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

Percentage Accurate: 94.4% → 98.2%

Time: 14.1s

Alternatives: 12

Speedup: 1.0×

• 32.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 94.4% 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: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 0.91893853320467 + \left(\left(0.083333333333333 \cdot \frac{1}{x} + \left(z \cdot \frac{0.0007936500793651 + y}{\frac{x}{z}} + \log x \cdot \left(x - 0.5\right)\right)\right) - x\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+
  0.91893853320467
  (-
   (+
    (* 0.083333333333333 (/ 1.0 x))
    (+ (* z (/ (+ 0.0007936500793651 y) (/ x z))) (* (log x) (- x 0.5))))
   x)))

C

double code(double x, double y, double z) {
	return 0.91893853320467 + (((0.083333333333333 * (1.0 / x)) + ((z * ((0.0007936500793651 + y) / (x / z))) + (log(x) * (x - 0.5)))) - x);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 0.91893853320467d0 + (((0.083333333333333d0 * (1.0d0 / x)) + ((z * ((0.0007936500793651d0 + y) / (x / z))) + (log(x) * (x - 0.5d0)))) - x)
end function

Java

public static double code(double x, double y, double z) {
	return 0.91893853320467 + (((0.083333333333333 * (1.0 / x)) + ((z * ((0.0007936500793651 + y) / (x / z))) + (Math.log(x) * (x - 0.5)))) - x);
}

Python

def code(x, y, z):
	return 0.91893853320467 + (((0.083333333333333 * (1.0 / x)) + ((z * ((0.0007936500793651 + y) / (x / z))) + (math.log(x) * (x - 0.5)))) - x)

Julia

function code(x, y, z)
	return Float64(0.91893853320467 + Float64(Float64(Float64(0.083333333333333 * Float64(1.0 / x)) + Float64(Float64(z * Float64(Float64(0.0007936500793651 + y) / Float64(x / z))) + Float64(log(x) * Float64(x - 0.5)))) - x))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 0.91893853320467 + (((0.083333333333333 * (1.0 / x)) + ((z * ((0.0007936500793651 + y) / (x / z))) + (log(x) * (x - 0.5)))) - x);
end

Wolfram

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

Derivation

1. Initial program 92.4%

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

   1. +-commutative 92.4%

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

   2. associate-+l+ 92.4%

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

   3. associate-+l- 92.4%

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

   4. fma-neg 92.5%

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

   5. sub-neg 92.5%

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

   6. metadata-eval 92.5%

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

   7. neg-sub0 92.5%

      \[\leadsto 0.91893853320467 + \mathsf{fma}\left(x + -0.5, \log x, \color{blue}{0 - \left(x - \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\right)}\right) \]

   8. associate-+l- 92.5%

      \[\leadsto 0.91893853320467 + \mathsf{fma}\left(x + -0.5, \log x, \color{blue}{\left(0 - x\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}}\right) \]

   9. neg-sub0 92.5%

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

   10. +-commutative 92.5%

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

   11. unsub-neg 92.5%

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

3. Simplified 92.5%

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

5. Taylor expanded in z around 0 93.2%

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

6. Taylor expanded in z around inf 87.6%

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

   1. unpow2 87.6%

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

   2. associate-*l* 93.0%

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

   3. distribute-rgt-in 90.7%

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

   4. associate-*r/ 90.7%

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

   5. metadata-eval 90.7%

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

   6. associate-*l/ 90.7%

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

   7. associate-*r/ 90.7%

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

   8. associate-*l/ 95.3%

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

   9. associate-/l* 94.0%

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

   10. distribute-rgt-out 99.0%

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

8. Simplified 99.0%

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

   1. *-commutative 99.0%

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

   2. clear-num 99.0%

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

   3. un-div-inv 99.1%

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

10. Applied egg-rr 99.1%

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

Alternative 2: 84.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{+75}:\\ \;\;\;\;0.91893853320467 + \left(\frac{y}{x} + \frac{0.0007936500793651}{x}\right) \cdot {z}^{2}\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+104}:\\ \;\;\;\;0.91893853320467 + \left(\left(0.083333333333333 \cdot \frac{1}{x} + \log x \cdot \left(x - 0.5\right)\right) - x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333 + t\_0}{x} + \left(0.91893853320467 + \log x \cdot -0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- (* z (+ 0.0007936500793651 y)) 0.0027777777777778))))
   (if (<= t_0 -5e+75)
     (+ 0.91893853320467 (* (+ (/ y x) (/ 0.0007936500793651 x)) (pow z 2.0)))
     (if (<= t_0 2e+104)
       (+
        0.91893853320467
        (- (+ (* 0.083333333333333 (/ 1.0 x)) (* (log x) (- x 0.5))) x))
       (+
        (/ (+ 0.083333333333333 t_0) x)
        (+ 0.91893853320467 (* (log x) -0.5)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778);
	double tmp;
	if (t_0 <= -5e+75) {
		tmp = 0.91893853320467 + (((y / x) + (0.0007936500793651 / x)) * pow(z, 2.0));
	} else if (t_0 <= 2e+104) {
		tmp = 0.91893853320467 + (((0.083333333333333 * (1.0 / x)) + (log(x) * (x - 0.5))) - x);
	} else {
		tmp = ((0.083333333333333 + t_0) / x) + (0.91893853320467 + (log(x) * -0.5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * ((z * (0.0007936500793651d0 + y)) - 0.0027777777777778d0)
    if (t_0 <= (-5d+75)) then
        tmp = 0.91893853320467d0 + (((y / x) + (0.0007936500793651d0 / x)) * (z ** 2.0d0))
    else if (t_0 <= 2d+104) then
        tmp = 0.91893853320467d0 + (((0.083333333333333d0 * (1.0d0 / x)) + (log(x) * (x - 0.5d0))) - x)
    else
        tmp = ((0.083333333333333d0 + t_0) / x) + (0.91893853320467d0 + (log(x) * (-0.5d0)))
    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 tmp;
	if (t_0 <= -5e+75) {
		tmp = 0.91893853320467 + (((y / x) + (0.0007936500793651 / x)) * Math.pow(z, 2.0));
	} else if (t_0 <= 2e+104) {
		tmp = 0.91893853320467 + (((0.083333333333333 * (1.0 / x)) + (Math.log(x) * (x - 0.5))) - x);
	} else {
		tmp = ((0.083333333333333 + t_0) / x) + (0.91893853320467 + (Math.log(x) * -0.5));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778)
	tmp = 0
	if t_0 <= -5e+75:
		tmp = 0.91893853320467 + (((y / x) + (0.0007936500793651 / x)) * math.pow(z, 2.0))
	elif t_0 <= 2e+104:
		tmp = 0.91893853320467 + (((0.083333333333333 * (1.0 / x)) + (math.log(x) * (x - 0.5))) - x)
	else:
		tmp = ((0.083333333333333 + t_0) / x) + (0.91893853320467 + (math.log(x) * -0.5))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(Float64(z * Float64(0.0007936500793651 + y)) - 0.0027777777777778))
	tmp = 0.0
	if (t_0 <= -5e+75)
		tmp = Float64(0.91893853320467 + Float64(Float64(Float64(y / x) + Float64(0.0007936500793651 / x)) * (z ^ 2.0)));
	elseif (t_0 <= 2e+104)
		tmp = Float64(0.91893853320467 + Float64(Float64(Float64(0.083333333333333 * Float64(1.0 / x)) + Float64(log(x) * Float64(x - 0.5))) - x));
	else
		tmp = Float64(Float64(Float64(0.083333333333333 + t_0) / x) + Float64(0.91893853320467 + Float64(log(x) * -0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778);
	tmp = 0.0;
	if (t_0 <= -5e+75)
		tmp = 0.91893853320467 + (((y / x) + (0.0007936500793651 / x)) * (z ^ 2.0));
	elseif (t_0 <= 2e+104)
		tmp = 0.91893853320467 + (((0.083333333333333 * (1.0 / x)) + (log(x) * (x - 0.5))) - x);
	else
		tmp = ((0.083333333333333 + t_0) / x) + (0.91893853320467 + (log(x) * -0.5));
	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]}, If[LessEqual[t$95$0, -5e+75], N[(0.91893853320467 + N[(N[(N[(y / x), $MachinePrecision] + N[(0.0007936500793651 / x), $MachinePrecision]), $MachinePrecision] * N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 2e+104], N[(0.91893853320467 + N[(N[(N[(0.083333333333333 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision] + N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(0.083333333333333 + t$95$0), $MachinePrecision] / x), $MachinePrecision] + N[(0.91893853320467 + N[(N[Log[x], $MachinePrecision] * -0.5), $MachinePrecision]), $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) < -5.0000000000000002e75

   1. Initial program 86.8%

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

      1. +-commutative 86.8%

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

      2. associate-+l+ 86.8%

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

      3. associate-+l- 86.8%

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

      4. fma-neg 86.9%

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

      5. sub-neg 86.9%

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

      6. metadata-eval 86.9%

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

      7. neg-sub0 86.9%

         \[\leadsto 0.91893853320467 + \mathsf{fma}\left(x + -0.5, \log x, \color{blue}{0 - \left(x - \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\right)}\right) \]

      8. associate-+l- 86.9%

         \[\leadsto 0.91893853320467 + \mathsf{fma}\left(x + -0.5, \log x, \color{blue}{\left(0 - x\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}}\right) \]

      9. neg-sub0 86.9%

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

      10. +-commutative 86.9%

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

      11. unsub-neg 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in z around inf 87.4%

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

      1. *-commutative 87.4%

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

      2. associate-*r/ 87.4%

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

      3. metadata-eval 87.4%

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

   7. Simplified 87.4%

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

   if -5.0000000000000002e75 < (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) < 2e104

   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. Step-by-step derivation

      1. +-commutative 99.5%

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

      2. associate-+l+ 99.5%

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

      3. associate-+l- 99.5%

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

      4. fma-neg 99.6%

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

      5. sub-neg 99.6%

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

      6. metadata-eval 99.6%

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

      7. neg-sub0 99.6%

         \[\leadsto 0.91893853320467 + \mathsf{fma}\left(x + -0.5, \log x, \color{blue}{0 - \left(x - \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\right)}\right) \]

      8. associate-+l- 99.6%

         \[\leadsto 0.91893853320467 + \mathsf{fma}\left(x + -0.5, \log x, \color{blue}{\left(0 - x\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}}\right) \]

      9. neg-sub0 99.6%

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

      10. +-commutative 99.6%

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

      11. unsub-neg 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around 0 96.3%

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

   if 2e104 < (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z)

   1. Initial program 85.4%

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

   3. Taylor expanded in x around 0 82.2%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right) \leq -5 \cdot 10^{+75}:\\ \;\;\;\;0.91893853320467 + \left(\frac{y}{x} + \frac{0.0007936500793651}{x}\right) \cdot {z}^{2}\\ \mathbf{elif}\;z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right) \leq 2 \cdot 10^{+104}:\\ \;\;\;\;0.91893853320467 + \left(\left(0.083333333333333 \cdot \frac{1}{x} + \log x \cdot \left(x - 0.5\right)\right) - x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x} + \left(0.91893853320467 + \log x \cdot -0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-93} \lor \neg \left(y \leq 6 \cdot 10^{-126}\right):\\ \;\;\;\;\left(0.91893853320467 + \left(x \cdot \log x - x\right)\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;0.91893853320467 + \left(\left(0.083333333333333 \cdot \frac{1}{x} + \left(\log x \cdot \left(x - 0.5\right) + z \cdot \left(z \cdot \frac{0.0007936500793651}{x}\right)\right)\right) - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4e-93) (not (<= y 6e-126)))
   (+
    (+ 0.91893853320467 (- (* x (log x)) x))
    (/
     (+
      0.083333333333333
      (* z (- (* z (+ 0.0007936500793651 y)) 0.0027777777777778)))
     x))
   (+
    0.91893853320467
    (-
     (+
      (* 0.083333333333333 (/ 1.0 x))
      (+ (* (log x) (- x 0.5)) (* z (* z (/ 0.0007936500793651 x)))))
     x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4e-93) || !(y <= 6e-126)) {
		tmp = (0.91893853320467 + ((x * log(x)) - x)) + ((0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x);
	} else {
		tmp = 0.91893853320467 + (((0.083333333333333 * (1.0 / x)) + ((log(x) * (x - 0.5)) + (z * (z * (0.0007936500793651 / x))))) - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-4d-93)) .or. (.not. (y <= 6d-126))) then
        tmp = (0.91893853320467d0 + ((x * log(x)) - x)) + ((0.083333333333333d0 + (z * ((z * (0.0007936500793651d0 + y)) - 0.0027777777777778d0))) / x)
    else
        tmp = 0.91893853320467d0 + (((0.083333333333333d0 * (1.0d0 / x)) + ((log(x) * (x - 0.5d0)) + (z * (z * (0.0007936500793651d0 / x))))) - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4e-93) || !(y <= 6e-126)) {
		tmp = (0.91893853320467 + ((x * Math.log(x)) - x)) + ((0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x);
	} else {
		tmp = 0.91893853320467 + (((0.083333333333333 * (1.0 / x)) + ((Math.log(x) * (x - 0.5)) + (z * (z * (0.0007936500793651 / x))))) - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4e-93) or not (y <= 6e-126):
		tmp = (0.91893853320467 + ((x * math.log(x)) - x)) + ((0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x)
	else:
		tmp = 0.91893853320467 + (((0.083333333333333 * (1.0 / x)) + ((math.log(x) * (x - 0.5)) + (z * (z * (0.0007936500793651 / x))))) - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4e-93) || !(y <= 6e-126))
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(x * log(x)) - x)) + Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * Float64(0.0007936500793651 + y)) - 0.0027777777777778))) / x));
	else
		tmp = Float64(0.91893853320467 + Float64(Float64(Float64(0.083333333333333 * Float64(1.0 / x)) + Float64(Float64(log(x) * Float64(x - 0.5)) + Float64(z * Float64(z * Float64(0.0007936500793651 / x))))) - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4e-93) || ~((y <= 6e-126)))
		tmp = (0.91893853320467 + ((x * log(x)) - x)) + ((0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x);
	else
		tmp = 0.91893853320467 + (((0.083333333333333 * (1.0 / x)) + ((log(x) * (x - 0.5)) + (z * (z * (0.0007936500793651 / x))))) - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4e-93], N[Not[LessEqual[y, 6e-126]], $MachinePrecision]], N[(N[(0.91893853320467 + N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $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[(0.91893853320467 + N[(N[(N[(0.083333333333333 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision] + N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] + N[(z * N[(z * N[(0.0007936500793651 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.9999999999999996e-93 or 6.0000000000000003e-126 < y

   1. Initial program 93.5%

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

   3. Taylor expanded in x around inf 93.1%

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

      1. mul-1-neg 93.1%

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

      2. distribute-rgt-neg-in 93.1%

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

      3. log-rec 93.1%

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

      4. remove-double-neg 93.1%

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

   5. Simplified 93.1%

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

   if -3.9999999999999996e-93 < y < 6.0000000000000003e-126

   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. Step-by-step derivation

      1. +-commutative 90.3%

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

      2. associate-+l+ 90.3%

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

      3. associate-+l- 90.3%

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

      4. fma-neg 90.4%

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

      5. sub-neg 90.4%

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

      6. metadata-eval 90.4%

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

      7. neg-sub0 90.4%

         \[\leadsto 0.91893853320467 + \mathsf{fma}\left(x + -0.5, \log x, \color{blue}{0 - \left(x - \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\right)}\right) \]

      8. associate-+l- 90.4%

         \[\leadsto 0.91893853320467 + \mathsf{fma}\left(x + -0.5, \log x, \color{blue}{\left(0 - x\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}}\right) \]

      9. neg-sub0 90.4%

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

      10. +-commutative 90.4%

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

      11. unsub-neg 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in z around 0 99.6%

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

   6. Taylor expanded in z around inf 90.4%

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

      1. unpow2 90.4%

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

      2. associate-*l* 99.6%

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

      3. distribute-rgt-in 99.6%

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

      4. associate-*r/ 99.7%

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

      5. metadata-eval 99.7%

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

      6. associate-*l/ 99.7%

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

      7. associate-*r/ 99.7%

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

      8. associate-*l/ 99.7%

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

      9. associate-/l* 92.8%

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

      10. distribute-rgt-out 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in y around 0 99.7%

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

       1. *-commutative 99.7%

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

       2. associate-*l/ 99.7%

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

       3. associate-*r/ 99.7%

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

   11. Simplified 99.7%

       \[\leadsto 0.91893853320467 + \left(\left(0.083333333333333 \cdot \frac{1}{x} + \left(z \cdot \color{blue}{\left(z \cdot \frac{0.0007936500793651}{x}\right)} + \log x \cdot \left(x - 0.5\right)\right)\right) - x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-93} \lor \neg \left(y \leq 6 \cdot 10^{-126}\right):\\ \;\;\;\;\left(0.91893853320467 + \left(x \cdot \log x - x\right)\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;0.91893853320467 + \left(\left(0.083333333333333 \cdot \frac{1}{x} + \left(\log x \cdot \left(x - 0.5\right) + z \cdot \left(z \cdot \frac{0.0007936500793651}{x}\right)\right)\right) - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.8 \cdot 10^{+121}:\\ \;\;\;\;\left(0.91893853320467 + \left(x \cdot \log x - x\right)\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;0.91893853320467 + \left(\left(0.083333333333333 \cdot \frac{1}{x} + \left(\log x \cdot \left(x - 0.5\right) + z \cdot \left(z \cdot \frac{y}{x}\right)\right)\right) - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 4.8e+121)
   (+
    (+ 0.91893853320467 (- (* x (log x)) x))
    (/
     (+
      0.083333333333333
      (* z (- (* z (+ 0.0007936500793651 y)) 0.0027777777777778)))
     x))
   (+
    0.91893853320467
    (-
     (+
      (* 0.083333333333333 (/ 1.0 x))
      (+ (* (log x) (- x 0.5)) (* z (* z (/ y x)))))
     x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 4.8e+121) {
		tmp = (0.91893853320467 + ((x * log(x)) - x)) + ((0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x);
	} else {
		tmp = 0.91893853320467 + (((0.083333333333333 * (1.0 / x)) + ((log(x) * (x - 0.5)) + (z * (z * (y / x))))) - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 4.8d+121) then
        tmp = (0.91893853320467d0 + ((x * log(x)) - x)) + ((0.083333333333333d0 + (z * ((z * (0.0007936500793651d0 + y)) - 0.0027777777777778d0))) / x)
    else
        tmp = 0.91893853320467d0 + (((0.083333333333333d0 * (1.0d0 / x)) + ((log(x) * (x - 0.5d0)) + (z * (z * (y / x))))) - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 4.8e+121) {
		tmp = (0.91893853320467 + ((x * Math.log(x)) - x)) + ((0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x);
	} else {
		tmp = 0.91893853320467 + (((0.083333333333333 * (1.0 / x)) + ((Math.log(x) * (x - 0.5)) + (z * (z * (y / x))))) - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 4.8e+121:
		tmp = (0.91893853320467 + ((x * math.log(x)) - x)) + ((0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x)
	else:
		tmp = 0.91893853320467 + (((0.083333333333333 * (1.0 / x)) + ((math.log(x) * (x - 0.5)) + (z * (z * (y / x))))) - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 4.8e+121)
		tmp = Float64(Float64(0.91893853320467 + Float64(Float64(x * log(x)) - x)) + Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * Float64(0.0007936500793651 + y)) - 0.0027777777777778))) / x));
	else
		tmp = Float64(0.91893853320467 + Float64(Float64(Float64(0.083333333333333 * Float64(1.0 / x)) + Float64(Float64(log(x) * Float64(x - 0.5)) + Float64(z * Float64(z * Float64(y / x))))) - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 4.8e+121)
		tmp = (0.91893853320467 + ((x * log(x)) - x)) + ((0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x);
	else
		tmp = 0.91893853320467 + (((0.083333333333333 * (1.0 / x)) + ((log(x) * (x - 0.5)) + (z * (z * (y / x))))) - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 4.8e+121], N[(N[(0.91893853320467 + N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $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[(0.91893853320467 + N[(N[(N[(0.083333333333333 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision] + N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision] + N[(z * N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.8e121

   1. Initial program 98.1%

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

   3. Taylor expanded in x around inf 97.2%

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

      1. mul-1-neg 97.2%

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

      2. distribute-rgt-neg-in 97.2%

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

      3. log-rec 97.2%

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

      4. remove-double-neg 97.2%

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

   5. Simplified 97.2%

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

   if 4.8e121 < x

   1. Initial program 81.6%

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

      1. +-commutative 81.6%

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

      2. associate-+l+ 81.6%

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

      3. associate-+l- 81.6%

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

      4. fma-neg 81.8%

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

      5. sub-neg 81.8%

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

      6. metadata-eval 81.8%

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

      7. neg-sub0 81.8%

         \[\leadsto 0.91893853320467 + \mathsf{fma}\left(x + -0.5, \log x, \color{blue}{0 - \left(x - \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\right)}\right) \]

      8. associate-+l- 81.8%

         \[\leadsto 0.91893853320467 + \mathsf{fma}\left(x + -0.5, \log x, \color{blue}{\left(0 - x\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}}\right) \]

      9. neg-sub0 81.8%

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

      10. +-commutative 81.8%

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

      11. unsub-neg 81.8%

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

   3. Simplified 81.8%

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

   5. Taylor expanded in z around 0 99.5%

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

   6. Taylor expanded in z around inf 87.0%

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

      1. unpow2 87.0%

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

      2. associate-*l* 99.5%

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

      3. distribute-rgt-in 99.5%

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

      4. associate-*r/ 99.5%

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

      5. metadata-eval 99.5%

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

      6. associate-*l/ 99.5%

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

      7. associate-*r/ 99.5%

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

      8. associate-*l/ 95.3%

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

      9. associate-/l* 99.4%

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

      10. distribute-rgt-out 99.4%

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

   8. Simplified 99.4%

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

   9. Taylor expanded in y around inf 90.0%

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

       1. *-commutative 90.0%

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

       2. associate-*r/ 94.2%

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

   11. Simplified 94.2%

       \[\leadsto 0.91893853320467 + \left(\left(0.083333333333333 \cdot \frac{1}{x} + \left(z \cdot \color{blue}{\left(z \cdot \frac{y}{x}\right)} + \log x \cdot \left(x - 0.5\right)\right)\right) - x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4.8 \cdot 10^{+121}:\\ \;\;\;\;\left(0.91893853320467 + \left(x \cdot \log x - x\right)\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;0.91893853320467 + \left(\left(0.083333333333333 \cdot \frac{1}{x} + \left(\log x \cdot \left(x - 0.5\right) + z \cdot \left(z \cdot \frac{y}{x}\right)\right)\right) - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+22} \lor \neg \left(z \leq 2.6 \cdot 10^{+33}\right):\\ \;\;\;\;0.91893853320467 + \left(\frac{y}{x} + \frac{0.0007936500793651}{x}\right) \cdot {z}^{2}\\ \mathbf{else}:\\ \;\;\;\;0.91893853320467 + \left(\left(0.083333333333333 \cdot \frac{1}{x} + \log x \cdot \left(x - 0.5\right)\right) - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -7.2e+22) (not (<= z 2.6e+33)))
   (+ 0.91893853320467 (* (+ (/ y x) (/ 0.0007936500793651 x)) (pow z 2.0)))
   (+
    0.91893853320467
    (- (+ (* 0.083333333333333 (/ 1.0 x)) (* (log x) (- x 0.5))) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.2e+22) || !(z <= 2.6e+33)) {
		tmp = 0.91893853320467 + (((y / x) + (0.0007936500793651 / x)) * pow(z, 2.0));
	} else {
		tmp = 0.91893853320467 + (((0.083333333333333 * (1.0 / x)) + (log(x) * (x - 0.5))) - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-7.2d+22)) .or. (.not. (z <= 2.6d+33))) then
        tmp = 0.91893853320467d0 + (((y / x) + (0.0007936500793651d0 / x)) * (z ** 2.0d0))
    else
        tmp = 0.91893853320467d0 + (((0.083333333333333d0 * (1.0d0 / x)) + (log(x) * (x - 0.5d0))) - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.2e+22) || !(z <= 2.6e+33)) {
		tmp = 0.91893853320467 + (((y / x) + (0.0007936500793651 / x)) * Math.pow(z, 2.0));
	} else {
		tmp = 0.91893853320467 + (((0.083333333333333 * (1.0 / x)) + (Math.log(x) * (x - 0.5))) - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -7.2e+22) or not (z <= 2.6e+33):
		tmp = 0.91893853320467 + (((y / x) + (0.0007936500793651 / x)) * math.pow(z, 2.0))
	else:
		tmp = 0.91893853320467 + (((0.083333333333333 * (1.0 / x)) + (math.log(x) * (x - 0.5))) - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -7.2e+22) || !(z <= 2.6e+33))
		tmp = Float64(0.91893853320467 + Float64(Float64(Float64(y / x) + Float64(0.0007936500793651 / x)) * (z ^ 2.0)));
	else
		tmp = Float64(0.91893853320467 + Float64(Float64(Float64(0.083333333333333 * Float64(1.0 / x)) + Float64(log(x) * Float64(x - 0.5))) - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -7.2e+22) || ~((z <= 2.6e+33)))
		tmp = 0.91893853320467 + (((y / x) + (0.0007936500793651 / x)) * (z ^ 2.0));
	else
		tmp = 0.91893853320467 + (((0.083333333333333 * (1.0 / x)) + (log(x) * (x - 0.5))) - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -7.2e+22], N[Not[LessEqual[z, 2.6e+33]], $MachinePrecision]], N[(0.91893853320467 + N[(N[(N[(y / x), $MachinePrecision] + N[(0.0007936500793651 / x), $MachinePrecision]), $MachinePrecision] * N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.91893853320467 + N[(N[(N[(0.083333333333333 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision] + N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.2e22 or 2.5999999999999997e33 < z

   1. Initial program 85.2%

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

      1. +-commutative 85.2%

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

      2. associate-+l+ 85.2%

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

      3. associate-+l- 85.2%

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

      4. fma-neg 85.3%

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

      5. sub-neg 85.3%

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

      6. metadata-eval 85.3%

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

      7. neg-sub0 85.3%

         \[\leadsto 0.91893853320467 + \mathsf{fma}\left(x + -0.5, \log x, \color{blue}{0 - \left(x - \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\right)}\right) \]

      8. associate-+l- 85.3%

         \[\leadsto 0.91893853320467 + \mathsf{fma}\left(x + -0.5, \log x, \color{blue}{\left(0 - x\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}}\right) \]

      9. neg-sub0 85.3%

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

      10. +-commutative 85.3%

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

      11. unsub-neg 85.3%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in z around inf 81.5%

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

      1. *-commutative 81.5%

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

      2. associate-*r/ 81.5%

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

      3. metadata-eval 81.5%

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

   7. Simplified 81.5%

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

   if -7.2e22 < z < 2.5999999999999997e33

   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. Step-by-step derivation

      1. +-commutative 99.5%

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

      2. associate-+l+ 99.5%

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

      3. associate-+l- 99.5%

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

      4. fma-neg 99.6%

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

      5. sub-neg 99.6%

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

      6. metadata-eval 99.6%

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

      7. neg-sub0 99.6%

         \[\leadsto 0.91893853320467 + \mathsf{fma}\left(x + -0.5, \log x, \color{blue}{0 - \left(x - \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\right)}\right) \]

      8. associate-+l- 99.6%

         \[\leadsto 0.91893853320467 + \mathsf{fma}\left(x + -0.5, \log x, \color{blue}{\left(0 - x\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}}\right) \]

      9. neg-sub0 99.6%

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

      10. +-commutative 99.6%

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

      11. unsub-neg 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around 0 90.4%

      \[\leadsto 0.91893853320467 + \color{blue}{\left(\left(0.083333333333333 \cdot \frac{1}{x} + \log x \cdot \left(x - 0.5\right)\right) - x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+22} \lor \neg \left(z \leq 2.6 \cdot 10^{+33}\right):\\ \;\;\;\;0.91893853320467 + \left(\frac{y}{x} + \frac{0.0007936500793651}{x}\right) \cdot {z}^{2}\\ \mathbf{else}:\\ \;\;\;\;0.91893853320467 + \left(\left(0.083333333333333 \cdot \frac{1}{x} + \log x \cdot \left(x - 0.5\right)\right) - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.4%

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

   1. +-commutative 92.4%

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

   2. associate-+l+ 92.4%

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

   3. associate-+l- 92.4%

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

   4. fma-neg 92.5%

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

   5. sub-neg 92.5%

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

   6. metadata-eval 92.5%

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

   7. neg-sub0 92.5%

      \[\leadsto 0.91893853320467 + \mathsf{fma}\left(x + -0.5, \log x, \color{blue}{0 - \left(x - \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\right)}\right) \]

   8. associate-+l- 92.5%

      \[\leadsto 0.91893853320467 + \mathsf{fma}\left(x + -0.5, \log x, \color{blue}{\left(0 - x\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}}\right) \]

   9. neg-sub0 92.5%

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

   10. +-commutative 92.5%

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

   11. unsub-neg 92.5%

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

3. Simplified 92.5%

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

5. Taylor expanded in z around 0 93.2%

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

6. Taylor expanded in z around inf 87.6%

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

   1. unpow2 87.6%

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

   2. associate-*l* 93.0%

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

   3. distribute-rgt-in 90.7%

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

   4. associate-*r/ 90.7%

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

   5. metadata-eval 90.7%

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

   6. associate-*l/ 90.7%

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

   7. associate-*r/ 90.7%

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

   8. associate-*l/ 95.3%

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

   9. associate-/l* 94.0%

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

   10. distribute-rgt-out 99.0%

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

8. Simplified 99.0%

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

   1. *-commutative 99.0%

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

   2. clear-num 99.0%

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

   3. un-div-inv 99.1%

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

10. Applied egg-rr 99.1%

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

11. Taylor expanded in x around 0 99.1%

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

12. Final simplification 99.1%

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

Alternative 7: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return 0.91893853320467 + (((0.083333333333333 / x) + ((log(x) * (x - 0.5)) + (z * ((0.0007936500793651 + y) * (z / 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 = 0.91893853320467d0 + (((0.083333333333333d0 / x) + ((log(x) * (x - 0.5d0)) + (z * ((0.0007936500793651d0 + y) * (z / x))))) - x)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.4%

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

   1. +-commutative 92.4%

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

   2. associate-+l+ 92.4%

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

   3. associate-+l- 92.4%

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

   4. fma-neg 92.5%

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

   5. sub-neg 92.5%

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

   6. metadata-eval 92.5%

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

   7. neg-sub0 92.5%

      \[\leadsto 0.91893853320467 + \mathsf{fma}\left(x + -0.5, \log x, \color{blue}{0 - \left(x - \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\right)}\right) \]

   8. associate-+l- 92.5%

      \[\leadsto 0.91893853320467 + \mathsf{fma}\left(x + -0.5, \log x, \color{blue}{\left(0 - x\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}}\right) \]

   9. neg-sub0 92.5%

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

   10. +-commutative 92.5%

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

   11. unsub-neg 92.5%

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

3. Simplified 92.5%

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

5. Taylor expanded in z around 0 93.2%

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

6. Taylor expanded in z around inf 87.6%

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

   1. unpow2 87.6%

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

   2. associate-*l* 93.0%

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

   3. distribute-rgt-in 90.7%

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

   4. associate-*r/ 90.7%

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

   5. metadata-eval 90.7%

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

   6. associate-*l/ 90.7%

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

   7. associate-*r/ 90.7%

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

   8. associate-*l/ 95.3%

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

   9. associate-/l* 94.0%

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

   10. distribute-rgt-out 99.0%

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

8. Simplified 99.0%

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

9. Taylor expanded in x around 0 99.0%

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

10. Final simplification 99.0%

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

Alternative 8: 83.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+22} \lor \neg \left(z \leq 2.5 \cdot 10^{+33}\right):\\ \;\;\;\;0.91893853320467 + \left(\frac{y}{x} + \frac{0.0007936500793651}{x}\right) \cdot {z}^{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x} + \left(0.91893853320467 + \left(x \cdot \log x - x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.75e+22) (not (<= z 2.5e+33)))
   (+ 0.91893853320467 (* (+ (/ y x) (/ 0.0007936500793651 x)) (pow z 2.0)))
   (+ (/ 0.083333333333333 x) (+ 0.91893853320467 (- (* x (log x)) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.75e+22) || !(z <= 2.5e+33)) {
		tmp = 0.91893853320467 + (((y / x) + (0.0007936500793651 / x)) * pow(z, 2.0));
	} else {
		tmp = (0.083333333333333 / x) + (0.91893853320467 + ((x * log(x)) - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.75d+22)) .or. (.not. (z <= 2.5d+33))) then
        tmp = 0.91893853320467d0 + (((y / x) + (0.0007936500793651d0 / x)) * (z ** 2.0d0))
    else
        tmp = (0.083333333333333d0 / x) + (0.91893853320467d0 + ((x * log(x)) - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.75e+22) || !(z <= 2.5e+33)) {
		tmp = 0.91893853320467 + (((y / x) + (0.0007936500793651 / x)) * Math.pow(z, 2.0));
	} else {
		tmp = (0.083333333333333 / x) + (0.91893853320467 + ((x * Math.log(x)) - x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.75e+22) or not (z <= 2.5e+33):
		tmp = 0.91893853320467 + (((y / x) + (0.0007936500793651 / x)) * math.pow(z, 2.0))
	else:
		tmp = (0.083333333333333 / x) + (0.91893853320467 + ((x * math.log(x)) - x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.75e+22) || !(z <= 2.5e+33))
		tmp = Float64(0.91893853320467 + Float64(Float64(Float64(y / x) + Float64(0.0007936500793651 / x)) * (z ^ 2.0)));
	else
		tmp = Float64(Float64(0.083333333333333 / x) + Float64(0.91893853320467 + Float64(Float64(x * log(x)) - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.75e+22) || ~((z <= 2.5e+33)))
		tmp = 0.91893853320467 + (((y / x) + (0.0007936500793651 / x)) * (z ^ 2.0));
	else
		tmp = (0.083333333333333 / x) + (0.91893853320467 + ((x * log(x)) - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.75e+22], N[Not[LessEqual[z, 2.5e+33]], $MachinePrecision]], N[(0.91893853320467 + N[(N[(N[(y / x), $MachinePrecision] + N[(0.0007936500793651 / x), $MachinePrecision]), $MachinePrecision] * N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.083333333333333 / x), $MachinePrecision] + N[(0.91893853320467 + N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.75e22 or 2.49999999999999986e33 < z

   1. Initial program 85.2%

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

      1. +-commutative 85.2%

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

      2. associate-+l+ 85.2%

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

      3. associate-+l- 85.2%

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

      4. fma-neg 85.3%

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

      5. sub-neg 85.3%

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

      6. metadata-eval 85.3%

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

      7. neg-sub0 85.3%

         \[\leadsto 0.91893853320467 + \mathsf{fma}\left(x + -0.5, \log x, \color{blue}{0 - \left(x - \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\right)}\right) \]

      8. associate-+l- 85.3%

         \[\leadsto 0.91893853320467 + \mathsf{fma}\left(x + -0.5, \log x, \color{blue}{\left(0 - x\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}}\right) \]

      9. neg-sub0 85.3%

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

      10. +-commutative 85.3%

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

      11. unsub-neg 85.3%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in z around inf 81.5%

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

      1. *-commutative 81.5%

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

      2. associate-*r/ 81.5%

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

      3. metadata-eval 81.5%

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

   7. Simplified 81.5%

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

   if -1.75e22 < z < 2.49999999999999986e33

   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 x around inf 98.4%

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

      1. mul-1-neg 98.4%

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

      2. distribute-rgt-neg-in 98.4%

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

      3. log-rec 98.4%

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

      4. remove-double-neg 98.4%

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

   5. Simplified 98.4%

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

   6. Taylor expanded in z around 0 89.1%

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

      1. *-commutative 89.1%

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

   8. Simplified 89.1%

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

   9. Taylor expanded in z around 0 89.2%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+22} \lor \neg \left(z \leq 2.5 \cdot 10^{+33}\right):\\ \;\;\;\;0.91893853320467 + \left(\frac{y}{x} + \frac{0.0007936500793651}{x}\right) \cdot {z}^{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x} + \left(0.91893853320467 + \left(x \cdot \log x - x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 93.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.4%

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

3. Taylor expanded in x around inf 91.9%

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

   1. mul-1-neg 91.9%

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

   2. distribute-rgt-neg-in 91.9%

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

   3. log-rec 91.9%

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

   4. remove-double-neg 91.9%

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

5. Simplified 91.9%

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

6. Final simplification 91.9%

   \[\leadsto \left(0.91893853320467 + \left(x \cdot \log x - x\right)\right) + \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x} \]
7. 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 92.4%

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

3. Taylor expanded in x around inf 91.9%

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

   1. mul-1-neg 91.9%

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

   2. distribute-rgt-neg-in 91.9%

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

   3. log-rec 91.9%

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

   4. remove-double-neg 91.9%

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

5. Simplified 91.9%

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

6. Taylor expanded in z around 0 60.1%

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

   1. *-commutative 60.1%

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

8. Simplified 60.1%

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

9. Taylor expanded in z around 0 52.3%

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

10. Final simplification 52.3%

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

Alternative 11: 36.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ 0.91893853320467 + x \cdot \left(\log x + -1\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 0.91893853320467 (* x (+ (log x) -1.0))))

C

double code(double x, double y, double z) {
	return 0.91893853320467 + (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 = 0.91893853320467d0 + (x * (log(x) + (-1.0d0)))
end function

Java

public static double code(double x, double y, double z) {
	return 0.91893853320467 + (x * (Math.log(x) + -1.0));
}

Python

def code(x, y, z):
	return 0.91893853320467 + (x * (math.log(x) + -1.0))

Julia

function code(x, y, z)
	return Float64(0.91893853320467 + Float64(x * Float64(log(x) + -1.0)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 0.91893853320467 + (x * (log(x) + -1.0));
end

Wolfram

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

Derivation

1. Initial program 92.4%

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

   1. +-commutative 92.4%

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

   2. associate-+l+ 92.4%

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

   3. associate-+l- 92.4%

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

   4. fma-neg 92.5%

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

   5. sub-neg 92.5%

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

   6. metadata-eval 92.5%

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

   7. neg-sub0 92.5%

      \[\leadsto 0.91893853320467 + \mathsf{fma}\left(x + -0.5, \log x, \color{blue}{0 - \left(x - \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\right)}\right) \]

   8. associate-+l- 92.5%

      \[\leadsto 0.91893853320467 + \mathsf{fma}\left(x + -0.5, \log x, \color{blue}{\left(0 - x\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}}\right) \]

   9. neg-sub0 92.5%

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

   10. +-commutative 92.5%

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

   11. unsub-neg 92.5%

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

3. Simplified 92.5%

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

5. Taylor expanded in x around inf 33.4%

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

   1. sub-neg 33.4%

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

   2. mul-1-neg 33.4%

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

   3. log-rec 33.4%

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

   4. remove-double-neg 33.4%

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

   5. metadata-eval 33.4%

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

7. Simplified 33.4%

   \[\leadsto 0.91893853320467 + \color{blue}{x \cdot \left(\log x + -1\right)} \]
8. Add Preprocessing

Alternative 12: 4.0% accurate, 123.0× speedup

Math

\[\begin{array}{l} \\ 0.91893853320467 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 0.91893853320467)

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return 0.91893853320467

Julia

function code(x, y, z)
	return 0.91893853320467
end

MATLAB

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

Wolfram

code[x_, y_, z_] := 0.91893853320467

Derivation

1. Initial program 92.4%

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

   1. +-commutative 92.4%

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

   2. associate-+l+ 92.4%

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

   3. associate-+l- 92.4%

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

   4. fma-neg 92.5%

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

   5. sub-neg 92.5%

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

   6. metadata-eval 92.5%

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

   7. neg-sub0 92.5%

      \[\leadsto 0.91893853320467 + \mathsf{fma}\left(x + -0.5, \log x, \color{blue}{0 - \left(x - \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\right)}\right) \]

   8. associate-+l- 92.5%

      \[\leadsto 0.91893853320467 + \mathsf{fma}\left(x + -0.5, \log x, \color{blue}{\left(0 - x\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}}\right) \]

   9. neg-sub0 92.5%

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

   10. +-commutative 92.5%

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

   11. unsub-neg 92.5%

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

3. Simplified 92.5%

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

5. Taylor expanded in x around inf 33.4%

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

   1. sub-neg 33.4%

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

   2. mul-1-neg 33.4%

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

   3. log-rec 33.4%

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

   4. remove-double-neg 33.4%

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

   5. metadata-eval 33.4%

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

7. Simplified 33.4%

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

8. Taylor expanded in x around 0 3.8%

   \[\leadsto \color{blue}{0.91893853320467} \]
9. 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 2024096 
(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)))