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

Percentage Accurate: 93.9% → 99.0%

Time: 13.9s

Alternatives: 11

Speedup: 1.0×

• 31.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.9 \cdot 10^{-88}:\\ \;\;\;\;\left(0.91893853320467 + \log x \cdot -0.5\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\frac{0.083333333333333}{x} + z \cdot \left(z \cdot \left(\frac{0.0007936500793651}{x} + \frac{y}{x}\right) - \frac{0.0027777777777778}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 4.9e-88)
   (+
    (+ 0.91893853320467 (* (log x) -0.5))
    (/
     (+
      0.083333333333333
      (* z (- (* z (+ 0.0007936500793651 y)) 0.0027777777777778)))
     x))
   (+
    (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
    (+
     (/ 0.083333333333333 x)
     (*
      z
      (-
       (* z (+ (/ 0.0007936500793651 x) (/ y x)))
       (/ 0.0027777777777778 x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 4.9e-88) {
		tmp = (0.91893853320467 + (log(x) * -0.5)) + ((0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x);
	} else {
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((0.083333333333333 / x) + (z * ((z * ((0.0007936500793651 / x) + (y / x))) - (0.0027777777777778 / x))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 4.9d-88) then
        tmp = (0.91893853320467d0 + (log(x) * (-0.5d0))) + ((0.083333333333333d0 + (z * ((z * (0.0007936500793651d0 + y)) - 0.0027777777777778d0))) / x)
    else
        tmp = ((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + ((0.083333333333333d0 / x) + (z * ((z * ((0.0007936500793651d0 / x) + (y / x))) - (0.0027777777777778d0 / x))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 4.9e-88) {
		tmp = (0.91893853320467 + (Math.log(x) * -0.5)) + ((0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x);
	} else {
		tmp = ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + ((0.083333333333333 / x) + (z * ((z * ((0.0007936500793651 / x) + (y / x))) - (0.0027777777777778 / x))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 4.9e-88:
		tmp = (0.91893853320467 + (math.log(x) * -0.5)) + ((0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x)
	else:
		tmp = ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + ((0.083333333333333 / x) + (z * ((z * ((0.0007936500793651 / x) + (y / x))) - (0.0027777777777778 / x))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 4.9e-88)
		tmp = Float64(Float64(0.91893853320467 + Float64(log(x) * -0.5)) + Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * Float64(0.0007936500793651 + y)) - 0.0027777777777778))) / x));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(Float64(0.083333333333333 / x) + Float64(z * Float64(Float64(z * Float64(Float64(0.0007936500793651 / x) + Float64(y / x))) - Float64(0.0027777777777778 / x)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 4.9e-88)
		tmp = (0.91893853320467 + (log(x) * -0.5)) + ((0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x);
	else
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((0.083333333333333 / x) + (z * ((z * ((0.0007936500793651 / x) + (y / x))) - (0.0027777777777778 / x))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 4.9e-88], N[(N[(0.91893853320467 + N[(N[Log[x], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision] + N[(N[(0.083333333333333 + N[(z * N[(N[(z * N[(0.0007936500793651 + y), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(N[(0.083333333333333 / x), $MachinePrecision] + N[(z * N[(N[(z * N[(N[(0.0007936500793651 / x), $MachinePrecision] + N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(0.0027777777777778 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.90000000000000028e-88

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 99.7%

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

   if 4.90000000000000028e-88 < x

   1. Initial program 90.3%

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

   3. Taylor expanded in z around 0 99.6%

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

      1. fma-define 99.6%

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

      2. associate-*r/ 99.6%

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

      3. metadata-eval 99.6%

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

      4. associate-*r/ 99.6%

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

      5. metadata-eval 99.6%

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

      6. associate-*r/ 99.6%

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

      7. metadata-eval 99.6%

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

   5. Simplified 99.6%

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

      1. fma-undefine 99.6%

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

   7. Applied egg-rr 99.6%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\left(z \cdot \left(z \cdot \left(\frac{0.0007936500793651}{x} + \frac{y}{x}\right) - \frac{0.0027777777777778}{x}\right) + \frac{0.083333333333333}{x}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4.9 \cdot 10^{-88}:\\ \;\;\;\;\left(0.91893853320467 + \log x \cdot -0.5\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\frac{0.083333333333333}{x} + z \cdot \left(z \cdot \left(\frac{0.0007936500793651}{x} + \frac{y}{x}\right) - \frac{0.0027777777777778}{x}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.7% accurate, 0.6× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((fma(z, (0.0007936500793651 + y), -0.0027777777777778) * (z / x)) + (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(fma(z, Float64(0.0007936500793651 + y), -0.0027777777777778) * Float64(z / x)) + Float64(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[(z * N[(0.0007936500793651 + y), $MachinePrecision] + -0.0027777777777778), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 93.9%

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

3. Taylor expanded in z around 0 94.4%

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

   1. fma-define 94.4%

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

   2. associate-*r/ 94.4%

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

   3. metadata-eval 94.4%

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

   4. associate-*r/ 94.4%

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

   5. metadata-eval 94.4%

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

   6. associate-*r/ 94.4%

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

   7. metadata-eval 94.4%

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

5. Simplified 94.4%

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

   1. fma-undefine 94.4%

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

7. Applied egg-rr 94.4%

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

8. Taylor expanded in x around 0 93.9%

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

   1. fma-neg 93.9%

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

   2. metadata-eval 93.9%

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

   3. *-commutative 93.9%

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

   4. associate-/l* 98.2%

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

10. Simplified 98.2%

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

Alternative 3: 84.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)\\ t_1 := 0.91893853320467 + \log x \cdot -0.5\\ \mathbf{if}\;t\_0 \leq -0.05:\\ \;\;\;\;t\_1 + \frac{0.083333333333333 + z \cdot \left(z \cdot y - 0.0027777777777778\right)}{x}\\ \mathbf{elif}\;t\_0 \leq 10^{+132}:\\ \;\;\;\;\frac{0.083333333333333}{x} + \left(\log x \cdot \left(x + -0.5\right) - \left(x + -0.91893853320467\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{0.083333333333333 + t\_0}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- (* z (+ 0.0007936500793651 y)) 0.0027777777777778)))
        (t_1 (+ 0.91893853320467 (* (log x) -0.5))))
   (if (<= t_0 -0.05)
     (+ t_1 (/ (+ 0.083333333333333 (* z (- (* z y) 0.0027777777777778))) x))
     (if (<= t_0 1e+132)
       (+
        (/ 0.083333333333333 x)
        (- (* (log x) (+ x -0.5)) (+ x -0.91893853320467)))
       (+ t_1 (/ (+ 0.083333333333333 t_0) x))))))

C

double code(double x, double y, double z) {
	double t_0 = z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778);
	double t_1 = 0.91893853320467 + (log(x) * -0.5);
	double tmp;
	if (t_0 <= -0.05) {
		tmp = t_1 + ((0.083333333333333 + (z * ((z * y) - 0.0027777777777778))) / x);
	} else if (t_0 <= 1e+132) {
		tmp = (0.083333333333333 / x) + ((log(x) * (x + -0.5)) - (x + -0.91893853320467));
	} else {
		tmp = t_1 + ((0.083333333333333 + t_0) / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = z * ((z * (0.0007936500793651d0 + y)) - 0.0027777777777778d0)
    t_1 = 0.91893853320467d0 + (log(x) * (-0.5d0))
    if (t_0 <= (-0.05d0)) then
        tmp = t_1 + ((0.083333333333333d0 + (z * ((z * y) - 0.0027777777777778d0))) / x)
    else if (t_0 <= 1d+132) then
        tmp = (0.083333333333333d0 / x) + ((log(x) * (x + (-0.5d0))) - (x + (-0.91893853320467d0)))
    else
        tmp = t_1 + ((0.083333333333333d0 + t_0) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778);
	double t_1 = 0.91893853320467 + (Math.log(x) * -0.5);
	double tmp;
	if (t_0 <= -0.05) {
		tmp = t_1 + ((0.083333333333333 + (z * ((z * y) - 0.0027777777777778))) / x);
	} else if (t_0 <= 1e+132) {
		tmp = (0.083333333333333 / x) + ((Math.log(x) * (x + -0.5)) - (x + -0.91893853320467));
	} else {
		tmp = t_1 + ((0.083333333333333 + t_0) / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778)
	t_1 = 0.91893853320467 + (math.log(x) * -0.5)
	tmp = 0
	if t_0 <= -0.05:
		tmp = t_1 + ((0.083333333333333 + (z * ((z * y) - 0.0027777777777778))) / x)
	elif t_0 <= 1e+132:
		tmp = (0.083333333333333 / x) + ((math.log(x) * (x + -0.5)) - (x + -0.91893853320467))
	else:
		tmp = t_1 + ((0.083333333333333 + t_0) / x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(Float64(z * Float64(0.0007936500793651 + y)) - 0.0027777777777778))
	t_1 = Float64(0.91893853320467 + Float64(log(x) * -0.5))
	tmp = 0.0
	if (t_0 <= -0.05)
		tmp = Float64(t_1 + Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * y) - 0.0027777777777778))) / x));
	elseif (t_0 <= 1e+132)
		tmp = Float64(Float64(0.083333333333333 / x) + Float64(Float64(log(x) * Float64(x + -0.5)) - Float64(x + -0.91893853320467)));
	else
		tmp = Float64(t_1 + Float64(Float64(0.083333333333333 + t_0) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778);
	t_1 = 0.91893853320467 + (log(x) * -0.5);
	tmp = 0.0;
	if (t_0 <= -0.05)
		tmp = t_1 + ((0.083333333333333 + (z * ((z * y) - 0.0027777777777778))) / x);
	elseif (t_0 <= 1e+132)
		tmp = (0.083333333333333 / x) + ((log(x) * (x + -0.5)) - (x + -0.91893853320467));
	else
		tmp = t_1 + ((0.083333333333333 + t_0) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(N[(z * N[(0.0007936500793651 + y), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(0.91893853320467 + N[(N[Log[x], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -0.05], N[(t$95$1 + N[(N[(0.083333333333333 + N[(z * N[(N[(z * y), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 1e+132], N[(N[(0.083333333333333 / x), $MachinePrecision] + N[(N[(N[Log[x], $MachinePrecision] * N[(x + -0.5), $MachinePrecision]), $MachinePrecision] - N[(x + -0.91893853320467), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(0.083333333333333 + t$95$0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) < -0.050000000000000003

   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. Add Preprocessing

   3. Taylor expanded in x around 0 74.7%

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

   4. Taylor expanded in y around inf 74.7%

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

      1. *-commutative 74.7%

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

   6. Simplified 74.7%

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

   if -0.050000000000000003 < (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) < 9.99999999999999991e131

   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. Add Preprocessing

   3. Taylor expanded in z around 0 93.5%

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

      1. associate-+l- 99.5%

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

      2. sub-neg 99.5%

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

      3. metadata-eval 99.5%

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

      4. sub-neg 99.5%

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

      5. metadata-eval 99.5%

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

   5. Applied egg-rr 93.5%

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

   if 9.99999999999999991e131 < (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z)

   1. Initial program 88.6%

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

   3. Taylor expanded in x around 0 84.0%

      \[\leadsto \left(\color{blue}{-0.5 \cdot \log x} + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right) \leq -0.05:\\ \;\;\;\;\left(0.91893853320467 + \log x \cdot -0.5\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot y - 0.0027777777777778\right)}{x}\\ \mathbf{elif}\;z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right) \leq 10^{+132}:\\ \;\;\;\;\frac{0.083333333333333}{x} + \left(\log x \cdot \left(x + -0.5\right) - \left(x + -0.91893853320467\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \log x \cdot -0.5\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.91893853320467 + \log x \cdot -0.5\\ t_1 := t\_0 + \frac{0.083333333333333 + z \cdot \left(z \cdot 0.0007936500793651 - 0.0027777777777778\right)}{x}\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-30}:\\ \;\;\;\;t\_0 + \frac{0.083333333333333 + z \cdot \left(z \cdot y - 0.0027777777777778\right)}{x}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+102}:\\ \;\;\;\;\frac{0.083333333333333}{x} + \left(\log x \cdot \left(x + -0.5\right) - \left(x + -0.91893853320467\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 0.91893853320467 (* (log x) -0.5)))
        (t_1
         (+
          t_0
          (/
           (+
            0.083333333333333
            (* z (- (* z 0.0007936500793651) 0.0027777777777778)))
           x))))
   (if (<= z -1.25e+69)
     t_1
     (if (<= z -5.2e-30)
       (+ t_0 (/ (+ 0.083333333333333 (* z (- (* z y) 0.0027777777777778))) x))
       (if (<= z 3.6e+102)
         (+
          (/ 0.083333333333333 x)
          (- (* (log x) (+ x -0.5)) (+ x -0.91893853320467)))
         t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = 0.91893853320467 + (log(x) * -0.5);
	double t_1 = t_0 + ((0.083333333333333 + (z * ((z * 0.0007936500793651) - 0.0027777777777778))) / x);
	double tmp;
	if (z <= -1.25e+69) {
		tmp = t_1;
	} else if (z <= -5.2e-30) {
		tmp = t_0 + ((0.083333333333333 + (z * ((z * y) - 0.0027777777777778))) / x);
	} else if (z <= 3.6e+102) {
		tmp = (0.083333333333333 / x) + ((log(x) * (x + -0.5)) - (x + -0.91893853320467));
	} 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 = 0.91893853320467d0 + (log(x) * (-0.5d0))
    t_1 = t_0 + ((0.083333333333333d0 + (z * ((z * 0.0007936500793651d0) - 0.0027777777777778d0))) / x)
    if (z <= (-1.25d+69)) then
        tmp = t_1
    else if (z <= (-5.2d-30)) then
        tmp = t_0 + ((0.083333333333333d0 + (z * ((z * y) - 0.0027777777777778d0))) / x)
    else if (z <= 3.6d+102) then
        tmp = (0.083333333333333d0 / x) + ((log(x) * (x + (-0.5d0))) - (x + (-0.91893853320467d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 0.91893853320467 + (Math.log(x) * -0.5);
	double t_1 = t_0 + ((0.083333333333333 + (z * ((z * 0.0007936500793651) - 0.0027777777777778))) / x);
	double tmp;
	if (z <= -1.25e+69) {
		tmp = t_1;
	} else if (z <= -5.2e-30) {
		tmp = t_0 + ((0.083333333333333 + (z * ((z * y) - 0.0027777777777778))) / x);
	} else if (z <= 3.6e+102) {
		tmp = (0.083333333333333 / x) + ((Math.log(x) * (x + -0.5)) - (x + -0.91893853320467));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 0.91893853320467 + (math.log(x) * -0.5)
	t_1 = t_0 + ((0.083333333333333 + (z * ((z * 0.0007936500793651) - 0.0027777777777778))) / x)
	tmp = 0
	if z <= -1.25e+69:
		tmp = t_1
	elif z <= -5.2e-30:
		tmp = t_0 + ((0.083333333333333 + (z * ((z * y) - 0.0027777777777778))) / x)
	elif z <= 3.6e+102:
		tmp = (0.083333333333333 / x) + ((math.log(x) * (x + -0.5)) - (x + -0.91893853320467))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(0.91893853320467 + Float64(log(x) * -0.5))
	t_1 = Float64(t_0 + Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * 0.0007936500793651) - 0.0027777777777778))) / x))
	tmp = 0.0
	if (z <= -1.25e+69)
		tmp = t_1;
	elseif (z <= -5.2e-30)
		tmp = Float64(t_0 + Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * y) - 0.0027777777777778))) / x));
	elseif (z <= 3.6e+102)
		tmp = Float64(Float64(0.083333333333333 / x) + Float64(Float64(log(x) * Float64(x + -0.5)) - Float64(x + -0.91893853320467)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 0.91893853320467 + (log(x) * -0.5);
	t_1 = t_0 + ((0.083333333333333 + (z * ((z * 0.0007936500793651) - 0.0027777777777778))) / x);
	tmp = 0.0;
	if (z <= -1.25e+69)
		tmp = t_1;
	elseif (z <= -5.2e-30)
		tmp = t_0 + ((0.083333333333333 + (z * ((z * y) - 0.0027777777777778))) / x);
	elseif (z <= 3.6e+102)
		tmp = (0.083333333333333 / x) + ((log(x) * (x + -0.5)) - (x + -0.91893853320467));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(0.91893853320467 + N[(N[Log[x], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(N[(0.083333333333333 + N[(z * N[(N[(z * 0.0007936500793651), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.25e+69], t$95$1, If[LessEqual[z, -5.2e-30], N[(t$95$0 + N[(N[(0.083333333333333 + N[(z * N[(N[(z * y), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+102], N[(N[(0.083333333333333 / x), $MachinePrecision] + N[(N[(N[Log[x], $MachinePrecision] * N[(x + -0.5), $MachinePrecision]), $MachinePrecision] - N[(x + -0.91893853320467), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.25000000000000009e69 or 3.6000000000000002e102 < z

   1. Initial program 87.2%

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

   3. Taylor expanded in x around 0 85.4%

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

   4. Taylor expanded in y around 0 65.0%

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

      1. *-commutative 65.0%

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

   6. Simplified 65.0%

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

   if -1.25000000000000009e69 < z < -5.19999999999999973e-30

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0 68.1%

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

   4. Taylor expanded in y around inf 59.7%

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

      1. *-commutative 59.7%

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

   6. Simplified 59.7%

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

   if -5.19999999999999973e-30 < z < 3.6000000000000002e102

   1. Initial program 97.6%

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

   3. Taylor expanded in z around 0 88.0%

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

      1. associate-+l- 97.6%

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

      2. sub-neg 97.6%

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

      3. metadata-eval 97.6%

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

      4. sub-neg 97.6%

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

      5. metadata-eval 97.6%

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

   5. Applied egg-rr 88.0%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+69}:\\ \;\;\;\;\left(0.91893853320467 + \log x \cdot -0.5\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot 0.0007936500793651 - 0.0027777777777778\right)}{x}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-30}:\\ \;\;\;\;\left(0.91893853320467 + \log x \cdot -0.5\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot y - 0.0027777777777778\right)}{x}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+102}:\\ \;\;\;\;\frac{0.083333333333333}{x} + \left(\log x \cdot \left(x + -0.5\right) - \left(x + -0.91893853320467\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + \log x \cdot -0.5\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot 0.0007936500793651 - 0.0027777777777778\right)}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 7.2 \cdot 10^{+14}:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x} + \left(\log x \cdot \left(x + -0.5\right) - \left(x + -0.91893853320467\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + z \cdot \left(\left(0.0007936500793651 + y\right) \cdot \frac{z}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 7.2e+14)
   (+
    (/
     (+
      0.083333333333333
      (* z (- (* z (+ 0.0007936500793651 y)) 0.0027777777777778)))
     x)
    (- (* (log x) (+ x -0.5)) (+ x -0.91893853320467)))
   (+
    (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
    (* z (* (+ 0.0007936500793651 y) (/ z x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 7.2e+14) {
		tmp = ((0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x) + ((log(x) * (x + -0.5)) - (x + -0.91893853320467));
	} else {
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (z * ((0.0007936500793651 + y) * (z / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 7.2d+14) then
        tmp = ((0.083333333333333d0 + (z * ((z * (0.0007936500793651d0 + y)) - 0.0027777777777778d0))) / x) + ((log(x) * (x + (-0.5d0))) - (x + (-0.91893853320467d0)))
    else
        tmp = ((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + (z * ((0.0007936500793651d0 + y) * (z / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 7.2e+14) {
		tmp = ((0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x) + ((Math.log(x) * (x + -0.5)) - (x + -0.91893853320467));
	} else {
		tmp = ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + (z * ((0.0007936500793651 + y) * (z / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 7.2e+14:
		tmp = ((0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x) + ((math.log(x) * (x + -0.5)) - (x + -0.91893853320467))
	else:
		tmp = ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + (z * ((0.0007936500793651 + y) * (z / x)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 7.2e+14)
		tmp = Float64(Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * Float64(0.0007936500793651 + y)) - 0.0027777777777778))) / x) + Float64(Float64(log(x) * Float64(x + -0.5)) - Float64(x + -0.91893853320467)));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(z * Float64(Float64(0.0007936500793651 + y) * Float64(z / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 7.2e+14)
		tmp = ((0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x) + ((log(x) * (x + -0.5)) - (x + -0.91893853320467));
	else
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (z * ((0.0007936500793651 + y) * (z / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 7.2e+14], N[(N[(N[(0.083333333333333 + N[(z * N[(N[(z * N[(0.0007936500793651 + y), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] + N[(N[(N[Log[x], $MachinePrecision] * N[(x + -0.5), $MachinePrecision]), $MachinePrecision] - N[(x + -0.91893853320467), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(z * N[(N[(0.0007936500793651 + y), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 7.2e14

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

      2. sub-neg 99.7%

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

      3. metadata-eval 99.7%

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

      4. sub-neg 99.7%

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

      5. metadata-eval 99.7%

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

   4. Applied egg-rr 99.7%

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

   if 7.2e14 < x

   1. Initial program 87.4%

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

   3. Taylor expanded in z around 0 99.6%

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

      1. fma-define 99.6%

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

      2. associate-*r/ 99.6%

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

      3. metadata-eval 99.6%

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

      4. associate-*r/ 99.6%

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

      5. metadata-eval 99.6%

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

      6. associate-*r/ 99.6%

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

      7. metadata-eval 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in z around inf 93.3%

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

      1. unpow2 93.3%

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

      2. associate-*l* 99.6%

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

      3. distribute-rgt-in 99.6%

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

      4. associate-*r/ 99.6%

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

      5. metadata-eval 99.6%

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

      6. associate-*l/ 99.5%

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

      7. associate-*r/ 99.6%

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

      8. associate-*l/ 96.5%

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

      9. associate-/l* 99.6%

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

      10. distribute-rgt-out 99.6%

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

   8. Simplified 99.6%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 7.2 \cdot 10^{+14}:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x} + \left(\log x \cdot \left(x + -0.5\right) - \left(x + -0.91893853320467\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + z \cdot \left(\left(0.0007936500793651 + y\right) \cdot \frac{z}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+68} \lor \neg \left(z \leq 9.5 \cdot 10^{+101}\right):\\ \;\;\;\;\left(0.91893853320467 + \log x \cdot -0.5\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot 0.0007936500793651 - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x} + \left(\log x \cdot \left(x + -0.5\right) - \left(x + -0.91893853320467\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6.8e+68) (not (<= z 9.5e+101)))
   (+
    (+ 0.91893853320467 (* (log x) -0.5))
    (/
     (+
      0.083333333333333
      (* z (- (* z 0.0007936500793651) 0.0027777777777778)))
     x))
   (+
    (/ 0.083333333333333 x)
    (- (* (log x) (+ x -0.5)) (+ x -0.91893853320467)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.8e+68) || !(z <= 9.5e+101)) {
		tmp = (0.91893853320467 + (log(x) * -0.5)) + ((0.083333333333333 + (z * ((z * 0.0007936500793651) - 0.0027777777777778))) / x);
	} else {
		tmp = (0.083333333333333 / x) + ((log(x) * (x + -0.5)) - (x + -0.91893853320467));
	}
	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 <= (-6.8d+68)) .or. (.not. (z <= 9.5d+101))) then
        tmp = (0.91893853320467d0 + (log(x) * (-0.5d0))) + ((0.083333333333333d0 + (z * ((z * 0.0007936500793651d0) - 0.0027777777777778d0))) / x)
    else
        tmp = (0.083333333333333d0 / x) + ((log(x) * (x + (-0.5d0))) - (x + (-0.91893853320467d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.8e+68) || !(z <= 9.5e+101)) {
		tmp = (0.91893853320467 + (Math.log(x) * -0.5)) + ((0.083333333333333 + (z * ((z * 0.0007936500793651) - 0.0027777777777778))) / x);
	} else {
		tmp = (0.083333333333333 / x) + ((Math.log(x) * (x + -0.5)) - (x + -0.91893853320467));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6.8e+68) or not (z <= 9.5e+101):
		tmp = (0.91893853320467 + (math.log(x) * -0.5)) + ((0.083333333333333 + (z * ((z * 0.0007936500793651) - 0.0027777777777778))) / x)
	else:
		tmp = (0.083333333333333 / x) + ((math.log(x) * (x + -0.5)) - (x + -0.91893853320467))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6.8e+68) || !(z <= 9.5e+101))
		tmp = Float64(Float64(0.91893853320467 + Float64(log(x) * -0.5)) + Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * 0.0007936500793651) - 0.0027777777777778))) / x));
	else
		tmp = Float64(Float64(0.083333333333333 / x) + Float64(Float64(log(x) * Float64(x + -0.5)) - Float64(x + -0.91893853320467)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -6.8e+68) || ~((z <= 9.5e+101)))
		tmp = (0.91893853320467 + (log(x) * -0.5)) + ((0.083333333333333 + (z * ((z * 0.0007936500793651) - 0.0027777777777778))) / x);
	else
		tmp = (0.083333333333333 / x) + ((log(x) * (x + -0.5)) - (x + -0.91893853320467));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6.8e+68], N[Not[LessEqual[z, 9.5e+101]], $MachinePrecision]], N[(N[(0.91893853320467 + N[(N[Log[x], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision] + N[(N[(0.083333333333333 + N[(z * N[(N[(z * 0.0007936500793651), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(0.083333333333333 / x), $MachinePrecision] + N[(N[(N[Log[x], $MachinePrecision] * N[(x + -0.5), $MachinePrecision]), $MachinePrecision] - N[(x + -0.91893853320467), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.8000000000000003e68 or 9.49999999999999947e101 < z

   1. Initial program 87.2%

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

   3. Taylor expanded in x around 0 85.4%

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

   4. Taylor expanded in y around 0 65.0%

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

      1. *-commutative 65.0%

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

   6. Simplified 65.0%

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

   if -6.8000000000000003e68 < z < 9.49999999999999947e101

   1. Initial program 97.8%

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

   3. Taylor expanded in z around 0 81.0%

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

      1. associate-+l- 97.8%

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

      2. sub-neg 97.8%

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

      3. metadata-eval 97.8%

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

      4. sub-neg 97.8%

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

      5. metadata-eval 97.8%

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

   5. Applied egg-rr 81.0%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+68} \lor \neg \left(z \leq 9.5 \cdot 10^{+101}\right):\\ \;\;\;\;\left(0.91893853320467 + \log x \cdot -0.5\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot 0.0007936500793651 - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x} + \left(\log x \cdot \left(x + -0.5\right) - \left(x + -0.91893853320467\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.00255:\\ \;\;\;\;\left(0.91893853320467 + \log x \cdot -0.5\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + z \cdot \left(\left(0.0007936500793651 + y\right) \cdot \frac{z}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 0.00255)
   (+
    (+ 0.91893853320467 (* (log x) -0.5))
    (/
     (+
      0.083333333333333
      (* z (- (* z (+ 0.0007936500793651 y)) 0.0027777777777778)))
     x))
   (+
    (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
    (* z (* (+ 0.0007936500793651 y) (/ z x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 0.00255) {
		tmp = (0.91893853320467 + (log(x) * -0.5)) + ((0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x);
	} else {
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (z * ((0.0007936500793651 + y) * (z / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 0.00255d0) then
        tmp = (0.91893853320467d0 + (log(x) * (-0.5d0))) + ((0.083333333333333d0 + (z * ((z * (0.0007936500793651d0 + y)) - 0.0027777777777778d0))) / x)
    else
        tmp = ((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + (z * ((0.0007936500793651d0 + y) * (z / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 0.00255) {
		tmp = (0.91893853320467 + (Math.log(x) * -0.5)) + ((0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x);
	} else {
		tmp = ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + (z * ((0.0007936500793651 + y) * (z / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 0.00255:
		tmp = (0.91893853320467 + (math.log(x) * -0.5)) + ((0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x)
	else:
		tmp = ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + (z * ((0.0007936500793651 + y) * (z / x)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 0.00255)
		tmp = Float64(Float64(0.91893853320467 + Float64(log(x) * -0.5)) + Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * Float64(0.0007936500793651 + y)) - 0.0027777777777778))) / x));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(z * Float64(Float64(0.0007936500793651 + y) * Float64(z / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 0.00255)
		tmp = (0.91893853320467 + (log(x) * -0.5)) + ((0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x);
	else
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (z * ((0.0007936500793651 + y) * (z / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 0.00255], N[(N[(0.91893853320467 + N[(N[Log[x], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision] + N[(N[(0.083333333333333 + N[(z * N[(N[(z * N[(0.0007936500793651 + y), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(z * N[(N[(0.0007936500793651 + y), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 0.0025500000000000002

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 99.7%

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

   if 0.0025500000000000002 < x

   1. Initial program 88.2%

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

   3. Taylor expanded in z around 0 99.6%

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

      1. fma-define 99.6%

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

      2. associate-*r/ 99.6%

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

      3. metadata-eval 99.6%

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

      4. associate-*r/ 99.6%

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

      5. metadata-eval 99.6%

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

      6. associate-*r/ 99.6%

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

      7. metadata-eval 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in z around inf 93.7%

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

      1. unpow2 93.7%

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

      2. associate-*l* 99.6%

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

      3. distribute-rgt-in 99.6%

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

      4. associate-*r/ 99.6%

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

      5. metadata-eval 99.6%

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

      6. associate-*l/ 99.5%

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

      7. associate-*r/ 99.6%

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

      8. associate-*l/ 96.7%

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

      9. associate-/l* 99.6%

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

      10. distribute-rgt-out 99.6%

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

   8. Simplified 99.6%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.00255:\\ \;\;\;\;\left(0.91893853320467 + \log x \cdot -0.5\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + z \cdot \left(\left(0.0007936500793651 + y\right) \cdot \frac{z}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < 1

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 99.7%

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

   4. Taylor expanded in z around 0 60.0%

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

   if 1 < x

   1. Initial program 87.8%

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

      1. sub-neg 87.8%

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

      2. associate-+l+ 87.8%

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

      3. fma-define 87.9%

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

      4. sub-neg 87.9%

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

      5. metadata-eval 87.9%

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

      6. +-commutative 87.9%

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

      7. unsub-neg 87.9%

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

      8. *-commutative 87.9%

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

      9. fma-define 87.9%

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

      10. fma-neg 87.9%

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

      11. metadata-eval 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in z around 0 61.7%

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

   6. Taylor expanded in x around inf 61.7%

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

      1. sub-neg 61.7%

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

      2. mul-1-neg 61.7%

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

      3. log-rec 61.7%

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

      4. remove-double-neg 61.7%

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

      5. metadata-eval 61.7%

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

      6. +-commutative 61.7%

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

   8. Simplified 61.7%

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

4. Final simplification 60.8%

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

Alternative 9: 56.6% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < 1

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 48.8%

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

   4. Taylor expanded in x around 0 48.8%

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

   if 1 < x

   1. Initial program 87.8%

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

      1. sub-neg 87.8%

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

      2. associate-+l+ 87.8%

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

      3. fma-define 87.9%

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

      4. sub-neg 87.9%

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

      5. metadata-eval 87.9%

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

      6. +-commutative 87.9%

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

      7. unsub-neg 87.9%

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

      8. *-commutative 87.9%

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

      9. fma-define 87.9%

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

      10. fma-neg 87.9%

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

      11. metadata-eval 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in z around 0 61.7%

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

   6. Taylor expanded in x around inf 61.7%

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

      1. sub-neg 61.7%

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

      2. mul-1-neg 61.7%

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

      3. log-rec 61.7%

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

      4. remove-double-neg 61.7%

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

      5. metadata-eval 61.7%

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

      6. +-commutative 61.7%

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

   8. Simplified 61.7%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1:\\ \;\;\;\;\frac{0.083333333333333}{x} + \left(0.91893853320467 + \log x \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 56.2% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.9%

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

3. Taylor expanded in z around 0 55.0%

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

4. Taylor expanded in x around inf 54.9%

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

   1. mul-1-neg 54.9%

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

   2. distribute-rgt-neg-in 54.9%

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

   3. log-rec 54.9%

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

   4. remove-double-neg 54.9%

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

6. Simplified 54.9%

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

7. Final simplification 54.9%

   \[\leadsto \frac{0.083333333333333}{x} + \left(0.91893853320467 + \left(x \cdot \log x - x\right)\right) \]
8. Add Preprocessing

Alternative 11: 34.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.9%

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

   1. sub-neg 93.9%

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

   2. associate-+l+ 93.9%

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

   3. fma-define 94.0%

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

   4. sub-neg 94.0%

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

   5. metadata-eval 94.0%

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

   6. +-commutative 94.0%

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

   7. unsub-neg 94.0%

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

   8. *-commutative 94.0%

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

   9. fma-define 94.0%

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

   10. fma-neg 94.0%

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

   11. metadata-eval 94.0%

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

3. Simplified 94.0%

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

5. Taylor expanded in z around 0 55.1%

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

6. Taylor expanded in x around inf 30.7%

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

   1. sub-neg 30.7%

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

   2. mul-1-neg 30.7%

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

   3. log-rec 30.7%

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

   4. remove-double-neg 30.7%

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

   5. metadata-eval 30.7%

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

   6. +-commutative 30.7%

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

8. Simplified 30.7%

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

9. Final simplification 30.7%

   \[\leadsto x \cdot \left(\log x + -1\right) \]
10. Add Preprocessing

Developer target: 98.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024101 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, B"
  :precision binary64

  :alt
  (+ (+ (+ (* (- 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)))