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

Percentage Accurate: 94.7% → 96.0%

Time: 18.4s

Alternatives: 14

Speedup: 1.0×

• 28.7% 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: 94.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\\ \mathbf{if}\;x \leq 12.5:\\ \;\;\;\;t_0 + {\left(\frac{x}{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(y + 0.0007936500793651\right) \cdot \left(\left(z \cdot z\right) \cdot \frac{1}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)))
   (if (<= x 12.5)
     (+
      t_0
      (pow
       (/
        x
        (fma
         z
         (fma (+ y 0.0007936500793651) z -0.0027777777777778)
         0.083333333333333))
       -1.0))
     (+ t_0 (* (+ y 0.0007936500793651) (* (* z z) (/ 1.0 x)))))))

C

double code(double x, double y, double z) {
	double t_0 = (((x - 0.5) * log(x)) - x) + 0.91893853320467;
	double tmp;
	if (x <= 12.5) {
		tmp = t_0 + pow((x / fma(z, fma((y + 0.0007936500793651), z, -0.0027777777777778), 0.083333333333333)), -1.0);
	} else {
		tmp = t_0 + ((y + 0.0007936500793651) * ((z * z) * (1.0 / x)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467)
	tmp = 0.0
	if (x <= 12.5)
		tmp = Float64(t_0 + (Float64(x / fma(z, fma(Float64(y + 0.0007936500793651), z, -0.0027777777777778), 0.083333333333333)) ^ -1.0));
	else
		tmp = Float64(t_0 + Float64(Float64(y + 0.0007936500793651) * Float64(Float64(z * z) * Float64(1.0 / x))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision]}, If[LessEqual[x, 12.5], N[(t$95$0 + N[Power[N[(x / N[(z * N[(N[(y + 0.0007936500793651), $MachinePrecision] * z + -0.0027777777777778), $MachinePrecision] + 0.083333333333333), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(N[(z * z), $MachinePrecision] * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 12.5

   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. clear-num 99.7%

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

      2. inv-pow 99.7%

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

      3. *-commutative 99.7%

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

      4. fma-udef 99.7%

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

      5. fma-neg 99.7%

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

      6. metadata-eval 99.7%

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

   3. Applied egg-rr 99.7%

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

   if 12.5 < x

   1. Initial program 91.5%

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

   2. Taylor expanded in z around inf 91.5%

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

      1. associate-/l* 96.3%

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

      2. unpow2 96.3%

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

   4. Simplified 96.3%

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

      1. associate-/r/ 96.3%

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

      2. +-commutative 96.3%

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

   6. Applied egg-rr 96.3%

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

      1. div-inv 96.4%

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

   8. Applied egg-rr 96.4%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 12.5:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + {\left(\frac{x}{\mathsf{fma}\left(z, \mathsf{fma}\left(y + 0.0007936500793651, z, -0.0027777777777778\right), 0.083333333333333\right)}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(y + 0.0007936500793651\right) \cdot \left(\left(z \cdot z\right) \cdot \frac{1}{x}\right)\\ \end{array} \]

Alternative 2: 96.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\\ \mathbf{if}\;x \leq 6000000:\\ \;\;\;\;t_0 + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(y + 0.0007936500793651\right) \cdot \left(\left(z \cdot z\right) \cdot \frac{1}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)))
   (if (<= x 6000000.0)
     (+
      t_0
      (/
       (+
        0.083333333333333
        (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))
       x))
     (+ t_0 (* (+ y 0.0007936500793651) (* (* z z) (/ 1.0 x)))))))

C

double code(double x, double y, double z) {
	double t_0 = (((x - 0.5) * log(x)) - x) + 0.91893853320467;
	double tmp;
	if (x <= 6000000.0) {
		tmp = t_0 + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = t_0 + ((y + 0.0007936500793651) * ((z * z) * (1.0 / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0
    if (x <= 6000000.0d0) then
        tmp = t_0 + ((0.083333333333333d0 + (z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0))) / x)
    else
        tmp = t_0 + ((y + 0.0007936500793651d0) * ((z * z) * (1.0d0 / x)))
    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 (x <= 6000000.0) {
		tmp = t_0 + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	} else {
		tmp = t_0 + ((y + 0.0007936500793651) * ((z * z) * (1.0 / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (((x - 0.5) * math.log(x)) - x) + 0.91893853320467
	tmp = 0
	if x <= 6000000.0:
		tmp = t_0 + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x)
	else:
		tmp = t_0 + ((y + 0.0007936500793651) * ((z * z) * (1.0 / x)))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467)
	tmp = 0.0
	if (x <= 6000000.0)
		tmp = Float64(t_0 + Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778))) / x));
	else
		tmp = Float64(t_0 + Float64(Float64(y + 0.0007936500793651) * Float64(Float64(z * z) * Float64(1.0 / x))));
	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 (x <= 6000000.0)
		tmp = t_0 + ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x);
	else
		tmp = t_0 + ((y + 0.0007936500793651) * ((z * z) * (1.0 / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision]}, If[LessEqual[x, 6000000.0], N[(t$95$0 + N[(N[(0.083333333333333 + N[(z * N[(N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(N[(z * z), $MachinePrecision] * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 6e6

   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 6e6 < x

   1. Initial program 91.3%

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

   2. Taylor expanded in z around inf 91.3%

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

      1. associate-/l* 96.2%

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

      2. unpow2 96.2%

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

   4. Simplified 96.2%

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

      1. associate-/r/ 96.3%

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

      2. +-commutative 96.3%

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

   6. Applied egg-rr 96.3%

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

      1. div-inv 96.3%

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

   8. Applied egg-rr 96.3%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 6000000:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(y + 0.0007936500793651\right) \cdot \left(\left(z \cdot z\right) \cdot \frac{1}{x}\right)\\ \end{array} \]

Alternative 3: 95.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5300000:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} + x \cdot \left(\log x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(y + 0.0007936500793651\right) \cdot \left(\left(z \cdot z\right) \cdot \frac{1}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 5300000.0)
   (+
    (/
     (+
      0.083333333333333
      (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))
     x)
    (* x (+ (log x) -1.0)))
   (+
    (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
    (* (+ y 0.0007936500793651) (* (* z z) (/ 1.0 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 5300000.0) {
		tmp = ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) + (x * (log(x) + -1.0));
	} else {
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((y + 0.0007936500793651) * ((z * z) * (1.0 / 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 <= 5300000.0d0) then
        tmp = ((0.083333333333333d0 + (z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0))) / x) + (x * (log(x) + (-1.0d0)))
    else
        tmp = ((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + ((y + 0.0007936500793651d0) * ((z * z) * (1.0d0 / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 5300000.0) {
		tmp = ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) + (x * (Math.log(x) + -1.0));
	} else {
		tmp = ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + ((y + 0.0007936500793651) * ((z * z) * (1.0 / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 5300000.0:
		tmp = ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) + (x * (math.log(x) + -1.0))
	else:
		tmp = ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + ((y + 0.0007936500793651) * ((z * z) * (1.0 / x)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 5300000.0)
		tmp = Float64(Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778))) / x) + Float64(x * Float64(log(x) + -1.0)));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(Float64(y + 0.0007936500793651) * Float64(Float64(z * z) * Float64(1.0 / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 5300000.0)
		tmp = ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) + (x * (log(x) + -1.0));
	else
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((y + 0.0007936500793651) * ((z * z) * (1.0 / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 5300000.0], N[(N[(N[(0.083333333333333 + N[(z * N[(N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] + N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(N[(z * z), $MachinePrecision] * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 5.3e6

   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. Taylor expanded in x around inf 99.2%

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

      1. sub-neg 37.8%

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

      2. mul-1-neg 37.8%

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

      3. log-rec 37.8%

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

      4. remove-double-neg 37.8%

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

      5. metadata-eval 37.8%

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

   4. Simplified 99.2%

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

   if 5.3e6 < x

   1. Initial program 91.3%

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

   2. Taylor expanded in z around inf 91.3%

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

      1. associate-/l* 96.2%

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

      2. unpow2 96.2%

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

   4. Simplified 96.2%

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

      1. associate-/r/ 96.3%

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

      2. +-commutative 96.3%

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

   6. Applied egg-rr 96.3%

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

      1. div-inv 96.3%

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

   8. Applied egg-rr 96.3%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5300000:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} + x \cdot \left(\log x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(y + 0.0007936500793651\right) \cdot \left(\left(z \cdot z\right) \cdot \frac{1}{x}\right)\\ \end{array} \]

Alternative 4: 92.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-70} \lor \neg \left(z \leq 5.5 \cdot 10^{-14}\right):\\ \;\;\;\;\left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x} + \left(x \cdot \log x - x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.2e-70) (not (<= z 5.5e-14)))
   (+ (* (+ y 0.0007936500793651) (/ (* z z) x)) (- (* x (log x)) x))
   (+
    (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
    (/ (+ 0.083333333333333 (* z -0.0027777777777778)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.2e-70) || !(z <= 5.5e-14)) {
		tmp = ((y + 0.0007936500793651) * ((z * z) / x)) + ((x * log(x)) - x);
	} else {
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((0.083333333333333 + (z * -0.0027777777777778)) / 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 <= (-5.2d-70)) .or. (.not. (z <= 5.5d-14))) then
        tmp = ((y + 0.0007936500793651d0) * ((z * z) / x)) + ((x * log(x)) - x)
    else
        tmp = ((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + ((0.083333333333333d0 + (z * (-0.0027777777777778d0))) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.2e-70) || !(z <= 5.5e-14)) {
		tmp = ((y + 0.0007936500793651) * ((z * z) / x)) + ((x * Math.log(x)) - x);
	} else {
		tmp = ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + ((0.083333333333333 + (z * -0.0027777777777778)) / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.2e-70) or not (z <= 5.5e-14):
		tmp = ((y + 0.0007936500793651) * ((z * z) / x)) + ((x * math.log(x)) - x)
	else:
		tmp = ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + ((0.083333333333333 + (z * -0.0027777777777778)) / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.2e-70) || !(z <= 5.5e-14))
		tmp = Float64(Float64(Float64(y + 0.0007936500793651) * Float64(Float64(z * z) / x)) + Float64(Float64(x * log(x)) - x));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(Float64(0.083333333333333 + Float64(z * -0.0027777777777778)) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.2e-70) || ~((z <= 5.5e-14)))
		tmp = ((y + 0.0007936500793651) * ((z * z) / x)) + ((x * log(x)) - x);
	else
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((0.083333333333333 + (z * -0.0027777777777778)) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.2e-70], N[Not[LessEqual[z, 5.5e-14]], $MachinePrecision]], N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(N[(z * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(N[(0.083333333333333 + N[(z * -0.0027777777777778), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.20000000000000004e-70 or 5.49999999999999991e-14 < z

   1. Initial program 93.4%

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

   2. Taylor expanded in z around inf 93.1%

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

      1. associate-/l* 96.9%

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

      2. unpow2 96.9%

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

   4. Simplified 96.9%

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

      1. associate-/r/ 96.9%

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

      2. +-commutative 96.9%

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

   6. Applied egg-rr 96.9%

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

   7. Taylor expanded in x around inf 96.9%

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

      1. sub-neg 96.9%

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

      2. mul-1-neg 96.9%

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

      3. log-rec 96.9%

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

      4. remove-double-neg 96.9%

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

      5. metadata-eval 96.9%

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

      6. distribute-rgt-in 96.9%

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

      7. neg-mul-1 96.9%

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

      8. sub-neg 96.9%

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

      9. *-commutative 96.9%

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

   9. Simplified 96.9%

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

   if -5.20000000000000004e-70 < z < 5.49999999999999991e-14

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0 96.0%

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

      1. *-commutative 96.0%

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

   4. Simplified 96.0%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{z \cdot -0.0027777777777778} + 0.083333333333333}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-70} \lor \neg \left(z \leq 5.5 \cdot 10^{-14}\right):\\ \;\;\;\;\left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x} + \left(x \cdot \log x - x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \end{array} \]

Alternative 5: 95.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 10000000:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} + x \cdot \left(\log x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x} + \left(x \cdot \log x - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 10000000.0)
   (+
    (/
     (+
      0.083333333333333
      (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))
     x)
    (* x (+ (log x) -1.0)))
   (+ (* (+ y 0.0007936500793651) (/ (* z z) x)) (- (* x (log x)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 10000000.0) {
		tmp = ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) + (x * (log(x) + -1.0));
	} else {
		tmp = ((y + 0.0007936500793651) * ((z * z) / x)) + ((x * log(x)) - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 10000000.0d0) then
        tmp = ((0.083333333333333d0 + (z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0))) / x) + (x * (log(x) + (-1.0d0)))
    else
        tmp = ((y + 0.0007936500793651d0) * ((z * z) / x)) + ((x * log(x)) - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 10000000.0) {
		tmp = ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) + (x * (Math.log(x) + -1.0));
	} else {
		tmp = ((y + 0.0007936500793651) * ((z * z) / x)) + ((x * Math.log(x)) - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 10000000.0:
		tmp = ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) + (x * (math.log(x) + -1.0))
	else:
		tmp = ((y + 0.0007936500793651) * ((z * z) / x)) + ((x * math.log(x)) - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 10000000.0)
		tmp = Float64(Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778))) / x) + Float64(x * Float64(log(x) + -1.0)));
	else
		tmp = Float64(Float64(Float64(y + 0.0007936500793651) * Float64(Float64(z * z) / x)) + Float64(Float64(x * log(x)) - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 10000000.0)
		tmp = ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) + (x * (log(x) + -1.0));
	else
		tmp = ((y + 0.0007936500793651) * ((z * z) / x)) + ((x * log(x)) - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 10000000.0], N[(N[(N[(0.083333333333333 + N[(z * N[(N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] + N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(N[(z * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1e7

   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. Taylor expanded in x around inf 99.2%

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

      1. sub-neg 37.8%

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

      2. mul-1-neg 37.8%

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

      3. log-rec 37.8%

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

      4. remove-double-neg 37.8%

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

      5. metadata-eval 37.8%

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

   4. Simplified 99.2%

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

   if 1e7 < x

   1. Initial program 91.3%

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

   2. Taylor expanded in z around inf 91.3%

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

      1. associate-/l* 96.2%

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

      2. unpow2 96.2%

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

   4. Simplified 96.2%

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

      1. associate-/r/ 96.3%

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

      2. +-commutative 96.3%

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

   6. Applied egg-rr 96.3%

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

   7. Taylor expanded in x around inf 95.9%

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

      1. sub-neg 95.9%

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

      2. mul-1-neg 95.9%

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

      3. log-rec 95.9%

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

      4. remove-double-neg 95.9%

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

      5. metadata-eval 95.9%

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

      6. distribute-rgt-in 95.9%

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

      7. neg-mul-1 95.9%

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

      8. sub-neg 95.9%

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

      9. *-commutative 95.9%

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

   9. Simplified 95.9%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 10000000:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} + x \cdot \left(\log x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x} + \left(x \cdot \log x - x\right)\\ \end{array} \]

Alternative 6: 95.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5300000:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} + x \cdot \left(\log x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 5300000.0)
   (+
    (/
     (+
      0.083333333333333
      (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))
     x)
    (* x (+ (log x) -1.0)))
   (+
    (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
    (* (+ y 0.0007936500793651) (/ (* z z) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 5300000.0) {
		tmp = ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) + (x * (log(x) + -1.0));
	} else {
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((y + 0.0007936500793651) * ((z * z) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 5300000.0d0) then
        tmp = ((0.083333333333333d0 + (z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0))) / x) + (x * (log(x) + (-1.0d0)))
    else
        tmp = ((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + ((y + 0.0007936500793651d0) * ((z * z) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 5300000.0) {
		tmp = ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) + (x * (Math.log(x) + -1.0));
	} else {
		tmp = ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + ((y + 0.0007936500793651) * ((z * z) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 5300000.0:
		tmp = ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) + (x * (math.log(x) + -1.0))
	else:
		tmp = ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + ((y + 0.0007936500793651) * ((z * z) / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 5300000.0)
		tmp = Float64(Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778))) / x) + Float64(x * Float64(log(x) + -1.0)));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(Float64(y + 0.0007936500793651) * Float64(Float64(z * z) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 5300000.0)
		tmp = ((0.083333333333333 + (z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778))) / x) + (x * (log(x) + -1.0));
	else
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((y + 0.0007936500793651) * ((z * z) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 5300000.0], N[(N[(N[(0.083333333333333 + N[(z * N[(N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] + N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(N[(z * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 5.3e6

   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. Taylor expanded in x around inf 99.2%

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

      1. sub-neg 37.8%

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

      2. mul-1-neg 37.8%

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

      3. log-rec 37.8%

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

      4. remove-double-neg 37.8%

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

      5. metadata-eval 37.8%

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

   4. Simplified 99.2%

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

   if 5.3e6 < x

   1. Initial program 91.3%

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

   2. Taylor expanded in z around inf 91.3%

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

      1. associate-/l* 96.2%

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

      2. unpow2 96.2%

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

   4. Simplified 96.2%

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

      1. associate-/r/ 96.3%

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

      2. +-commutative 96.3%

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

   6. Applied egg-rr 96.3%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5300000:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} + x \cdot \left(\log x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x}\\ \end{array} \]

Alternative 7: 92.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-70} \lor \neg \left(z \leq 1.95 \cdot 10^{-13}\right):\\ \;\;\;\;\left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x} + \left(x \cdot \log x - x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.3e-70) (not (<= z 1.95e-13)))
   (+ (* (+ y 0.0007936500793651) (/ (* z z) x)) (- (* x (log x)) x))
   (+
    (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
    (/ 0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.3e-70) || !(z <= 1.95e-13)) {
		tmp = ((y + 0.0007936500793651) * ((z * z) / x)) + ((x * log(x)) - x);
	} 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 <= (-5.3d-70)) .or. (.not. (z <= 1.95d-13))) then
        tmp = ((y + 0.0007936500793651d0) * ((z * z) / x)) + ((x * log(x)) - x)
    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 <= -5.3e-70) || !(z <= 1.95e-13)) {
		tmp = ((y + 0.0007936500793651) * ((z * z) / x)) + ((x * Math.log(x)) - x);
	} 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 <= -5.3e-70) or not (z <= 1.95e-13):
		tmp = ((y + 0.0007936500793651) * ((z * z) / x)) + ((x * math.log(x)) - x)
	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 <= -5.3e-70) || !(z <= 1.95e-13))
		tmp = Float64(Float64(Float64(y + 0.0007936500793651) * Float64(Float64(z * z) / x)) + Float64(Float64(x * log(x)) - x));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.3e-70) || ~((z <= 1.95e-13)))
		tmp = ((y + 0.0007936500793651) * ((z * z) / x)) + ((x * log(x)) - x);
	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, -5.3e-70], N[Not[LessEqual[z, 1.95e-13]], $MachinePrecision]], N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(N[(z * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.29999999999999983e-70 or 1.95000000000000002e-13 < z

   1. Initial program 93.4%

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

   2. Taylor expanded in z around inf 93.1%

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

      1. associate-/l* 96.9%

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

      2. unpow2 96.9%

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

   4. Simplified 96.9%

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

      1. associate-/r/ 96.9%

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

      2. +-commutative 96.9%

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

   6. Applied egg-rr 96.9%

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

   7. Taylor expanded in x around inf 96.9%

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

      1. sub-neg 96.9%

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

      2. mul-1-neg 96.9%

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

      3. log-rec 96.9%

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

      4. remove-double-neg 96.9%

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

      5. metadata-eval 96.9%

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

      6. distribute-rgt-in 96.9%

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

      7. neg-mul-1 96.9%

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

      8. sub-neg 96.9%

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

      9. *-commutative 96.9%

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

   9. Simplified 96.9%

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

   if -5.29999999999999983e-70 < z < 1.95000000000000002e-13

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0 95.9%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-70} \lor \neg \left(z \leq 1.95 \cdot 10^{-13}\right):\\ \;\;\;\;\left(y + 0.0007936500793651\right) \cdot \frac{z \cdot z}{x} + \left(x \cdot \log x - x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 8: 80.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(\log x + -1\right)\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{-70} \lor \neg \left(z \leq 1.35 \cdot 10^{-11}\right):\\ \;\;\;\;t_0 + \frac{y}{\frac{x}{z \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{1}{x \cdot 12.000000000000048}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ (log x) -1.0))))
   (if (or (<= z -1.5e-70) (not (<= z 1.35e-11)))
     (+ t_0 (/ y (/ x (* z z))))
     (+ t_0 (/ 1.0 (* x 12.000000000000048))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (log(x) + -1.0);
	double tmp;
	if ((z <= -1.5e-70) || !(z <= 1.35e-11)) {
		tmp = t_0 + (y / (x / (z * z)));
	} else {
		tmp = t_0 + (1.0 / (x * 12.000000000000048));
	}
	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 * (log(x) + (-1.0d0))
    if ((z <= (-1.5d-70)) .or. (.not. (z <= 1.35d-11))) then
        tmp = t_0 + (y / (x / (z * z)))
    else
        tmp = t_0 + (1.0d0 / (x * 12.000000000000048d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (Math.log(x) + -1.0);
	double tmp;
	if ((z <= -1.5e-70) || !(z <= 1.35e-11)) {
		tmp = t_0 + (y / (x / (z * z)));
	} else {
		tmp = t_0 + (1.0 / (x * 12.000000000000048));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (math.log(x) + -1.0)
	tmp = 0
	if (z <= -1.5e-70) or not (z <= 1.35e-11):
		tmp = t_0 + (y / (x / (z * z)))
	else:
		tmp = t_0 + (1.0 / (x * 12.000000000000048))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(log(x) + -1.0))
	tmp = 0.0
	if ((z <= -1.5e-70) || !(z <= 1.35e-11))
		tmp = Float64(t_0 + Float64(y / Float64(x / Float64(z * z))));
	else
		tmp = Float64(t_0 + Float64(1.0 / Float64(x * 12.000000000000048)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (log(x) + -1.0);
	tmp = 0.0;
	if ((z <= -1.5e-70) || ~((z <= 1.35e-11)))
		tmp = t_0 + (y / (x / (z * z)));
	else
		tmp = t_0 + (1.0 / (x * 12.000000000000048));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -1.5e-70], N[Not[LessEqual[z, 1.35e-11]], $MachinePrecision]], N[(t$95$0 + N[(y / N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(1.0 / N[(x * 12.000000000000048), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5000000000000001e-70 or 1.35000000000000002e-11 < z

   1. Initial program 93.4%

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

   2. Taylor expanded in x around inf 93.5%

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

      1. sub-neg 24.0%

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

      2. mul-1-neg 24.0%

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

      3. log-rec 24.0%

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

      4. remove-double-neg 24.0%

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

      5. metadata-eval 24.0%

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

   4. Simplified 93.5%

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

   5. Taylor expanded in y around inf 71.6%

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

      1. associate-/l* 77.4%

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

      2. unpow2 77.4%

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

   7. Simplified 77.4%

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

   if -1.5000000000000001e-70 < z < 1.35000000000000002e-11

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0 95.9%

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

   3. Taylor expanded in x around inf 94.9%

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

      1. sub-neg 94.9%

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

      2. mul-1-neg 94.9%

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

      3. log-rec 94.9%

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

      4. remove-double-neg 94.9%

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

      5. metadata-eval 94.9%

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

   5. Simplified 94.9%

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

      1. add-sqr-sqrt 94.8%

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

   7. Applied egg-rr 94.8%

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

      1. add-sqr-sqrt 94.9%

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

      2. clear-num 94.9%

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

      3. div-inv 95.0%

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

      4. metadata-eval 95.0%

         \[\leadsto x \cdot \left(\log x + -1\right) + \frac{1}{x \cdot \color{blue}{12.000000000000048}} \]

   9. Applied egg-rr 95.0%

      \[\leadsto x \cdot \left(\log x + -1\right) + \color{blue}{\frac{1}{x \cdot 12.000000000000048}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-70} \lor \neg \left(z \leq 1.35 \cdot 10^{-11}\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{y}{\frac{x}{z \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{1}{x \cdot 12.000000000000048}\\ \end{array} \]

Alternative 9: 81.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-70} \lor \neg \left(z \leq 3.2 \cdot 10^{-14}\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{y}{\frac{x}{z \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.3e-70) (not (<= z 3.2e-14)))
   (+ (* x (+ (log x) -1.0)) (/ 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 <= -5.3e-70) || !(z <= 3.2e-14)) {
		tmp = (x * (log(x) + -1.0)) + (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 <= (-5.3d-70)) .or. (.not. (z <= 3.2d-14))) then
        tmp = (x * (log(x) + (-1.0d0))) + (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 <= -5.3e-70) || !(z <= 3.2e-14)) {
		tmp = (x * (Math.log(x) + -1.0)) + (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 <= -5.3e-70) or not (z <= 3.2e-14):
		tmp = (x * (math.log(x) + -1.0)) + (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 <= -5.3e-70) || !(z <= 3.2e-14))
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(y / Float64(x / Float64(z * z))));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.3e-70) || ~((z <= 3.2e-14)))
		tmp = (x * (log(x) + -1.0)) + (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, -5.3e-70], N[Not[LessEqual[z, 3.2e-14]], $MachinePrecision]], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.29999999999999983e-70 or 3.2000000000000002e-14 < z

   1. Initial program 93.4%

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

   2. Taylor expanded in x around inf 93.5%

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

      1. sub-neg 24.0%

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

      2. mul-1-neg 24.0%

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

      3. log-rec 24.0%

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

      4. remove-double-neg 24.0%

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

      5. metadata-eval 24.0%

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

   4. Simplified 93.5%

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

   5. Taylor expanded in y around inf 71.6%

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

      1. associate-/l* 77.4%

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

      2. unpow2 77.4%

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

   7. Simplified 77.4%

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

   if -5.29999999999999983e-70 < z < 3.2000000000000002e-14

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0 95.9%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-70} \lor \neg \left(z \leq 3.2 \cdot 10^{-14}\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{y}{\frac{x}{z \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 10: 53.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5300000:\\ \;\;\;\;\frac{\frac{0.0069444444444443885}{x \cdot x} - x \cdot x}{x + \frac{0.083333333333333}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{-0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 5300000.0)
   (/
    (- (/ 0.0069444444444443885 (* x x)) (* x x))
    (+ x (/ 0.083333333333333 x)))
   (+ (* x (+ (log x) -1.0)) (/ -0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 5300000.0) {
		tmp = ((0.0069444444444443885 / (x * x)) - (x * x)) / (x + (0.083333333333333 / 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 <= 5300000.0d0) then
        tmp = ((0.0069444444444443885d0 / (x * x)) - (x * x)) / (x + (0.083333333333333d0 / 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 <= 5300000.0) {
		tmp = ((0.0069444444444443885 / (x * x)) - (x * x)) / (x + (0.083333333333333 / x));
	} else {
		tmp = (x * (Math.log(x) + -1.0)) + (-0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 5300000.0:
		tmp = ((0.0069444444444443885 / (x * x)) - (x * x)) / (x + (0.083333333333333 / 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 <= 5300000.0)
		tmp = Float64(Float64(Float64(0.0069444444444443885 / Float64(x * x)) - Float64(x * x)) / Float64(x + Float64(0.083333333333333 / 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 <= 5300000.0)
		tmp = ((0.0069444444444443885 / (x * x)) - (x * x)) / (x + (0.083333333333333 / x));
	else
		tmp = (x * (log(x) + -1.0)) + (-0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 5300000.0], N[(N[(N[(0.0069444444444443885 / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(x * x), $MachinePrecision]), $MachinePrecision] / N[(x + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(-0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 5.3e6

   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. Taylor expanded in z around 0 38.3%

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

      1. add-cube-cbrt 38.3%

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

      2. pow3 38.3%

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

      3. sub-neg 38.3%

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

      4. metadata-eval 38.3%

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

   4. Applied egg-rr 38.3%

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

   5. Taylor expanded in x around inf 37.9%

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

      1. neg-mul-1 37.9%

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

   7. Simplified 37.9%

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

      1. +-commutative 37.9%

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

      2. flip-+ 49.1%

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

      3. frac-times 49.2%

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

      4. metadata-eval 49.2%

         \[\leadsto \frac{\frac{\color{blue}{0.0069444444444443885}}{x \cdot x} - \left(-x\right) \cdot \left(-x\right)}{\frac{0.083333333333333}{x} - \left(-x\right)} \]

      5. sqr-neg 49.2%

         \[\leadsto \frac{\frac{0.0069444444444443885}{x \cdot x} - \color{blue}{x \cdot x}}{\frac{0.083333333333333}{x} - \left(-x\right)} \]

      6. add-sqr-sqrt 0.0%

         \[\leadsto \frac{\frac{0.0069444444444443885}{x \cdot x} - x \cdot x}{\frac{0.083333333333333}{x} - \color{blue}{\sqrt{-x} \cdot \sqrt{-x}}} \]

      7. sqrt-unprod 49.1%

         \[\leadsto \frac{\frac{0.0069444444444443885}{x \cdot x} - x \cdot x}{\frac{0.083333333333333}{x} - \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}} \]

      8. sqr-neg 49.1%

         \[\leadsto \frac{\frac{0.0069444444444443885}{x \cdot x} - x \cdot x}{\frac{0.083333333333333}{x} - \sqrt{\color{blue}{x \cdot x}}} \]

      9. sqrt-unprod 49.1%

         \[\leadsto \frac{\frac{0.0069444444444443885}{x \cdot x} - x \cdot x}{\frac{0.083333333333333}{x} - \color{blue}{\sqrt{x} \cdot \sqrt{x}}} \]

      10. add-sqr-sqrt 49.1%

          \[\leadsto \frac{\frac{0.0069444444444443885}{x \cdot x} - x \cdot x}{\frac{0.083333333333333}{x} - \color{blue}{x}} \]

      11. unsub-neg 49.1%

          \[\leadsto \frac{\frac{0.0069444444444443885}{x \cdot x} - x \cdot x}{\color{blue}{\frac{0.083333333333333}{x} + \left(-x\right)}} \]

      12. +-commutative 49.1%

          \[\leadsto \frac{\frac{0.0069444444444443885}{x \cdot x} - x \cdot x}{\color{blue}{\left(-x\right) + \frac{0.083333333333333}{x}}} \]

      13. add-sqr-sqrt 0.0%

          \[\leadsto \frac{\frac{0.0069444444444443885}{x \cdot x} - x \cdot x}{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}} + \frac{0.083333333333333}{x}} \]

      14. sqrt-unprod 49.2%

          \[\leadsto \frac{\frac{0.0069444444444443885}{x \cdot x} - x \cdot x}{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} + \frac{0.083333333333333}{x}} \]

      15. sqr-neg 49.2%

          \[\leadsto \frac{\frac{0.0069444444444443885}{x \cdot x} - x \cdot x}{\sqrt{\color{blue}{x \cdot x}} + \frac{0.083333333333333}{x}} \]

      16. sqrt-unprod 49.2%

          \[\leadsto \frac{\frac{0.0069444444444443885}{x \cdot x} - x \cdot x}{\color{blue}{\sqrt{x} \cdot \sqrt{x}} + \frac{0.083333333333333}{x}} \]

      17. add-sqr-sqrt 49.2%

          \[\leadsto \frac{\frac{0.0069444444444443885}{x \cdot x} - x \cdot x}{\color{blue}{x} + \frac{0.083333333333333}{x}} \]

   9. Applied egg-rr 49.2%

      \[\leadsto \color{blue}{\frac{\frac{0.0069444444444443885}{x \cdot x} - x \cdot x}{x + \frac{0.083333333333333}{x}}} \]

   if 5.3e6 < x

   1. Initial program 91.3%

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

   2. Taylor expanded in z around 0 74.2%

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

   3. Taylor expanded in x around inf 73.9%

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

      1. sub-neg 73.9%

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

      2. mul-1-neg 73.9%

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

      3. log-rec 73.9%

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

      4. remove-double-neg 73.9%

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

      5. metadata-eval 73.9%

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

   5. Simplified 73.9%

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

      1. add-sqr-sqrt 73.9%

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

   7. Applied egg-rr 73.9%

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

      1. add-sqr-sqrt 73.9%

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

      2. frac-2neg 73.9%

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

      3. metadata-eval 73.9%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 73.9%

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

      6. sqr-neg 73.9%

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

      7. sqrt-unprod 73.9%

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

      8. add-sqr-sqrt 73.9%

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

   9. Applied egg-rr 73.9%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5300000:\\ \;\;\;\;\frac{\frac{0.0069444444444443885}{x \cdot x} - x \cdot x}{x + \frac{0.083333333333333}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{-0.083333333333333}{x}\\ \end{array} \]

Alternative 11: 34.6% accurate, 6.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{0.083333333333333}{x}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+16} \lor \neg \left(z \leq 1.05 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{\frac{0.0069444444444443885}{x \cdot x} - x \cdot x}{t_0}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (/ 0.083333333333333 x))))
   (if (or (<= z -3.1e+16) (not (<= z 1.05e-8)))
     (/ (- (/ 0.0069444444444443885 (* x x)) (* x x)) t_0)
     t_0)))

C

double code(double x, double y, double z) {
	double t_0 = x + (0.083333333333333 / x);
	double tmp;
	if ((z <= -3.1e+16) || !(z <= 1.05e-8)) {
		tmp = ((0.0069444444444443885 / (x * x)) - (x * x)) / t_0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x + (0.083333333333333d0 / x)
    if ((z <= (-3.1d+16)) .or. (.not. (z <= 1.05d-8))) then
        tmp = ((0.0069444444444443885d0 / (x * x)) - (x * x)) / t_0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (0.083333333333333 / x);
	double tmp;
	if ((z <= -3.1e+16) || !(z <= 1.05e-8)) {
		tmp = ((0.0069444444444443885 / (x * x)) - (x * x)) / t_0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (0.083333333333333 / x)
	tmp = 0
	if (z <= -3.1e+16) or not (z <= 1.05e-8):
		tmp = ((0.0069444444444443885 / (x * x)) - (x * x)) / t_0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(0.083333333333333 / x))
	tmp = 0.0
	if ((z <= -3.1e+16) || !(z <= 1.05e-8))
		tmp = Float64(Float64(Float64(0.0069444444444443885 / Float64(x * x)) - Float64(x * x)) / t_0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (0.083333333333333 / x);
	tmp = 0.0;
	if ((z <= -3.1e+16) || ~((z <= 1.05e-8)))
		tmp = ((0.0069444444444443885 / (x * x)) - (x * x)) / t_0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -3.1e+16], N[Not[LessEqual[z, 1.05e-8]], $MachinePrecision]], N[(N[(N[(0.0069444444444443885 / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(x * x), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision], t$95$0]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1e16 or 1.04999999999999997e-8 < z

   1. Initial program 92.9%

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

   2. Taylor expanded in z around 0 21.5%

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

      1. add-cube-cbrt 21.4%

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

      2. pow3 21.3%

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

      3. sub-neg 21.3%

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

      4. metadata-eval 21.3%

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

   4. Applied egg-rr 21.3%

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

   5. Taylor expanded in x around inf 3.0%

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

      1. neg-mul-1 3.0%

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

   7. Simplified 3.0%

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

      1. +-commutative 3.0%

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

      2. flip-+ 29.1%

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

      3. frac-times 29.1%

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

      4. metadata-eval 29.1%

         \[\leadsto \frac{\frac{\color{blue}{0.0069444444444443885}}{x \cdot x} - \left(-x\right) \cdot \left(-x\right)}{\frac{0.083333333333333}{x} - \left(-x\right)} \]

      5. sqr-neg 29.1%

         \[\leadsto \frac{\frac{0.0069444444444443885}{x \cdot x} - \color{blue}{x \cdot x}}{\frac{0.083333333333333}{x} - \left(-x\right)} \]

      6. add-sqr-sqrt 0.0%

         \[\leadsto \frac{\frac{0.0069444444444443885}{x \cdot x} - x \cdot x}{\frac{0.083333333333333}{x} - \color{blue}{\sqrt{-x} \cdot \sqrt{-x}}} \]

      7. sqrt-unprod 27.1%

         \[\leadsto \frac{\frac{0.0069444444444443885}{x \cdot x} - x \cdot x}{\frac{0.083333333333333}{x} - \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}} \]

      8. sqr-neg 27.1%

         \[\leadsto \frac{\frac{0.0069444444444443885}{x \cdot x} - x \cdot x}{\frac{0.083333333333333}{x} - \sqrt{\color{blue}{x \cdot x}}} \]

      9. sqrt-unprod 32.4%

         \[\leadsto \frac{\frac{0.0069444444444443885}{x \cdot x} - x \cdot x}{\frac{0.083333333333333}{x} - \color{blue}{\sqrt{x} \cdot \sqrt{x}}} \]

      10. add-sqr-sqrt 32.4%

          \[\leadsto \frac{\frac{0.0069444444444443885}{x \cdot x} - x \cdot x}{\frac{0.083333333333333}{x} - \color{blue}{x}} \]

      11. unsub-neg 32.4%

          \[\leadsto \frac{\frac{0.0069444444444443885}{x \cdot x} - x \cdot x}{\color{blue}{\frac{0.083333333333333}{x} + \left(-x\right)}} \]

      12. +-commutative 32.4%

          \[\leadsto \frac{\frac{0.0069444444444443885}{x \cdot x} - x \cdot x}{\color{blue}{\left(-x\right) + \frac{0.083333333333333}{x}}} \]

      13. add-sqr-sqrt 0.0%

          \[\leadsto \frac{\frac{0.0069444444444443885}{x \cdot x} - x \cdot x}{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}} + \frac{0.083333333333333}{x}} \]

      14. sqrt-unprod 26.2%

          \[\leadsto \frac{\frac{0.0069444444444443885}{x \cdot x} - x \cdot x}{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} + \frac{0.083333333333333}{x}} \]

      15. sqr-neg 26.2%

          \[\leadsto \frac{\frac{0.0069444444444443885}{x \cdot x} - x \cdot x}{\sqrt{\color{blue}{x \cdot x}} + \frac{0.083333333333333}{x}} \]

      16. sqrt-unprod 29.1%

          \[\leadsto \frac{\frac{0.0069444444444443885}{x \cdot x} - x \cdot x}{\color{blue}{\sqrt{x} \cdot \sqrt{x}} + \frac{0.083333333333333}{x}} \]

      17. add-sqr-sqrt 29.1%

          \[\leadsto \frac{\frac{0.0069444444444443885}{x \cdot x} - x \cdot x}{\color{blue}{x} + \frac{0.083333333333333}{x}} \]

   9. Applied egg-rr 29.1%

      \[\leadsto \color{blue}{\frac{\frac{0.0069444444444443885}{x \cdot x} - x \cdot x}{x + \frac{0.083333333333333}{x}}} \]

   if -3.1e16 < z < 1.04999999999999997e-8

   1. Initial program 99.5%

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

   2. Taylor expanded in z around 0 91.5%

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

      1. add-cube-cbrt 90.6%

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

      2. pow3 90.6%

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

      3. sub-neg 90.6%

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

      4. metadata-eval 90.6%

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

   4. Applied egg-rr 90.6%

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

   5. Taylor expanded in x around inf 42.3%

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

      1. neg-mul-1 42.3%

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

   7. Simplified 42.3%

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

      1. expm1-log1p-u 38.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(-x\right) + \frac{0.083333333333333}{x}\right)\right)} \]

      2. expm1-udef 38.6%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\left(-x\right) + \frac{0.083333333333333}{x}\right)} - 1} \]

      3. add-sqr-sqrt 0.0%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\sqrt{-x} \cdot \sqrt{-x}} + \frac{0.083333333333333}{x}\right)} - 1 \]

      4. sqrt-unprod 43.7%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} + \frac{0.083333333333333}{x}\right)} - 1 \]

      5. sqr-neg 43.7%

         \[\leadsto e^{\mathsf{log1p}\left(\sqrt{\color{blue}{x \cdot x}} + \frac{0.083333333333333}{x}\right)} - 1 \]

      6. sqrt-unprod 45.6%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\sqrt{x} \cdot \sqrt{x}} + \frac{0.083333333333333}{x}\right)} - 1 \]

      7. add-sqr-sqrt 45.6%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{x} + \frac{0.083333333333333}{x}\right)} - 1 \]

   9. Applied egg-rr 45.6%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(x + \frac{0.083333333333333}{x}\right)} - 1} \]
   10. Step-by-step derivation

       1. expm1-def 45.6%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x + \frac{0.083333333333333}{x}\right)\right)} \]

       2. expm1-log1p 48.8%

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

   11. Simplified 48.8%

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

4. Final simplification 38.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+16} \lor \neg \left(z \leq 1.05 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{\frac{0.0069444444444443885}{x \cdot x} - x \cdot x}{x + \frac{0.083333333333333}{x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 12: 27.3% accurate, 24.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.0%

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

2. Taylor expanded in z around 0 54.3%

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

   1. add-cube-cbrt 53.8%

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

   2. pow3 53.8%

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

   3. sub-neg 53.8%

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

   4. metadata-eval 53.8%

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

4. Applied egg-rr 53.8%

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

5. Taylor expanded in x around inf 21.4%

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

   1. neg-mul-1 21.4%

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

7. Simplified 21.4%

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

   1. expm1-log1p-u 19.4%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(-x\right) + \frac{0.083333333333333}{x}\right)\right)} \]

   2. expm1-udef 19.4%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\left(-x\right) + \frac{0.083333333333333}{x}\right)} - 1} \]

   3. add-sqr-sqrt 0.0%

      \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\sqrt{-x} \cdot \sqrt{-x}} + \frac{0.083333333333333}{x}\right)} - 1 \]

   4. sqrt-unprod 25.3%

      \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} + \frac{0.083333333333333}{x}\right)} - 1 \]

   5. sqr-neg 25.3%

      \[\leadsto e^{\mathsf{log1p}\left(\sqrt{\color{blue}{x \cdot x}} + \frac{0.083333333333333}{x}\right)} - 1 \]

   6. sqrt-unprod 24.5%

      \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\sqrt{x} \cdot \sqrt{x}} + \frac{0.083333333333333}{x}\right)} - 1 \]

   7. add-sqr-sqrt 24.5%

      \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{x} + \frac{0.083333333333333}{x}\right)} - 1 \]

9. Applied egg-rr 24.5%

   \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(x + \frac{0.083333333333333}{x}\right)} - 1} \]
10. Step-by-step derivation

    1. expm1-def 24.5%

       \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x + \frac{0.083333333333333}{x}\right)\right)} \]

    2. expm1-log1p 26.0%

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

11. Simplified 26.0%

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

12. Final simplification 26.0%

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

Alternative 13: 23.4% accurate, 41.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.0%

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

2. Taylor expanded in z around 0 54.3%

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

   1. add-cube-cbrt 53.8%

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

   2. pow3 53.8%

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

   3. sub-neg 53.8%

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

   4. metadata-eval 53.8%

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

4. Applied egg-rr 53.8%

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

5. Taylor expanded in x around inf 21.4%

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

   1. neg-mul-1 21.4%

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

7. Simplified 21.4%

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

8. Taylor expanded in x around 0 22.3%

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

9. Final simplification 22.3%

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

Alternative 14: 1.3% accurate, 61.5× speedup

Math

\[\begin{array}{l} \\ -x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- x))

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = -x
end function

Java

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

Python

def code(x, y, z):
	return -x

Julia

function code(x, y, z)
	return Float64(-x)
end

MATLAB

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

Wolfram

code[x_, y_, z_] := (-x)

Derivation

1. Initial program 96.0%

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

2. Taylor expanded in z around 0 54.3%

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

   1. add-cube-cbrt 53.8%

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

   2. pow3 53.8%

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

   3. sub-neg 53.8%

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

   4. metadata-eval 53.8%

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

4. Applied egg-rr 53.8%

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

5. Taylor expanded in x around inf 21.4%

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

   1. neg-mul-1 21.4%

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

7. Simplified 21.4%

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

8. Taylor expanded in x around inf 1.3%

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

   1. mul-1-neg 1.3%

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

10. Simplified 1.3%

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

11. Final simplification 1.3%

    \[\leadsto -x \]

Developer target: 98.8% 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 2023277 
(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)))