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

Percentage Accurate: 93.8% → 99.6%

Time: 14.7s

Alternatives: 13

Speedup: 1.0×

• 28.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 90000000000:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + z \cdot \left(z \cdot \frac{y + 0.0007936500793651}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 90000000000.0)
   (+
    (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
    (/
     (+
      (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778))
      0.083333333333333)
     x))
   (+ (* x (+ (log x) -1.0)) (* z (* z (/ (+ y 0.0007936500793651) x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 90000000000.0) {
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x);
	} else {
		tmp = (x * (log(x) + -1.0)) + (z * (z * ((y + 0.0007936500793651) / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 90000000000.0d0) then
        tmp = ((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + (((z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0)) + 0.083333333333333d0) / x)
    else
        tmp = (x * (log(x) + (-1.0d0))) + (z * (z * ((y + 0.0007936500793651d0) / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 90000000000.0) {
		tmp = ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x);
	} else {
		tmp = (x * (Math.log(x) + -1.0)) + (z * (z * ((y + 0.0007936500793651) / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 90000000000.0:
		tmp = ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x)
	else:
		tmp = (x * (math.log(x) + -1.0)) + (z * (z * ((y + 0.0007936500793651) / x)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 90000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(Float64(Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x));
	else
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(z * Float64(z * Float64(Float64(y + 0.0007936500793651) / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 90000000000.0)
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x);
	else
		tmp = (x * (log(x) + -1.0)) + (z * (z * ((y + 0.0007936500793651) / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 90000000000.0], N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(N[(N[(z * N[(N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(z * N[(z * N[(N[(y + 0.0007936500793651), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 9e10

   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 9e10 < x

   1. Initial program 87.0%

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

   2. Taylor expanded in x around inf 87.1%

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

      1. *-commutative 87.1%

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

      2. sub-neg 87.1%

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

      3. mul-1-neg 87.1%

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

      4. log-rec 87.1%

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

      5. remove-double-neg 87.1%

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

      6. metadata-eval 87.1%

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

   4. Simplified 87.1%

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

   5. Taylor expanded in z around inf 87.1%

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

      1. associate-/l* 91.2%

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

      2. unpow2 91.2%

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

   7. Simplified 91.2%

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

   8. Taylor expanded in z around 0 87.1%

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

      1. associate-/l* 91.2%

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

      2. *-rgt-identity 91.2%

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

      3. associate-*r/ 91.2%

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

      4. unpow2 91.2%

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

      5. associate-*l* 99.6%

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

      6. associate-/r/ 99.7%

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

      7. associate-*l/ 99.7%

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

      8. *-lft-identity 99.7%

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

   10. Simplified 99.7%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 90000000000:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + z \cdot \left(z \cdot \frac{y + 0.0007936500793651}{x}\right)\\ \end{array} \]

Alternative 2: 98.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(\log x + -1\right)\\ \mathbf{if}\;x \leq 10000000000:\\ \;\;\;\;\frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x} + t_0\\ \mathbf{else}:\\ \;\;\;\;t_0 + z \cdot \left(z \cdot \frac{y + 0.0007936500793651}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ (log x) -1.0))))
   (if (<= x 10000000000.0)
     (+
      (/
       (+
        (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778))
        0.083333333333333)
       x)
      t_0)
     (+ t_0 (* z (* z (/ (+ y 0.0007936500793651) x)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (log(x) + -1.0);
	double tmp;
	if (x <= 10000000000.0) {
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + t_0;
	} else {
		tmp = t_0 + (z * (z * ((y + 0.0007936500793651) / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (log(x) + (-1.0d0))
    if (x <= 10000000000.0d0) then
        tmp = (((z * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0)) + 0.083333333333333d0) / x) + t_0
    else
        tmp = t_0 + (z * (z * ((y + 0.0007936500793651d0) / x)))
    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 (x <= 10000000000.0) {
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + t_0;
	} else {
		tmp = t_0 + (z * (z * ((y + 0.0007936500793651) / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (math.log(x) + -1.0)
	tmp = 0
	if x <= 10000000000.0:
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + t_0
	else:
		tmp = t_0 + (z * (z * ((y + 0.0007936500793651) / x)))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(log(x) + -1.0))
	tmp = 0.0
	if (x <= 10000000000.0)
		tmp = Float64(Float64(Float64(Float64(z * Float64(Float64(z * Float64(y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + t_0);
	else
		tmp = Float64(t_0 + Float64(z * Float64(z * Float64(Float64(y + 0.0007936500793651) / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (log(x) + -1.0);
	tmp = 0.0;
	if (x <= 10000000000.0)
		tmp = (((z * ((z * (y + 0.0007936500793651)) - 0.0027777777777778)) + 0.083333333333333) / x) + t_0;
	else
		tmp = t_0 + (z * (z * ((y + 0.0007936500793651) / x)));
	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[LessEqual[x, 10000000000.0], N[(N[(N[(N[(z * N[(N[(z * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision] + t$95$0), $MachinePrecision], N[(t$95$0 + N[(z * N[(z * N[(N[(y + 0.0007936500793651), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 1e10

   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 99.5%

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

      1. *-commutative 99.5%

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

      2. sub-neg 99.5%

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

      3. mul-1-neg 99.5%

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

      4. log-rec 99.5%

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

      5. remove-double-neg 99.5%

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

      6. metadata-eval 99.5%

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

   4. Simplified 99.5%

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

   if 1e10 < x

   1. Initial program 87.0%

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

   2. Taylor expanded in x around inf 87.1%

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

      1. *-commutative 87.1%

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

      2. sub-neg 87.1%

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

      3. mul-1-neg 87.1%

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

      4. log-rec 87.1%

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

      5. remove-double-neg 87.1%

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

      6. metadata-eval 87.1%

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

   4. Simplified 87.1%

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

   5. Taylor expanded in z around inf 87.1%

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

      1. associate-/l* 91.2%

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

      2. unpow2 91.2%

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

   7. Simplified 91.2%

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

   8. Taylor expanded in z around 0 87.1%

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

      1. associate-/l* 91.2%

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

      2. *-rgt-identity 91.2%

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

      3. associate-*r/ 91.2%

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

      4. unpow2 91.2%

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

      5. associate-*l* 99.6%

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

      6. associate-/r/ 99.7%

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

      7. associate-*l/ 99.7%

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

      8. *-lft-identity 99.7%

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

   10. Simplified 99.7%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 10000000000:\\ \;\;\;\;\frac{z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right) + 0.083333333333333}{x} + x \cdot \left(\log x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + z \cdot \left(z \cdot \frac{y + 0.0007936500793651}{x}\right)\\ \end{array} \]

Alternative 3: 80.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(\log x + -1\right)\\ t_1 := t_0 + y \cdot \left(z \cdot \frac{z}{x}\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 205:\\ \;\;\;\;t_0 + \frac{0.083333333333333}{x}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+224}:\\ \;\;\;\;t_0 + 0.0007936500793651 \cdot \frac{z}{\frac{x}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ (log x) -1.0))) (t_1 (+ t_0 (* y (* z (/ z x))))))
   (if (<= z -2e-94)
     t_1
     (if (<= z 205.0)
       (+ t_0 (/ 0.083333333333333 x))
       (if (<= z 5.3e+224)
         (+ t_0 (* 0.0007936500793651 (/ z (/ x z))))
         t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = x * (log(x) + -1.0);
	double t_1 = t_0 + (y * (z * (z / x)));
	double tmp;
	if (z <= -2e-94) {
		tmp = t_1;
	} else if (z <= 205.0) {
		tmp = t_0 + (0.083333333333333 / x);
	} else if (z <= 5.3e+224) {
		tmp = t_0 + (0.0007936500793651 * (z / (x / z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * (log(x) + (-1.0d0))
    t_1 = t_0 + (y * (z * (z / x)))
    if (z <= (-2d-94)) then
        tmp = t_1
    else if (z <= 205.0d0) then
        tmp = t_0 + (0.083333333333333d0 / x)
    else if (z <= 5.3d+224) then
        tmp = t_0 + (0.0007936500793651d0 * (z / (x / z)))
    else
        tmp = t_1
    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 t_1 = t_0 + (y * (z * (z / x)));
	double tmp;
	if (z <= -2e-94) {
		tmp = t_1;
	} else if (z <= 205.0) {
		tmp = t_0 + (0.083333333333333 / x);
	} else if (z <= 5.3e+224) {
		tmp = t_0 + (0.0007936500793651 * (z / (x / z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (math.log(x) + -1.0)
	t_1 = t_0 + (y * (z * (z / x)))
	tmp = 0
	if z <= -2e-94:
		tmp = t_1
	elif z <= 205.0:
		tmp = t_0 + (0.083333333333333 / x)
	elif z <= 5.3e+224:
		tmp = t_0 + (0.0007936500793651 * (z / (x / z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(log(x) + -1.0))
	t_1 = Float64(t_0 + Float64(y * Float64(z * Float64(z / x))))
	tmp = 0.0
	if (z <= -2e-94)
		tmp = t_1;
	elseif (z <= 205.0)
		tmp = Float64(t_0 + Float64(0.083333333333333 / x));
	elseif (z <= 5.3e+224)
		tmp = Float64(t_0 + Float64(0.0007936500793651 * Float64(z / Float64(x / z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (log(x) + -1.0);
	t_1 = t_0 + (y * (z * (z / x)));
	tmp = 0.0;
	if (z <= -2e-94)
		tmp = t_1;
	elseif (z <= 205.0)
		tmp = t_0 + (0.083333333333333 / x);
	elseif (z <= 5.3e+224)
		tmp = t_0 + (0.0007936500793651 * (z / (x / z)));
	else
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(t$95$0 + N[(y * N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e-94], t$95$1, If[LessEqual[z, 205.0], N[(t$95$0 + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.3e+224], N[(t$95$0 + N[(0.0007936500793651 * N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9999999999999999e-94 or 5.2999999999999999e224 < z

   1. Initial program 91.7%

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

   2. Taylor expanded in x around inf 91.8%

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

      1. *-commutative 91.8%

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

      2. sub-neg 91.8%

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

      3. mul-1-neg 91.8%

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

      4. log-rec 91.8%

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

      5. remove-double-neg 91.8%

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

      6. metadata-eval 91.8%

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

   4. Simplified 91.8%

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

   5. Taylor expanded in z around inf 85.4%

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

      1. associate-/l* 85.9%

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

      2. unpow2 85.9%

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

   7. Simplified 85.9%

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

   8. Taylor expanded in y around inf 69.6%

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

      1. associate-*r/ 73.1%

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

      2. unpow2 73.1%

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

      3. associate-/l* 77.0%

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

   10. Simplified 77.0%

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

       1. associate-/r/ 77.0%

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

   12. Applied egg-rr 77.0%

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

   if -1.9999999999999999e-94 < z < 205

   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 x around inf 99.3%

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

      1. *-commutative 99.3%

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

      2. sub-neg 99.3%

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

      3. mul-1-neg 99.3%

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

      4. log-rec 99.3%

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

      5. remove-double-neg 99.3%

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

      6. metadata-eval 99.3%

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

   4. Simplified 99.3%

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

   5. Taylor expanded in z around 0 94.5%

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

   if 205 < z < 5.2999999999999999e224

   1. Initial program 89.6%

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

   2. Taylor expanded in x around inf 89.6%

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

      1. *-commutative 89.6%

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

      2. sub-neg 89.6%

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

      3. mul-1-neg 89.6%

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

      4. log-rec 89.6%

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

      5. remove-double-neg 89.6%

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

      6. metadata-eval 89.6%

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

   4. Simplified 89.6%

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

   5. Taylor expanded in z around inf 88.7%

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

      1. associate-/l* 92.1%

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

      2. unpow2 92.1%

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

   7. Simplified 92.1%

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

   8. Taylor expanded in y around 0 77.1%

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

      1. unpow2 77.1%

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

      2. associate-/l* 80.3%

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

   10. Simplified 80.3%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-94}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + y \cdot \left(z \cdot \frac{z}{x}\right)\\ \mathbf{elif}\;z \leq 205:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333}{x}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+224}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + 0.0007936500793651 \cdot \frac{z}{\frac{x}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + y \cdot \left(z \cdot \frac{z}{x}\right)\\ \end{array} \]

Alternative 4: 80.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(\log x + -1\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{-94}:\\ \;\;\;\;t_0 + \frac{y}{\frac{\frac{x}{z}}{z}}\\ \mathbf{elif}\;z \leq 205:\\ \;\;\;\;t_0 + \frac{0.083333333333333}{x}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+226}:\\ \;\;\;\;t_0 + 0.0007936500793651 \cdot \frac{z}{\frac{x}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + y \cdot \left(z \cdot \frac{z}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ (log x) -1.0))))
   (if (<= z -2e-94)
     (+ t_0 (/ y (/ (/ x z) z)))
     (if (<= z 205.0)
       (+ t_0 (/ 0.083333333333333 x))
       (if (<= z 3.2e+226)
         (+ t_0 (* 0.0007936500793651 (/ z (/ x z))))
         (+ t_0 (* y (* z (/ z x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (log(x) + -1.0);
	double tmp;
	if (z <= -2e-94) {
		tmp = t_0 + (y / ((x / z) / z));
	} else if (z <= 205.0) {
		tmp = t_0 + (0.083333333333333 / x);
	} else if (z <= 3.2e+226) {
		tmp = t_0 + (0.0007936500793651 * (z / (x / z)));
	} else {
		tmp = t_0 + (y * (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) :: t_0
    real(8) :: tmp
    t_0 = x * (log(x) + (-1.0d0))
    if (z <= (-2d-94)) then
        tmp = t_0 + (y / ((x / z) / z))
    else if (z <= 205.0d0) then
        tmp = t_0 + (0.083333333333333d0 / x)
    else if (z <= 3.2d+226) then
        tmp = t_0 + (0.0007936500793651d0 * (z / (x / z)))
    else
        tmp = t_0 + (y * (z * (z / x)))
    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 <= -2e-94) {
		tmp = t_0 + (y / ((x / z) / z));
	} else if (z <= 205.0) {
		tmp = t_0 + (0.083333333333333 / x);
	} else if (z <= 3.2e+226) {
		tmp = t_0 + (0.0007936500793651 * (z / (x / z)));
	} else {
		tmp = t_0 + (y * (z * (z / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (math.log(x) + -1.0)
	tmp = 0
	if z <= -2e-94:
		tmp = t_0 + (y / ((x / z) / z))
	elif z <= 205.0:
		tmp = t_0 + (0.083333333333333 / x)
	elif z <= 3.2e+226:
		tmp = t_0 + (0.0007936500793651 * (z / (x / z)))
	else:
		tmp = t_0 + (y * (z * (z / x)))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(log(x) + -1.0))
	tmp = 0.0
	if (z <= -2e-94)
		tmp = Float64(t_0 + Float64(y / Float64(Float64(x / z) / z)));
	elseif (z <= 205.0)
		tmp = Float64(t_0 + Float64(0.083333333333333 / x));
	elseif (z <= 3.2e+226)
		tmp = Float64(t_0 + Float64(0.0007936500793651 * Float64(z / Float64(x / z))));
	else
		tmp = Float64(t_0 + Float64(y * Float64(z * Float64(z / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (log(x) + -1.0);
	tmp = 0.0;
	if (z <= -2e-94)
		tmp = t_0 + (y / ((x / z) / z));
	elseif (z <= 205.0)
		tmp = t_0 + (0.083333333333333 / x);
	elseif (z <= 3.2e+226)
		tmp = t_0 + (0.0007936500793651 * (z / (x / z)));
	else
		tmp = t_0 + (y * (z * (z / x)));
	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[LessEqual[z, -2e-94], N[(t$95$0 + N[(y / N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 205.0], N[(t$95$0 + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+226], N[(t$95$0 + N[(0.0007936500793651 * N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(y * N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.9999999999999999e-94

   1. Initial program 93.6%

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

   2. Taylor expanded in x around inf 93.6%

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

      1. *-commutative 93.6%

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

      2. sub-neg 93.6%

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

      3. mul-1-neg 93.6%

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

      4. log-rec 93.6%

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

      5. remove-double-neg 93.6%

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

      6. metadata-eval 93.6%

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

   4. Simplified 93.6%

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

   5. Taylor expanded in y around inf 69.0%

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

      1. associate-/l* 73.0%

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

      2. unpow2 73.0%

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

      3. associate-/r* 76.3%

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

   7. Simplified 76.3%

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

   if -1.9999999999999999e-94 < z < 205

   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 x around inf 99.3%

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

      1. *-commutative 99.3%

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

      2. sub-neg 99.3%

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

      3. mul-1-neg 99.3%

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

      4. log-rec 99.3%

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

      5. remove-double-neg 99.3%

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

      6. metadata-eval 99.3%

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

   4. Simplified 99.3%

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

   5. Taylor expanded in z around 0 94.5%

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

   if 205 < z < 3.19999999999999977e226

   1. Initial program 89.6%

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

   2. Taylor expanded in x around inf 89.6%

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

      1. *-commutative 89.6%

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

      2. sub-neg 89.6%

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

      3. mul-1-neg 89.6%

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

      4. log-rec 89.6%

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

      5. remove-double-neg 89.6%

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

      6. metadata-eval 89.6%

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

   4. Simplified 89.6%

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

   5. Taylor expanded in z around inf 88.7%

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

      1. associate-/l* 92.1%

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

      2. unpow2 92.1%

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

   7. Simplified 92.1%

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

   8. Taylor expanded in y around 0 77.1%

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

      1. unpow2 77.1%

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

      2. associate-/l* 80.3%

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

   10. Simplified 80.3%

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

   if 3.19999999999999977e226 < z

   1. Initial program 81.1%

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

   2. Taylor expanded in x around inf 81.1%

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

      1. *-commutative 81.1%

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

      2. sub-neg 81.1%

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

      3. mul-1-neg 81.1%

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

      4. log-rec 81.1%

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

      5. remove-double-neg 81.1%

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

      6. metadata-eval 81.1%

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

   4. Simplified 81.1%

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

   5. Taylor expanded in z around inf 81.1%

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

      1. associate-/l* 81.1%

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

      2. unpow2 81.1%

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

   7. Simplified 81.1%

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

   8. Taylor expanded in y around inf 73.3%

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

      1. associate-*r/ 73.3%

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

      2. unpow2 73.3%

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

      3. associate-/l* 81.1%

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

   10. Simplified 81.1%

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

       1. associate-/r/ 81.1%

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

   12. Applied egg-rr 81.1%

       \[\leadsto x \cdot \left(\log x + -1\right) + y \cdot \color{blue}{\left(\frac{z}{x} \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-94}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{y}{\frac{\frac{x}{z}}{z}}\\ \mathbf{elif}\;z \leq 205:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333}{x}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+226}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + 0.0007936500793651 \cdot \frac{z}{\frac{x}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + y \cdot \left(z \cdot \frac{z}{x}\right)\\ \end{array} \]

Alternative 5: 80.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(\log x + -1\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{-94}:\\ \;\;\;\;t_0 + \frac{y}{\frac{\frac{x}{z}}{z}}\\ \mathbf{elif}\;z \leq 205:\\ \;\;\;\;t_0 + \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+224}:\\ \;\;\;\;t_0 + 0.0007936500793651 \cdot \frac{z}{\frac{x}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + y \cdot \left(z \cdot \frac{z}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ (log x) -1.0))))
   (if (<= z -2e-94)
     (+ t_0 (/ y (/ (/ x z) z)))
     (if (<= z 205.0)
       (+ t_0 (/ (+ 0.083333333333333 (* z -0.0027777777777778)) x))
       (if (<= z 4.8e+224)
         (+ t_0 (* 0.0007936500793651 (/ z (/ x z))))
         (+ t_0 (* y (* z (/ z x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (log(x) + -1.0);
	double tmp;
	if (z <= -2e-94) {
		tmp = t_0 + (y / ((x / z) / z));
	} else if (z <= 205.0) {
		tmp = t_0 + ((0.083333333333333 + (z * -0.0027777777777778)) / x);
	} else if (z <= 4.8e+224) {
		tmp = t_0 + (0.0007936500793651 * (z / (x / z)));
	} else {
		tmp = t_0 + (y * (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) :: t_0
    real(8) :: tmp
    t_0 = x * (log(x) + (-1.0d0))
    if (z <= (-2d-94)) then
        tmp = t_0 + (y / ((x / z) / z))
    else if (z <= 205.0d0) then
        tmp = t_0 + ((0.083333333333333d0 + (z * (-0.0027777777777778d0))) / x)
    else if (z <= 4.8d+224) then
        tmp = t_0 + (0.0007936500793651d0 * (z / (x / z)))
    else
        tmp = t_0 + (y * (z * (z / x)))
    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 <= -2e-94) {
		tmp = t_0 + (y / ((x / z) / z));
	} else if (z <= 205.0) {
		tmp = t_0 + ((0.083333333333333 + (z * -0.0027777777777778)) / x);
	} else if (z <= 4.8e+224) {
		tmp = t_0 + (0.0007936500793651 * (z / (x / z)));
	} else {
		tmp = t_0 + (y * (z * (z / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (math.log(x) + -1.0)
	tmp = 0
	if z <= -2e-94:
		tmp = t_0 + (y / ((x / z) / z))
	elif z <= 205.0:
		tmp = t_0 + ((0.083333333333333 + (z * -0.0027777777777778)) / x)
	elif z <= 4.8e+224:
		tmp = t_0 + (0.0007936500793651 * (z / (x / z)))
	else:
		tmp = t_0 + (y * (z * (z / x)))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(log(x) + -1.0))
	tmp = 0.0
	if (z <= -2e-94)
		tmp = Float64(t_0 + Float64(y / Float64(Float64(x / z) / z)));
	elseif (z <= 205.0)
		tmp = Float64(t_0 + Float64(Float64(0.083333333333333 + Float64(z * -0.0027777777777778)) / x));
	elseif (z <= 4.8e+224)
		tmp = Float64(t_0 + Float64(0.0007936500793651 * Float64(z / Float64(x / z))));
	else
		tmp = Float64(t_0 + Float64(y * Float64(z * Float64(z / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (log(x) + -1.0);
	tmp = 0.0;
	if (z <= -2e-94)
		tmp = t_0 + (y / ((x / z) / z));
	elseif (z <= 205.0)
		tmp = t_0 + ((0.083333333333333 + (z * -0.0027777777777778)) / x);
	elseif (z <= 4.8e+224)
		tmp = t_0 + (0.0007936500793651 * (z / (x / z)));
	else
		tmp = t_0 + (y * (z * (z / x)));
	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[LessEqual[z, -2e-94], N[(t$95$0 + N[(y / N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 205.0], N[(t$95$0 + N[(N[(0.083333333333333 + N[(z * -0.0027777777777778), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e+224], N[(t$95$0 + N[(0.0007936500793651 * N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(y * N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.9999999999999999e-94

   1. Initial program 93.6%

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

   2. Taylor expanded in x around inf 93.6%

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

      1. *-commutative 93.6%

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

      2. sub-neg 93.6%

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

      3. mul-1-neg 93.6%

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

      4. log-rec 93.6%

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

      5. remove-double-neg 93.6%

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

      6. metadata-eval 93.6%

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

   4. Simplified 93.6%

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

   5. Taylor expanded in y around inf 69.0%

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

      1. associate-/l* 73.0%

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

      2. unpow2 73.0%

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

      3. associate-/r* 76.3%

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

   7. Simplified 76.3%

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

   if -1.9999999999999999e-94 < z < 205

   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 x around inf 99.3%

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

      1. *-commutative 99.3%

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

      2. sub-neg 99.3%

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

      3. mul-1-neg 99.3%

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

      4. log-rec 99.3%

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

      5. remove-double-neg 99.3%

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

      6. metadata-eval 99.3%

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

   4. Simplified 99.3%

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

   5. Taylor expanded in z around 0 94.5%

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

      1. *-commutative 94.5%

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

   7. Simplified 94.5%

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

   if 205 < z < 4.80000000000000002e224

   1. Initial program 89.6%

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

   2. Taylor expanded in x around inf 89.6%

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

      1. *-commutative 89.6%

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

      2. sub-neg 89.6%

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

      3. mul-1-neg 89.6%

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

      4. log-rec 89.6%

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

      5. remove-double-neg 89.6%

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

      6. metadata-eval 89.6%

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

   4. Simplified 89.6%

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

   5. Taylor expanded in z around inf 88.7%

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

      1. associate-/l* 92.1%

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

      2. unpow2 92.1%

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

   7. Simplified 92.1%

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

   8. Taylor expanded in y around 0 77.1%

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

      1. unpow2 77.1%

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

      2. associate-/l* 80.3%

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

   10. Simplified 80.3%

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

   if 4.80000000000000002e224 < z

   1. Initial program 81.1%

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

   2. Taylor expanded in x around inf 81.1%

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

      1. *-commutative 81.1%

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

      2. sub-neg 81.1%

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

      3. mul-1-neg 81.1%

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

      4. log-rec 81.1%

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

      5. remove-double-neg 81.1%

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

      6. metadata-eval 81.1%

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

   4. Simplified 81.1%

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

   5. Taylor expanded in z around inf 81.1%

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

      1. associate-/l* 81.1%

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

      2. unpow2 81.1%

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

   7. Simplified 81.1%

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

   8. Taylor expanded in y around inf 73.3%

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

      1. associate-*r/ 73.3%

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

      2. unpow2 73.3%

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

      3. associate-/l* 81.1%

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

   10. Simplified 81.1%

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

       1. associate-/r/ 81.1%

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

   12. Applied egg-rr 81.1%

       \[\leadsto x \cdot \left(\log x + -1\right) + y \cdot \color{blue}{\left(\frac{z}{x} \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-94}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{y}{\frac{\frac{x}{z}}{z}}\\ \mathbf{elif}\;z \leq 205:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+224}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + 0.0007936500793651 \cdot \frac{z}{\frac{x}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + y \cdot \left(z \cdot \frac{z}{x}\right)\\ \end{array} \]

Alternative 6: 81.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(\log x + -1\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{-94}:\\ \;\;\;\;t_0 + \frac{y}{\frac{\frac{x}{z}}{z}}\\ \mathbf{elif}\;z \leq 205:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \mathbf{elif}\;z \leq 7.1 \cdot 10^{+224}:\\ \;\;\;\;t_0 + 0.0007936500793651 \cdot \frac{z}{\frac{x}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + y \cdot \left(z \cdot \frac{z}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ (log x) -1.0))))
   (if (<= z -2e-94)
     (+ t_0 (/ y (/ (/ x z) z)))
     (if (<= z 205.0)
       (+
        (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
        (/ 0.083333333333333 x))
       (if (<= z 7.1e+224)
         (+ t_0 (* 0.0007936500793651 (/ z (/ x z))))
         (+ t_0 (* y (* z (/ z x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (log(x) + -1.0);
	double tmp;
	if (z <= -2e-94) {
		tmp = t_0 + (y / ((x / z) / z));
	} else if (z <= 205.0) {
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	} else if (z <= 7.1e+224) {
		tmp = t_0 + (0.0007936500793651 * (z / (x / z)));
	} else {
		tmp = t_0 + (y * (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) :: t_0
    real(8) :: tmp
    t_0 = x * (log(x) + (-1.0d0))
    if (z <= (-2d-94)) then
        tmp = t_0 + (y / ((x / z) / z))
    else if (z <= 205.0d0) then
        tmp = ((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + (0.083333333333333d0 / x)
    else if (z <= 7.1d+224) then
        tmp = t_0 + (0.0007936500793651d0 * (z / (x / z)))
    else
        tmp = t_0 + (y * (z * (z / x)))
    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 <= -2e-94) {
		tmp = t_0 + (y / ((x / z) / z));
	} else if (z <= 205.0) {
		tmp = ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	} else if (z <= 7.1e+224) {
		tmp = t_0 + (0.0007936500793651 * (z / (x / z)));
	} else {
		tmp = t_0 + (y * (z * (z / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (math.log(x) + -1.0)
	tmp = 0
	if z <= -2e-94:
		tmp = t_0 + (y / ((x / z) / z))
	elif z <= 205.0:
		tmp = ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x)
	elif z <= 7.1e+224:
		tmp = t_0 + (0.0007936500793651 * (z / (x / z)))
	else:
		tmp = t_0 + (y * (z * (z / x)))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(log(x) + -1.0))
	tmp = 0.0
	if (z <= -2e-94)
		tmp = Float64(t_0 + Float64(y / Float64(Float64(x / z) / z)));
	elseif (z <= 205.0)
		tmp = Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(0.083333333333333 / x));
	elseif (z <= 7.1e+224)
		tmp = Float64(t_0 + Float64(0.0007936500793651 * Float64(z / Float64(x / z))));
	else
		tmp = Float64(t_0 + Float64(y * Float64(z * Float64(z / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (log(x) + -1.0);
	tmp = 0.0;
	if (z <= -2e-94)
		tmp = t_0 + (y / ((x / z) / z));
	elseif (z <= 205.0)
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	elseif (z <= 7.1e+224)
		tmp = t_0 + (0.0007936500793651 * (z / (x / z)));
	else
		tmp = t_0 + (y * (z * (z / x)));
	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[LessEqual[z, -2e-94], N[(t$95$0 + N[(y / N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 205.0], 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], If[LessEqual[z, 7.1e+224], N[(t$95$0 + N[(0.0007936500793651 * N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(y * N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.9999999999999999e-94

   1. Initial program 93.6%

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

   2. Taylor expanded in x around inf 93.6%

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

      1. *-commutative 93.6%

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

      2. sub-neg 93.6%

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

      3. mul-1-neg 93.6%

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

      4. log-rec 93.6%

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

      5. remove-double-neg 93.6%

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

      6. metadata-eval 93.6%

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

   4. Simplified 93.6%

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

   5. Taylor expanded in y around inf 69.0%

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

      1. associate-/l* 73.0%

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

      2. unpow2 73.0%

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

      3. associate-/r* 76.3%

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

   7. Simplified 76.3%

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

   if -1.9999999999999999e-94 < z < 205

   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 94.7%

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

   if 205 < z < 7.0999999999999998e224

   1. Initial program 89.6%

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

   2. Taylor expanded in x around inf 89.6%

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

      1. *-commutative 89.6%

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

      2. sub-neg 89.6%

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

      3. mul-1-neg 89.6%

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

      4. log-rec 89.6%

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

      5. remove-double-neg 89.6%

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

      6. metadata-eval 89.6%

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

   4. Simplified 89.6%

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

   5. Taylor expanded in z around inf 88.7%

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

      1. associate-/l* 92.1%

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

      2. unpow2 92.1%

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

   7. Simplified 92.1%

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

   8. Taylor expanded in y around 0 77.1%

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

      1. unpow2 77.1%

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

      2. associate-/l* 80.3%

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

   10. Simplified 80.3%

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

   if 7.0999999999999998e224 < z

   1. Initial program 81.1%

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

   2. Taylor expanded in x around inf 81.1%

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

      1. *-commutative 81.1%

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

      2. sub-neg 81.1%

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

      3. mul-1-neg 81.1%

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

      4. log-rec 81.1%

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

      5. remove-double-neg 81.1%

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

      6. metadata-eval 81.1%

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

   4. Simplified 81.1%

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

   5. Taylor expanded in z around inf 81.1%

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

      1. associate-/l* 81.1%

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

      2. unpow2 81.1%

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

   7. Simplified 81.1%

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

   8. Taylor expanded in y around inf 73.3%

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

      1. associate-*r/ 73.3%

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

      2. unpow2 73.3%

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

      3. associate-/l* 81.1%

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

   10. Simplified 81.1%

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

       1. associate-/r/ 81.1%

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

   12. Applied egg-rr 81.1%

       \[\leadsto x \cdot \left(\log x + -1\right) + y \cdot \color{blue}{\left(\frac{z}{x} \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-94}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{y}{\frac{\frac{x}{z}}{z}}\\ \mathbf{elif}\;z \leq 205:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \mathbf{elif}\;z \leq 7.1 \cdot 10^{+224}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + 0.0007936500793651 \cdot \frac{z}{\frac{x}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + y \cdot \left(z \cdot \frac{z}{x}\right)\\ \end{array} \]

Alternative 7: 95.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-13} \lor \neg \left(z \leq 9.2 \cdot 10^{-36}\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + z \cdot \left(z \cdot \frac{y + 0.0007936500793651}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.6e-13) (not (<= z 9.2e-36)))
   (+ (* x (+ (log x) -1.0)) (* z (* z (/ (+ y 0.0007936500793651) 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 <= -2.6e-13) || !(z <= 9.2e-36)) {
		tmp = (x * (log(x) + -1.0)) + (z * (z * ((y + 0.0007936500793651) / 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 <= (-2.6d-13)) .or. (.not. (z <= 9.2d-36))) then
        tmp = (x * (log(x) + (-1.0d0))) + (z * (z * ((y + 0.0007936500793651d0) / 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 <= -2.6e-13) || !(z <= 9.2e-36)) {
		tmp = (x * (Math.log(x) + -1.0)) + (z * (z * ((y + 0.0007936500793651) / 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 <= -2.6e-13) or not (z <= 9.2e-36):
		tmp = (x * (math.log(x) + -1.0)) + (z * (z * ((y + 0.0007936500793651) / 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 <= -2.6e-13) || !(z <= 9.2e-36))
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(z * Float64(z * Float64(Float64(y + 0.0007936500793651) / 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 <= -2.6e-13) || ~((z <= 9.2e-36)))
		tmp = (x * (log(x) + -1.0)) + (z * (z * ((y + 0.0007936500793651) / 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, -2.6e-13], N[Not[LessEqual[z, 9.2e-36]], $MachinePrecision]], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(z * N[(z * N[(N[(y + 0.0007936500793651), $MachinePrecision] / x), $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 < -2.6e-13 or 9.19999999999999986e-36 < z

   1. Initial program 90.0%

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

   2. Taylor expanded in x around inf 90.1%

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

      1. *-commutative 90.1%

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

      2. sub-neg 90.1%

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

      3. mul-1-neg 90.1%

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

      4. log-rec 90.1%

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

      5. remove-double-neg 90.1%

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

      6. metadata-eval 90.1%

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

   4. Simplified 90.1%

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

   5. Taylor expanded in z around inf 89.2%

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

      1. associate-/l* 92.4%

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

      2. unpow2 92.4%

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

   7. Simplified 92.4%

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

   8. Taylor expanded in z around 0 89.2%

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

      1. associate-/l* 92.4%

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

      2. *-rgt-identity 92.4%

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

      3. associate-*r/ 92.3%

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

      4. unpow2 92.3%

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

      5. associate-*l* 98.9%

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

      6. associate-/r/ 98.9%

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

      7. associate-*l/ 99.0%

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

      8. *-lft-identity 99.0%

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

   10. Simplified 99.0%

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

   if -2.6e-13 < z < 9.19999999999999986e-36

   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 90.6%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-13} \lor \neg \left(z \leq 9.2 \cdot 10^{-36}\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + z \cdot \left(z \cdot \frac{y + 0.0007936500793651}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 8: 94.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(\log x + -1\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{-94}:\\ \;\;\;\;t_0 + \left(y + 0.0007936500793651\right) \cdot \frac{z}{\frac{x}{z}}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-32}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;t_0 + z \cdot \left(z \cdot \frac{y + 0.0007936500793651}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ (log x) -1.0))))
   (if (<= z -2e-94)
     (+ t_0 (* (+ y 0.0007936500793651) (/ z (/ x z))))
     (if (<= z 3e-32)
       (+
        (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
        (/ 0.083333333333333 x))
       (+ t_0 (* z (* z (/ (+ y 0.0007936500793651) x))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (log(x) + -1.0);
	double tmp;
	if (z <= -2e-94) {
		tmp = t_0 + ((y + 0.0007936500793651) * (z / (x / z)));
	} else if (z <= 3e-32) {
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	} else {
		tmp = t_0 + (z * (z * ((y + 0.0007936500793651) / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (log(x) + (-1.0d0))
    if (z <= (-2d-94)) then
        tmp = t_0 + ((y + 0.0007936500793651d0) * (z / (x / z)))
    else if (z <= 3d-32) then
        tmp = ((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + (0.083333333333333d0 / x)
    else
        tmp = t_0 + (z * (z * ((y + 0.0007936500793651d0) / x)))
    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 <= -2e-94) {
		tmp = t_0 + ((y + 0.0007936500793651) * (z / (x / z)));
	} else if (z <= 3e-32) {
		tmp = ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	} else {
		tmp = t_0 + (z * (z * ((y + 0.0007936500793651) / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (math.log(x) + -1.0)
	tmp = 0
	if z <= -2e-94:
		tmp = t_0 + ((y + 0.0007936500793651) * (z / (x / z)))
	elif z <= 3e-32:
		tmp = ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x)
	else:
		tmp = t_0 + (z * (z * ((y + 0.0007936500793651) / x)))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(log(x) + -1.0))
	tmp = 0.0
	if (z <= -2e-94)
		tmp = Float64(t_0 + Float64(Float64(y + 0.0007936500793651) * Float64(z / Float64(x / z))));
	elseif (z <= 3e-32)
		tmp = Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(0.083333333333333 / x));
	else
		tmp = Float64(t_0 + Float64(z * Float64(z * Float64(Float64(y + 0.0007936500793651) / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (log(x) + -1.0);
	tmp = 0.0;
	if (z <= -2e-94)
		tmp = t_0 + ((y + 0.0007936500793651) * (z / (x / z)));
	elseif (z <= 3e-32)
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	else
		tmp = t_0 + (z * (z * ((y + 0.0007936500793651) / x)));
	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[LessEqual[z, -2e-94], N[(t$95$0 + N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e-32], 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], N[(t$95$0 + N[(z * N[(z * N[(N[(y + 0.0007936500793651), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9999999999999999e-94

   1. Initial program 93.6%

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

   2. Taylor expanded in x around inf 93.6%

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

      1. *-commutative 93.6%

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

      2. sub-neg 93.6%

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

      3. mul-1-neg 93.6%

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

      4. log-rec 93.6%

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

      5. remove-double-neg 93.6%

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

      6. metadata-eval 93.6%

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

   4. Simplified 93.6%

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

   5. Taylor expanded in z around inf 86.1%

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

      1. associate-/l* 86.8%

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

      2. unpow2 86.8%

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

   7. Simplified 86.8%

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

   8. Taylor expanded in z around 0 86.1%

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

      1. associate-*l/ 89.3%

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

      2. unpow2 89.3%

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

      3. *-commutative 89.3%

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

      4. associate-/l* 92.3%

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

   10. Simplified 92.3%

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

   if -1.9999999999999999e-94 < z < 3e-32

   1. Initial program 99.5%

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

   2. Taylor expanded in z around 0 96.5%

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

   if 3e-32 < z

   1. Initial program 88.4%

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

   2. Taylor expanded in x around inf 88.5%

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

      1. *-commutative 88.5%

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

      2. sub-neg 88.5%

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

      3. mul-1-neg 88.5%

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

      4. log-rec 88.5%

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

      5. remove-double-neg 88.5%

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

      6. metadata-eval 88.5%

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

   4. Simplified 88.5%

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

   5. Taylor expanded in z around inf 87.7%

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

      1. associate-/l* 90.3%

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

      2. unpow2 90.3%

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

   7. Simplified 90.3%

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

   8. Taylor expanded in z around 0 87.7%

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

      1. associate-/l* 90.3%

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

      2. *-rgt-identity 90.3%

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

      3. associate-*r/ 90.3%

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

      4. unpow2 90.3%

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

      5. associate-*l* 99.0%

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

      6. associate-/r/ 99.0%

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

      7. associate-*l/ 99.0%

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

      8. *-lft-identity 99.0%

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

   10. Simplified 99.0%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-94}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z}{\frac{x}{z}}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-32}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + z \cdot \left(z \cdot \frac{y + 0.0007936500793651}{x}\right)\\ \end{array} \]

Alternative 9: 97.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(\log x + -1\right)\\ \mathbf{if}\;z \leq -19000:\\ \;\;\;\;t_0 + z \cdot \left(z \cdot \frac{y + 0.0007936500793651}{x}\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-13}:\\ \;\;\;\;t_0 + \frac{0.083333333333333 + z \cdot \left(y \cdot z\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(y + 0.0007936500793651\right) \cdot \frac{z}{\frac{x}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ (log x) -1.0))))
   (if (<= z -19000.0)
     (+ t_0 (* z (* z (/ (+ y 0.0007936500793651) x))))
     (if (<= z 1.2e-13)
       (+ t_0 (/ (+ 0.083333333333333 (* z (* y z))) x))
       (+ t_0 (* (+ y 0.0007936500793651) (/ z (/ x z))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (log(x) + -1.0);
	double tmp;
	if (z <= -19000.0) {
		tmp = t_0 + (z * (z * ((y + 0.0007936500793651) / x)));
	} else if (z <= 1.2e-13) {
		tmp = t_0 + ((0.083333333333333 + (z * (y * z))) / x);
	} else {
		tmp = t_0 + ((y + 0.0007936500793651) * (z / (x / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (log(x) + (-1.0d0))
    if (z <= (-19000.0d0)) then
        tmp = t_0 + (z * (z * ((y + 0.0007936500793651d0) / x)))
    else if (z <= 1.2d-13) then
        tmp = t_0 + ((0.083333333333333d0 + (z * (y * z))) / x)
    else
        tmp = t_0 + ((y + 0.0007936500793651d0) * (z / (x / z)))
    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 <= -19000.0) {
		tmp = t_0 + (z * (z * ((y + 0.0007936500793651) / x)));
	} else if (z <= 1.2e-13) {
		tmp = t_0 + ((0.083333333333333 + (z * (y * z))) / x);
	} else {
		tmp = t_0 + ((y + 0.0007936500793651) * (z / (x / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (math.log(x) + -1.0)
	tmp = 0
	if z <= -19000.0:
		tmp = t_0 + (z * (z * ((y + 0.0007936500793651) / x)))
	elif z <= 1.2e-13:
		tmp = t_0 + ((0.083333333333333 + (z * (y * z))) / x)
	else:
		tmp = t_0 + ((y + 0.0007936500793651) * (z / (x / z)))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(log(x) + -1.0))
	tmp = 0.0
	if (z <= -19000.0)
		tmp = Float64(t_0 + Float64(z * Float64(z * Float64(Float64(y + 0.0007936500793651) / x))));
	elseif (z <= 1.2e-13)
		tmp = Float64(t_0 + Float64(Float64(0.083333333333333 + Float64(z * Float64(y * z))) / x));
	else
		tmp = Float64(t_0 + Float64(Float64(y + 0.0007936500793651) * Float64(z / Float64(x / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (log(x) + -1.0);
	tmp = 0.0;
	if (z <= -19000.0)
		tmp = t_0 + (z * (z * ((y + 0.0007936500793651) / x)));
	elseif (z <= 1.2e-13)
		tmp = t_0 + ((0.083333333333333 + (z * (y * z))) / x);
	else
		tmp = t_0 + ((y + 0.0007936500793651) * (z / (x / z)));
	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[LessEqual[z, -19000.0], N[(t$95$0 + N[(z * N[(z * N[(N[(y + 0.0007936500793651), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e-13], N[(t$95$0 + N[(N[(0.083333333333333 + N[(z * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(N[(y + 0.0007936500793651), $MachinePrecision] * N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -19000

   1. Initial program 91.4%

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

   2. Taylor expanded in x around inf 91.4%

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

      1. *-commutative 91.4%

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

      2. sub-neg 91.4%

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

      3. mul-1-neg 91.4%

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

      4. log-rec 91.4%

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

      5. remove-double-neg 91.4%

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

      6. metadata-eval 91.4%

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

   4. Simplified 91.4%

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

   5. Taylor expanded in z around inf 90.4%

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

      1. associate-/l* 94.4%

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

      2. unpow2 94.4%

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

   7. Simplified 94.4%

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

   8. Taylor expanded in z around 0 90.4%

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

      1. associate-/l* 94.4%

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

      2. *-rgt-identity 94.4%

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

      3. associate-*r/ 94.4%

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

      4. unpow2 94.4%

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

      5. associate-*l* 98.9%

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

      6. associate-/r/ 98.9%

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

      7. associate-*l/ 98.9%

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

      8. *-lft-identity 98.9%

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

   10. Simplified 98.9%

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

   if -19000 < z < 1.1999999999999999e-13

   1. Initial program 99.5%

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

   2. Taylor expanded in x around inf 99.3%

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

      1. *-commutative 99.3%

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

      2. sub-neg 99.3%

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

      3. mul-1-neg 99.3%

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

      4. log-rec 99.3%

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

      5. remove-double-neg 99.3%

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

      6. metadata-eval 99.3%

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

   4. Simplified 99.3%

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

   5. Taylor expanded in y around inf 99.3%

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

      1. *-commutative 99.3%

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

      2. unpow2 99.3%

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

      3. associate-*l* 99.3%

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

   7. Simplified 99.3%

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

   if 1.1999999999999999e-13 < z

   1. Initial program 88.3%

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

   2. Taylor expanded in x around inf 88.3%

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

      1. *-commutative 88.3%

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

      2. sub-neg 88.3%

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

      3. mul-1-neg 88.3%

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

      4. log-rec 88.3%

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

      5. remove-double-neg 88.3%

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

      6. metadata-eval 88.3%

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

   4. Simplified 88.3%

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

   5. Taylor expanded in z around inf 87.6%

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

      1. associate-/l* 90.2%

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

      2. unpow2 90.2%

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

   7. Simplified 90.2%

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

   8. Taylor expanded in z around 0 87.6%

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

      1. associate-*l/ 90.1%

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

      2. unpow2 90.1%

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

      3. *-commutative 90.1%

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

      4. associate-/l* 99.0%

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

   10. Simplified 99.0%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -19000:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + z \cdot \left(z \cdot \frac{y + 0.0007936500793651}{x}\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333 + z \cdot \left(y \cdot z\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \left(y + 0.0007936500793651\right) \cdot \frac{z}{\frac{x}{z}}\\ \end{array} \]

Alternative 10: 79.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(\log x + -1\right)\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{-12} \lor \neg \left(z \leq 205\right):\\ \;\;\;\;t_0 + 0.0007936500793651 \cdot \frac{z}{\frac{x}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ (log x) -1.0))))
   (if (or (<= z -6.2e-12) (not (<= z 205.0)))
     (+ t_0 (* 0.0007936500793651 (/ z (/ x z))))
     (+ t_0 (/ 0.083333333333333 x)))))

C

double code(double x, double y, double z) {
	double t_0 = x * (log(x) + -1.0);
	double tmp;
	if ((z <= -6.2e-12) || !(z <= 205.0)) {
		tmp = t_0 + (0.0007936500793651 * (z / (x / z)));
	} else {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = x * (log(x) + (-1.0d0))
    if ((z <= (-6.2d-12)) .or. (.not. (z <= 205.0d0))) then
        tmp = t_0 + (0.0007936500793651d0 * (z / (x / z)))
    else
        tmp = t_0 + (0.083333333333333d0 / x)
    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 <= -6.2e-12) || !(z <= 205.0)) {
		tmp = t_0 + (0.0007936500793651 * (z / (x / z)));
	} else {
		tmp = t_0 + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (math.log(x) + -1.0)
	tmp = 0
	if (z <= -6.2e-12) or not (z <= 205.0):
		tmp = t_0 + (0.0007936500793651 * (z / (x / z)))
	else:
		tmp = t_0 + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(log(x) + -1.0))
	tmp = 0.0
	if ((z <= -6.2e-12) || !(z <= 205.0))
		tmp = Float64(t_0 + Float64(0.0007936500793651 * Float64(z / Float64(x / z))));
	else
		tmp = Float64(t_0 + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (log(x) + -1.0);
	tmp = 0.0;
	if ((z <= -6.2e-12) || ~((z <= 205.0)))
		tmp = t_0 + (0.0007936500793651 * (z / (x / z)));
	else
		tmp = t_0 + (0.083333333333333 / x);
	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, -6.2e-12], N[Not[LessEqual[z, 205.0]], $MachinePrecision]], N[(t$95$0 + N[(0.0007936500793651 * N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.2000000000000002e-12 or 205 < z

   1. Initial program 89.7%

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

   2. Taylor expanded in x around inf 89.8%

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

      1. *-commutative 89.8%

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

      2. sub-neg 89.8%

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

      3. mul-1-neg 89.8%

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

      4. log-rec 89.8%

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

      5. remove-double-neg 89.8%

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

      6. metadata-eval 89.8%

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

   4. Simplified 89.8%

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

   5. Taylor expanded in z around inf 88.9%

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

      1. associate-/l* 92.1%

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

      2. unpow2 92.1%

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

   7. Simplified 92.1%

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

   8. Taylor expanded in y around 0 68.2%

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

      1. unpow2 68.2%

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

      2. associate-/l* 70.4%

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

   10. Simplified 70.4%

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

   if -6.2000000000000002e-12 < z < 205

   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 x around inf 99.3%

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

      1. *-commutative 99.3%

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

      2. sub-neg 99.3%

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

      3. mul-1-neg 99.3%

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

      4. log-rec 99.3%

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

      5. remove-double-neg 99.3%

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

      6. metadata-eval 99.3%

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

   4. Simplified 99.3%

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

   5. Taylor expanded in z around 0 89.1%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-12} \lor \neg \left(z \leq 205\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + 0.0007936500793651 \cdot \frac{z}{\frac{x}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 11: 56.3% accurate, 1.1× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x * (log(x) + -1.0)) + (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 * (log(x) + (-1.0d0))) + (0.083333333333333d0 / x)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.3%

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

2. Taylor expanded in x around inf 94.2%

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

   1. *-commutative 94.2%

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

   2. sub-neg 94.2%

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

   3. mul-1-neg 94.2%

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

   4. log-rec 94.2%

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

   5. remove-double-neg 94.2%

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

   6. metadata-eval 94.2%

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

4. Simplified 94.2%

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

5. Taylor expanded in z around 0 55.9%

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

6. Final simplification 55.9%

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

Alternative 12: 55.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 6.8 \cdot 10^{-13}:\\ \;\;\;\;\frac{0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 6.8e-13) (/ 0.083333333333333 x) (* x (+ (log x) -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 6.8e-13) {
		tmp = 0.083333333333333 / x;
	} else {
		tmp = x * (log(x) + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 6.8d-13) then
        tmp = 0.083333333333333d0 / x
    else
        tmp = x * (log(x) + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 6.8e-13) {
		tmp = 0.083333333333333 / x;
	} else {
		tmp = x * (Math.log(x) + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 6.8e-13:
		tmp = 0.083333333333333 / x
	else:
		tmp = x * (math.log(x) + -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 6.8e-13)
		tmp = Float64(0.083333333333333 / x);
	else
		tmp = Float64(x * Float64(log(x) + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 6.8e-13)
		tmp = 0.083333333333333 / x;
	else
		tmp = x * (log(x) + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 6.8e-13], N[(0.083333333333333 / x), $MachinePrecision], N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 6.80000000000000031e-13

   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 99.5%

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

      1. *-commutative 99.5%

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

      2. sub-neg 99.5%

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

      3. mul-1-neg 99.5%

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

      4. log-rec 99.5%

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

      5. remove-double-neg 99.5%

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

      6. metadata-eval 99.5%

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

   4. Simplified 99.5%

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

   5. Taylor expanded in z around 0 44.2%

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

   6. Taylor expanded in x around 0 44.2%

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

   if 6.80000000000000031e-13 < x

   1. Initial program 87.6%

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

   2. Taylor expanded in x around inf 87.8%

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

      1. *-commutative 87.8%

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

      2. sub-neg 87.8%

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

      3. mul-1-neg 87.8%

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

      4. log-rec 87.8%

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

      5. remove-double-neg 87.8%

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

      6. metadata-eval 87.8%

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

   4. Simplified 87.8%

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

   5. Taylor expanded in z around 0 70.1%

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

   6. Taylor expanded in x around inf 70.2%

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

      1. *-commutative 70.2%

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

      2. sub-neg 70.2%

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

      3. mul-1-neg 70.2%

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

      4. log-rec 70.2%

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

      5. remove-double-neg 70.2%

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

      6. metadata-eval 70.2%

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

   8. Simplified 70.2%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 6.8 \cdot 10^{-13}:\\ \;\;\;\;\frac{0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right)\\ \end{array} \]

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 94.3%

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

2. Taylor expanded in x around inf 94.2%

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

   1. *-commutative 94.2%

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

   2. sub-neg 94.2%

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

   3. mul-1-neg 94.2%

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

   4. log-rec 94.2%

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

   5. remove-double-neg 94.2%

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

   6. metadata-eval 94.2%

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

4. Simplified 94.2%

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

5. Taylor expanded in z around 0 55.9%

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

6. Taylor expanded in x around 0 25.6%

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

7. Final simplification 25.6%

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

Developer target: 98.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023196 
(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)))