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

Percentage Accurate: 93.8% → 96.7%

Time: 16.7s

Alternatives: 14

Speedup: 1.0×

• 27.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5 \cdot 10^{+90}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(z \cdot \left(\left(y + 0.0007936500793651\right) \cdot z\right) + z \cdot -0.0027777777777778\right) + 0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{y}{\frac{1}{z} \cdot \frac{x}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 5e+90)
   (+
    (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
    (/
     (+
      (+ (* z (* (+ y 0.0007936500793651) z)) (* z -0.0027777777777778))
      0.083333333333333)
     x))
   (+ (* x (+ (log x) -1.0)) (/ y (* (/ 1.0 z) (/ x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 5e+90) {
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((((z * ((y + 0.0007936500793651) * z)) + (z * -0.0027777777777778)) + 0.083333333333333) / x);
	} else {
		tmp = (x * (log(x) + -1.0)) + (y / ((1.0 / z) * (x / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 5d+90) then
        tmp = ((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + ((((z * ((y + 0.0007936500793651d0) * z)) + (z * (-0.0027777777777778d0))) + 0.083333333333333d0) / x)
    else
        tmp = (x * (log(x) + (-1.0d0))) + (y / ((1.0d0 / z) * (x / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 5e+90) {
		tmp = ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + ((((z * ((y + 0.0007936500793651) * z)) + (z * -0.0027777777777778)) + 0.083333333333333) / x);
	} else {
		tmp = (x * (Math.log(x) + -1.0)) + (y / ((1.0 / z) * (x / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 5e+90:
		tmp = ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + ((((z * ((y + 0.0007936500793651) * z)) + (z * -0.0027777777777778)) + 0.083333333333333) / x)
	else:
		tmp = (x * (math.log(x) + -1.0)) + (y / ((1.0 / z) * (x / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 5e+90)
		tmp = Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(Float64(Float64(Float64(z * Float64(Float64(y + 0.0007936500793651) * z)) + Float64(z * -0.0027777777777778)) + 0.083333333333333) / x));
	else
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(y / Float64(Float64(1.0 / z) * Float64(x / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 5e+90)
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((((z * ((y + 0.0007936500793651) * z)) + (z * -0.0027777777777778)) + 0.083333333333333) / x);
	else
		tmp = (x * (log(x) + -1.0)) + (y / ((1.0 / z) * (x / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 5e+90], N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(N[(N[(N[(z * N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + N[(z * -0.0027777777777778), $MachinePrecision]), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(N[(1.0 / z), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 5.0000000000000004e90

   1. Initial program 98.6%

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

      1. *-commutative 98.6%

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

      2. sub-neg 98.6%

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

      3. metadata-eval 98.6%

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

      4. distribute-rgt-in 98.6%

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

   3. Applied egg-rr 98.6%

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

   if 5.0000000000000004e90 < x

   1. Initial program 88.1%

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

   2. Taylor expanded in x around inf 88.2%

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

      1. sub-neg 88.2%

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

      2. mul-1-neg 88.2%

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

      3. log-rec 88.2%

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

      4. remove-double-neg 88.2%

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

      5. metadata-eval 88.2%

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

   4. Simplified 88.2%

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

   5. Taylor expanded in y around inf 85.1%

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

      1. associate-/l* 89.1%

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

   7. Simplified 89.1%

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

      1. *-un-lft-identity 89.1%

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

      2. unpow2 89.1%

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

      3. times-frac 97.2%

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

   9. Applied egg-rr 97.2%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5 \cdot 10^{+90}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(z \cdot \left(\left(y + 0.0007936500793651\right) \cdot z\right) + z \cdot -0.0027777777777778\right) + 0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{y}{\frac{1}{z} \cdot \frac{x}{z}}\\ \end{array} \]

Alternative 2: 96.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5.8 \cdot 10^{+90}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333 + z \cdot \left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{y}{\frac{1}{z} \cdot \frac{x}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 5.8e+90)
   (+
    (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
    (/
     (+
      0.083333333333333
      (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)))
     x))
   (+ (* x (+ (log x) -1.0)) (/ y (* (/ 1.0 z) (/ x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 5.8e+90) {
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((0.083333333333333 + (z * (((y + 0.0007936500793651) * z) - 0.0027777777777778))) / x);
	} else {
		tmp = (x * (log(x) + -1.0)) + (y / ((1.0 / z) * (x / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 5.8d+90) then
        tmp = ((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + ((0.083333333333333d0 + (z * (((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0))) / x)
    else
        tmp = (x * (log(x) + (-1.0d0))) + (y / ((1.0d0 / z) * (x / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 5.8e+90) {
		tmp = ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + ((0.083333333333333 + (z * (((y + 0.0007936500793651) * z) - 0.0027777777777778))) / x);
	} else {
		tmp = (x * (Math.log(x) + -1.0)) + (y / ((1.0 / z) * (x / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 5.8e+90:
		tmp = ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + ((0.083333333333333 + (z * (((y + 0.0007936500793651) * z) - 0.0027777777777778))) / x)
	else:
		tmp = (x * (math.log(x) + -1.0)) + (y / ((1.0 / z) * (x / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 5.8e+90)
		tmp = Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778))) / x));
	else
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(y / Float64(Float64(1.0 / z) * Float64(x / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 5.8e+90)
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((0.083333333333333 + (z * (((y + 0.0007936500793651) * z) - 0.0027777777777778))) / x);
	else
		tmp = (x * (log(x) + -1.0)) + (y / ((1.0 / z) * (x / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 5.8e+90], N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(N[(0.083333333333333 + N[(z * N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(N[(1.0 / z), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 5.8000000000000003e90

   1. Initial program 98.6%

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

   if 5.8000000000000003e90 < x

   1. Initial program 88.1%

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

   2. Taylor expanded in x around inf 88.2%

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

      1. sub-neg 88.2%

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

      2. mul-1-neg 88.2%

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

      3. log-rec 88.2%

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

      4. remove-double-neg 88.2%

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

      5. metadata-eval 88.2%

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

   4. Simplified 88.2%

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

   5. Taylor expanded in y around inf 85.1%

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

      1. associate-/l* 89.1%

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

   7. Simplified 89.1%

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

      1. *-un-lft-identity 89.1%

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

      2. unpow2 89.1%

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

      3. times-frac 97.2%

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

   9. Applied egg-rr 97.2%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5.8 \cdot 10^{+90}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333 + z \cdot \left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{y}{\frac{1}{z} \cdot \frac{x}{z}}\\ \end{array} \]

Alternative 3: 86.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(\log x + -1\right)\\ \mathbf{if}\;y \leq -3500000000 \lor \neg \left(y \leq 1.02 \cdot 10^{+235}\right) \land y \leq 1.45 \cdot 10^{+276}:\\ \;\;\;\;t_0 + \frac{y}{\frac{1}{z} \cdot \frac{x}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{0.083333333333333 + z \cdot \left(0.0007936500793651 \cdot z - 0.0027777777777778\right)}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ (log x) -1.0))))
   (if (or (<= y -3500000000.0) (and (not (<= y 1.02e+235)) (<= y 1.45e+276)))
     (+ t_0 (/ y (* (/ 1.0 z) (/ x z))))
     (+
      t_0
      (/
       (+
        0.083333333333333
        (* z (- (* 0.0007936500793651 z) 0.0027777777777778)))
       x)))))

C

double code(double x, double y, double z) {
	double t_0 = x * (log(x) + -1.0);
	double tmp;
	if ((y <= -3500000000.0) || (!(y <= 1.02e+235) && (y <= 1.45e+276))) {
		tmp = t_0 + (y / ((1.0 / z) * (x / z)));
	} else {
		tmp = t_0 + ((0.083333333333333 + (z * ((0.0007936500793651 * z) - 0.0027777777777778))) / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (log(x) + (-1.0d0))
    if ((y <= (-3500000000.0d0)) .or. (.not. (y <= 1.02d+235)) .and. (y <= 1.45d+276)) then
        tmp = t_0 + (y / ((1.0d0 / z) * (x / z)))
    else
        tmp = t_0 + ((0.083333333333333d0 + (z * ((0.0007936500793651d0 * z) - 0.0027777777777778d0))) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (Math.log(x) + -1.0);
	double tmp;
	if ((y <= -3500000000.0) || (!(y <= 1.02e+235) && (y <= 1.45e+276))) {
		tmp = t_0 + (y / ((1.0 / z) * (x / z)));
	} else {
		tmp = t_0 + ((0.083333333333333 + (z * ((0.0007936500793651 * z) - 0.0027777777777778))) / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (math.log(x) + -1.0)
	tmp = 0
	if (y <= -3500000000.0) or (not (y <= 1.02e+235) and (y <= 1.45e+276)):
		tmp = t_0 + (y / ((1.0 / z) * (x / z)))
	else:
		tmp = t_0 + ((0.083333333333333 + (z * ((0.0007936500793651 * z) - 0.0027777777777778))) / x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(log(x) + -1.0))
	tmp = 0.0
	if ((y <= -3500000000.0) || (!(y <= 1.02e+235) && (y <= 1.45e+276)))
		tmp = Float64(t_0 + Float64(y / Float64(Float64(1.0 / z) * Float64(x / z))));
	else
		tmp = Float64(t_0 + Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(0.0007936500793651 * z) - 0.0027777777777778))) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (log(x) + -1.0);
	tmp = 0.0;
	if ((y <= -3500000000.0) || (~((y <= 1.02e+235)) && (y <= 1.45e+276)))
		tmp = t_0 + (y / ((1.0 / z) * (x / z)));
	else
		tmp = t_0 + ((0.083333333333333 + (z * ((0.0007936500793651 * z) - 0.0027777777777778))) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[y, -3500000000.0], And[N[Not[LessEqual[y, 1.02e+235]], $MachinePrecision], LessEqual[y, 1.45e+276]]], N[(t$95$0 + N[(y / N[(N[(1.0 / z), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(N[(0.083333333333333 + N[(z * N[(N[(0.0007936500793651 * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.5e9 or 1.02e235 < y < 1.44999999999999996e276

   1. Initial program 94.1%

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

   2. Taylor expanded in x around inf 93.5%

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

      1. sub-neg 93.5%

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

      2. mul-1-neg 93.5%

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

      3. log-rec 93.5%

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

      4. remove-double-neg 93.5%

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

      5. metadata-eval 93.5%

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

   4. Simplified 93.5%

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

   5. Taylor expanded in y around inf 75.8%

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

      1. associate-/l* 80.0%

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

   7. Simplified 80.0%

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

      1. *-un-lft-identity 80.0%

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

      2. unpow2 80.0%

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

      3. times-frac 81.3%

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

   9. Applied egg-rr 81.3%

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

   if -3.5e9 < y < 1.02e235 or 1.44999999999999996e276 < y

   1. Initial program 96.2%

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

   2. Taylor expanded in x around inf 94.7%

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

      1. sub-neg 94.7%

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

      2. mul-1-neg 94.7%

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

      3. log-rec 94.7%

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

      4. remove-double-neg 94.7%

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

      5. metadata-eval 94.7%

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

   4. Simplified 94.7%

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

   5. Taylor expanded in y around 0 90.6%

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

      1. *-commutative 90.6%

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

   7. Simplified 90.6%

      \[\leadsto x \cdot \left(\log x + -1\right) + \frac{\left(\color{blue}{z \cdot 0.0007936500793651} - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3500000000 \lor \neg \left(y \leq 1.02 \cdot 10^{+235}\right) \land y \leq 1.45 \cdot 10^{+276}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{y}{\frac{1}{z} \cdot \frac{x}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333 + z \cdot \left(0.0007936500793651 \cdot z - 0.0027777777777778\right)}{x}\\ \end{array} \]

Alternative 4: 94.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 18000:\\ \;\;\;\;\frac{\left(z \cdot \left(\left(y + 0.0007936500793651\right) \cdot z\right) + z \cdot -0.0027777777777778\right) + 0.083333333333333}{x} + \left(0.91893853320467 + \log x \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{y}{\frac{1}{z} \cdot \frac{x}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 18000.0)
   (+
    (/
     (+
      (+ (* z (* (+ y 0.0007936500793651) z)) (* z -0.0027777777777778))
      0.083333333333333)
     x)
    (+ 0.91893853320467 (* (log x) -0.5)))
   (+ (* x (+ (log x) -1.0)) (/ y (* (/ 1.0 z) (/ x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 18000.0) {
		tmp = ((((z * ((y + 0.0007936500793651) * z)) + (z * -0.0027777777777778)) + 0.083333333333333) / x) + (0.91893853320467 + (log(x) * -0.5));
	} else {
		tmp = (x * (log(x) + -1.0)) + (y / ((1.0 / z) * (x / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 18000.0d0) then
        tmp = ((((z * ((y + 0.0007936500793651d0) * z)) + (z * (-0.0027777777777778d0))) + 0.083333333333333d0) / x) + (0.91893853320467d0 + (log(x) * (-0.5d0)))
    else
        tmp = (x * (log(x) + (-1.0d0))) + (y / ((1.0d0 / z) * (x / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 18000.0) {
		tmp = ((((z * ((y + 0.0007936500793651) * z)) + (z * -0.0027777777777778)) + 0.083333333333333) / x) + (0.91893853320467 + (Math.log(x) * -0.5));
	} else {
		tmp = (x * (Math.log(x) + -1.0)) + (y / ((1.0 / z) * (x / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 18000.0:
		tmp = ((((z * ((y + 0.0007936500793651) * z)) + (z * -0.0027777777777778)) + 0.083333333333333) / x) + (0.91893853320467 + (math.log(x) * -0.5))
	else:
		tmp = (x * (math.log(x) + -1.0)) + (y / ((1.0 / z) * (x / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 18000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(z * Float64(Float64(y + 0.0007936500793651) * z)) + Float64(z * -0.0027777777777778)) + 0.083333333333333) / x) + Float64(0.91893853320467 + Float64(log(x) * -0.5)));
	else
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(y / Float64(Float64(1.0 / z) * Float64(x / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 18000.0)
		tmp = ((((z * ((y + 0.0007936500793651) * z)) + (z * -0.0027777777777778)) + 0.083333333333333) / x) + (0.91893853320467 + (log(x) * -0.5));
	else
		tmp = (x * (log(x) + -1.0)) + (y / ((1.0 / z) * (x / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 18000.0], N[(N[(N[(N[(N[(z * N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + N[(z * -0.0027777777777778), $MachinePrecision]), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision] + N[(0.91893853320467 + N[(N[Log[x], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(N[(1.0 / z), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 18000

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. sub-neg 99.6%

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

      3. metadata-eval 99.6%

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

      4. distribute-rgt-in 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in x around 0 98.7%

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

   if 18000 < x

   1. Initial program 89.9%

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

   2. Taylor expanded in x around inf 89.5%

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

      1. sub-neg 89.5%

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

      2. mul-1-neg 89.5%

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

      3. log-rec 89.5%

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

      4. remove-double-neg 89.5%

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

      5. metadata-eval 89.5%

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

   4. Simplified 89.5%

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

   5. Taylor expanded in y around inf 85.7%

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

      1. associate-/l* 89.2%

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

   7. Simplified 89.2%

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

      1. *-un-lft-identity 89.2%

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

      2. unpow2 89.2%

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

      3. times-frac 94.9%

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

   9. Applied egg-rr 94.9%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 18000:\\ \;\;\;\;\frac{\left(z \cdot \left(\left(y + 0.0007936500793651\right) \cdot z\right) + z \cdot -0.0027777777777778\right) + 0.083333333333333}{x} + \left(0.91893853320467 + \log x \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{y}{\frac{1}{z} \cdot \frac{x}{z}}\\ \end{array} \]

Alternative 5: 92.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(\log x + -1\right)\\ \mathbf{if}\;y \leq -26000000 \lor \neg \left(y \leq 5 \cdot 10^{-7}\right):\\ \;\;\;\;t_0 + \frac{0.083333333333333 + z \cdot \left(y \cdot z - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{0.083333333333333 + z \cdot \left(0.0007936500793651 \cdot z - 0.0027777777777778\right)}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ (log x) -1.0))))
   (if (or (<= y -26000000.0) (not (<= y 5e-7)))
     (+ t_0 (/ (+ 0.083333333333333 (* z (- (* y z) 0.0027777777777778))) x))
     (+
      t_0
      (/
       (+
        0.083333333333333
        (* z (- (* 0.0007936500793651 z) 0.0027777777777778)))
       x)))))

C

double code(double x, double y, double z) {
	double t_0 = x * (log(x) + -1.0);
	double tmp;
	if ((y <= -26000000.0) || !(y <= 5e-7)) {
		tmp = t_0 + ((0.083333333333333 + (z * ((y * z) - 0.0027777777777778))) / x);
	} else {
		tmp = t_0 + ((0.083333333333333 + (z * ((0.0007936500793651 * z) - 0.0027777777777778))) / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (log(x) + (-1.0d0))
    if ((y <= (-26000000.0d0)) .or. (.not. (y <= 5d-7))) then
        tmp = t_0 + ((0.083333333333333d0 + (z * ((y * z) - 0.0027777777777778d0))) / x)
    else
        tmp = t_0 + ((0.083333333333333d0 + (z * ((0.0007936500793651d0 * z) - 0.0027777777777778d0))) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (Math.log(x) + -1.0);
	double tmp;
	if ((y <= -26000000.0) || !(y <= 5e-7)) {
		tmp = t_0 + ((0.083333333333333 + (z * ((y * z) - 0.0027777777777778))) / x);
	} else {
		tmp = t_0 + ((0.083333333333333 + (z * ((0.0007936500793651 * z) - 0.0027777777777778))) / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (math.log(x) + -1.0)
	tmp = 0
	if (y <= -26000000.0) or not (y <= 5e-7):
		tmp = t_0 + ((0.083333333333333 + (z * ((y * z) - 0.0027777777777778))) / x)
	else:
		tmp = t_0 + ((0.083333333333333 + (z * ((0.0007936500793651 * z) - 0.0027777777777778))) / x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(log(x) + -1.0))
	tmp = 0.0
	if ((y <= -26000000.0) || !(y <= 5e-7))
		tmp = Float64(t_0 + Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(y * z) - 0.0027777777777778))) / x));
	else
		tmp = Float64(t_0 + Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(0.0007936500793651 * z) - 0.0027777777777778))) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (log(x) + -1.0);
	tmp = 0.0;
	if ((y <= -26000000.0) || ~((y <= 5e-7)))
		tmp = t_0 + ((0.083333333333333 + (z * ((y * z) - 0.0027777777777778))) / x);
	else
		tmp = t_0 + ((0.083333333333333 + (z * ((0.0007936500793651 * z) - 0.0027777777777778))) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[y, -26000000.0], N[Not[LessEqual[y, 5e-7]], $MachinePrecision]], N[(t$95$0 + N[(N[(0.083333333333333 + N[(z * N[(N[(y * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(N[(0.083333333333333 + N[(z * N[(N[(0.0007936500793651 * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6e7 or 4.99999999999999977e-7 < y

   1. Initial program 96.1%

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

   2. Taylor expanded in x around inf 94.0%

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

      1. sub-neg 94.0%

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

      2. mul-1-neg 94.0%

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

      3. log-rec 94.0%

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

      4. remove-double-neg 94.0%

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

      5. metadata-eval 94.0%

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

   4. Simplified 94.0%

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

   5. Taylor expanded in y around inf 94.0%

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

      1. *-commutative 94.0%

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

   7. Simplified 94.0%

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

   if -2.6e7 < y < 4.99999999999999977e-7

   1. Initial program 95.2%

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

   2. Taylor expanded in x around inf 94.8%

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

      1. sub-neg 94.8%

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

      2. mul-1-neg 94.8%

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

      3. log-rec 94.8%

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

      4. remove-double-neg 94.8%

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

      5. metadata-eval 94.8%

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

   4. Simplified 94.8%

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

   5. Taylor expanded in y around 0 94.3%

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

      1. *-commutative 94.3%

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

   7. Simplified 94.3%

      \[\leadsto x \cdot \left(\log x + -1\right) + \frac{\left(\color{blue}{z \cdot 0.0007936500793651} - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -26000000 \lor \neg \left(y \leq 5 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333 + z \cdot \left(y \cdot z - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333 + z \cdot \left(0.0007936500793651 \cdot z - 0.0027777777777778\right)}{x}\\ \end{array} \]

Alternative 6: 95.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(\log x + -1\right)\\ \mathbf{if}\;x \leq 5.6 \cdot 10^{+88}:\\ \;\;\;\;t_0 + \frac{0.083333333333333 + z \cdot \left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{y}{\frac{1}{z} \cdot \frac{x}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ (log x) -1.0))))
   (if (<= x 5.6e+88)
     (+
      t_0
      (/
       (+
        0.083333333333333
        (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)))
       x))
     (+ t_0 (/ y (* (/ 1.0 z) (/ x z)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (log(x) + -1.0);
	double tmp;
	if (x <= 5.6e+88) {
		tmp = t_0 + ((0.083333333333333 + (z * (((y + 0.0007936500793651) * z) - 0.0027777777777778))) / x);
	} else {
		tmp = t_0 + (y / ((1.0 / z) * (x / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (log(x) + (-1.0d0))
    if (x <= 5.6d+88) then
        tmp = t_0 + ((0.083333333333333d0 + (z * (((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0))) / x)
    else
        tmp = t_0 + (y / ((1.0d0 / z) * (x / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (Math.log(x) + -1.0);
	double tmp;
	if (x <= 5.6e+88) {
		tmp = t_0 + ((0.083333333333333 + (z * (((y + 0.0007936500793651) * z) - 0.0027777777777778))) / x);
	} else {
		tmp = t_0 + (y / ((1.0 / z) * (x / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (math.log(x) + -1.0)
	tmp = 0
	if x <= 5.6e+88:
		tmp = t_0 + ((0.083333333333333 + (z * (((y + 0.0007936500793651) * z) - 0.0027777777777778))) / x)
	else:
		tmp = t_0 + (y / ((1.0 / z) * (x / z)))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(log(x) + -1.0))
	tmp = 0.0
	if (x <= 5.6e+88)
		tmp = Float64(t_0 + Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778))) / x));
	else
		tmp = Float64(t_0 + Float64(y / Float64(Float64(1.0 / z) * Float64(x / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (log(x) + -1.0);
	tmp = 0.0;
	if (x <= 5.6e+88)
		tmp = t_0 + ((0.083333333333333 + (z * (((y + 0.0007936500793651) * z) - 0.0027777777777778))) / x);
	else
		tmp = t_0 + (y / ((1.0 / z) * (x / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 5.6e+88], N[(t$95$0 + N[(N[(0.083333333333333 + N[(z * N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(y / N[(N[(1.0 / z), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 5.59999999999999977e88

   1. Initial program 98.6%

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

   2. Taylor expanded in x around inf 96.9%

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

      1. sub-neg 96.9%

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

      2. mul-1-neg 96.9%

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

      3. log-rec 96.9%

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

      4. remove-double-neg 96.9%

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

      5. metadata-eval 96.9%

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

   4. Simplified 96.9%

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

   if 5.59999999999999977e88 < x

   1. Initial program 88.1%

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

   2. Taylor expanded in x around inf 88.2%

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

      1. sub-neg 88.2%

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

      2. mul-1-neg 88.2%

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

      3. log-rec 88.2%

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

      4. remove-double-neg 88.2%

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

      5. metadata-eval 88.2%

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

   4. Simplified 88.2%

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

   5. Taylor expanded in y around inf 85.1%

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

      1. associate-/l* 89.1%

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

   7. Simplified 89.1%

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

      1. *-un-lft-identity 89.1%

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

      2. unpow2 89.1%

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

      3. times-frac 97.2%

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

   9. Applied egg-rr 97.2%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5.6 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333 + z \cdot \left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{y}{\frac{1}{z} \cdot \frac{x}{z}}\\ \end{array} \]

Alternative 7: 82.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -30000000 \lor \neg \left(z \leq 3.5\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{y}{\frac{1}{z} \cdot \frac{x}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -30000000.0) (not (<= z 3.5)))
   (+ (* x (+ (log x) -1.0)) (/ y (* (/ 1.0 z) (/ x z))))
   (+
    (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
    (/ 0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -30000000.0) || !(z <= 3.5)) {
		tmp = (x * (log(x) + -1.0)) + (y / ((1.0 / z) * (x / z)));
	} else {
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-30000000.0d0)) .or. (.not. (z <= 3.5d0))) then
        tmp = (x * (log(x) + (-1.0d0))) + (y / ((1.0d0 / z) * (x / z)))
    else
        tmp = ((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -30000000.0) || !(z <= 3.5)) {
		tmp = (x * (Math.log(x) + -1.0)) + (y / ((1.0 / z) * (x / z)));
	} else {
		tmp = ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -30000000.0) or not (z <= 3.5):
		tmp = (x * (math.log(x) + -1.0)) + (y / ((1.0 / z) * (x / z)))
	else:
		tmp = ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -30000000.0) || !(z <= 3.5))
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(y / Float64(Float64(1.0 / z) * Float64(x / z))));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -30000000.0) || ~((z <= 3.5)))
		tmp = (x * (log(x) + -1.0)) + (y / ((1.0 / z) * (x / z)));
	else
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -30000000.0], N[Not[LessEqual[z, 3.5]], $MachinePrecision]], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(N[(1.0 / z), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3e7 or 3.5 < z

   1. Initial program 91.4%

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

   2. Taylor expanded in x around inf 91.5%

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

      1. sub-neg 91.5%

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

      2. mul-1-neg 91.5%

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

      3. log-rec 91.5%

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

      4. remove-double-neg 91.5%

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

      5. metadata-eval 91.5%

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

   4. Simplified 91.5%

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

   5. Taylor expanded in y around inf 71.4%

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

      1. associate-/l* 74.4%

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

   7. Simplified 74.4%

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

      1. *-un-lft-identity 74.4%

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

      2. unpow2 74.4%

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

      3. times-frac 79.3%

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

   9. Applied egg-rr 79.3%

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

   if -3e7 < z < 3.5

   1. Initial program 99.5%

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

   2. Taylor expanded in z around 0 91.3%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -30000000 \lor \neg \left(z \leq 3.5\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{y}{\frac{1}{z} \cdot \frac{x}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 8: 79.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -30000000 \lor \neg \left(z \leq 0.26\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + z \cdot \left(z \cdot \frac{y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x} + \left(0.91893853320467 + \left(x \cdot \log x - x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -30000000.0) (not (<= z 0.26)))
   (+ (* x (+ (log x) -1.0)) (* z (* z (/ y x))))
   (+ (/ 0.083333333333333 x) (+ 0.91893853320467 (- (* x (log x)) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -30000000.0) || !(z <= 0.26)) {
		tmp = (x * (log(x) + -1.0)) + (z * (z * (y / x)));
	} 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 <= (-30000000.0d0)) .or. (.not. (z <= 0.26d0))) then
        tmp = (x * (log(x) + (-1.0d0))) + (z * (z * (y / x)))
    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 <= -30000000.0) || !(z <= 0.26)) {
		tmp = (x * (Math.log(x) + -1.0)) + (z * (z * (y / x)));
	} else {
		tmp = (0.083333333333333 / x) + (0.91893853320467 + ((x * Math.log(x)) - x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -30000000.0) or not (z <= 0.26):
		tmp = (x * (math.log(x) + -1.0)) + (z * (z * (y / x)))
	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 <= -30000000.0) || !(z <= 0.26))
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(z * Float64(z * Float64(y / x))));
	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 <= -30000000.0) || ~((z <= 0.26)))
		tmp = (x * (log(x) + -1.0)) + (z * (z * (y / x)));
	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, -30000000.0], N[Not[LessEqual[z, 0.26]], $MachinePrecision]], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(z * N[(z * N[(y / x), $MachinePrecision]), $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 < -3e7 or 0.26000000000000001 < z

   1. Initial program 91.5%

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

   2. Taylor expanded in x around inf 91.3%

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

      1. sub-neg 91.3%

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

      2. mul-1-neg 91.3%

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

      3. log-rec 91.3%

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

      4. remove-double-neg 91.3%

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

      5. metadata-eval 91.3%

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

   4. Simplified 91.3%

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

   5. Taylor expanded in y around inf 71.4%

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

      1. associate-/l* 74.4%

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

   7. Simplified 74.4%

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

      1. associate-/r/ 73.4%

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

      2. unpow2 73.4%

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

      3. associate-*r* 75.5%

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

   9. Applied egg-rr 75.5%

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

   if -3e7 < z < 0.26000000000000001

   1. Initial program 99.5%

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

   2. Taylor expanded in z around 0 91.2%

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

   3. Taylor expanded in x around inf 89.1%

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

      1. mul-1-neg 89.1%

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

      2. distribute-rgt-neg-in 89.1%

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

      3. log-rec 89.1%

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

      4. remove-double-neg 89.1%

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

   5. Simplified 89.1%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -30000000 \lor \neg \left(z \leq 0.26\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + z \cdot \left(z \cdot \frac{y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{x} + \left(0.91893853320467 + \left(x \cdot \log x - x\right)\right)\\ \end{array} \]

Alternative 9: 79.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(\log x + -1\right)\\ \mathbf{if}\;z \leq -30000000 \lor \neg \left(z \leq 0.26\right):\\ \;\;\;\;t_0 + z \cdot \left(z \cdot \frac{y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{z \cdot -0.0027777777777778 + 0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ (log x) -1.0))))
   (if (or (<= z -30000000.0) (not (<= z 0.26)))
     (+ t_0 (* z (* z (/ y x))))
     (+ t_0 (/ (+ (* z -0.0027777777777778) 0.083333333333333) x)))))

C

double code(double x, double y, double z) {
	double t_0 = x * (log(x) + -1.0);
	double tmp;
	if ((z <= -30000000.0) || !(z <= 0.26)) {
		tmp = t_0 + (z * (z * (y / x)));
	} else {
		tmp = t_0 + (((z * -0.0027777777777778) + 0.083333333333333) / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (log(x) + (-1.0d0))
    if ((z <= (-30000000.0d0)) .or. (.not. (z <= 0.26d0))) then
        tmp = t_0 + (z * (z * (y / x)))
    else
        tmp = t_0 + (((z * (-0.0027777777777778d0)) + 0.083333333333333d0) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (Math.log(x) + -1.0);
	double tmp;
	if ((z <= -30000000.0) || !(z <= 0.26)) {
		tmp = t_0 + (z * (z * (y / x)));
	} else {
		tmp = t_0 + (((z * -0.0027777777777778) + 0.083333333333333) / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (math.log(x) + -1.0)
	tmp = 0
	if (z <= -30000000.0) or not (z <= 0.26):
		tmp = t_0 + (z * (z * (y / x)))
	else:
		tmp = t_0 + (((z * -0.0027777777777778) + 0.083333333333333) / x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(log(x) + -1.0))
	tmp = 0.0
	if ((z <= -30000000.0) || !(z <= 0.26))
		tmp = Float64(t_0 + Float64(z * Float64(z * Float64(y / x))));
	else
		tmp = Float64(t_0 + Float64(Float64(Float64(z * -0.0027777777777778) + 0.083333333333333) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (log(x) + -1.0);
	tmp = 0.0;
	if ((z <= -30000000.0) || ~((z <= 0.26)))
		tmp = t_0 + (z * (z * (y / x)));
	else
		tmp = t_0 + (((z * -0.0027777777777778) + 0.083333333333333) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -30000000.0], N[Not[LessEqual[z, 0.26]], $MachinePrecision]], N[(t$95$0 + N[(z * N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(N[(N[(z * -0.0027777777777778), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3e7 or 0.26000000000000001 < z

   1. Initial program 91.5%

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

   2. Taylor expanded in x around inf 91.3%

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

      1. sub-neg 91.3%

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

      2. mul-1-neg 91.3%

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

      3. log-rec 91.3%

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

      4. remove-double-neg 91.3%

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

      5. metadata-eval 91.3%

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

   4. Simplified 91.3%

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

   5. Taylor expanded in y around inf 71.4%

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

      1. associate-/l* 74.4%

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

   7. Simplified 74.4%

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

      1. associate-/r/ 73.4%

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

      2. unpow2 73.4%

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

      3. associate-*r* 75.5%

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

   9. Applied egg-rr 75.5%

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

   if -3e7 < z < 0.26000000000000001

   1. Initial program 99.5%

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

   2. Taylor expanded in x around inf 97.3%

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

      1. sub-neg 97.3%

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

      2. mul-1-neg 97.3%

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

      3. log-rec 97.3%

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

      4. remove-double-neg 97.3%

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

      5. metadata-eval 97.3%

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

   4. Simplified 97.3%

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

   5. Taylor expanded in z around 0 89.6%

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

      1. *-commutative 89.6%

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

   7. Simplified 89.6%

      \[\leadsto x \cdot \left(\log x + -1\right) + \frac{\color{blue}{z \cdot -0.0027777777777778} + 0.083333333333333}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -30000000 \lor \neg \left(z \leq 0.26\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + z \cdot \left(z \cdot \frac{y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{z \cdot -0.0027777777777778 + 0.083333333333333}{x}\\ \end{array} \]

Alternative 10: 80.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -30000000 \lor \neg \left(z \leq 3.6\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + z \cdot \left(z \cdot \frac{y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -30000000.0) (not (<= z 3.6)))
   (+ (* x (+ (log x) -1.0)) (* z (* z (/ y x))))
   (+
    (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
    (/ 0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -30000000.0) || !(z <= 3.6)) {
		tmp = (x * (log(x) + -1.0)) + (z * (z * (y / x)));
	} else {
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-30000000.0d0)) .or. (.not. (z <= 3.6d0))) then
        tmp = (x * (log(x) + (-1.0d0))) + (z * (z * (y / x)))
    else
        tmp = ((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -30000000.0) || !(z <= 3.6)) {
		tmp = (x * (Math.log(x) + -1.0)) + (z * (z * (y / x)));
	} else {
		tmp = ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -30000000.0) or not (z <= 3.6):
		tmp = (x * (math.log(x) + -1.0)) + (z * (z * (y / x)))
	else:
		tmp = ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -30000000.0) || !(z <= 3.6))
		tmp = Float64(Float64(x * Float64(log(x) + -1.0)) + Float64(z * Float64(z * Float64(y / x))));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -30000000.0) || ~((z <= 3.6)))
		tmp = (x * (log(x) + -1.0)) + (z * (z * (y / x)));
	else
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -30000000.0], N[Not[LessEqual[z, 3.6]], $MachinePrecision]], N[(N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(z * N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3e7 or 3.60000000000000009 < z

   1. Initial program 91.4%

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

   2. Taylor expanded in x around inf 91.5%

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

      1. sub-neg 91.5%

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

      2. mul-1-neg 91.5%

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

      3. log-rec 91.5%

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

      4. remove-double-neg 91.5%

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

      5. metadata-eval 91.5%

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

   4. Simplified 91.5%

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

   5. Taylor expanded in y around inf 71.4%

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

      1. associate-/l* 74.4%

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

   7. Simplified 74.4%

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

      1. associate-/r/ 73.5%

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

      2. unpow2 73.5%

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

      3. associate-*r* 75.5%

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

   9. Applied egg-rr 75.5%

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

   if -3e7 < z < 3.60000000000000009

   1. Initial program 99.5%

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

   2. Taylor expanded in z around 0 91.3%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -30000000 \lor \neg \left(z \leq 3.6\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + z \cdot \left(z \cdot \frac{y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 11: 61.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(\log x + -1\right)\\ \mathbf{if}\;z \leq -30000000 \lor \neg \left(z \leq 3.4 \cdot 10^{+211}\right):\\ \;\;\;\;t_0 + -0.0027777777777778 \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{0.083333333333333}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ (log x) -1.0))))
   (if (or (<= z -30000000.0) (not (<= z 3.4e+211)))
     (+ t_0 (* -0.0027777777777778 (/ z x)))
     (+ t_0 (/ 0.083333333333333 x)))))

C

double code(double x, double y, double z) {
	double t_0 = x * (log(x) + -1.0);
	double tmp;
	if ((z <= -30000000.0) || !(z <= 3.4e+211)) {
		tmp = t_0 + (-0.0027777777777778 * (z / x));
	} else {
		tmp = t_0 + (0.083333333333333 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (log(x) + (-1.0d0))
    if ((z <= (-30000000.0d0)) .or. (.not. (z <= 3.4d+211))) then
        tmp = t_0 + ((-0.0027777777777778d0) * (z / x))
    else
        tmp = t_0 + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (Math.log(x) + -1.0);
	double tmp;
	if ((z <= -30000000.0) || !(z <= 3.4e+211)) {
		tmp = t_0 + (-0.0027777777777778 * (z / x));
	} else {
		tmp = t_0 + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (math.log(x) + -1.0)
	tmp = 0
	if (z <= -30000000.0) or not (z <= 3.4e+211):
		tmp = t_0 + (-0.0027777777777778 * (z / x))
	else:
		tmp = t_0 + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(log(x) + -1.0))
	tmp = 0.0
	if ((z <= -30000000.0) || !(z <= 3.4e+211))
		tmp = Float64(t_0 + Float64(-0.0027777777777778 * Float64(z / x)));
	else
		tmp = Float64(t_0 + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (log(x) + -1.0);
	tmp = 0.0;
	if ((z <= -30000000.0) || ~((z <= 3.4e+211)))
		tmp = t_0 + (-0.0027777777777778 * (z / x));
	else
		tmp = t_0 + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(N[Log[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -30000000.0], N[Not[LessEqual[z, 3.4e+211]], $MachinePrecision]], N[(t$95$0 + N[(-0.0027777777777778 * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3e7 or 3.3999999999999999e211 < z

   1. Initial program 91.3%

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

   2. Taylor expanded in x around inf 91.3%

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

      1. sub-neg 91.3%

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

      2. mul-1-neg 91.3%

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

      3. log-rec 91.3%

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

      4. remove-double-neg 91.3%

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

      5. metadata-eval 91.3%

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

   4. Simplified 91.3%

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

   5. Taylor expanded in z around 0 43.2%

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

   6. Taylor expanded in z around inf 43.2%

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

   if -3e7 < z < 3.3999999999999999e211

   1. Initial program 97.8%

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

   2. Taylor expanded in z around 0 79.3%

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

   3. Taylor expanded in x around inf 77.4%

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

      1. sub-neg 96.0%

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

      2. mul-1-neg 96.0%

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

      3. log-rec 96.0%

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

      4. remove-double-neg 96.0%

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

      5. metadata-eval 96.0%

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

   5. Simplified 77.4%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -30000000 \lor \neg \left(z \leq 3.4 \cdot 10^{+211}\right):\\ \;\;\;\;x \cdot \left(\log x + -1\right) + -0.0027777777777778 \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x + -1\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

Alternative 12: 56.9% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.6%

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

2. Taylor expanded in z around 0 60.0%

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

3. Taylor expanded in x around inf 58.8%

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

   1. sub-neg 94.4%

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

   2. mul-1-neg 94.4%

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

   3. log-rec 94.4%

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

   4. remove-double-neg 94.4%

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

   5. metadata-eval 94.4%

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

5. Simplified 58.8%

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

6. Final simplification 58.8%

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

Alternative 13: 23.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ {\left(x \cdot 12.000000000000048\right)}^{-1} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (pow (* x 12.000000000000048) -1.0))

C

double code(double x, double y, double z) {
	return pow((x * 12.000000000000048), -1.0);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * 12.000000000000048d0) ** (-1.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return Math.pow((x * 12.000000000000048), -1.0);
}

Python

def code(x, y, z):
	return math.pow((x * 12.000000000000048), -1.0)

Julia

function code(x, y, z)
	return Float64(x * 12.000000000000048) ^ -1.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * 12.000000000000048) ^ -1.0;
end

Wolfram

code[x_, y_, z_] := N[Power[N[(x * 12.000000000000048), $MachinePrecision], -1.0], $MachinePrecision]

Derivation

1. Initial program 95.6%

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

2. Taylor expanded in z around 0 60.0%

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

3. Taylor expanded in x around inf 58.8%

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

   1. sub-neg 94.4%

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

   2. mul-1-neg 94.4%

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

   3. log-rec 94.4%

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

   4. remove-double-neg 94.4%

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

   5. metadata-eval 94.4%

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

5. Simplified 58.8%

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

6. Taylor expanded in x around 0 28.5%

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

   1. clear-num 28.5%

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

   2. inv-pow 28.5%

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

   3. div-inv 28.5%

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

   4. metadata-eval 28.5%

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

8. Applied egg-rr 28.5%

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

9. Final simplification 28.5%

   \[\leadsto {\left(x \cdot 12.000000000000048\right)}^{-1} \]

Alternative 14: 23.6% accurate, 41.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.6%

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

2. Taylor expanded in z around 0 60.0%

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

3. Taylor expanded in x around inf 58.8%

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

   1. sub-neg 94.4%

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

   2. mul-1-neg 94.4%

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

   3. log-rec 94.4%

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

   4. remove-double-neg 94.4%

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

   5. metadata-eval 94.4%

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

5. Simplified 58.8%

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

6. Taylor expanded in x around 0 28.5%

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

7. Final simplification 28.5%

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

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 2023318 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (+ (+ (+ (* (- x 0.5) (log x)) (- 0.91893853320467 x)) (/ 0.083333333333333 x)) (* (/ z x) (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))

  (+ (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467) (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)))