Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, B

Percentage Accurate: 69.3% → 99.1%

Time: 16.2s

Alternatives: 11

Speedup: 1.4×

Specification

Math

\[\begin{array}{l} \\ x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+
  x
  (/
   (*
    y
    (+
     (* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
     0.279195317918525))
   (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))

C

double code(double x, double y, double z) {
	return x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304));
}

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 + ((y * ((((z * 0.0692910599291889d0) + 0.4917317610505968d0) * z) + 0.279195317918525d0)) / (((z + 6.012459259764103d0) * z) + 3.350343815022304d0))
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304));
}

Python

def code(x, y, z):
	return x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / Float64(Float64(Float64(z + 6.012459259764103) * z) + 3.350343815022304)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y * N[(N[(N[(N[(z * 0.0692910599291889), $MachinePrecision] + 0.4917317610505968), $MachinePrecision] * z), $MachinePrecision] + 0.279195317918525), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(z + 6.012459259764103), $MachinePrecision] * z), $MachinePrecision] + 3.350343815022304), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 69.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+
  x
  (/
   (*
    y
    (+
     (* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
     0.279195317918525))
   (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))

C

double code(double x, double y, double z) {
	return x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304));
}

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 + ((y * ((((z * 0.0692910599291889d0) + 0.4917317610505968d0) * z) + 0.279195317918525d0)) / (((z + 6.012459259764103d0) * z) + 3.350343815022304d0))
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304));
}

Python

def code(x, y, z):
	return x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / Float64(Float64(Float64(z + 6.012459259764103) * z) + 3.350343815022304)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y * N[(N[(N[(N[(z * 0.0692910599291889), $MachinePrecision] + 0.4917317610505968), $MachinePrecision] * z), $MachinePrecision] + 0.279195317918525), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(z + 6.012459259764103), $MachinePrecision] * z), $MachinePrecision] + 3.350343815022304), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot 0.0692910599291889 - \left(\frac{y \cdot -0.07512208616047561 - \frac{y \cdot -0.4046220386999212}{z}}{z} - x\right)\\ \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-8}:\\ \;\;\;\;y \cdot 0.08333333333333323 + \left(z \cdot \left(y \cdot -0.00277777777751721 + z \cdot \left(y \cdot 0.0007936505811533442\right)\right) + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (-
          (* y 0.0692910599291889)
          (-
           (/ (- (* y -0.07512208616047561) (/ (* y -0.4046220386999212) z)) z)
           x))))
   (if (<= z -5.4)
     t_0
     (if (<= z 5.1e-8)
       (+
        (* y 0.08333333333333323)
        (+
         (* z (+ (* y -0.00277777777751721) (* z (* y 0.0007936505811533442))))
         x))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (y * 0.0692910599291889) - ((((y * -0.07512208616047561) - ((y * -0.4046220386999212) / z)) / z) - x);
	double tmp;
	if (z <= -5.4) {
		tmp = t_0;
	} else if (z <= 5.1e-8) {
		tmp = (y * 0.08333333333333323) + ((z * ((y * -0.00277777777751721) + (z * (y * 0.0007936505811533442)))) + x);
	} 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) :: tmp
    t_0 = (y * 0.0692910599291889d0) - ((((y * (-0.07512208616047561d0)) - ((y * (-0.4046220386999212d0)) / z)) / z) - x)
    if (z <= (-5.4d0)) then
        tmp = t_0
    else if (z <= 5.1d-8) then
        tmp = (y * 0.08333333333333323d0) + ((z * ((y * (-0.00277777777751721d0)) + (z * (y * 0.0007936505811533442d0)))) + x)
    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 * 0.0692910599291889) - ((((y * -0.07512208616047561) - ((y * -0.4046220386999212) / z)) / z) - x);
	double tmp;
	if (z <= -5.4) {
		tmp = t_0;
	} else if (z <= 5.1e-8) {
		tmp = (y * 0.08333333333333323) + ((z * ((y * -0.00277777777751721) + (z * (y * 0.0007936505811533442)))) + x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y * 0.0692910599291889) - ((((y * -0.07512208616047561) - ((y * -0.4046220386999212) / z)) / z) - x)
	tmp = 0
	if z <= -5.4:
		tmp = t_0
	elif z <= 5.1e-8:
		tmp = (y * 0.08333333333333323) + ((z * ((y * -0.00277777777751721) + (z * (y * 0.0007936505811533442)))) + x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * 0.0692910599291889) - Float64(Float64(Float64(Float64(y * -0.07512208616047561) - Float64(Float64(y * -0.4046220386999212) / z)) / z) - x))
	tmp = 0.0
	if (z <= -5.4)
		tmp = t_0;
	elseif (z <= 5.1e-8)
		tmp = Float64(Float64(y * 0.08333333333333323) + Float64(Float64(z * Float64(Float64(y * -0.00277777777751721) + Float64(z * Float64(y * 0.0007936505811533442)))) + x));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y * 0.0692910599291889) - ((((y * -0.07512208616047561) - ((y * -0.4046220386999212) / z)) / z) - x);
	tmp = 0.0;
	if (z <= -5.4)
		tmp = t_0;
	elseif (z <= 5.1e-8)
		tmp = (y * 0.08333333333333323) + ((z * ((y * -0.00277777777751721) + (z * (y * 0.0007936505811533442)))) + x);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * 0.0692910599291889), $MachinePrecision] - N[(N[(N[(N[(y * -0.07512208616047561), $MachinePrecision] - N[(N[(y * -0.4046220386999212), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.4], t$95$0, If[LessEqual[z, 5.1e-8], N[(N[(y * 0.08333333333333323), $MachinePrecision] + N[(N[(z * N[(N[(y * -0.00277777777751721), $MachinePrecision] + N[(z * N[(y * 0.0007936505811533442), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4000000000000004 or 5.10000000000000001e-8 < z

   1. Initial program 44.9%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around -inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -5.4000000000000004 < z < 5.10000000000000001e-8

   1. Initial program 99.6%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot 0.0692910599291889 + 0.4917317610505968\\ \mathbf{if}\;\frac{y \cdot \left(t\_0 \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \leq 5 \cdot 10^{+305}:\\ \;\;\;\;x + \frac{y}{\frac{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304}{z \cdot t\_0 + 0.279195317918525}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.0692910599291889 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* z 0.0692910599291889) 0.4917317610505968)))
   (if (<=
        (/
         (* y (+ (* t_0 z) 0.279195317918525))
         (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
        5e+305)
     (+
      x
      (/
       y
       (/
        (+ (* z (+ z 6.012459259764103)) 3.350343815022304)
        (+ (* z t_0) 0.279195317918525))))
     (+ (* y 0.0692910599291889) x))))

C

double code(double x, double y, double z) {
	double t_0 = (z * 0.0692910599291889) + 0.4917317610505968;
	double tmp;
	if (((y * ((t_0 * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304)) <= 5e+305) {
		tmp = x + (y / (((z * (z + 6.012459259764103)) + 3.350343815022304) / ((z * t_0) + 0.279195317918525)));
	} else {
		tmp = (y * 0.0692910599291889) + 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 = (z * 0.0692910599291889d0) + 0.4917317610505968d0
    if (((y * ((t_0 * z) + 0.279195317918525d0)) / (((z + 6.012459259764103d0) * z) + 3.350343815022304d0)) <= 5d+305) then
        tmp = x + (y / (((z * (z + 6.012459259764103d0)) + 3.350343815022304d0) / ((z * t_0) + 0.279195317918525d0)))
    else
        tmp = (y * 0.0692910599291889d0) + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z * 0.0692910599291889) + 0.4917317610505968;
	double tmp;
	if (((y * ((t_0 * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304)) <= 5e+305) {
		tmp = x + (y / (((z * (z + 6.012459259764103)) + 3.350343815022304) / ((z * t_0) + 0.279195317918525)));
	} else {
		tmp = (y * 0.0692910599291889) + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z * 0.0692910599291889) + 0.4917317610505968
	tmp = 0
	if ((y * ((t_0 * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304)) <= 5e+305:
		tmp = x + (y / (((z * (z + 6.012459259764103)) + 3.350343815022304) / ((z * t_0) + 0.279195317918525)))
	else:
		tmp = (y * 0.0692910599291889) + x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * 0.0692910599291889) + 0.4917317610505968)
	tmp = 0.0
	if (Float64(Float64(y * Float64(Float64(t_0 * z) + 0.279195317918525)) / Float64(Float64(Float64(z + 6.012459259764103) * z) + 3.350343815022304)) <= 5e+305)
		tmp = Float64(x + Float64(y / Float64(Float64(Float64(z * Float64(z + 6.012459259764103)) + 3.350343815022304) / Float64(Float64(z * t_0) + 0.279195317918525))));
	else
		tmp = Float64(Float64(y * 0.0692910599291889) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z * 0.0692910599291889) + 0.4917317610505968;
	tmp = 0.0;
	if (((y * ((t_0 * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304)) <= 5e+305)
		tmp = x + (y / (((z * (z + 6.012459259764103)) + 3.350343815022304) / ((z * t_0) + 0.279195317918525)));
	else
		tmp = (y * 0.0692910599291889) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * 0.0692910599291889), $MachinePrecision] + 0.4917317610505968), $MachinePrecision]}, If[LessEqual[N[(N[(y * N[(N[(t$95$0 * z), $MachinePrecision] + 0.279195317918525), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(z + 6.012459259764103), $MachinePrecision] * z), $MachinePrecision] + 3.350343815022304), $MachinePrecision]), $MachinePrecision], 5e+305], N[(x + N[(y / N[(N[(N[(z * N[(z + 6.012459259764103), $MachinePrecision]), $MachinePrecision] + 3.350343815022304), $MachinePrecision] / N[(N[(z * t$95$0), $MachinePrecision] + 0.279195317918525), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 0.0692910599291889), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 692910599291889/10000000000000000 binary64)) #s(literal 307332350656623/625000000000000 binary64)) z) #s(literal 11167812716741/40000000000000 binary64))) (+.f64 (*.f64 (+.f64 z #s(literal 6012459259764103/1000000000000000 binary64)) z) #s(literal 104698244219447/31250000000000 binary64))) < 5.00000000000000009e305

   1. Initial program 98.2%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   if 5.00000000000000009e305 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 692910599291889/10000000000000000 binary64)) #s(literal 307332350656623/625000000000000 binary64)) z) #s(literal 11167812716741/40000000000000 binary64))) (+.f64 (*.f64 (+.f64 z #s(literal 6012459259764103/1000000000000000 binary64)) z) #s(literal 104698244219447/31250000000000 binary64)))

   1. Initial program 0.9%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 99.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(0.0692910599291889 - \frac{-0.07512208616047561}{z}\right) + x\\ \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-8}:\\ \;\;\;\;y \cdot 0.08333333333333323 + \left(z \cdot \left(y \cdot -0.00277777777751721 + z \cdot \left(y \cdot 0.0007936505811533442\right)\right) + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* y (- 0.0692910599291889 (/ -0.07512208616047561 z))) x)))
   (if (<= z -5.4)
     t_0
     (if (<= z 5.1e-8)
       (+
        (* y 0.08333333333333323)
        (+
         (* z (+ (* y -0.00277777777751721) (* z (* y 0.0007936505811533442))))
         x))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (y * (0.0692910599291889 - (-0.07512208616047561 / z))) + x;
	double tmp;
	if (z <= -5.4) {
		tmp = t_0;
	} else if (z <= 5.1e-8) {
		tmp = (y * 0.08333333333333323) + ((z * ((y * -0.00277777777751721) + (z * (y * 0.0007936505811533442)))) + x);
	} 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) :: tmp
    t_0 = (y * (0.0692910599291889d0 - ((-0.07512208616047561d0) / z))) + x
    if (z <= (-5.4d0)) then
        tmp = t_0
    else if (z <= 5.1d-8) then
        tmp = (y * 0.08333333333333323d0) + ((z * ((y * (-0.00277777777751721d0)) + (z * (y * 0.0007936505811533442d0)))) + x)
    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 * (0.0692910599291889 - (-0.07512208616047561 / z))) + x;
	double tmp;
	if (z <= -5.4) {
		tmp = t_0;
	} else if (z <= 5.1e-8) {
		tmp = (y * 0.08333333333333323) + ((z * ((y * -0.00277777777751721) + (z * (y * 0.0007936505811533442)))) + x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y * (0.0692910599291889 - (-0.07512208616047561 / z))) + x
	tmp = 0
	if z <= -5.4:
		tmp = t_0
	elif z <= 5.1e-8:
		tmp = (y * 0.08333333333333323) + ((z * ((y * -0.00277777777751721) + (z * (y * 0.0007936505811533442)))) + x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * Float64(0.0692910599291889 - Float64(-0.07512208616047561 / z))) + x)
	tmp = 0.0
	if (z <= -5.4)
		tmp = t_0;
	elseif (z <= 5.1e-8)
		tmp = Float64(Float64(y * 0.08333333333333323) + Float64(Float64(z * Float64(Float64(y * -0.00277777777751721) + Float64(z * Float64(y * 0.0007936505811533442)))) + x));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y * (0.0692910599291889 - (-0.07512208616047561 / z))) + x;
	tmp = 0.0;
	if (z <= -5.4)
		tmp = t_0;
	elseif (z <= 5.1e-8)
		tmp = (y * 0.08333333333333323) + ((z * ((y * -0.00277777777751721) + (z * (y * 0.0007936505811533442)))) + x);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * N[(0.0692910599291889 - N[(-0.07512208616047561 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -5.4], t$95$0, If[LessEqual[z, 5.1e-8], N[(N[(y * 0.08333333333333323), $MachinePrecision] + N[(N[(z * N[(N[(y * -0.00277777777751721), $MachinePrecision] + N[(z * N[(y * 0.0007936505811533442), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4000000000000004 or 5.10000000000000001e-8 < z

   1. Initial program 44.9%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -5.4000000000000004 < z < 5.10000000000000001e-8

   1. Initial program 99.6%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 60.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+146}:\\ \;\;\;\;0.08333333333333323 \cdot y\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{+77}:\\ \;\;\;\;y \cdot 0.0692910599291889\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+20}:\\ \;\;\;\;0.08333333333333323 \cdot y\\ \mathbf{elif}\;y \leq 1750:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;0.08333333333333323 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.25e+146)
   (* 0.08333333333333323 y)
   (if (<= y -2.05e+77)
     (* y 0.0692910599291889)
     (if (<= y -1.05e+20)
       (* 0.08333333333333323 y)
       (if (<= y 1750.0) x (* 0.08333333333333323 y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.25e+146) {
		tmp = 0.08333333333333323 * y;
	} else if (y <= -2.05e+77) {
		tmp = y * 0.0692910599291889;
	} else if (y <= -1.05e+20) {
		tmp = 0.08333333333333323 * y;
	} else if (y <= 1750.0) {
		tmp = x;
	} else {
		tmp = 0.08333333333333323 * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.25d+146)) then
        tmp = 0.08333333333333323d0 * y
    else if (y <= (-2.05d+77)) then
        tmp = y * 0.0692910599291889d0
    else if (y <= (-1.05d+20)) then
        tmp = 0.08333333333333323d0 * y
    else if (y <= 1750.0d0) then
        tmp = x
    else
        tmp = 0.08333333333333323d0 * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.25e+146) {
		tmp = 0.08333333333333323 * y;
	} else if (y <= -2.05e+77) {
		tmp = y * 0.0692910599291889;
	} else if (y <= -1.05e+20) {
		tmp = 0.08333333333333323 * y;
	} else if (y <= 1750.0) {
		tmp = x;
	} else {
		tmp = 0.08333333333333323 * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.25e+146:
		tmp = 0.08333333333333323 * y
	elif y <= -2.05e+77:
		tmp = y * 0.0692910599291889
	elif y <= -1.05e+20:
		tmp = 0.08333333333333323 * y
	elif y <= 1750.0:
		tmp = x
	else:
		tmp = 0.08333333333333323 * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.25e+146)
		tmp = Float64(0.08333333333333323 * y);
	elseif (y <= -2.05e+77)
		tmp = Float64(y * 0.0692910599291889);
	elseif (y <= -1.05e+20)
		tmp = Float64(0.08333333333333323 * y);
	elseif (y <= 1750.0)
		tmp = x;
	else
		tmp = Float64(0.08333333333333323 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.25e+146)
		tmp = 0.08333333333333323 * y;
	elseif (y <= -2.05e+77)
		tmp = y * 0.0692910599291889;
	elseif (y <= -1.05e+20)
		tmp = 0.08333333333333323 * y;
	elseif (y <= 1750.0)
		tmp = x;
	else
		tmp = 0.08333333333333323 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.25e+146], N[(0.08333333333333323 * y), $MachinePrecision], If[LessEqual[y, -2.05e+77], N[(y * 0.0692910599291889), $MachinePrecision], If[LessEqual[y, -1.05e+20], N[(0.08333333333333323 * y), $MachinePrecision], If[LessEqual[y, 1750.0], x, N[(0.08333333333333323 * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.25e146 or -2.05e77 < y < -1.05e20 or 1750 < y

   1. Initial program 66.8%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -1.25e146 < y < -2.05e77

   1. Initial program 49.7%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -1.05e20 < y < 1750

   1. Initial program 77.7%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 99.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(0.0692910599291889 - \frac{-0.07512208616047561}{z}\right) + x\\ \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-8}:\\ \;\;\;\;\left(y \cdot \left(z \cdot -0.00277777777751721\right) + y \cdot 0.08333333333333323\right) + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* y (- 0.0692910599291889 (/ -0.07512208616047561 z))) x)))
   (if (<= z -5.4)
     t_0
     (if (<= z 5.1e-8)
       (+ (+ (* y (* z -0.00277777777751721)) (* y 0.08333333333333323)) x)
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (y * (0.0692910599291889 - (-0.07512208616047561 / z))) + x;
	double tmp;
	if (z <= -5.4) {
		tmp = t_0;
	} else if (z <= 5.1e-8) {
		tmp = ((y * (z * -0.00277777777751721)) + (y * 0.08333333333333323)) + x;
	} 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) :: tmp
    t_0 = (y * (0.0692910599291889d0 - ((-0.07512208616047561d0) / z))) + x
    if (z <= (-5.4d0)) then
        tmp = t_0
    else if (z <= 5.1d-8) then
        tmp = ((y * (z * (-0.00277777777751721d0))) + (y * 0.08333333333333323d0)) + x
    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 * (0.0692910599291889 - (-0.07512208616047561 / z))) + x;
	double tmp;
	if (z <= -5.4) {
		tmp = t_0;
	} else if (z <= 5.1e-8) {
		tmp = ((y * (z * -0.00277777777751721)) + (y * 0.08333333333333323)) + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y * (0.0692910599291889 - (-0.07512208616047561 / z))) + x
	tmp = 0
	if z <= -5.4:
		tmp = t_0
	elif z <= 5.1e-8:
		tmp = ((y * (z * -0.00277777777751721)) + (y * 0.08333333333333323)) + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * Float64(0.0692910599291889 - Float64(-0.07512208616047561 / z))) + x)
	tmp = 0.0
	if (z <= -5.4)
		tmp = t_0;
	elseif (z <= 5.1e-8)
		tmp = Float64(Float64(Float64(y * Float64(z * -0.00277777777751721)) + Float64(y * 0.08333333333333323)) + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y * (0.0692910599291889 - (-0.07512208616047561 / z))) + x;
	tmp = 0.0;
	if (z <= -5.4)
		tmp = t_0;
	elseif (z <= 5.1e-8)
		tmp = ((y * (z * -0.00277777777751721)) + (y * 0.08333333333333323)) + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * N[(0.0692910599291889 - N[(-0.07512208616047561 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -5.4], t$95$0, If[LessEqual[z, 5.1e-8], N[(N[(N[(y * N[(z * -0.00277777777751721), $MachinePrecision]), $MachinePrecision] + N[(y * 0.08333333333333323), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4000000000000004 or 5.10000000000000001e-8 < z

   1. Initial program 44.9%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -5.4000000000000004 < z < 5.10000000000000001e-8

   1. Initial program 99.6%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 99.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(0.0692910599291889 - \frac{-0.07512208616047561}{z}\right) + x\\ \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \left(0.08333333333333323 + z \cdot -0.00277777777751721\right) + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* y (- 0.0692910599291889 (/ -0.07512208616047561 z))) x)))
   (if (<= z -5.4)
     t_0
     (if (<= z 5.1e-8)
       (+ (* y (+ 0.08333333333333323 (* z -0.00277777777751721))) x)
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (y * (0.0692910599291889 - (-0.07512208616047561 / z))) + x;
	double tmp;
	if (z <= -5.4) {
		tmp = t_0;
	} else if (z <= 5.1e-8) {
		tmp = (y * (0.08333333333333323 + (z * -0.00277777777751721))) + x;
	} 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) :: tmp
    t_0 = (y * (0.0692910599291889d0 - ((-0.07512208616047561d0) / z))) + x
    if (z <= (-5.4d0)) then
        tmp = t_0
    else if (z <= 5.1d-8) then
        tmp = (y * (0.08333333333333323d0 + (z * (-0.00277777777751721d0)))) + x
    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 * (0.0692910599291889 - (-0.07512208616047561 / z))) + x;
	double tmp;
	if (z <= -5.4) {
		tmp = t_0;
	} else if (z <= 5.1e-8) {
		tmp = (y * (0.08333333333333323 + (z * -0.00277777777751721))) + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y * (0.0692910599291889 - (-0.07512208616047561 / z))) + x
	tmp = 0
	if z <= -5.4:
		tmp = t_0
	elif z <= 5.1e-8:
		tmp = (y * (0.08333333333333323 + (z * -0.00277777777751721))) + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * Float64(0.0692910599291889 - Float64(-0.07512208616047561 / z))) + x)
	tmp = 0.0
	if (z <= -5.4)
		tmp = t_0;
	elseif (z <= 5.1e-8)
		tmp = Float64(Float64(y * Float64(0.08333333333333323 + Float64(z * -0.00277777777751721))) + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y * (0.0692910599291889 - (-0.07512208616047561 / z))) + x;
	tmp = 0.0;
	if (z <= -5.4)
		tmp = t_0;
	elseif (z <= 5.1e-8)
		tmp = (y * (0.08333333333333323 + (z * -0.00277777777751721))) + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * N[(0.0692910599291889 - N[(-0.07512208616047561 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -5.4], t$95$0, If[LessEqual[z, 5.1e-8], N[(N[(y * N[(0.08333333333333323 + N[(z * -0.00277777777751721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4000000000000004 or 5.10000000000000001e-8 < z

   1. Initial program 44.9%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -5.4000000000000004 < z < 5.10000000000000001e-8

   1. Initial program 99.6%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 98.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot 0.0692910599291889 + x\\ \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \left(0.08333333333333323 + z \cdot -0.00277777777751721\right) + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* y 0.0692910599291889) x)))
   (if (<= z -5.4)
     t_0
     (if (<= z 5.1e-8)
       (+ (* y (+ 0.08333333333333323 (* z -0.00277777777751721))) x)
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (y * 0.0692910599291889) + x;
	double tmp;
	if (z <= -5.4) {
		tmp = t_0;
	} else if (z <= 5.1e-8) {
		tmp = (y * (0.08333333333333323 + (z * -0.00277777777751721))) + x;
	} 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) :: tmp
    t_0 = (y * 0.0692910599291889d0) + x
    if (z <= (-5.4d0)) then
        tmp = t_0
    else if (z <= 5.1d-8) then
        tmp = (y * (0.08333333333333323d0 + (z * (-0.00277777777751721d0)))) + x
    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 * 0.0692910599291889) + x;
	double tmp;
	if (z <= -5.4) {
		tmp = t_0;
	} else if (z <= 5.1e-8) {
		tmp = (y * (0.08333333333333323 + (z * -0.00277777777751721))) + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y * 0.0692910599291889) + x
	tmp = 0
	if z <= -5.4:
		tmp = t_0
	elif z <= 5.1e-8:
		tmp = (y * (0.08333333333333323 + (z * -0.00277777777751721))) + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * 0.0692910599291889) + x)
	tmp = 0.0
	if (z <= -5.4)
		tmp = t_0;
	elseif (z <= 5.1e-8)
		tmp = Float64(Float64(y * Float64(0.08333333333333323 + Float64(z * -0.00277777777751721))) + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y * 0.0692910599291889) + x;
	tmp = 0.0;
	if (z <= -5.4)
		tmp = t_0;
	elseif (z <= 5.1e-8)
		tmp = (y * (0.08333333333333323 + (z * -0.00277777777751721))) + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * 0.0692910599291889), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -5.4], t$95$0, If[LessEqual[z, 5.1e-8], N[(N[(y * N[(0.08333333333333323 + N[(z * -0.00277777777751721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4000000000000004 or 5.10000000000000001e-8 < z

   1. Initial program 44.9%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -5.4000000000000004 < z < 5.10000000000000001e-8

   1. Initial program 99.6%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 98.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot 0.0692910599291889 + x\\ \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-8}:\\ \;\;\;\;y \cdot 0.08333333333333323 + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* y 0.0692910599291889) x)))
   (if (<= z -5.4)
     t_0
     (if (<= z 5.1e-8) (+ (* y 0.08333333333333323) x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (y * 0.0692910599291889) + x;
	double tmp;
	if (z <= -5.4) {
		tmp = t_0;
	} else if (z <= 5.1e-8) {
		tmp = (y * 0.08333333333333323) + x;
	} 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) :: tmp
    t_0 = (y * 0.0692910599291889d0) + x
    if (z <= (-5.4d0)) then
        tmp = t_0
    else if (z <= 5.1d-8) then
        tmp = (y * 0.08333333333333323d0) + x
    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 * 0.0692910599291889) + x;
	double tmp;
	if (z <= -5.4) {
		tmp = t_0;
	} else if (z <= 5.1e-8) {
		tmp = (y * 0.08333333333333323) + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y * 0.0692910599291889) + x
	tmp = 0
	if z <= -5.4:
		tmp = t_0
	elif z <= 5.1e-8:
		tmp = (y * 0.08333333333333323) + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * 0.0692910599291889) + x)
	tmp = 0.0
	if (z <= -5.4)
		tmp = t_0;
	elseif (z <= 5.1e-8)
		tmp = Float64(Float64(y * 0.08333333333333323) + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y * 0.0692910599291889) + x;
	tmp = 0.0;
	if (z <= -5.4)
		tmp = t_0;
	elseif (z <= 5.1e-8)
		tmp = (y * 0.08333333333333323) + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * 0.0692910599291889), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -5.4], t$95$0, If[LessEqual[z, 5.1e-8], N[(N[(y * 0.08333333333333323), $MachinePrecision] + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4000000000000004 or 5.10000000000000001e-8 < z

   1. Initial program 44.9%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -5.4000000000000004 < z < 5.10000000000000001e-8

   1. Initial program 99.6%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 76.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot 0.0692910599291889 + x\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{-59}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-239}:\\ \;\;\;\;0.08333333333333323 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* y 0.0692910599291889) x)))
   (if (<= z -1.1e-59)
     t_0
     (if (<= z 1.7e-239) (* 0.08333333333333323 y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (y * 0.0692910599291889) + x;
	double tmp;
	if (z <= -1.1e-59) {
		tmp = t_0;
	} else if (z <= 1.7e-239) {
		tmp = 0.08333333333333323 * y;
	} 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) :: tmp
    t_0 = (y * 0.0692910599291889d0) + x
    if (z <= (-1.1d-59)) then
        tmp = t_0
    else if (z <= 1.7d-239) then
        tmp = 0.08333333333333323d0 * y
    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 * 0.0692910599291889) + x;
	double tmp;
	if (z <= -1.1e-59) {
		tmp = t_0;
	} else if (z <= 1.7e-239) {
		tmp = 0.08333333333333323 * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y * 0.0692910599291889) + x
	tmp = 0
	if z <= -1.1e-59:
		tmp = t_0
	elif z <= 1.7e-239:
		tmp = 0.08333333333333323 * y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * 0.0692910599291889) + x)
	tmp = 0.0
	if (z <= -1.1e-59)
		tmp = t_0;
	elseif (z <= 1.7e-239)
		tmp = Float64(0.08333333333333323 * y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y * 0.0692910599291889) + x;
	tmp = 0.0;
	if (z <= -1.1e-59)
		tmp = t_0;
	elseif (z <= 1.7e-239)
		tmp = 0.08333333333333323 * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * 0.0692910599291889), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -1.1e-59], t$95$0, If[LessEqual[z, 1.7e-239], N[(0.08333333333333323 * y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0999999999999999e-59 or 1.7e-239 < z

   1. Initial program 63.1%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.0999999999999999e-59 < z < 1.7e-239

   1. Initial program 99.4%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 60.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+23}:\\ \;\;\;\;0.08333333333333323 \cdot y\\ \mathbf{elif}\;y \leq 8200:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;0.08333333333333323 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.8e+23)
   (* 0.08333333333333323 y)
   (if (<= y 8200.0) x (* 0.08333333333333323 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.8e+23) {
		tmp = 0.08333333333333323 * y;
	} else if (y <= 8200.0) {
		tmp = x;
	} else {
		tmp = 0.08333333333333323 * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-2.8d+23)) then
        tmp = 0.08333333333333323d0 * y
    else if (y <= 8200.0d0) then
        tmp = x
    else
        tmp = 0.08333333333333323d0 * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.8e+23) {
		tmp = 0.08333333333333323 * y;
	} else if (y <= 8200.0) {
		tmp = x;
	} else {
		tmp = 0.08333333333333323 * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.8e+23:
		tmp = 0.08333333333333323 * y
	elif y <= 8200.0:
		tmp = x
	else:
		tmp = 0.08333333333333323 * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.8e+23)
		tmp = Float64(0.08333333333333323 * y);
	elseif (y <= 8200.0)
		tmp = x;
	else
		tmp = Float64(0.08333333333333323 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.8e+23)
		tmp = 0.08333333333333323 * y;
	elseif (y <= 8200.0)
		tmp = x;
	else
		tmp = 0.08333333333333323 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.8e+23], N[(0.08333333333333323 * y), $MachinePrecision], If[LessEqual[y, 8200.0], x, N[(0.08333333333333323 * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.8e23 or 8200 < y

   1. Initial program 65.2%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -2.8e23 < y < 8200

   1. Initial program 77.7%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 51.0% accurate, 21.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return 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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 71.6%

   \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
2. Add Preprocessing

3. Taylor expanded in x around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Developer target: 99.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\frac{0.07512208616047561}{z} + 0.0692910599291889\right) \cdot y - \left(\frac{0.40462203869992125 \cdot y}{z \cdot z} - x\right)\\ \mathbf{if}\;z < -8120153.652456675:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z < 6.576118972787377 \cdot 10^{+20}:\\ \;\;\;\;x + \left(y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)\right) \cdot \frac{1}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (-
          (* (+ (/ 0.07512208616047561 z) 0.0692910599291889) y)
          (- (/ (* 0.40462203869992125 y) (* z z)) x))))
   (if (< z -8120153.652456675)
     t_0
     (if (< z 6.576118972787377e+20)
       (+
        x
        (*
         (*
          y
          (+
           (* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
           0.279195317918525))
         (/ 1.0 (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (((0.07512208616047561 / z) + 0.0692910599291889) * y) - (((0.40462203869992125 * y) / (z * z)) - x);
	double tmp;
	if (z < -8120153.652456675) {
		tmp = t_0;
	} else if (z < 6.576118972787377e+20) {
		tmp = x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) * (1.0 / (((z + 6.012459259764103) * z) + 3.350343815022304)));
	} 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) :: tmp
    t_0 = (((0.07512208616047561d0 / z) + 0.0692910599291889d0) * y) - (((0.40462203869992125d0 * y) / (z * z)) - x)
    if (z < (-8120153.652456675d0)) then
        tmp = t_0
    else if (z < 6.576118972787377d+20) then
        tmp = x + ((y * ((((z * 0.0692910599291889d0) + 0.4917317610505968d0) * z) + 0.279195317918525d0)) * (1.0d0 / (((z + 6.012459259764103d0) * z) + 3.350343815022304d0)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (((0.07512208616047561 / z) + 0.0692910599291889) * y) - (((0.40462203869992125 * y) / (z * z)) - x);
	double tmp;
	if (z < -8120153.652456675) {
		tmp = t_0;
	} else if (z < 6.576118972787377e+20) {
		tmp = x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) * (1.0 / (((z + 6.012459259764103) * z) + 3.350343815022304)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (((0.07512208616047561 / z) + 0.0692910599291889) * y) - (((0.40462203869992125 * y) / (z * z)) - x)
	tmp = 0
	if z < -8120153.652456675:
		tmp = t_0
	elif z < 6.576118972787377e+20:
		tmp = x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) * (1.0 / (((z + 6.012459259764103) * z) + 3.350343815022304)))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(0.07512208616047561 / z) + 0.0692910599291889) * y) - Float64(Float64(Float64(0.40462203869992125 * y) / Float64(z * z)) - x))
	tmp = 0.0
	if (z < -8120153.652456675)
		tmp = t_0;
	elseif (z < 6.576118972787377e+20)
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) * Float64(1.0 / Float64(Float64(Float64(z + 6.012459259764103) * z) + 3.350343815022304))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (((0.07512208616047561 / z) + 0.0692910599291889) * y) - (((0.40462203869992125 * y) / (z * z)) - x);
	tmp = 0.0;
	if (z < -8120153.652456675)
		tmp = t_0;
	elseif (z < 6.576118972787377e+20)
		tmp = x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) * (1.0 / (((z + 6.012459259764103) * z) + 3.350343815022304)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(0.07512208616047561 / z), $MachinePrecision] + 0.0692910599291889), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(0.40462203869992125 * y), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -8120153.652456675], t$95$0, If[Less[z, 6.576118972787377e+20], N[(x + N[(N[(y * N[(N[(N[(N[(z * 0.0692910599291889), $MachinePrecision] + 0.4917317610505968), $MachinePrecision] * z), $MachinePrecision] + 0.279195317918525), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(N[(N[(z + 6.012459259764103), $MachinePrecision] * z), $MachinePrecision] + 3.350343815022304), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024110 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :alt
  (if (< z -8120153.652456675) (- (* (+ (/ 0.07512208616047561 z) 0.0692910599291889) y) (- (/ (* 0.40462203869992125 y) (* z z)) x)) (if (< z 6.576118972787377e+20) (+ x (* (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (/ 1.0 (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (- (* (+ (/ 0.07512208616047561 z) 0.0692910599291889) y) (- (/ (* 0.40462203869992125 y) (* z z)) x))))

  (+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))