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

Percentage Accurate: 93.9% → 93.9%

Time: 3.3s

Alternatives: 15

Speedup: 1.0×

• 31.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

\[\mathsf{TRUE}\left(\right)\]

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Add Preprocessing
3. Add Preprocessing

Alternative 2: 31.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z\\ t_1 := \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{t\_0 + 0.083333333333333}{x}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+190}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\left(x - 0.5\right) + 0.91893853320467\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z))
        (t_1
         (+
          (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
          (/ (+ t_0 0.083333333333333) x))))
   (if (<= t_1 -1e+190)
     t_0
     (if (<= t_1 5e+305) (+ (- x 0.5) 0.91893853320467) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z;
	double t_1 = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((t_0 + 0.083333333333333) / x);
	double tmp;
	if (t_1 <= -1e+190) {
		tmp = t_0;
	} else if (t_1 <= 5e+305) {
		tmp = (x - 0.5) + 0.91893853320467;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0) * z
    t_1 = ((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + ((t_0 + 0.083333333333333d0) / x)
    if (t_1 <= (-1d+190)) then
        tmp = t_0
    else if (t_1 <= 5d+305) then
        tmp = (x - 0.5d0) + 0.91893853320467d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z;
	double t_1 = ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + ((t_0 + 0.083333333333333) / x);
	double tmp;
	if (t_1 <= -1e+190) {
		tmp = t_0;
	} else if (t_1 <= 5e+305) {
		tmp = (x - 0.5) + 0.91893853320467;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z
	t_1 = ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + ((t_0 + 0.083333333333333) / x)
	tmp = 0
	if t_1 <= -1e+190:
		tmp = t_0
	elif t_1 <= 5e+305:
		tmp = (x - 0.5) + 0.91893853320467
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z)
	t_1 = Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(Float64(t_0 + 0.083333333333333) / x))
	tmp = 0.0
	if (t_1 <= -1e+190)
		tmp = t_0;
	elseif (t_1 <= 5e+305)
		tmp = Float64(Float64(x - 0.5) + 0.91893853320467);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z;
	t_1 = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((t_0 + 0.083333333333333) / x);
	tmp = 0.0;
	if (t_1 <= -1e+190)
		tmp = t_0;
	elseif (t_1 <= 5e+305)
		tmp = (x - 0.5) + 0.91893853320467;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(N[(t$95$0 + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+190], t$95$0, If[LessEqual[t$95$1, 5e+305], N[(N[(x - 0.5), $MachinePrecision] + 0.91893853320467), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) (log.f64 x)) x) #s(literal 91893853320467/100000000000000 binary64)) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) #s(literal 83333333333333/1000000000000000 binary64)) x)) < -1.0000000000000001e190 or 5.00000000000000009e305 < (+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) (log.f64 x)) x) #s(literal 91893853320467/100000000000000 binary64)) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) #s(literal 83333333333333/1000000000000000 binary64)) x))

   1. Initial program 88.6%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{\frac{83333333333333}{1000000000000000} + \left(x \cdot \left(\frac{91893853320467}{100000000000000} + \frac{-1}{2} \cdot \log x\right) + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)\right)}{x}} \]

   5. Applied rewrites 8.7%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(-1 \cdot \log \left(\frac{1}{x}\right) + \left(\frac{1}{2} \cdot \frac{\log \left(\frac{1}{x}\right)}{x} + \left(\frac{\frac{83333333333333}{1000000000000000}}{{x}^{2}} + \left(\frac{91893853320467}{100000000000000} \cdot \frac{1}{x} + \frac{z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}{{x}^{2}}\right)\right)\right)\right) - 1\right)} \]

   8. Applied rewrites 65.7%

      \[\leadsto \color{blue}{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z} \]

   if -1.0000000000000001e190 < (+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) (log.f64 x)) x) #s(literal 91893853320467/100000000000000 binary64)) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) #s(literal 83333333333333/1000000000000000 binary64)) x)) < 5.00000000000000009e305

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{\frac{83333333333333}{1000000000000000} + \left(x \cdot \left(\frac{91893853320467}{100000000000000} + \frac{-1}{2} \cdot \log x\right) + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)\right)}{x}} \]

   5. Applied rewrites 51.8%

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

   6. Taylor expanded in x around 0

      \[\leadsto \frac{-1}{2} \cdot \log x + \frac{91893853320467}{100000000000000} \]

   8. Applied rewrites 9.5%

      \[\leadsto \left(x - 0.5\right) + 0.91893853320467 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 84.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x - 0.5\right) \cdot \log x\\ \mathbf{if}\;x \leq 1.4 \cdot 10^{+97}:\\ \;\;\;\;\left(t\_0 + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\right) + 0.91893853320467\\ \mathbf{else}:\\ \;\;\;\;t\_0 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- x 0.5) (log x))))
   (if (<= x 1.4e+97)
     (+
      (+
       t_0
       (/
        (+
         (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
         0.083333333333333)
        x))
      0.91893853320467)
     (- t_0 x))))

C

double code(double x, double y, double z) {
	double t_0 = (x - 0.5) * log(x);
	double tmp;
	if (x <= 1.4e+97) {
		tmp = (t_0 + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)) + 0.91893853320467;
	} else {
		tmp = t_0 - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x - 0.5d0) * log(x)
    if (x <= 1.4d+97) then
        tmp = (t_0 + ((((((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0) * z) + 0.083333333333333d0) / x)) + 0.91893853320467d0
    else
        tmp = t_0 - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x - 0.5) * Math.log(x);
	double tmp;
	if (x <= 1.4e+97) {
		tmp = (t_0 + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)) + 0.91893853320467;
	} else {
		tmp = t_0 - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x - 0.5) * math.log(x)
	tmp = 0
	if x <= 1.4e+97:
		tmp = (t_0 + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)) + 0.91893853320467
	else:
		tmp = t_0 - x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - 0.5) * log(x))
	tmp = 0.0
	if (x <= 1.4e+97)
		tmp = Float64(Float64(t_0 + Float64(Float64(Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)) + 0.91893853320467);
	else
		tmp = Float64(t_0 - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x - 0.5) * log(x);
	tmp = 0.0;
	if (x <= 1.4e+97)
		tmp = (t_0 + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)) + 0.91893853320467;
	else
		tmp = t_0 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 1.4e+97], N[(N[(t$95$0 + N[(N[(N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + 0.91893853320467), $MachinePrecision], N[(t$95$0 - x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 1.4e97

   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. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{\frac{83333333333333}{1000000000000000} + \left(x \cdot \left(\frac{91893853320467}{100000000000000} + \frac{-1}{2} \cdot \log x\right) + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)\right)}{x}} \]

   5. Applied rewrites 15.8%

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

   6. Taylor expanded in x around 0

      \[\leadsto \left(\frac{-1}{2} \cdot \log x + x \cdot \left(\log x - 1\right)\right) + \frac{91893853320467}{100000000000000} \]

   8. Applied rewrites 88.8%

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

   if 1.4e97 < x

   1. Initial program 87.8%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{\frac{83333333333333}{1000000000000000} + \left(x \cdot \left(\frac{91893853320467}{100000000000000} + \left(\frac{-1}{2} \cdot \log x + x \cdot \left(\log x - 1\right)\right)\right) + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)\right)}{x}} \]

   5. Applied rewrites 79.1%

      \[\leadsto \color{blue}{\left(x - 0.5\right) \cdot \log x - x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 84.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x - 0.5\right) \cdot \log x\\ \mathbf{if}\;x \leq 1.4 \cdot 10^{+97}:\\ \;\;\;\;t\_0 + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;t\_0 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- x 0.5) (log x))))
   (if (<= x 1.4e+97)
     (+
      t_0
      (/
       (+
        (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
        0.083333333333333)
       x))
     (- t_0 x))))

C

double code(double x, double y, double z) {
	double t_0 = (x - 0.5) * log(x);
	double tmp;
	if (x <= 1.4e+97) {
		tmp = t_0 + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
	} else {
		tmp = t_0 - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x - 0.5d0) * log(x)
    if (x <= 1.4d+97) then
        tmp = t_0 + ((((((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0) * z) + 0.083333333333333d0) / x)
    else
        tmp = t_0 - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x - 0.5) * Math.log(x);
	double tmp;
	if (x <= 1.4e+97) {
		tmp = t_0 + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
	} else {
		tmp = t_0 - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x - 0.5) * math.log(x)
	tmp = 0
	if x <= 1.4e+97:
		tmp = t_0 + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)
	else:
		tmp = t_0 - x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - 0.5) * log(x))
	tmp = 0.0
	if (x <= 1.4e+97)
		tmp = Float64(t_0 + Float64(Float64(Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x));
	else
		tmp = Float64(t_0 - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x - 0.5) * log(x);
	tmp = 0.0;
	if (x <= 1.4e+97)
		tmp = t_0 + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
	else
		tmp = t_0 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 1.4e+97], N[(t$95$0 + N[(N[(N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(t$95$0 - x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 1.4e97

   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. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(\frac{91893853320467}{100000000000000} + \frac{-1}{2} \cdot \log x\right)} + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x} \]

   5. Applied rewrites 88.5%

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

   if 1.4e97 < x

   1. Initial program 87.8%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{\frac{83333333333333}{1000000000000000} + \left(x \cdot \left(\frac{91893853320467}{100000000000000} + \left(\frac{-1}{2} \cdot \log x + x \cdot \left(\log x - 1\right)\right)\right) + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)\right)}{x}} \]

   5. Applied rewrites 79.1%

      \[\leadsto \color{blue}{\left(x - 0.5\right) \cdot \log x - x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 83.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.4 \cdot 10^{+97}:\\ \;\;\;\;\left(\left(x - 0.5\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(x - 0.5\right) \cdot \log x - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.4e+97)
   (+
    (+ (- x 0.5) 0.91893853320467)
    (/
     (+
      (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
      0.083333333333333)
     x))
   (- (* (- x 0.5) (log x)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.4e+97) {
		tmp = ((x - 0.5) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
	} else {
		tmp = ((x - 0.5) * log(x)) - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 1.4d+97) then
        tmp = ((x - 0.5d0) + 0.91893853320467d0) + ((((((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0) * z) + 0.083333333333333d0) / x)
    else
        tmp = ((x - 0.5d0) * log(x)) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.4e+97) {
		tmp = ((x - 0.5) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
	} else {
		tmp = ((x - 0.5) * Math.log(x)) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1.4e+97:
		tmp = ((x - 0.5) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)
	else:
		tmp = ((x - 0.5) * math.log(x)) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.4e+97)
		tmp = Float64(Float64(Float64(x - 0.5) + 0.91893853320467) + Float64(Float64(Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x));
	else
		tmp = Float64(Float64(Float64(x - 0.5) * log(x)) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1.4e+97)
		tmp = ((x - 0.5) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
	else
		tmp = ((x - 0.5) * log(x)) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.4e+97], N[(N[(N[(x - 0.5), $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], N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.4e97

   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. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(\frac{91893853320467}{100000000000000} + \frac{-1}{2} \cdot \log x\right)} + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x} \]

   5. Applied rewrites 88.5%

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

   6. Taylor expanded in x around 0

      \[\leadsto \left(x - \frac{1}{2}\right) \cdot \log x + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x} \]

   8. Applied rewrites 16.5%

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

   9. Taylor expanded in x around 0

      \[\leadsto \left(x - \frac{1}{2}\right) \cdot \log x + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x} \]

   11. Applied rewrites 77.4%

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

   12. Taylor expanded in x around 0

       \[\leadsto \color{blue}{\left(\frac{91893853320467}{100000000000000} + \left(\frac{-1}{2} \cdot \log x + x \cdot \left(\log x - 1\right)\right)\right)} + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x} \]

   14. Applied rewrites 86.8%

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

   if 1.4e97 < x

   1. Initial program 87.8%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{\frac{83333333333333}{1000000000000000} + \left(x \cdot \left(\frac{91893853320467}{100000000000000} + \left(\frac{-1}{2} \cdot \log x + x \cdot \left(\log x - 1\right)\right)\right) + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)\right)}{x}} \]

   5. Applied rewrites 79.1%

      \[\leadsto \color{blue}{\left(x - 0.5\right) \cdot \log x - x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 67.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5.5 \cdot 10^{+226}:\\ \;\;\;\;\left(\left(x - 0.5\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(x - 0.5\right) \cdot \log x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 5.5e+226)
   (+
    (+ (- x 0.5) 0.91893853320467)
    (/
     (+
      (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
      0.083333333333333)
     x))
   (* (- x 0.5) (log x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 5.5e+226) {
		tmp = ((x - 0.5) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
	} else {
		tmp = (x - 0.5) * log(x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 5.5d+226) then
        tmp = ((x - 0.5d0) + 0.91893853320467d0) + ((((((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0) * z) + 0.083333333333333d0) / x)
    else
        tmp = (x - 0.5d0) * log(x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 5.5e+226) {
		tmp = ((x - 0.5) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
	} else {
		tmp = (x - 0.5) * Math.log(x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 5.5e+226:
		tmp = ((x - 0.5) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)
	else:
		tmp = (x - 0.5) * math.log(x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 5.5e+226)
		tmp = Float64(Float64(Float64(x - 0.5) + 0.91893853320467) + Float64(Float64(Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x));
	else
		tmp = Float64(Float64(x - 0.5) * log(x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 5.5e+226)
		tmp = ((x - 0.5) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
	else
		tmp = (x - 0.5) * log(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 5.5e+226], N[(N[(N[(x - 0.5), $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], N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 5.5000000000000005e226

   1. Initial program 97.5%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(\frac{91893853320467}{100000000000000} + \frac{-1}{2} \cdot \log x\right)} + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x} \]

   5. Applied rewrites 80.3%

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

   6. Taylor expanded in x around 0

      \[\leadsto \left(x - \frac{1}{2}\right) \cdot \log x + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x} \]

   8. Applied rewrites 18.1%

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

   9. Taylor expanded in x around 0

      \[\leadsto \left(x - \frac{1}{2}\right) \cdot \log x + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x} \]

   11. Applied rewrites 68.2%

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

   12. Taylor expanded in x around 0

       \[\leadsto \color{blue}{\left(\frac{91893853320467}{100000000000000} + \left(\frac{-1}{2} \cdot \log x + x \cdot \left(\log x - 1\right)\right)\right)} + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x} \]

   14. Applied rewrites 76.7%

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

   if 5.5000000000000005e226 < x

   1. Initial program 81.9%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{\frac{83333333333333}{1000000000000000} + \left(x \cdot \left(\frac{91893853320467}{100000000000000} + \frac{-1}{2} \cdot \log x\right) + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)\right)}{x}} \]

   5. Applied rewrites 89.5%

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

   6. Taylor expanded in x around 0

      \[\leadsto \frac{91893853320467}{100000000000000} + \color{blue}{\frac{-1}{2} \cdot \log x} \]

   8. Applied rewrites 31.8%

      \[\leadsto \left(x - 0.5\right) \cdot \color{blue}{\log x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 66.4% accurate, 3.7× speedup

Math

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

FPCore

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

Python

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

Julia

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

Wolfram

code[x_, y_, z_] := N[(N[(N[(x - 0.5), $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]

Derivation

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. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\left(\frac{91893853320467}{100000000000000} + \frac{-1}{2} \cdot \log x\right)} + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x} \]

5. Applied rewrites 73.5%

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

6. Taylor expanded in x around 0

   \[\leadsto \left(x - \frac{1}{2}\right) \cdot \log x + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x} \]

8. Applied rewrites 17.0%

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

9. Taylor expanded in x around 0

   \[\leadsto \left(x - \frac{1}{2}\right) \cdot \log x + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x} \]

11. Applied rewrites 60.3%

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

12. Taylor expanded in x around 0

    \[\leadsto \color{blue}{\left(\frac{91893853320467}{100000000000000} + \left(\frac{-1}{2} \cdot \log x + x \cdot \left(\log x - 1\right)\right)\right)} + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x} \]

14. Applied rewrites 68.1%

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

Alternative 8: 66.4% accurate, 4.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

Wolfram

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

Derivation

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. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\left(\frac{91893853320467}{100000000000000} + \frac{-1}{2} \cdot \log x\right)} + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x} \]

5. Applied rewrites 73.5%

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

6. Taylor expanded in x around 0

   \[\leadsto \left(x - \frac{1}{2}\right) \cdot \log x + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x} \]

8. Applied rewrites 17.0%

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

9. Taylor expanded in x around 0

   \[\leadsto \left(x - \frac{1}{2}\right) \cdot \log x + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x} \]

11. Applied rewrites 60.3%

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

12. Taylor expanded in x around 0

    \[\leadsto \color{blue}{\left(\frac{91893853320467}{100000000000000} + \frac{-1}{2} \cdot \log x\right)} + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x} \]

14. Applied rewrites 68.1%

    \[\leadsto \color{blue}{\left(x - 0.5\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
15. Add Preprocessing

Alternative 9: 63.1% accurate, 4.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (((((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 = (((((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0) * z) + 0.083333333333333d0) / x
end function

Java

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

Python

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

Julia

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

Wolfram

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

Derivation

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. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\left(\frac{91893853320467}{100000000000000} + \frac{-1}{2} \cdot \log x\right)} + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x} \]

5. Applied rewrites 73.5%

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

6. Taylor expanded in x around 0

   \[\leadsto \left(x - \frac{1}{2}\right) \cdot \log x + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x} \]

8. Applied rewrites 17.0%

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

9. Taylor expanded in x around 0

   \[\leadsto \left(x - \frac{1}{2}\right) \cdot \log x + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x} \]

11. Applied rewrites 60.3%

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

12. Taylor expanded in x around -inf

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

14. Applied rewrites 64.8%

    \[\leadsto \color{blue}{\frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}} \]
15. Add Preprocessing

Alternative 10: 14.8% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+110}:\\ \;\;\;\;\left(x - 0.5\right) \cdot \left(y + 0.0007936500793651\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+44}:\\ \;\;\;\;\left(x - 0.5\right) + 0.91893853320467\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + 0.0007936500793651\right) \cdot z + 0.91893853320467\right) + 0.91893853320467\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.55e+110)
   (* (- x 0.5) (+ y 0.0007936500793651))
   (if (<= z 6.4e+44)
     (+ (- x 0.5) 0.91893853320467)
     (+
      (+ (* (+ y 0.0007936500793651) z) 0.91893853320467)
      0.91893853320467))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.55e+110) {
		tmp = (x - 0.5) * (y + 0.0007936500793651);
	} else if (z <= 6.4e+44) {
		tmp = (x - 0.5) + 0.91893853320467;
	} else {
		tmp = (((y + 0.0007936500793651) * z) + 0.91893853320467) + 0.91893853320467;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.55d+110)) then
        tmp = (x - 0.5d0) * (y + 0.0007936500793651d0)
    else if (z <= 6.4d+44) then
        tmp = (x - 0.5d0) + 0.91893853320467d0
    else
        tmp = (((y + 0.0007936500793651d0) * z) + 0.91893853320467d0) + 0.91893853320467d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.55e+110) {
		tmp = (x - 0.5) * (y + 0.0007936500793651);
	} else if (z <= 6.4e+44) {
		tmp = (x - 0.5) + 0.91893853320467;
	} else {
		tmp = (((y + 0.0007936500793651) * z) + 0.91893853320467) + 0.91893853320467;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.55e+110:
		tmp = (x - 0.5) * (y + 0.0007936500793651)
	elif z <= 6.4e+44:
		tmp = (x - 0.5) + 0.91893853320467
	else:
		tmp = (((y + 0.0007936500793651) * z) + 0.91893853320467) + 0.91893853320467
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.55e+110)
		tmp = Float64(Float64(x - 0.5) * Float64(y + 0.0007936500793651));
	elseif (z <= 6.4e+44)
		tmp = Float64(Float64(x - 0.5) + 0.91893853320467);
	else
		tmp = Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) + 0.91893853320467) + 0.91893853320467);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.55e+110)
		tmp = (x - 0.5) * (y + 0.0007936500793651);
	elseif (z <= 6.4e+44)
		tmp = (x - 0.5) + 0.91893853320467;
	else
		tmp = (((y + 0.0007936500793651) * z) + 0.91893853320467) + 0.91893853320467;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.55e+110], N[(N[(x - 0.5), $MachinePrecision] * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.4e+44], N[(N[(x - 0.5), $MachinePrecision] + 0.91893853320467), $MachinePrecision], N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + 0.91893853320467), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.55000000000000009e110

   1. Initial program 91.7%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(\frac{91893853320467}{100000000000000} + \frac{-1}{2} \cdot \log x\right)} + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x} \]

   5. Applied rewrites 88.8%

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

   6. Taylor expanded in x around 0

      \[\leadsto \left(x - \frac{1}{2}\right) \cdot \log x + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x} \]

   8. Applied rewrites 28.7%

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

   9. Taylor expanded in x around 0

      \[\leadsto \left(x - \frac{1}{2}\right) \cdot \log x + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x} \]

   11. Applied rewrites 87.9%

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

   12. Taylor expanded in x around 0

       \[\leadsto \color{blue}{\frac{\frac{83333333333333}{1000000000000000} + \left(x \cdot \left(\frac{91893853320467}{100000000000000} + \left(\frac{-1}{2} \cdot \log x + x \cdot \left(\log x - 1\right)\right)\right) + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)\right)}{x}} \]

   14. Applied rewrites 16.2%

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

   if -1.55000000000000009e110 < z < 6.40000000000000009e44

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{\frac{83333333333333}{1000000000000000} + \left(x \cdot \left(\frac{91893853320467}{100000000000000} + \frac{-1}{2} \cdot \log x\right) + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)\right)}{x}} \]

   5. Applied rewrites 49.3%

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

   6. Taylor expanded in x around 0

      \[\leadsto \frac{-1}{2} \cdot \log x + \frac{91893853320467}{100000000000000} \]

   8. Applied rewrites 9.1%

      \[\leadsto \left(x - 0.5\right) + 0.91893853320467 \]

   if 6.40000000000000009e44 < z

   1. Initial program 87.1%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{\frac{83333333333333}{1000000000000000} + \left(x \cdot \left(\frac{91893853320467}{100000000000000} + \frac{-1}{2} \cdot \log x\right) + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)\right)}{x}} \]

   5. Applied rewrites 18.3%

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

   6. Taylor expanded in x around 0

      \[\leadsto \frac{-1}{2} \cdot \log x + \frac{91893853320467}{100000000000000} \]

   8. Applied rewrites 5.0%

      \[\leadsto \left(x - 0.5\right) + 0.91893853320467 \]

   9. Taylor expanded in x around 0

      \[\leadsto \left(x - \frac{1}{2}\right) + \frac{91893853320467}{100000000000000} \]

   11. Applied rewrites 30.7%

       \[\leadsto \left(\left(y + 0.0007936500793651\right) \cdot z + 0.91893853320467\right) + 0.91893853320467 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 14.8% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+110}:\\ \;\;\;\;\left(x - 0.5\right) \cdot \left(y + 0.0007936500793651\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+44}:\\ \;\;\;\;\left(x - 0.5\right) + 0.91893853320467\\ \mathbf{else}:\\ \;\;\;\;\left(y + 0.0007936500793651\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.55e+110)
   (* (- x 0.5) (+ y 0.0007936500793651))
   (if (<= z 6.4e+44)
     (+ (- x 0.5) 0.91893853320467)
     (* (+ y 0.0007936500793651) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.55e+110) {
		tmp = (x - 0.5) * (y + 0.0007936500793651);
	} else if (z <= 6.4e+44) {
		tmp = (x - 0.5) + 0.91893853320467;
	} else {
		tmp = (y + 0.0007936500793651) * 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 (z <= (-1.55d+110)) then
        tmp = (x - 0.5d0) * (y + 0.0007936500793651d0)
    else if (z <= 6.4d+44) then
        tmp = (x - 0.5d0) + 0.91893853320467d0
    else
        tmp = (y + 0.0007936500793651d0) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.55e+110) {
		tmp = (x - 0.5) * (y + 0.0007936500793651);
	} else if (z <= 6.4e+44) {
		tmp = (x - 0.5) + 0.91893853320467;
	} else {
		tmp = (y + 0.0007936500793651) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.55e+110:
		tmp = (x - 0.5) * (y + 0.0007936500793651)
	elif z <= 6.4e+44:
		tmp = (x - 0.5) + 0.91893853320467
	else:
		tmp = (y + 0.0007936500793651) * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.55e+110)
		tmp = Float64(Float64(x - 0.5) * Float64(y + 0.0007936500793651));
	elseif (z <= 6.4e+44)
		tmp = Float64(Float64(x - 0.5) + 0.91893853320467);
	else
		tmp = Float64(Float64(y + 0.0007936500793651) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.55e+110)
		tmp = (x - 0.5) * (y + 0.0007936500793651);
	elseif (z <= 6.4e+44)
		tmp = (x - 0.5) + 0.91893853320467;
	else
		tmp = (y + 0.0007936500793651) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.55e+110], N[(N[(x - 0.5), $MachinePrecision] * N[(y + 0.0007936500793651), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.4e+44], N[(N[(x - 0.5), $MachinePrecision] + 0.91893853320467), $MachinePrecision], N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.55000000000000009e110

   1. Initial program 91.7%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(\frac{91893853320467}{100000000000000} + \frac{-1}{2} \cdot \log x\right)} + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x} \]

   5. Applied rewrites 88.8%

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

   6. Taylor expanded in x around 0

      \[\leadsto \left(x - \frac{1}{2}\right) \cdot \log x + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x} \]

   8. Applied rewrites 28.7%

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

   9. Taylor expanded in x around 0

      \[\leadsto \left(x - \frac{1}{2}\right) \cdot \log x + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x} \]

   11. Applied rewrites 87.9%

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

   12. Taylor expanded in x around 0

       \[\leadsto \color{blue}{\frac{\frac{83333333333333}{1000000000000000} + \left(x \cdot \left(\frac{91893853320467}{100000000000000} + \left(\frac{-1}{2} \cdot \log x + x \cdot \left(\log x - 1\right)\right)\right) + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)\right)}{x}} \]

   14. Applied rewrites 16.2%

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

   if -1.55000000000000009e110 < z < 6.40000000000000009e44

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{\frac{83333333333333}{1000000000000000} + \left(x \cdot \left(\frac{91893853320467}{100000000000000} + \frac{-1}{2} \cdot \log x\right) + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)\right)}{x}} \]

   5. Applied rewrites 49.3%

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

   6. Taylor expanded in x around 0

      \[\leadsto \frac{-1}{2} \cdot \log x + \frac{91893853320467}{100000000000000} \]

   8. Applied rewrites 9.1%

      \[\leadsto \left(x - 0.5\right) + 0.91893853320467 \]

   if 6.40000000000000009e44 < z

   1. Initial program 87.1%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{\frac{83333333333333}{1000000000000000} + \left(x \cdot \left(\frac{91893853320467}{100000000000000} + \left(\frac{-1}{2} \cdot \log x + x \cdot \left(\log x - 1\right)\right)\right) + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)\right)}{x}} \]

   5. Applied rewrites 18.3%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 30.7%

      \[\leadsto \left(y + 0.0007936500793651\right) \cdot \color{blue}{z} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 13.4% accurate, 9.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 6.4 \cdot 10^{+44}:\\ \;\;\;\;\left(x - 0.5\right) + 0.91893853320467\\ \mathbf{else}:\\ \;\;\;\;\left(y + 0.0007936500793651\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 6.4e+44)
   (+ (- x 0.5) 0.91893853320467)
   (* (+ y 0.0007936500793651) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 6.4e+44) {
		tmp = (x - 0.5) + 0.91893853320467;
	} else {
		tmp = (y + 0.0007936500793651) * 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 (z <= 6.4d+44) then
        tmp = (x - 0.5d0) + 0.91893853320467d0
    else
        tmp = (y + 0.0007936500793651d0) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 6.4e+44) {
		tmp = (x - 0.5) + 0.91893853320467;
	} else {
		tmp = (y + 0.0007936500793651) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 6.4e+44:
		tmp = (x - 0.5) + 0.91893853320467
	else:
		tmp = (y + 0.0007936500793651) * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 6.4e+44)
		tmp = Float64(Float64(x - 0.5) + 0.91893853320467);
	else
		tmp = Float64(Float64(y + 0.0007936500793651) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 6.4e+44)
		tmp = (x - 0.5) + 0.91893853320467;
	else
		tmp = (y + 0.0007936500793651) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 6.4e+44], N[(N[(x - 0.5), $MachinePrecision] + 0.91893853320467), $MachinePrecision], N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 6.40000000000000009e44

   1. Initial program 97.6%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{\frac{83333333333333}{1000000000000000} + \left(x \cdot \left(\frac{91893853320467}{100000000000000} + \frac{-1}{2} \cdot \log x\right) + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)\right)}{x}} \]

   5. Applied rewrites 40.3%

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

   6. Taylor expanded in x around 0

      \[\leadsto \frac{-1}{2} \cdot \log x + \frac{91893853320467}{100000000000000} \]

   8. Applied rewrites 7.9%

      \[\leadsto \left(x - 0.5\right) + 0.91893853320467 \]

   if 6.40000000000000009e44 < z

   1. Initial program 87.1%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{\frac{83333333333333}{1000000000000000} + \left(x \cdot \left(\frac{91893853320467}{100000000000000} + \left(\frac{-1}{2} \cdot \log x + x \cdot \left(\log x - 1\right)\right)\right) + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)\right)}{x}} \]

   5. Applied rewrites 18.3%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 30.7%

      \[\leadsto \left(y + 0.0007936500793651\right) \cdot \color{blue}{z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 7.8% accurate, 11.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.7:\\ \;\;\;\;\left(y + 0.0007936500793651\right) + 0.91893853320467\\ \mathbf{else}:\\ \;\;\;\;x - 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 2.7) (+ (+ y 0.0007936500793651) 0.91893853320467) (- x 0.5)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 2.7) {
		tmp = (y + 0.0007936500793651) + 0.91893853320467;
	} else {
		tmp = x - 0.5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 2.7d0) then
        tmp = (y + 0.0007936500793651d0) + 0.91893853320467d0
    else
        tmp = x - 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 2.7) {
		tmp = (y + 0.0007936500793651) + 0.91893853320467;
	} else {
		tmp = x - 0.5;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 2.7:
		tmp = (y + 0.0007936500793651) + 0.91893853320467
	else:
		tmp = x - 0.5
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 2.7)
		tmp = Float64(Float64(y + 0.0007936500793651) + 0.91893853320467);
	else
		tmp = Float64(x - 0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 2.7)
		tmp = (y + 0.0007936500793651) + 0.91893853320467;
	else
		tmp = x - 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 2.7], N[(N[(y + 0.0007936500793651), $MachinePrecision] + 0.91893853320467), $MachinePrecision], N[(x - 0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.7000000000000002

   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. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{\frac{83333333333333}{1000000000000000} + \left(x \cdot \left(\frac{91893853320467}{100000000000000} + \frac{-1}{2} \cdot \log x\right) + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)\right)}{x}} \]

   5. Applied rewrites 3.6%

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

   6. Taylor expanded in x around 0

      \[\leadsto \frac{-1}{2} \cdot \log x + \frac{91893853320467}{100000000000000} \]

   8. Applied rewrites 3.5%

      \[\leadsto \left(x - 0.5\right) + 0.91893853320467 \]

   9. Taylor expanded in x around inf

      \[\leadsto x \cdot \left(\left(-1 \cdot \log \left(\frac{1}{x}\right) + \frac{1}{2} \cdot \frac{\log \left(\frac{1}{x}\right)}{x}\right) - 1\right) + \frac{91893853320467}{100000000000000} \]

   11. Applied rewrites 4.5%

       \[\leadsto \left(y + 0.0007936500793651\right) + 0.91893853320467 \]

   if 2.7000000000000002 < x

   1. Initial program 90.8%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{\frac{83333333333333}{1000000000000000} + \left(x \cdot \left(\frac{91893853320467}{100000000000000} + \left(\frac{-1}{2} \cdot \log x + x \cdot \left(\log x - 1\right)\right)\right) + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)\right)}{x}} \]

   5. Applied rewrites 66.7%

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

   6. Taylor expanded in x around 0

      \[\leadsto \frac{-1}{2} \cdot \color{blue}{\log x} \]

   8. Applied rewrites 10.9%

      \[\leadsto x - \color{blue}{0.5} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 7.4% accurate, 21.1× speedup

Math

\[\begin{array}{l} \\ \left(x - 0.5\right) + 0.91893853320467 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (- x 0.5) 0.91893853320467))

C

double code(double x, double y, double z) {
	return (x - 0.5) + 0.91893853320467;
}

Fortran

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

Java

public static double code(double x, double y, double z) {
	return (x - 0.5) + 0.91893853320467;
}

Python

def code(x, y, z):
	return (x - 0.5) + 0.91893853320467

Julia

function code(x, y, z)
	return Float64(Float64(x - 0.5) + 0.91893853320467)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x - 0.5) + 0.91893853320467;
end

Wolfram

code[x_, y_, z_] := N[(N[(x - 0.5), $MachinePrecision] + 0.91893853320467), $MachinePrecision]

Derivation

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. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{\frac{83333333333333}{1000000000000000} + \left(x \cdot \left(\frac{91893853320467}{100000000000000} + \frac{-1}{2} \cdot \log x\right) + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)\right)}{x}} \]

5. Applied rewrites 35.3%

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

6. Taylor expanded in x around 0

   \[\leadsto \frac{-1}{2} \cdot \log x + \frac{91893853320467}{100000000000000} \]

8. Applied rewrites 7.2%

   \[\leadsto \left(x - 0.5\right) + 0.91893853320467 \]
9. Add Preprocessing

Alternative 15: 6.1% accurate, 37.0× speedup

Math

\[\begin{array}{l} \\ x - 0.5 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- x 0.5))

C

double code(double x, double y, double z) {
	return x - 0.5;
}

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
end function

Java

public static double code(double x, double y, double z) {
	return x - 0.5;
}

Python

def code(x, y, z):
	return x - 0.5

Julia

function code(x, y, z)
	return Float64(x - 0.5)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x - 0.5;
end

Wolfram

code[x_, y_, z_] := N[(x - 0.5), $MachinePrecision]

Derivation

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. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{\frac{83333333333333}{1000000000000000} + \left(x \cdot \left(\frac{91893853320467}{100000000000000} + \left(\frac{-1}{2} \cdot \log x + x \cdot \left(\log x - 1\right)\right)\right) + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)\right)}{x}} \]

5. Applied rewrites 34.9%

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

6. Taylor expanded in x around 0

   \[\leadsto \frac{-1}{2} \cdot \color{blue}{\log x} \]

8. Applied rewrites 6.1%

   \[\leadsto x - \color{blue}{0.5} \]
9. Add Preprocessing

Developer Target 1: 98.8% accurate, 0.9× 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 2024321 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, B"
  :precision binary64
  :pre (TRUE)

  :alt
  (! :herbie-platform default (+ (+ (+ (* (- x 1/2) (log x)) (- 91893853320467/100000000000000 x)) (/ 83333333333333/1000000000000000 x)) (* (/ z x) (- (* z (+ y 7936500793651/10000000000000000)) 13888888888889/5000000000000000))))

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