+ t_0 (/ 0.083333333333333 x))
       (+ t_0 (* y (/ z (/ x z))))))))

C

double code(double x, double y, double z) {
	double t_0 = ((x + -0.5) * log(x)) - (x + -0.91893853320467);
	double tmp;
	if (z <= -1.05e-9) {
		tmp = (((log(x) * (x - 0.5)) - x) + 0.91893853320467) + (y / ((x / z) / z));
	} else if (z <= 1.75e-8) {
		tmp = t_0 + (0.083333333333333 / x);
	} else {
		tmp = t_0 + (y * (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) :: t_0
    real(8) :: tmp
    t_0 = ((x + (-0.5d0)) * log(x)) - (x + (-0.91893853320467d0))
    if (z <= (-1.05d-9)) then
        tmp = (((log(x) * (x - 0.5d0)) - x) + 0.91893853320467d0) + (y / ((x / z) / z))
    else if (z <= 1.75d-8) then
        tmp = t_0 + (0.083333333333333d0 / x)
    else
        tmp = t_0 + (y * (z / (x / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((x + -0.5) * Math.log(x)) - (x + -0.91893853320467);
	double tmp;
	if (z <= -1.05e-9) {
		tmp = (((Math.log(x) * (x - 0.5)) - x) + 0.91893853320467) + (y / ((x / z) / z));
	} else if (z <= 1.75e-8) {
		tmp = t_0 + (0.083333333333333 / x);
	} else {
		tmp = t_0 + (y * (z / (x / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((x + -0.5) * math.log(x)) - (x + -0.91893853320467)
	tmp = 0
	if z <= -1.05e-9:
		tmp = (((math.log(x) * (x - 0.5)) - x) + 0.91893853320467) + (y / ((x / z) / z))
	elif z <= 1.75e-8:
		tmp = t_0 + (0.083333333333333 / x)
	else:
		tmp = t_0 + (y * (z / (x / z)))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(x + -0.5) * log(x)) - Float64(x + -0.91893853320467))
	tmp = 0.0
	if (z <= -1.05e-9)
		tmp = Float64(Float64(Float64(Float64(log(x) * Float64(x - 0.5)) - x) + 0.91893853320467) + Float64(y / Float64(Float64(x / z) / z)));
	elseif (z <= 1.75e-8)
		tmp = Float64(t_0 + Float64(0.083333333333333 / x));
	else
		tmp = Float64(t_0 + Float64(y * Float64(z / Float64(x / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((x + -0.5) * log(x)) - (x + -0.91893853320467);
	tmp = 0.0;
	if (z <= -1.05e-9)
		tmp = (((log(x) * (x - 0.5)) - x) + 0.91893853320467) + (y / ((x / z) / z));
	elseif (z <= 1.75e-8)
		tmp = t_0 + (0.083333333333333 / x);
	else
		tmp = t_0 + (y * (z / (x / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - N[(x + -0.91893853320467), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05e-9], N[(N[(N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(y / N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e-8], N[(t$95$0 + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(y * N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.0500000000000001e-9

   1. Initial program 85.5%

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

   2. Taylor expanded in y around inf 66.3%

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

      1. associate-/l* 73.6%

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

      2. unpow2 73.6%

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

      3. associate-/r* 82.0%

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

   4. Simplified 82.0%

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

   if -1.0500000000000001e-9 < z < 1.75000000000000012e-8

   1. Initial program 99.6%

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

      1. associate-+l- 99.6%

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

      2. sub-neg 99.6%

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

      3. metadata-eval 99.6%

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

      4. sub-neg 99.6%

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

      5. metadata-eval 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in z around 0 95.9%

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

   if 1.75000000000000012e-8 < z

   1. Initial program 91.2%

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

      1. associate-+l- 91.2%

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

      2. sub-neg 91.2%

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

      3. metadata-eval 91.2%

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

      4. sub-neg 91.2%

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

      5. metadata-eval 91.2%

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

   3. Applied egg-rr 91.2%

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

   4. Taylor expanded in y around inf 66.7%

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

      1. associate-/l* 74.0%

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

      2. unpow2 74.0%

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

   6. Simplified 74.0%

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

      1. clear-num 74.0%

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

      2. associate-/r/ 75.5%

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

      3. clear-num 75.5%

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

      4. associate-/l* 78.6%

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

   8. Applied egg-rr 78.6%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-9}:\\ \;\;\;\;\left(\left(\log x \cdot \left(x - 0.5\right) - x\right) + 0.91893853320467\right) + \frac{y}{\frac{\frac{x}{z}}{z}}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-8}:\\ \;\;\;\;\left(\left(x + -0.5\right) \cdot \log x - \left(x + -0.91893853320467\right)\right) + \frac{0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + -0.5\right) \cdot \log x - \left(x + -0.91893853320467\right)\right) + y \cdot \frac{z}{\frac{x}{z}}\\ \end{array} \]

Alternative 8: 84.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + -0.5\right) \cdot \log x - \left(x + -0.91893853320467\right)\\ \mathbf{if}\;z \leq -7 \cdot 10^{-11}:\\ \;\;\;\;\left(\left(\log x \cdot \left(x - 0.5\right) - x\right) + 0.91893853320467\right) + \frac{y}{\frac{\frac{x}{z}}{z}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-5}:\\ \;\;\;\;t_0 + \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \mathbf{else}:\\ \;\;\;\;t_0 + y \cdot \frac{z}{\frac{x}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* (+ x -0.5) (log x)) (+ x -0.91893853320467))))
   (if (<= z -7e-11)
     (+ (+ (- (* (log x) (- x 0.5)) x) 0.91893853320467) (/ y (/ (/ x z) z)))
     (if (<= z 2.6e-5)
       (+ t_0 (/ (+ 0.083333333333333 (* z -0.0027777777777778)) x))
       (+ t_0 (* y (/ z (/ x z))))))))

C

double code(double x, double y, double z) {
	double t_0 = ((x + -0.5) * log(x)) - (x + -0.91893853320467);
	double tmp;
	if (z <= -7e-11) {
		tmp = (((log(x) * (x - 0.5)) - x) + 0.91893853320467) + (y / ((x / z) / z));
	} else if (z <= 2.6e-5) {
		tmp = t_0 + ((0.083333333333333 + (z * -0.0027777777777778)) / x);
	} else {
		tmp = t_0 + (y * (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) :: t_0
    real(8) :: tmp
    t_0 = ((x + (-0.5d0)) * log(x)) - (x + (-0.91893853320467d0))
    if (z <= (-7d-11)) then
        tmp = (((log(x) * (x - 0.5d0)) - x) + 0.91893853320467d0) + (y / ((x / z) / z))
    else if (z <= 2.6d-5) then
        tmp = t_0 + ((0.083333333333333d0 + (z * (-0.0027777777777778d0))) / x)
    else
        tmp = t_0 + (y * (z / (x / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((x + -0.5) * Math.log(x)) - (x + -0.91893853320467);
	double tmp;
	if (z <= -7e-11) {
		tmp = (((Math.log(x) * (x - 0.5)) - x) + 0.91893853320467) + (y / ((x / z) / z));
	} else if (z <= 2.6e-5) {
		tmp = t_0 + ((0.083333333333333 + (z * -0.0027777777777778)) / x);
	} else {
		tmp = t_0 + (y * (z / (x / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((x + -0.5) * math.log(x)) - (x + -0.91893853320467)
	tmp = 0
	if z <= -7e-11:
		tmp = (((math.log(x) * (x - 0.5)) - x) + 0.91893853320467) + (y / ((x / z) / z))
	elif z <= 2.6e-5:
		tmp = t_0 + ((0.083333333333333 + (z * -0.0027777777777778)) / x)
	else:
		tmp = t_0 + (y * (z / (x / z)))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(x + -0.5) * log(x)) - Float64(x + -0.91893853320467))
	tmp = 0.0
	if (z <= -7e-11)
		tmp = Float64(Float64(Float64(Float64(log(x) * Float64(x - 0.5)) - x) + 0.91893853320467) + Float64(y / Float64(Float64(x / z) / z)));
	elseif (z <= 2.6e-5)
		tmp = Float64(t_0 + Float64(Float64(0.083333333333333 + Float64(z * -0.0027777777777778)) / x));
	else
		tmp = Float64(t_0 + Float64(y * Float64(z / Float64(x / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((x + -0.5) * log(x)) - (x + -0.91893853320467);
	tmp = 0.0;
	if (z <= -7e-11)
		tmp = (((log(x) * (x - 0.5)) - x) + 0.91893853320467) + (y / ((x / z) / z));
	elseif (z <= 2.6e-5)
		tmp = t_0 + ((0.083333333333333 + (z * -0.0027777777777778)) / x);
	else
		tmp = t_0 + (y * (z / (x / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - N[(x + -0.91893853320467), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7e-11], N[(N[(N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(y / N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e-5], N[(t$95$0 + N[(N[(0.083333333333333 + N[(z * -0.0027777777777778), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(y * N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.00000000000000038e-11

   1. Initial program 85.5%

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

   2. Taylor expanded in y around inf 66.3%

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

      1. associate-/l* 73.6%

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

      2. unpow2 73.6%

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

      3. associate-/r* 82.0%

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

   4. Simplified 82.0%

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

   if -7.00000000000000038e-11 < z < 2.59999999999999984e-5

   1. Initial program 99.6%

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

      1. associate-+l- 99.6%

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

      2. sub-neg 99.6%

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

      3. metadata-eval 99.6%

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

      4. sub-neg 99.6%

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

      5. metadata-eval 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in z around 0 96.4%

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

      1. *-commutative 96.4%

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

   6. Simplified 96.4%

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

   if 2.59999999999999984e-5 < z

   1. Initial program 91.2%

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

      1. associate-+l- 91.2%

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

      2. sub-neg 91.2%

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

      3. metadata-eval 91.2%

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

      4. sub-neg 91.2%

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

      5. metadata-eval 91.2%

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

   3. Applied egg-rr 91.2%

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

   4. Taylor expanded in y around inf 66.7%

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

      1. associate-/l* 74.0%

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

      2. unpow2 74.0%

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

   6. Simplified 74.0%

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

      1. clear-num 74.0%

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

      2. associate-/r/ 75.5%

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

      3. clear-num 75.5%

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

      4. associate-/l* 78.6%

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

   8. Applied egg-rr 78.6%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-11}:\\ \;\;\;\;\left(\left(\log x \cdot \left(x - 0.5\right) - x\right) + 0.91893853320467\right) + \frac{y}{\frac{\frac{x}{z}}{z}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-5}:\\ \;\;\;\;\left(\left(x + -0.5\right) \cdot \log x - \left(x + -0.91893853320467\right)\right) + \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + -0.5\right) \cdot \log x - \left(x + -0.91893853320467\right)\right) + y \cdot \frac{z}{\frac{x}{z}}\\ \end{array} \]

Alternative 9: 95.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.45 \cdot 10^{+103}:\\ \;\;\;\;\frac{z \cdot \left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) + 0.083333333333333}{x} + x \cdot \left(\log x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\log x \cdot \left(x - 0.5\right) - x\right) + 0.91893853320467\right) + \frac{y}{\frac{\frac{x}{z}}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.45e+103)
   (+
    (/
     (+
      (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778))
      0.083333333333333)
     x)
    (* x (+ (log x) -1.0)))
   (+ (+ (- (* (log x) (- x 0.5)) x) 0.91893853320467) (/ y (/ (/ x z) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.45e+103) {
		tmp = (((z * (((y + 0.0007936500793651) * z) - 0.0027777777777778)) + 0.083333333333333) / x) + (x * (log(x) + -1.0));
	} else {
		tmp = (((log(x) * (x - 0.5)) - x) + 0.91893853320467) + (y / ((x / z) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 1.45d+103) then
        tmp = (((z * (((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0)) + 0.083333333333333d0) / x) + (x * (log(x) + (-1.0d0)))
    else
        tmp = (((log(x) * (x - 0.5d0)) - x) + 0.91893853320467d0) + (y / ((x / z) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.45e+103) {
		tmp = (((z * (((y + 0.0007936500793651) * z) - 0.0027777777777778)) + 0.083333333333333) / x) + (x * (Math.log(x) + -1.0));
	} else {
		tmp = (((Math.log(x) * (x - 0.5)) - x) + 0.91893853320467) + (y / ((x / z) / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1.45e+103:
		tmp = (((z * (((y + 0.0007936500793651) * z) - 0.0027777777777778)) + 0.083333333333333) / x) + (x * (math.log(x) + -1.0))
	else:
		tmp = (((math.log(x) * (x - 0.5)) - x) + 0.91893853320467) + (y / ((x / z) / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.45e+103)
		tmp = Float64(Float64(Float64(Float64(z * Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778)) + 0.083333333333333) / x) + Float64(x * Float64(log(x) + -1.0)));
	else
		tmp = Float64(Float64(Float64(Float64(log(x) * Float64(x - 0.5)) - x) + 0.91893853320467) + Float64(y / Float64(Float64(x / z) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1.45e+103)
		tmp = (((z * (((y + 0.0007936500793651) * z) - 0.0027777777777778)) + 0.083333333333333) / x) + (x * (log(x) + -1.0));
	else
		tmp = (((log(x) * (x - 0.5)) - x) + 0.91893853320467) + (y / ((x / z) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.45e+103], N[(N[(N[(N[(z * N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision] + N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(y / N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.4499999999999999e103

   1. Initial program 99.2%

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

   2. Taylor expanded in x around inf 97.6%

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

      1. *-commutative 93.3%

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

      2. sub-neg 93.3%

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

      3. mul-1-neg 93.3%

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

      4. log-rec 93.3%

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

      5. remove-double-neg 93.3%

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

      6. metadata-eval 93.3%

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

   4. Simplified 97.6%

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

   if 1.4499999999999999e103 < x

   1. Initial program 80.9%

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

   2. Taylor expanded in y around inf 79.3%

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

      1. associate-/l* 87.1%

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

      2. unpow2 87.1%

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

      3. associate-/r* 97.2%

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

   4. Simplified 97.2%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.45 \cdot 10^{+103}:\\ \;\;\;\;\frac{z \cdot \left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) + 0.083333333333333}{x} + x \cdot \left(\log x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\log x \cdot \left(x - 0.5\right) - x\right) + 0.91893853320467\right) + \frac{y}{\frac{\frac{x}{z}}{z}}\\ \end{array} \]

Alternative 10: 95.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.3 \cdot 10^{+103}:\\ \;\;\;\;\frac{z \cdot \left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) + 0.083333333333333}{x} + \left(x \cdot \log x - x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\log x \cdot \left(x - 0.5\right) - x\right) + 0.91893853320467\right) + \frac{y}{\frac{\frac{x}{z}}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.3e+103)
   (+
    (/
     (+
      (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778))
      0.083333333333333)
     x)
    (- (* x (log x)) x))
   (+ (+ (- (* (log x) (- x 0.5)) x) 0.91893853320467) (/ y (/ (/ x z) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.3e+103) {
		tmp = (((z * (((y + 0.0007936500793651) * z) - 0.0027777777777778)) + 0.083333333333333) / x) + ((x * log(x)) - x);
	} else {
		tmp = (((log(x) * (x - 0.5)) - x) + 0.91893853320467) + (y / ((x / z) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 1.3d+103) then
        tmp = (((z * (((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0)) + 0.083333333333333d0) / x) + ((x * log(x)) - x)
    else
        tmp = (((log(x) * (x - 0.5d0)) - x) + 0.91893853320467d0) + (y / ((x / z) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.3e+103) {
		tmp = (((z * (((y + 0.0007936500793651) * z) - 0.0027777777777778)) + 0.083333333333333) / x) + ((x * Math.log(x)) - x);
	} else {
		tmp = (((Math.log(x) * (x - 0.5)) - x) + 0.91893853320467) + (y / ((x / z) / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1.3e+103:
		tmp = (((z * (((y + 0.0007936500793651) * z) - 0.0027777777777778)) + 0.083333333333333) / x) + ((x * math.log(x)) - x)
	else:
		tmp = (((math.log(x) * (x - 0.5)) - x) + 0.91893853320467) + (y / ((x / z) / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.3e+103)
		tmp = Float64(Float64(Float64(Float64(z * Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778)) + 0.083333333333333) / x) + Float64(Float64(x * log(x)) - x));
	else
		tmp = Float64(Float64(Float64(Float64(log(x) * Float64(x - 0.5)) - x) + 0.91893853320467) + Float64(y / Float64(Float64(x / z) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1.3e+103)
		tmp = (((z * (((y + 0.0007936500793651) * z) - 0.0027777777777778)) + 0.083333333333333) / x) + ((x * log(x)) - x);
	else
		tmp = (((log(x) * (x - 0.5)) - x) + 0.91893853320467) + (y / ((x / z) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.3e+103], N[(N[(N[(N[(z * N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision] + N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(y / N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.3000000000000001e103

   1. Initial program 99.2%

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

      1. associate-+l- 99.2%

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

      2. sub-neg 99.2%

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

      3. metadata-eval 99.2%

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

      4. sub-neg 99.2%

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

      5. metadata-eval 99.2%

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

   3. Applied egg-rr 99.2%

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

   4. Taylor expanded in x around inf 97.6%

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

      1. *-commutative 51.4%

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

      2. sub-neg 51.4%

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

      3. mul-1-neg 51.4%

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

      4. log-rec 51.4%

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

      5. remove-double-neg 51.4%

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

      6. metadata-eval 51.4%

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

      7. distribute-rgt-in 51.5%

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

      8. remove-double-neg 51.5%

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

      9. log-rec 51.5%

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

      10. distribute-lft-neg-in 51.5%

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

      11. mul-1-neg 51.5%

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

      12. neg-mul-1 51.5%

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

      13. unsub-neg 51.5%

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

      14. mul-1-neg 51.5%

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

      15. distribute-lft-neg-in 51.5%

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

      16. log-rec 51.5%

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

      17. remove-double-neg 51.5%

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

      18. *-commutative 51.5%

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

   6. Simplified 97.6%

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

   if 1.3000000000000001e103 < x

   1. Initial program 81.4%

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

   2. Taylor expanded in y around inf 79.7%

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

      1. associate-/l* 87.4%

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

      2. unpow2 87.4%

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

      3. associate-/r* 97.2%

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

   4. Simplified 97.2%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.3 \cdot 10^{+103}:\\ \;\;\;\;\frac{z \cdot \left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) + 0.083333333333333}{x} + \left(x \cdot \log x - x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\log x \cdot \left(x - 0.5\right) - x\right) + 0.91893853320467\right) + \frac{y}{\frac{\frac{x}{z}}{z}}\\ \end{array} \]

Alternative 11: 82.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-11} \lor \neg \left(z \leq 1.12 \cdot 10^{-8}\right):\\ \;\;\;\;\left(x \cdot \log x - x\right) + \frac{y}{\frac{x}{z \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\log x \cdot \left(x - 0.5\right) - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -7e-11) (not (<= z 1.12e-8)))
   (+ (- (* x (log x)) x) (/ y (/ x (* z z))))
   (+
    (+ (- (* (log x) (- x 0.5)) x) 0.91893853320467)
    (/ 0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7e-11) || !(z <= 1.12e-8)) {
		tmp = ((x * log(x)) - x) + (y / (x / (z * z)));
	} else {
		tmp = (((log(x) * (x - 0.5)) - x) + 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 <= (-7d-11)) .or. (.not. (z <= 1.12d-8))) then
        tmp = ((x * log(x)) - x) + (y / (x / (z * z)))
    else
        tmp = (((log(x) * (x - 0.5d0)) - x) + 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 <= -7e-11) || !(z <= 1.12e-8)) {
		tmp = ((x * Math.log(x)) - x) + (y / (x / (z * z)));
	} else {
		tmp = (((Math.log(x) * (x - 0.5)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -7e-11) or not (z <= 1.12e-8):
		tmp = ((x * math.log(x)) - x) + (y / (x / (z * z)))
	else:
		tmp = (((math.log(x) * (x - 0.5)) - x) + 0.91893853320467) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -7e-11) || !(z <= 1.12e-8))
		tmp = Float64(Float64(Float64(x * log(x)) - x) + Float64(y / Float64(x / Float64(z * z))));
	else
		tmp = Float64(Float64(Float64(Float64(log(x) * Float64(x - 0.5)) - x) + 0.91893853320467) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -7e-11) || ~((z <= 1.12e-8)))
		tmp = ((x * log(x)) - x) + (y / (x / (z * z)));
	else
		tmp = (((log(x) * (x - 0.5)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -7e-11], N[Not[LessEqual[z, 1.12e-8]], $MachinePrecision]], N[(N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + N[(y / N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.00000000000000038e-11 or 1.11999999999999994e-8 < z

   1. Initial program 88.1%

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

      1. associate-+l- 88.1%

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

      2. sub-neg 88.1%

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

      3. metadata-eval 88.1%

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

      4. sub-neg 88.1%

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

      5. metadata-eval 88.1%

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

   3. Applied egg-rr 88.1%

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

   4. Taylor expanded in y around inf 66.5%

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

      1. associate-/l* 73.8%

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

      2. unpow2 73.8%

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

   6. Simplified 73.8%

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

   7. Taylor expanded in x around inf 73.7%

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

      1. *-commutative 73.7%

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

      2. sub-neg 73.7%

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

      3. mul-1-neg 73.7%

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

      4. log-rec 73.7%

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

      5. remove-double-neg 73.7%

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

      6. metadata-eval 73.7%

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

      7. distribute-rgt-in 73.7%

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

      8. remove-double-neg 73.7%

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

      9. log-rec 73.7%

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

      10. distribute-lft-neg-in 73.7%

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

      11. mul-1-neg 73.7%

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

      12. neg-mul-1 73.7%

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

      13. unsub-neg 73.7%

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

      14. mul-1-neg 73.7%

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

      15. distribute-lft-neg-in 73.7%

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

      16. log-rec 73.7%

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

      17. remove-double-neg 73.7%

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

      18. *-commutative 73.7%

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

   9. Simplified 73.7%

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

   if -7.00000000000000038e-11 < z < 1.11999999999999994e-8

   1. Initial program 99.6%

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

   2. Taylor expanded in z around 0 95.8%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-11} \lor \neg \left(z \leq 1.12 \cdot 10^{-8}\right):\\ \;\;\;\;\left(x \cdot \log x - x\right) + \frac{y}{\frac{x}{z \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\log x \cdot \left(x - 0.5\right) - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 12: 82.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-10} \lor \neg \left(z \leq 4.8 \cdot 10^{-9}\right):\\ \;\;\;\;\left(x \cdot \log x - x\right) + \frac{y}{\frac{x}{z \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + -0.5\right) \cdot \log x - \left(x + -0.91893853320467\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.5e-10) (not (<= z 4.8e-9)))
   (+ (- (* x (log x)) x) (/ y (/ x (* z z))))
   (+
    (- (* (+ x -0.5) (log x)) (+ x -0.91893853320467))
    (/ 0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.5e-10) || !(z <= 4.8e-9)) {
		tmp = ((x * log(x)) - x) + (y / (x / (z * z)));
	} else {
		tmp = (((x + -0.5) * log(x)) - (x + -0.91893853320467)) + (0.083333333333333 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-2.5d-10)) .or. (.not. (z <= 4.8d-9))) then
        tmp = ((x * log(x)) - x) + (y / (x / (z * z)))
    else
        tmp = (((x + (-0.5d0)) * log(x)) - (x + (-0.91893853320467d0))) + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.5e-10) || !(z <= 4.8e-9)) {
		tmp = ((x * Math.log(x)) - x) + (y / (x / (z * z)));
	} else {
		tmp = (((x + -0.5) * Math.log(x)) - (x + -0.91893853320467)) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.5e-10) or not (z <= 4.8e-9):
		tmp = ((x * math.log(x)) - x) + (y / (x / (z * z)))
	else:
		tmp = (((x + -0.5) * math.log(x)) - (x + -0.91893853320467)) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.5e-10) || !(z <= 4.8e-9))
		tmp = Float64(Float64(Float64(x * log(x)) - x) + Float64(y / Float64(x / Float64(z * z))));
	else
		tmp = Float64(Float64(Float64(Float64(x + -0.5) * log(x)) - Float64(x + -0.91893853320467)) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.5e-10) || ~((z <= 4.8e-9)))
		tmp = ((x * log(x)) - x) + (y / (x / (z * z)));
	else
		tmp = (((x + -0.5) * log(x)) - (x + -0.91893853320467)) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.5e-10], N[Not[LessEqual[z, 4.8e-9]], $MachinePrecision]], N[(N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + N[(y / N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x + -0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - N[(x + -0.91893853320467), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.50000000000000016e-10 or 4.8e-9 < z

   1. Initial program 88.1%

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

      1. associate-+l- 88.1%

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

      2. sub-neg 88.1%

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

      3. metadata-eval 88.1%

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

      4. sub-neg 88.1%

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

      5. metadata-eval 88.1%

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

   3. Applied egg-rr 88.1%

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

   4. Taylor expanded in y around inf 66.5%

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

      1. associate-/l* 73.8%

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

      2. unpow2 73.8%

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

   6. Simplified 73.8%

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

   7. Taylor expanded in x around inf 73.7%

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

      1. *-commutative 73.7%

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

      2. sub-neg 73.7%

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

      3. mul-1-neg 73.7%

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

      4. log-rec 73.7%

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

      5. remove-double-neg 73.7%

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

      6. metadata-eval 73.7%

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

      7. distribute-rgt-in 73.7%

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

      8. remove-double-neg 73.7%

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

      9. log-rec 73.7%

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

      10. distribute-lft-neg-in 73.7%

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

      11. mul-1-neg 73.7%

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

      12. neg-mul-1 73.7%

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

      13. unsub-neg 73.7%

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

      14. mul-1-neg 73.7%

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

      15. distribute-lft-neg-in 73.7%

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

      16. log-rec 73.7%

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

      17. remove-double-neg 73.7%

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

      18. *-commutative 73.7%

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

   9. Simplified 73.7%

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

   if -2.50000000000000016e-10 < z < 4.8e-9

   1. Initial program 99.6%

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

      1. associate-+l- 99.6%

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

      2. sub-neg 99.6%

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

      3. metadata-eval 99.6%

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

      4. sub-neg 99.6%

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

      5. metadata-eval 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in z around 0 95.9%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-10} \lor \neg \left(z \leq 4.8 \cdot 10^{-9}\right):\\ \;\;\;\;\left(x \cdot \log x - x\right) + \frac{y}{\frac{x}{z \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + -0.5\right) \cdot \log x - \left(x + -0.91893853320467\right)\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 13: 63.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.8 \cdot 10^{-31}:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\log x \cdot \left(x - 0.5\right) - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 4.8e-31)
   (/ (+ 0.083333333333333 (* z -0.0027777777777778)) x)
   (+
    (+ (- (* (log x) (- x 0.5)) x) 0.91893853320467)
    (/ 0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 4.8e-31) {
		tmp = (0.083333333333333 + (z * -0.0027777777777778)) / x;
	} else {
		tmp = (((log(x) * (x - 0.5)) - x) + 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 (x <= 4.8d-31) then
        tmp = (0.083333333333333d0 + (z * (-0.0027777777777778d0))) / x
    else
        tmp = (((log(x) * (x - 0.5d0)) - x) + 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 (x <= 4.8e-31) {
		tmp = (0.083333333333333 + (z * -0.0027777777777778)) / x;
	} else {
		tmp = (((Math.log(x) * (x - 0.5)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 4.8e-31:
		tmp = (0.083333333333333 + (z * -0.0027777777777778)) / x
	else:
		tmp = (((math.log(x) * (x - 0.5)) - x) + 0.91893853320467) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 4.8e-31)
		tmp = Float64(Float64(0.083333333333333 + Float64(z * -0.0027777777777778)) / x);
	else
		tmp = Float64(Float64(Float64(Float64(log(x) * Float64(x - 0.5)) - x) + 0.91893853320467) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 4.8e-31)
		tmp = (0.083333333333333 + (z * -0.0027777777777778)) / x;
	else
		tmp = (((log(x) * (x - 0.5)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 4.8e-31], N[(N[(0.083333333333333 + N[(z * -0.0027777777777778), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], N[(N[(N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.8e-31

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 56.1%

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

   3. Taylor expanded in x around inf 56.1%

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

      1. *-commutative 91.9%

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

      2. sub-neg 91.9%

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

      3. mul-1-neg 91.9%

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

      4. log-rec 91.9%

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

      5. remove-double-neg 91.9%

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

      6. metadata-eval 91.9%

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

   5. Simplified 56.1%

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

   6. Taylor expanded in x around 0 56.2%

      \[\leadsto \color{blue}{\frac{0.083333333333333 + -0.0027777777777778 \cdot z}{x}} \]
   7. Step-by-step derivation

      1. *-commutative 56.2%

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

   8. Simplified 56.2%

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

   if 4.8e-31 < x

   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. Taylor expanded in z around 0 65.1%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4.8 \cdot 10^{-31}:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\log x \cdot \left(x - 0.5\right) - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 14: 62.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 340:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 340.0)
   (/ (+ 0.083333333333333 (* z -0.0027777777777778)) x)
   (+ (* x (+ (log x) -1.0)) (/ 0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 340.0) {
		tmp = (0.083333333333333 + (z * -0.0027777777777778)) / x;
	} else {
		tmp = (x * (log(x) + -1.0)) + (0.083333333333333 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 340.0d0) then
        tmp = (0.083333333333333d0 + (z * (-0.0027777777777778d0))) / x
    else
        tmp = (x * (log(x) + (-1.0d0))) + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 340.0) {
		tmp = (0.083333333333333 + (z * -0.0027777777777778)) / x;
	} else {
		tmp = (x * (Math.log(x) + -1.0)) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 340.0:
		tmp = (0.083333333333333 + (z * -0.0027777777777778)) / x
	else:
		tmp = (x * (math.log(x) + -1.0)) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 340.0)
		tmp = Float64(Float64(0.083333333333333 + Float64(z * -0.0027777777777778)) / x);
	else
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 340.0)
		tmp = (0.083333333333333 + (z * -0.0027777777777778)) / x;
	else
		tmp = (x * (log(x) + -1.0)) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 340.0], N[(N[(0.083333333333333 + N[(z * -0.0027777777777778), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 340

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 55.0%

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

   3. Taylor expanded in x around inf 54.2%

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

      1. *-commutative 92.4%

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

      2. sub-neg 92.4%

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

      3. mul-1-neg 92.4%

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

      4. log-rec 92.4%

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

      5. remove-double-neg 92.4%

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

      6. metadata-eval 92.4%

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

   5. Simplified 54.2%

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

   6. Taylor expanded in x around 0 53.7%

      \[\leadsto \color{blue}{\frac{0.083333333333333 + -0.0027777777777778 \cdot z}{x}} \]
   7. Step-by-step derivation

      1. *-commutative 53.7%

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

   8. Simplified 53.7%

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

   if 340 < x

   1. Initial program 86.7%

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

   2. Taylor expanded in z around 0 68.5%

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

   3. Taylor expanded in x around inf 67.2%

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

      1. *-commutative 98.4%

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

      2. sub-neg 98.4%

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

      3. mul-1-neg 98.4%

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

      4. log-rec 98.4%

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

      5. remove-double-neg 98.4%

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

      6. metadata-eval 98.4%

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

   5. Simplified 67.2%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 340:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 15: 62.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 340:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log x - x\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 340.0)
   (/ (+ 0.083333333333333 (* z -0.0027777777777778)) x)
   (+ (- (* x (log x)) x) (/ 0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 340.0) {
		tmp = (0.083333333333333 + (z * -0.0027777777777778)) / x;
	} else {
		tmp = ((x * log(x)) - x) + (0.083333333333333 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 340.0d0) then
        tmp = (0.083333333333333d0 + (z * (-0.0027777777777778d0))) / x
    else
        tmp = ((x * log(x)) - x) + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 340.0) {
		tmp = (0.083333333333333 + (z * -0.0027777777777778)) / x;
	} else {
		tmp = ((x * Math.log(x)) - x) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 340.0:
		tmp = (0.083333333333333 + (z * -0.0027777777777778)) / x
	else:
		tmp = ((x * math.log(x)) - x) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 340.0)
		tmp = Float64(Float64(0.083333333333333 + Float64(z * -0.0027777777777778)) / x);
	else
		tmp = Float64(Float64(Float64(x * log(x)) - x) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 340.0)
		tmp = (0.083333333333333 + (z * -0.0027777777777778)) / x;
	else
		tmp = ((x * log(x)) - x) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 340.0], N[(N[(0.083333333333333 + N[(z * -0.0027777777777778), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], N[(N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 340

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 55.0%

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

   3. Taylor expanded in x around inf 54.2%

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

      1. *-commutative 92.4%

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

      2. sub-neg 92.4%

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

      3. mul-1-neg 92.4%

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

      4. log-rec 92.4%

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

      5. remove-double-neg 92.4%

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

      6. metadata-eval 92.4%

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

   5. Simplified 54.2%

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

   6. Taylor expanded in x around 0 53.7%

      \[\leadsto \color{blue}{\frac{0.083333333333333 + -0.0027777777777778 \cdot z}{x}} \]
   7. Step-by-step derivation

      1. *-commutative 53.7%

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

   8. Simplified 53.7%

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

   if 340 < x

   1. Initial program 86.7%

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

   2. Taylor expanded in z around 0 68.5%

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

   3. Taylor expanded in x around inf 67.2%

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

      1. *-commutative 98.4%

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

      2. sub-neg 98.4%

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

      3. mul-1-neg 98.4%

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

      4. log-rec 98.4%

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

      5. remove-double-neg 98.4%

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

      6. metadata-eval 98.4%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in x around 0 67.2%

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

      1. sub-neg 67.2%

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

      2. metadata-eval 67.2%

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

      3. *-commutative 67.2%

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

      4. distribute-rgt-in 67.2%

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

      5. mul-1-neg 67.2%

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

      6. unsub-neg 67.2%

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

      7. *-commutative 67.2%

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

   8. Simplified 67.2%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 340:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log x - x\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 16: 33.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 340:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x \cdot \left(x \cdot 0.0069444444444443885\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 340.0)
   (/ (+ 0.083333333333333 (* z -0.0027777777777778)) x)
   (sqrt (* x (* x 0.0069444444444443885)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 340.0) {
		tmp = (0.083333333333333 + (z * -0.0027777777777778)) / x;
	} else {
		tmp = sqrt((x * (x * 0.0069444444444443885)));
	}
	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 <= 340.0d0) then
        tmp = (0.083333333333333d0 + (z * (-0.0027777777777778d0))) / x
    else
        tmp = sqrt((x * (x * 0.0069444444444443885d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 340.0) {
		tmp = (0.083333333333333 + (z * -0.0027777777777778)) / x;
	} else {
		tmp = Math.sqrt((x * (x * 0.0069444444444443885)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 340.0:
		tmp = (0.083333333333333 + (z * -0.0027777777777778)) / x
	else:
		tmp = math.sqrt((x * (x * 0.0069444444444443885)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 340.0)
		tmp = Float64(Float64(0.083333333333333 + Float64(z * -0.0027777777777778)) / x);
	else
		tmp = sqrt(Float64(x * Float64(x * 0.0069444444444443885)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 340.0)
		tmp = (0.083333333333333 + (z * -0.0027777777777778)) / x;
	else
		tmp = sqrt((x * (x * 0.0069444444444443885)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 340.0], N[(N[(0.083333333333333 + N[(z * -0.0027777777777778), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], N[Sqrt[N[(x * N[(x * 0.0069444444444443885), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 340

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 55.0%

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

   3. Taylor expanded in x around inf 54.2%

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

      1. *-commutative 92.4%

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

      2. sub-neg 92.4%

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

      3. mul-1-neg 92.4%

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

      4. log-rec 92.4%

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

      5. remove-double-neg 92.4%

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

      6. metadata-eval 92.4%

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

   5. Simplified 54.2%

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

   6. Taylor expanded in x around 0 53.7%

      \[\leadsto \color{blue}{\frac{0.083333333333333 + -0.0027777777777778 \cdot z}{x}} \]
   7. Step-by-step derivation

      1. *-commutative 53.7%

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

   8. Simplified 53.7%

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

   if 340 < x

   1. Initial program 86.7%

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

   2. Taylor expanded in z around 0 68.5%

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

   3. Taylor expanded in x around inf 67.2%

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

      1. *-commutative 98.4%

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

      2. sub-neg 98.4%

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

      3. mul-1-neg 98.4%

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

      4. log-rec 98.4%

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

      5. remove-double-neg 98.4%

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

      6. metadata-eval 98.4%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in x around 0 3.0%

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

      1. metadata-eval 3.0%

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

      2. associate-*l/ 3.0%

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

      3. rem-exp-log 3.0%

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

      4. log-rec 3.0%

         \[\leadsto e^{\color{blue}{-\log x}} \cdot 0.083333333333333 \]

      5. rem-square-sqrt 0.0%

         \[\leadsto e^{\color{blue}{\sqrt{-\log x} \cdot \sqrt{-\log x}}} \cdot 0.083333333333333 \]

      6. fabs-sqr 0.0%

         \[\leadsto e^{\color{blue}{\left|\sqrt{-\log x} \cdot \sqrt{-\log x}\right|}} \cdot 0.083333333333333 \]

      7. rem-square-sqrt 10.1%

         \[\leadsto e^{\left|\color{blue}{-\log x}\right|} \cdot 0.083333333333333 \]

      8. fabs-neg 10.1%

         \[\leadsto e^{\color{blue}{\left|\log x\right|}} \cdot 0.083333333333333 \]

      9. rem-square-sqrt 10.1%

         \[\leadsto e^{\left|\color{blue}{\sqrt{\log x} \cdot \sqrt{\log x}}\right|} \cdot 0.083333333333333 \]

      10. fabs-sqr 10.1%

          \[\leadsto e^{\color{blue}{\sqrt{\log x} \cdot \sqrt{\log x}}} \cdot 0.083333333333333 \]

      11. rem-square-sqrt 10.1%

          \[\leadsto e^{\color{blue}{\log x}} \cdot 0.083333333333333 \]

      12. rem-exp-log 10.1%

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

   8. Simplified 10.1%

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

      1. add-sqr-sqrt 10.1%

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

      2. sqrt-unprod 12.1%

         \[\leadsto \color{blue}{\sqrt{\left(x \cdot 0.083333333333333\right) \cdot \left(x \cdot 0.083333333333333\right)}} \]

      3. swap-sqr 12.0%

         \[\leadsto \sqrt{\color{blue}{\left(x \cdot x\right) \cdot \left(0.083333333333333 \cdot 0.083333333333333\right)}} \]

      4. metadata-eval 12.0%

         \[\leadsto \sqrt{\left(x \cdot x\right) \cdot \color{blue}{0.0069444444444443885}} \]

   10. Applied egg-rr 12.0%

       \[\leadsto \color{blue}{\sqrt{\left(x \cdot x\right) \cdot 0.0069444444444443885}} \]
   11. Step-by-step derivation

       1. associate-*l* 12.1%

          \[\leadsto \sqrt{\color{blue}{x \cdot \left(x \cdot 0.0069444444444443885\right)}} \]

   12. Simplified 12.1%

       \[\leadsto \color{blue}{\sqrt{x \cdot \left(x \cdot 0.0069444444444443885\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 340:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x \cdot \left(x \cdot 0.0069444444444443885\right)}\\ \end{array} \]

Alternative 17: 28.8% accurate, 13.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -30 \lor \neg \left(z \leq 2.7 \cdot 10^{+128}\right):\\ \;\;\;\;-0.0027777777777778 \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -30.0) (not (<= z 2.7e+128)))
   (* -0.0027777777777778 (/ z x))
   (/ 0.083333333333333 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -30.0) || !(z <= 2.7e+128)) {
		tmp = -0.0027777777777778 * (z / x);
	} else {
		tmp = 0.083333333333333 / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-30.0d0)) .or. (.not. (z <= 2.7d+128))) then
        tmp = (-0.0027777777777778d0) * (z / x)
    else
        tmp = 0.083333333333333d0 / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -30.0) || !(z <= 2.7e+128)) {
		tmp = -0.0027777777777778 * (z / x);
	} else {
		tmp = 0.083333333333333 / x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -30.0) or not (z <= 2.7e+128):
		tmp = -0.0027777777777778 * (z / x)
	else:
		tmp = 0.083333333333333 / x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -30.0) || !(z <= 2.7e+128))
		tmp = Float64(-0.0027777777777778 * Float64(z / x));
	else
		tmp = Float64(0.083333333333333 / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -30.0) || ~((z <= 2.7e+128)))
		tmp = -0.0027777777777778 * (z / x);
	else
		tmp = 0.083333333333333 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -30.0], N[Not[LessEqual[z, 2.7e+128]], $MachinePrecision]], N[(-0.0027777777777778 * N[(z / x), $MachinePrecision]), $MachinePrecision], N[(0.083333333333333 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -30 or 2.70000000000000001e128 < z

   1. Initial program 86.7%

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

   2. Taylor expanded in z around 0 33.6%

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

   3. Taylor expanded in x around inf 33.6%

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

      1. *-commutative 99.7%

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

      2. sub-neg 99.7%

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

      3. mul-1-neg 99.7%

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

      4. log-rec 99.7%

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

      5. remove-double-neg 99.7%

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

      6. metadata-eval 99.7%

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

   5. Simplified 33.6%

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

   6. Taylor expanded in z around inf 14.9%

      \[\leadsto \color{blue}{-0.0027777777777778 \cdot \frac{z}{x}} \]
   7. Step-by-step derivation

      1. *-commutative 14.9%

         \[\leadsto \color{blue}{\frac{z}{x} \cdot -0.0027777777777778} \]

   8. Simplified 14.9%

      \[\leadsto \color{blue}{\frac{z}{x} \cdot -0.0027777777777778} \]

   if -30 < z < 2.70000000000000001e128

   1. Initial program 98.4%

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

   2. Taylor expanded in z around 0 84.0%

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

   3. Taylor expanded in x around inf 82.1%

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

      1. *-commutative 91.9%

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

      2. sub-neg 91.9%

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

      3. mul-1-neg 91.9%

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

      4. log-rec 91.9%

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

      5. remove-double-neg 91.9%

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

      6. metadata-eval 91.9%

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

   5. Simplified 82.1%

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

   6. Taylor expanded in x around 0 39.6%

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

4. Final simplification 28.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -30 \lor \neg \left(z \leq 2.7 \cdot 10^{+128}\right):\\ \;\;\;\;-0.0027777777777778 \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 18: 32.5% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 340:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.083333333333333\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 340.0)
   (/ (+ 0.083333333333333 (* z -0.0027777777777778)) x)
   (* x 0.083333333333333)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 340.0) {
		tmp = (0.083333333333333 + (z * -0.0027777777777778)) / x;
	} else {
		tmp = x * 0.083333333333333;
	}
	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 <= 340.0d0) then
        tmp = (0.083333333333333d0 + (z * (-0.0027777777777778d0))) / x
    else
        tmp = x * 0.083333333333333d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 340.0) {
		tmp = (0.083333333333333 + (z * -0.0027777777777778)) / x;
	} else {
		tmp = x * 0.083333333333333;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 340.0:
		tmp = (0.083333333333333 + (z * -0.0027777777777778)) / x
	else:
		tmp = x * 0.083333333333333
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 340.0)
		tmp = Float64(Float64(0.083333333333333 + Float64(z * -0.0027777777777778)) / x);
	else
		tmp = Float64(x * 0.083333333333333);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 340.0)
		tmp = (0.083333333333333 + (z * -0.0027777777777778)) / x;
	else
		tmp = x * 0.083333333333333;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 340.0], N[(N[(0.083333333333333 + N[(z * -0.0027777777777778), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], N[(x * 0.083333333333333), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 340

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 55.0%

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

   3. Taylor expanded in x around inf 54.2%

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

      1. *-commutative 92.4%

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

      2. sub-neg 92.4%

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

      3. mul-1-neg 92.4%

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

      4. log-rec 92.4%

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

      5. remove-double-neg 92.4%

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

      6. metadata-eval 92.4%

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

   5. Simplified 54.2%

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

   6. Taylor expanded in x around 0 53.7%

      \[\leadsto \color{blue}{\frac{0.083333333333333 + -0.0027777777777778 \cdot z}{x}} \]
   7. Step-by-step derivation

      1. *-commutative 53.7%

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

   8. Simplified 53.7%

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

   if 340 < x

   1. Initial program 86.7%

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

   2. Taylor expanded in z around 0 68.5%

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

   3. Taylor expanded in x around inf 67.2%

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

      1. *-commutative 98.4%

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

      2. sub-neg 98.4%

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

      3. mul-1-neg 98.4%

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

      4. log-rec 98.4%

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

      5. remove-double-neg 98.4%

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

      6. metadata-eval 98.4%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in x around 0 3.0%

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

      1. metadata-eval 3.0%

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

      2. associate-*l/ 3.0%

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

      3. rem-exp-log 3.0%

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

      4. log-rec 3.0%

         \[\leadsto e^{\color{blue}{-\log x}} \cdot 0.083333333333333 \]

      5. rem-square-sqrt 0.0%

         \[\leadsto e^{\color{blue}{\sqrt{-\log x} \cdot \sqrt{-\log x}}} \cdot 0.083333333333333 \]

      6. fabs-sqr 0.0%

         \[\leadsto e^{\color{blue}{\left|\sqrt{-\log x} \cdot \sqrt{-\log x}\right|}} \cdot 0.083333333333333 \]

      7. rem-square-sqrt 10.1%

         \[\leadsto e^{\left|\color{blue}{-\log x}\right|} \cdot 0.083333333333333 \]

      8. fabs-neg 10.1%

         \[\leadsto e^{\color{blue}{\left|\log x\right|}} \cdot 0.083333333333333 \]

      9. rem-square-sqrt 10.1%

         \[\leadsto e^{\left|\color{blue}{\sqrt{\log x} \cdot \sqrt{\log x}}\right|} \cdot 0.083333333333333 \]

      10. fabs-sqr 10.1%

          \[\leadsto e^{\color{blue}{\sqrt{\log x} \cdot \sqrt{\log x}}} \cdot 0.083333333333333 \]

      11. rem-square-sqrt 10.1%

          \[\leadsto e^{\color{blue}{\log x}} \cdot 0.083333333333333 \]

      12. rem-exp-log 10.1%

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

   8. Simplified 10.1%

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

4. Final simplification 31.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 340:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.083333333333333\\ \end{array} \]

Alternative 19: 27.2% accurate, 24.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.9:\\ \;\;\;\;\frac{0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.083333333333333\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 0.9) (/ 0.083333333333333 x) (* x 0.083333333333333)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 0.9) {
		tmp = 0.083333333333333 / x;
	} else {
		tmp = x * 0.083333333333333;
	}
	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 <= 0.9d0) then
        tmp = 0.083333333333333d0 / x
    else
        tmp = x * 0.083333333333333d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 0.9) {
		tmp = 0.083333333333333 / x;
	} else {
		tmp = x * 0.083333333333333;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 0.9:
		tmp = 0.083333333333333 / x
	else:
		tmp = x * 0.083333333333333
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 0.9)
		tmp = Float64(0.083333333333333 / x);
	else
		tmp = Float64(x * 0.083333333333333);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 0.9)
		tmp = 0.083333333333333 / x;
	else
		tmp = x * 0.083333333333333;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 0.9], N[(0.083333333333333 / x), $MachinePrecision], N[(x * 0.083333333333333), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 0.900000000000000022

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 45.8%

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

   3. Taylor expanded in x around inf 45.0%

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

      1. *-commutative 92.2%

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

      2. sub-neg 92.2%

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

      3. mul-1-neg 92.2%

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

      4. log-rec 92.2%

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

      5. remove-double-neg 92.2%

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

      6. metadata-eval 92.2%

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

   5. Simplified 45.0%

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

   6. Taylor expanded in x around 0 45.0%

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

   if 0.900000000000000022 < x

   1. Initial program 87.0%

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

   2. Taylor expanded in z around 0 67.0%

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

   3. Taylor expanded in x around inf 65.7%

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

      1. *-commutative 98.4%

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

      2. sub-neg 98.4%

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

      3. mul-1-neg 98.4%

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

      4. log-rec 98.4%

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

      5. remove-double-neg 98.4%

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

      6. metadata-eval 98.4%

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

   5. Simplified 65.7%

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

   6. Taylor expanded in x around 0 3.0%

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

      1. metadata-eval 3.0%

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

      2. associate-*l/ 3.0%

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

      3. rem-exp-log 3.0%

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

      4. log-rec 3.0%

         \[\leadsto e^{\color{blue}{-\log x}} \cdot 0.083333333333333 \]

      5. rem-square-sqrt 0.0%

         \[\leadsto e^{\color{blue}{\sqrt{-\log x} \cdot \sqrt{-\log x}}} \cdot 0.083333333333333 \]

      6. fabs-sqr 0.0%

         \[\leadsto e^{\color{blue}{\left|\sqrt{-\log x} \cdot \sqrt{-\log x}\right|}} \cdot 0.083333333333333 \]

      7. rem-square-sqrt 9.9%

         \[\leadsto e^{\left|\color{blue}{-\log x}\right|} \cdot 0.083333333333333 \]

      8. fabs-neg 9.9%

         \[\leadsto e^{\color{blue}{\left|\log x\right|}} \cdot 0.083333333333333 \]

      9. rem-square-sqrt 9.9%

         \[\leadsto e^{\left|\color{blue}{\sqrt{\log x} \cdot \sqrt{\log x}}\right|} \cdot 0.083333333333333 \]

      10. fabs-sqr 9.9%

          \[\leadsto e^{\color{blue}{\sqrt{\log x} \cdot \sqrt{\log x}}} \cdot 0.083333333333333 \]

      11. rem-square-sqrt 9.9%

          \[\leadsto e^{\color{blue}{\log x}} \cdot 0.083333333333333 \]

      12. rem-exp-log 9.9%

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

   8. Simplified 9.9%

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

4. Final simplification 27.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.9:\\ \;\;\;\;\frac{0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.083333333333333\\ \end{array} \]

Alternative 20: 6.6% accurate, 41.0× speedup

Math

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

FPCore

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

C

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

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 * 0.083333333333333d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.2%

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

2. Taylor expanded in z around 0 56.6%

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

3. Taylor expanded in x around inf 55.6%

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

   1. *-commutative 95.4%

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

   2. sub-neg 95.4%

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

   3. mul-1-neg 95.4%

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

   4. log-rec 95.4%

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

   5. remove-double-neg 95.4%

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

   6. metadata-eval 95.4%

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

5. Simplified 55.6%

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

6. Taylor expanded in x around 0 23.5%

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

   1. metadata-eval 23.5%

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

   2. associate-*l/ 23.5%

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

   3. rem-exp-log 21.9%

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

   4. log-rec 21.9%

      \[\leadsto e^{\color{blue}{-\log x}} \cdot 0.083333333333333 \]

   5. rem-square-sqrt 20.0%

      \[\leadsto e^{\color{blue}{\sqrt{-\log x} \cdot \sqrt{-\log x}}} \cdot 0.083333333333333 \]

   6. fabs-sqr 20.0%

      \[\leadsto e^{\color{blue}{\left|\sqrt{-\log x} \cdot \sqrt{-\log x}\right|}} \cdot 0.083333333333333 \]

   7. rem-square-sqrt 25.5%

      \[\leadsto e^{\left|\color{blue}{-\log x}\right|} \cdot 0.083333333333333 \]

   8. fabs-neg 25.5%

      \[\leadsto e^{\color{blue}{\left|\log x\right|}} \cdot 0.083333333333333 \]

   9. rem-square-sqrt 5.1%

      \[\leadsto e^{\left|\color{blue}{\sqrt{\log x} \cdot \sqrt{\log x}}\right|} \cdot 0.083333333333333 \]

   10. fabs-sqr 5.1%

       \[\leadsto e^{\color{blue}{\sqrt{\log x} \cdot \sqrt{\log x}}} \cdot 0.083333333333333 \]

   11. rem-square-sqrt 6.6%

       \[\leadsto e^{\color{blue}{\log x}} \cdot 0.083333333333333 \]

   12. rem-exp-log 6.6%

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

8. Simplified 6.6%

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

9. Final simplification 6.6%

   \[\leadsto x \cdot 0.083333333333333 \]

Developer target: 98.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023200 
(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)))