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

Percentage Accurate: 69.3% → 99.1%

Time: 16.0s

Alternatives: 13

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, 0.9× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.4) (not (<= z 5.1e-8)))
   (+
    x
    (*
     y
     (-
      0.0692910599291889
      (/ (+ (/ 0.4046220386999212 z) -0.07512208616047561) z))))
   (+
    x
    (*
     y
     (+
      0.08333333333333323
      (* z (- (* z 0.0007936505811533442) 0.00277777777751721)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.4) || !(z <= 5.1e-8)) {
		tmp = x + (y * (0.0692910599291889 - (((0.4046220386999212 / z) + -0.07512208616047561) / z)));
	} else {
		tmp = x + (y * (0.08333333333333323 + (z * ((z * 0.0007936505811533442) - 0.00277777777751721))));
	}
	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 <= (-5.4d0)) .or. (.not. (z <= 5.1d-8))) then
        tmp = x + (y * (0.0692910599291889d0 - (((0.4046220386999212d0 / z) + (-0.07512208616047561d0)) / z)))
    else
        tmp = x + (y * (0.08333333333333323d0 + (z * ((z * 0.0007936505811533442d0) - 0.00277777777751721d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.4) || !(z <= 5.1e-8)) {
		tmp = x + (y * (0.0692910599291889 - (((0.4046220386999212 / z) + -0.07512208616047561) / z)));
	} else {
		tmp = x + (y * (0.08333333333333323 + (z * ((z * 0.0007936505811533442) - 0.00277777777751721))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.4) or not (z <= 5.1e-8):
		tmp = x + (y * (0.0692910599291889 - (((0.4046220386999212 / z) + -0.07512208616047561) / z)))
	else:
		tmp = x + (y * (0.08333333333333323 + (z * ((z * 0.0007936505811533442) - 0.00277777777751721))))
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.4], N[Not[LessEqual[z, 5.1e-8]], $MachinePrecision]], N[(x + N[(y * N[(0.0692910599291889 - N[(N[(N[(0.4046220386999212 / z), $MachinePrecision] + -0.07512208616047561), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(0.08333333333333323 + N[(z * N[(N[(z * 0.0007936505811533442), $MachinePrecision] - 0.00277777777751721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

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. Step-by-step derivation

      1. remove-double-neg 44.9%

         \[\leadsto x + \color{blue}{\left(-\left(-\frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      2. associate-/l* 54.8%

         \[\leadsto x + \left(-\left(-\color{blue}{y \cdot \frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}}\right)\right) \]

      3. distribute-rgt-neg-in 54.8%

         \[\leadsto x + \left(-\color{blue}{y \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)}\right) \]

      4. distribute-lft-neg-in 54.8%

         \[\leadsto x + \color{blue}{\left(-y\right) \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)} \]

      5. distribute-lft-neg-in 54.8%

         \[\leadsto x + \color{blue}{\left(-y \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      6. distribute-rgt-neg-in 54.8%

         \[\leadsto x + \color{blue}{y \cdot \left(-\left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      7. remove-double-neg 54.8%

         \[\leadsto x + y \cdot \color{blue}{\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}} \]

      8. fma-define 54.8%

         \[\leadsto x + y \cdot \frac{\color{blue}{\mathsf{fma}\left(z \cdot 0.0692910599291889 + 0.4917317610505968, z, 0.279195317918525\right)}}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

      9. fma-define 54.8%

         \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}, z, 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

      10. fma-define 54.8%

          \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}{\color{blue}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}} \]

   3. Simplified 54.8%

      \[\leadsto \color{blue}{x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around -inf 99.7%

      \[\leadsto x + y \cdot \color{blue}{\left(0.0692910599291889 + -1 \cdot \frac{0.4046220386999212 \cdot \frac{1}{z} - 0.07512208616047561}{z}\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 99.7%

         \[\leadsto x + y \cdot \left(0.0692910599291889 + \color{blue}{\left(-\frac{0.4046220386999212 \cdot \frac{1}{z} - 0.07512208616047561}{z}\right)}\right) \]

      2. unsub-neg 99.7%

         \[\leadsto x + y \cdot \color{blue}{\left(0.0692910599291889 - \frac{0.4046220386999212 \cdot \frac{1}{z} - 0.07512208616047561}{z}\right)} \]

      3. sub-neg 99.7%

         \[\leadsto x + y \cdot \left(0.0692910599291889 - \frac{\color{blue}{0.4046220386999212 \cdot \frac{1}{z} + \left(-0.07512208616047561\right)}}{z}\right) \]

      4. associate-*r/ 99.7%

         \[\leadsto x + y \cdot \left(0.0692910599291889 - \frac{\color{blue}{\frac{0.4046220386999212 \cdot 1}{z}} + \left(-0.07512208616047561\right)}{z}\right) \]

      5. metadata-eval 99.7%

         \[\leadsto x + y \cdot \left(0.0692910599291889 - \frac{\frac{\color{blue}{0.4046220386999212}}{z} + \left(-0.07512208616047561\right)}{z}\right) \]

      6. metadata-eval 99.7%

         \[\leadsto x + y \cdot \left(0.0692910599291889 - \frac{\frac{0.4046220386999212}{z} + \color{blue}{-0.07512208616047561}}{z}\right) \]

   7. Simplified 99.7%

      \[\leadsto x + y \cdot \color{blue}{\left(0.0692910599291889 - \frac{\frac{0.4046220386999212}{z} + -0.07512208616047561}{z}\right)} \]

   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. Step-by-step derivation

      1. remove-double-neg 99.6%

         \[\leadsto x + \color{blue}{\left(-\left(-\frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      2. associate-/l* 99.8%

         \[\leadsto x + \left(-\left(-\color{blue}{y \cdot \frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}}\right)\right) \]

      3. distribute-rgt-neg-in 99.8%

         \[\leadsto x + \left(-\color{blue}{y \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)}\right) \]

      4. distribute-lft-neg-in 99.8%

         \[\leadsto x + \color{blue}{\left(-y\right) \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)} \]

      5. distribute-lft-neg-in 99.8%

         \[\leadsto x + \color{blue}{\left(-y \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      6. distribute-rgt-neg-in 99.8%

         \[\leadsto x + \color{blue}{y \cdot \left(-\left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      7. remove-double-neg 99.8%

         \[\leadsto x + y \cdot \color{blue}{\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}} \]

      8. fma-define 99.8%

         \[\leadsto x + y \cdot \frac{\color{blue}{\mathsf{fma}\left(z \cdot 0.0692910599291889 + 0.4917317610505968, z, 0.279195317918525\right)}}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

      9. fma-define 99.8%

         \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}, z, 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

      10. fma-define 99.8%

          \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}{\color{blue}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 99.8%

      \[\leadsto x + y \cdot \color{blue}{\left(0.08333333333333323 + z \cdot \left(0.0007936505811533442 \cdot z - 0.00277777777751721\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \lor \neg \left(z \leq 5.1 \cdot 10^{-8}\right):\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 - \frac{\frac{0.4046220386999212}{z} + -0.07512208616047561}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.08333333333333323 + z \cdot \left(z \cdot 0.0007936505811533442 - 0.00277777777751721\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} \leq 5 \cdot 10^{+305}:\\ \;\;\;\;x + y \cdot \frac{\mathsf{fma}\left(\frac{0.24180012482592123 - {z}^{2} \cdot 0.004801250986110448}{0.4917317610505968 - z \cdot 0.0692910599291889}, z, 0.279195317918525\right)}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (/
       (*
        y
        (+
         (* z (+ (* z 0.0692910599291889) 0.4917317610505968))
         0.279195317918525))
       (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
      5e+305)
   (+
    x
    (*
     y
     (/
      (fma
       (/
        (- 0.24180012482592123 (* (pow z 2.0) 0.004801250986110448))
        (- 0.4917317610505968 (* z 0.0692910599291889)))
       z
       0.279195317918525)
      (fma (+ z 6.012459259764103) z 3.350343815022304))))
   (+ x (* y 0.0692910599291889))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((y * ((z * ((z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / ((z * (z + 6.012459259764103)) + 3.350343815022304)) <= 5e+305) {
		tmp = x + (y * (fma(((0.24180012482592123 - (pow(z, 2.0) * 0.004801250986110448)) / (0.4917317610505968 - (z * 0.0692910599291889))), z, 0.279195317918525) / fma((z + 6.012459259764103), z, 3.350343815022304)));
	} else {
		tmp = x + (y * 0.0692910599291889);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / Float64(Float64(z * Float64(z + 6.012459259764103)) + 3.350343815022304)) <= 5e+305)
		tmp = Float64(x + Float64(y * Float64(fma(Float64(Float64(0.24180012482592123 - Float64((z ^ 2.0) * 0.004801250986110448)) / Float64(0.4917317610505968 - Float64(z * 0.0692910599291889))), z, 0.279195317918525) / fma(Float64(z + 6.012459259764103), z, 3.350343815022304))));
	else
		tmp = Float64(x + Float64(y * 0.0692910599291889));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(y * N[(N[(z * N[(N[(z * 0.0692910599291889), $MachinePrecision] + 0.4917317610505968), $MachinePrecision]), $MachinePrecision] + 0.279195317918525), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(z + 6.012459259764103), $MachinePrecision]), $MachinePrecision] + 3.350343815022304), $MachinePrecision]), $MachinePrecision], 5e+305], N[(x + N[(y * N[(N[(N[(N[(0.24180012482592123 - N[(N[Power[z, 2.0], $MachinePrecision] * 0.004801250986110448), $MachinePrecision]), $MachinePrecision] / N[(0.4917317610505968 - N[(z * 0.0692910599291889), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z + 0.279195317918525), $MachinePrecision] / N[(N[(z + 6.012459259764103), $MachinePrecision] * z + 3.350343815022304), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 0.0692910599291889), $MachinePrecision]), $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. Step-by-step derivation

      1. remove-double-neg 98.2%

         \[\leadsto x + \color{blue}{\left(-\left(-\frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      2. associate-/l* 99.8%

         \[\leadsto x + \left(-\left(-\color{blue}{y \cdot \frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}}\right)\right) \]

      3. distribute-rgt-neg-in 99.8%

         \[\leadsto x + \left(-\color{blue}{y \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)}\right) \]

      4. distribute-lft-neg-in 99.8%

         \[\leadsto x + \color{blue}{\left(-y\right) \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)} \]

      5. distribute-lft-neg-in 99.8%

         \[\leadsto x + \color{blue}{\left(-y \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      6. distribute-rgt-neg-in 99.8%

         \[\leadsto x + \color{blue}{y \cdot \left(-\left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      7. remove-double-neg 99.8%

         \[\leadsto x + y \cdot \color{blue}{\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}} \]

      8. fma-define 99.8%

         \[\leadsto x + y \cdot \frac{\color{blue}{\mathsf{fma}\left(z \cdot 0.0692910599291889 + 0.4917317610505968, z, 0.279195317918525\right)}}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

      9. fma-define 99.8%

         \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}, z, 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

      10. fma-define 99.8%

          \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}{\color{blue}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-define 99.8%

         \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(\color{blue}{z \cdot 0.0692910599291889 + 0.4917317610505968}, z, 0.279195317918525\right)}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)} \]

      2. +-commutative 99.8%

         \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(\color{blue}{0.4917317610505968 + z \cdot 0.0692910599291889}, z, 0.279195317918525\right)}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)} \]

      3. flip-+ 99.8%

         \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{0.4917317610505968 \cdot 0.4917317610505968 - \left(z \cdot 0.0692910599291889\right) \cdot \left(z \cdot 0.0692910599291889\right)}{0.4917317610505968 - z \cdot 0.0692910599291889}}, z, 0.279195317918525\right)}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)} \]

      4. metadata-eval 99.8%

         \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(\frac{\color{blue}{0.24180012482592123} - \left(z \cdot 0.0692910599291889\right) \cdot \left(z \cdot 0.0692910599291889\right)}{0.4917317610505968 - z \cdot 0.0692910599291889}, z, 0.279195317918525\right)}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)} \]

      5. swap-sqr 99.7%

         \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(\frac{0.24180012482592123 - \color{blue}{\left(z \cdot z\right) \cdot \left(0.0692910599291889 \cdot 0.0692910599291889\right)}}{0.4917317610505968 - z \cdot 0.0692910599291889}, z, 0.279195317918525\right)}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)} \]

      6. pow2 99.7%

         \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(\frac{0.24180012482592123 - \color{blue}{{z}^{2}} \cdot \left(0.0692910599291889 \cdot 0.0692910599291889\right)}{0.4917317610505968 - z \cdot 0.0692910599291889}, z, 0.279195317918525\right)}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)} \]

      7. metadata-eval 99.8%

         \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(\frac{0.24180012482592123 - {z}^{2} \cdot \color{blue}{0.004801250986110448}}{0.4917317610505968 - z \cdot 0.0692910599291889}, z, 0.279195317918525\right)}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)} \]

   6. Applied egg-rr 99.8%

      \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(\color{blue}{\frac{0.24180012482592123 - {z}^{2} \cdot 0.004801250986110448}{0.4917317610505968 - z \cdot 0.0692910599291889}}, z, 0.279195317918525\right)}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)} \]

   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. Step-by-step derivation

      1. +-commutative 0.9%

         \[\leadsto \color{blue}{\frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} + x} \]

      2. *-commutative 0.9%

         \[\leadsto \frac{\color{blue}{\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right) \cdot y}}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} + x \]

      3. associate-/l* 15.6%

         \[\leadsto \color{blue}{\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right) \cdot \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}} + x \]

      4. fma-define 15.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right)} \]

      5. *-commutative 15.6%

         \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right)} + 0.279195317918525, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      6. fma-define 15.6%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z, z \cdot 0.0692910599291889 + 0.4917317610505968, 0.279195317918525\right)}, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      7. fma-define 15.6%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}, 0.279195317918525\right), \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      8. *-commutative 15.6%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\color{blue}{z \cdot \left(z + 6.012459259764103\right)} + 3.350343815022304}, x\right) \]

      9. fma-define 15.6%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\color{blue}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}}, x\right) \]

   3. Simplified 15.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 99.7%

      \[\leadsto \color{blue}{x + 0.0692910599291889 \cdot y} \]
   6. Step-by-step derivation

      1. +-commutative 99.7%

         \[\leadsto \color{blue}{0.0692910599291889 \cdot y + x} \]

   7. Simplified 99.7%

      \[\leadsto \color{blue}{0.0692910599291889 \cdot y + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} \leq 5 \cdot 10^{+305}:\\ \;\;\;\;x + y \cdot \frac{\mathsf{fma}\left(\frac{0.24180012482592123 - {z}^{2} \cdot 0.004801250986110448}{0.4917317610505968 - z \cdot 0.0692910599291889}, z, 0.279195317918525\right)}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(y * N[(N[(z * N[(N[(z * 0.0692910599291889), $MachinePrecision] + 0.4917317610505968), $MachinePrecision]), $MachinePrecision] + 0.279195317918525), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(z + 6.012459259764103), $MachinePrecision]), $MachinePrecision] + 3.350343815022304), $MachinePrecision]), $MachinePrecision], 5e+305], N[(x + N[(y * N[(N[(N[(z * 0.0692910599291889 + 0.4917317610505968), $MachinePrecision] * z + 0.279195317918525), $MachinePrecision] / N[(N[(z + 6.012459259764103), $MachinePrecision] * z + 3.350343815022304), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 0.0692910599291889), $MachinePrecision]), $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. Step-by-step derivation

      1. remove-double-neg 98.2%

         \[\leadsto x + \color{blue}{\left(-\left(-\frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      2. associate-/l* 99.8%

         \[\leadsto x + \left(-\left(-\color{blue}{y \cdot \frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}}\right)\right) \]

      3. distribute-rgt-neg-in 99.8%

         \[\leadsto x + \left(-\color{blue}{y \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)}\right) \]

      4. distribute-lft-neg-in 99.8%

         \[\leadsto x + \color{blue}{\left(-y\right) \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)} \]

      5. distribute-lft-neg-in 99.8%

         \[\leadsto x + \color{blue}{\left(-y \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      6. distribute-rgt-neg-in 99.8%

         \[\leadsto x + \color{blue}{y \cdot \left(-\left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      7. remove-double-neg 99.8%

         \[\leadsto x + y \cdot \color{blue}{\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}} \]

      8. fma-define 99.8%

         \[\leadsto x + y \cdot \frac{\color{blue}{\mathsf{fma}\left(z \cdot 0.0692910599291889 + 0.4917317610505968, z, 0.279195317918525\right)}}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

      9. fma-define 99.8%

         \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}, z, 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

      10. fma-define 99.8%

          \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}{\color{blue}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}} \]
   4. Add Preprocessing

   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. Step-by-step derivation

      1. +-commutative 0.9%

         \[\leadsto \color{blue}{\frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} + x} \]

      2. *-commutative 0.9%

         \[\leadsto \frac{\color{blue}{\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right) \cdot y}}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} + x \]

      3. associate-/l* 15.6%

         \[\leadsto \color{blue}{\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right) \cdot \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}} + x \]

      4. fma-define 15.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right)} \]

      5. *-commutative 15.6%

         \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right)} + 0.279195317918525, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      6. fma-define 15.6%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z, z \cdot 0.0692910599291889 + 0.4917317610505968, 0.279195317918525\right)}, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      7. fma-define 15.6%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}, 0.279195317918525\right), \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      8. *-commutative 15.6%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\color{blue}{z \cdot \left(z + 6.012459259764103\right)} + 3.350343815022304}, x\right) \]

      9. fma-define 15.6%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\color{blue}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}}, x\right) \]

   3. Simplified 15.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 99.7%

      \[\leadsto \color{blue}{x + 0.0692910599291889 \cdot y} \]
   6. Step-by-step derivation

      1. +-commutative 99.7%

         \[\leadsto \color{blue}{0.0692910599291889 \cdot y + x} \]

   7. Simplified 99.7%

      \[\leadsto \color{blue}{0.0692910599291889 \cdot y + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} \leq 5 \cdot 10^{+305}:\\ \;\;\;\;x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

   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. Step-by-step derivation

      1. +-commutative 0.9%

         \[\leadsto \color{blue}{\frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} + x} \]

      2. *-commutative 0.9%

         \[\leadsto \frac{\color{blue}{\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right) \cdot y}}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} + x \]

      3. associate-/l* 15.6%

         \[\leadsto \color{blue}{\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right) \cdot \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}} + x \]

      4. fma-define 15.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right)} \]

      5. *-commutative 15.6%

         \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right)} + 0.279195317918525, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      6. fma-define 15.6%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z, z \cdot 0.0692910599291889 + 0.4917317610505968, 0.279195317918525\right)}, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      7. fma-define 15.6%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}, 0.279195317918525\right), \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      8. *-commutative 15.6%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\color{blue}{z \cdot \left(z + 6.012459259764103\right)} + 3.350343815022304}, x\right) \]

      9. fma-define 15.6%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\color{blue}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}}, x\right) \]

   3. Simplified 15.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 99.7%

      \[\leadsto \color{blue}{x + 0.0692910599291889 \cdot y} \]
   6. Step-by-step derivation

      1. +-commutative 99.7%

         \[\leadsto \color{blue}{0.0692910599291889 \cdot y + x} \]

   7. Simplified 99.7%

      \[\leadsto \color{blue}{0.0692910599291889 \cdot y + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.6%

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

Alternative 5: 60.4% accurate, 0.9× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.25e+146)
   (* y 0.08333333333333323)
   (if (<= y -2.05e+77)
     (* y 0.0692910599291889)
     (if (or (<= y -1.05e+20) (not (<= y 1750.0)))
       (* y 0.08333333333333323)
       x))))

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.25d+146)) then
        tmp = y * 0.08333333333333323d0
    else if (y <= (-2.05d+77)) then
        tmp = y * 0.0692910599291889d0
    else if ((y <= (-1.05d+20)) .or. (.not. (y <= 1750.0d0))) then
        tmp = y * 0.08333333333333323d0
    else
        tmp = x
    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 = y * 0.08333333333333323;
	} else if (y <= -2.05e+77) {
		tmp = y * 0.0692910599291889;
	} else if ((y <= -1.05e+20) || !(y <= 1750.0)) {
		tmp = y * 0.08333333333333323;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.25e+146:
		tmp = y * 0.08333333333333323
	elif y <= -2.05e+77:
		tmp = y * 0.0692910599291889
	elif (y <= -1.05e+20) or not (y <= 1750.0):
		tmp = y * 0.08333333333333323
	else:
		tmp = x
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.25e+146], N[(y * 0.08333333333333323), $MachinePrecision], If[LessEqual[y, -2.05e+77], N[(y * 0.0692910599291889), $MachinePrecision], If[Or[LessEqual[y, -1.05e+20], N[Not[LessEqual[y, 1750.0]], $MachinePrecision]], N[(y * 0.08333333333333323), $MachinePrecision], x]]]

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. Step-by-step derivation

      1. +-commutative 66.8%

         \[\leadsto \color{blue}{\frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} + x} \]

      2. *-commutative 66.8%

         \[\leadsto \frac{\color{blue}{\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right) \cdot y}}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} + x \]

      3. associate-/l* 78.3%

         \[\leadsto \color{blue}{\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right) \cdot \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}} + x \]

      4. fma-define 78.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right)} \]

      5. *-commutative 78.3%

         \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right)} + 0.279195317918525, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      6. fma-define 78.3%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z, z \cdot 0.0692910599291889 + 0.4917317610505968, 0.279195317918525\right)}, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      7. fma-define 78.3%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}, 0.279195317918525\right), \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      8. *-commutative 78.3%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\color{blue}{z \cdot \left(z + 6.012459259764103\right)} + 3.350343815022304}, x\right) \]

      9. fma-define 78.3%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\color{blue}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}}, x\right) \]

   3. Simplified 78.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 73.2%

      \[\leadsto \color{blue}{x + 0.08333333333333323 \cdot y} \]
   6. Step-by-step derivation

      1. +-commutative 73.2%

         \[\leadsto \color{blue}{0.08333333333333323 \cdot y + x} \]

   7. Simplified 73.2%

      \[\leadsto \color{blue}{0.08333333333333323 \cdot y + x} \]

   8. Taylor expanded in y around inf 55.2%

      \[\leadsto \color{blue}{0.08333333333333323 \cdot y} \]

   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. Step-by-step derivation

      1. +-commutative 49.7%

         \[\leadsto \color{blue}{\frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} + x} \]

      2. *-commutative 49.7%

         \[\leadsto \frac{\color{blue}{\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right) \cdot y}}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} + x \]

      3. associate-/l* 49.7%

         \[\leadsto \color{blue}{\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right) \cdot \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}} + x \]

      4. fma-define 49.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right)} \]

      5. *-commutative 49.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right)} + 0.279195317918525, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      6. fma-define 49.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z, z \cdot 0.0692910599291889 + 0.4917317610505968, 0.279195317918525\right)}, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      7. fma-define 49.7%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}, 0.279195317918525\right), \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      8. *-commutative 49.7%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\color{blue}{z \cdot \left(z + 6.012459259764103\right)} + 3.350343815022304}, x\right) \]

      9. fma-define 49.7%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\color{blue}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}}, x\right) \]

   3. Simplified 49.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 86.7%

      \[\leadsto \color{blue}{x + 0.0692910599291889 \cdot y} \]
   6. Step-by-step derivation

      1. +-commutative 86.7%

         \[\leadsto \color{blue}{0.0692910599291889 \cdot y + x} \]

      2. fma-define 86.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(0.0692910599291889, y, x\right)} \]

   7. Simplified 86.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.0692910599291889, y, x\right)} \]

   8. Taylor expanded in y around inf 62.3%

      \[\leadsto \color{blue}{0.0692910599291889 \cdot y} \]
   9. Step-by-step derivation

      1. *-commutative 62.3%

         \[\leadsto \color{blue}{y \cdot 0.0692910599291889} \]

   10. Simplified 62.3%

       \[\leadsto \color{blue}{y \cdot 0.0692910599291889} \]

   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. Step-by-step derivation

      1. +-commutative 77.7%

         \[\leadsto \color{blue}{\frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} + x} \]

      2. *-commutative 77.7%

         \[\leadsto \frac{\color{blue}{\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right) \cdot y}}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} + x \]

      3. associate-/l* 76.3%

         \[\leadsto \color{blue}{\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right) \cdot \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}} + x \]

      4. fma-define 76.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right)} \]

      5. *-commutative 76.4%

         \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right)} + 0.279195317918525, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      6. fma-define 76.4%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z, z \cdot 0.0692910599291889 + 0.4917317610505968, 0.279195317918525\right)}, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      7. fma-define 76.4%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}, 0.279195317918525\right), \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      8. *-commutative 76.4%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\color{blue}{z \cdot \left(z + 6.012459259764103\right)} + 3.350343815022304}, x\right) \]

      9. fma-define 76.4%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\color{blue}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}}, x\right) \]

   3. Simplified 76.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 79.3%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+146}:\\ \;\;\;\;y \cdot 0.08333333333333323\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{+77}:\\ \;\;\;\;y \cdot 0.0692910599291889\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+20} \lor \neg \left(y \leq 1750\right):\\ \;\;\;\;y \cdot 0.08333333333333323\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.1% accurate, 0.9× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.4) (not (<= z 5.1e-8)))
   (+ x (* y (+ 0.0692910599291889 (/ 0.07512208616047561 z))))
   (+
    x
    (*
     y
     (+
      0.08333333333333323
      (* z (- (* z 0.0007936505811533442) 0.00277777777751721)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.4) || !(z <= 5.1e-8)) {
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)));
	} else {
		tmp = x + (y * (0.08333333333333323 + (z * ((z * 0.0007936505811533442) - 0.00277777777751721))));
	}
	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 <= (-5.4d0)) .or. (.not. (z <= 5.1d-8))) then
        tmp = x + (y * (0.0692910599291889d0 + (0.07512208616047561d0 / z)))
    else
        tmp = x + (y * (0.08333333333333323d0 + (z * ((z * 0.0007936505811533442d0) - 0.00277777777751721d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.4) || !(z <= 5.1e-8)) {
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)));
	} else {
		tmp = x + (y * (0.08333333333333323 + (z * ((z * 0.0007936505811533442) - 0.00277777777751721))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.4) or not (z <= 5.1e-8):
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)))
	else:
		tmp = x + (y * (0.08333333333333323 + (z * ((z * 0.0007936505811533442) - 0.00277777777751721))))
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.4], N[Not[LessEqual[z, 5.1e-8]], $MachinePrecision]], N[(x + N[(y * N[(0.0692910599291889 + N[(0.07512208616047561 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(0.08333333333333323 + N[(z * N[(N[(z * 0.0007936505811533442), $MachinePrecision] - 0.00277777777751721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

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. Step-by-step derivation

      1. remove-double-neg 44.9%

         \[\leadsto x + \color{blue}{\left(-\left(-\frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      2. associate-/l* 54.8%

         \[\leadsto x + \left(-\left(-\color{blue}{y \cdot \frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}}\right)\right) \]

      3. distribute-rgt-neg-in 54.8%

         \[\leadsto x + \left(-\color{blue}{y \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)}\right) \]

      4. distribute-lft-neg-in 54.8%

         \[\leadsto x + \color{blue}{\left(-y\right) \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)} \]

      5. distribute-lft-neg-in 54.8%

         \[\leadsto x + \color{blue}{\left(-y \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      6. distribute-rgt-neg-in 54.8%

         \[\leadsto x + \color{blue}{y \cdot \left(-\left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      7. remove-double-neg 54.8%

         \[\leadsto x + y \cdot \color{blue}{\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}} \]

      8. fma-define 54.8%

         \[\leadsto x + y \cdot \frac{\color{blue}{\mathsf{fma}\left(z \cdot 0.0692910599291889 + 0.4917317610505968, z, 0.279195317918525\right)}}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

      9. fma-define 54.8%

         \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}, z, 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

      10. fma-define 54.8%

          \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}{\color{blue}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}} \]

   3. Simplified 54.8%

      \[\leadsto \color{blue}{x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 99.6%

      \[\leadsto x + y \cdot \color{blue}{\left(0.0692910599291889 + 0.07512208616047561 \cdot \frac{1}{z}\right)} \]
   6. Step-by-step derivation

      1. associate-*r/ 99.6%

         \[\leadsto x + y \cdot \left(0.0692910599291889 + \color{blue}{\frac{0.07512208616047561 \cdot 1}{z}}\right) \]

      2. metadata-eval 99.6%

         \[\leadsto x + y \cdot \left(0.0692910599291889 + \frac{\color{blue}{0.07512208616047561}}{z}\right) \]

   7. Simplified 99.6%

      \[\leadsto x + y \cdot \color{blue}{\left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)} \]

   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. Step-by-step derivation

      1. remove-double-neg 99.6%

         \[\leadsto x + \color{blue}{\left(-\left(-\frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      2. associate-/l* 99.8%

         \[\leadsto x + \left(-\left(-\color{blue}{y \cdot \frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}}\right)\right) \]

      3. distribute-rgt-neg-in 99.8%

         \[\leadsto x + \left(-\color{blue}{y \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)}\right) \]

      4. distribute-lft-neg-in 99.8%

         \[\leadsto x + \color{blue}{\left(-y\right) \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)} \]

      5. distribute-lft-neg-in 99.8%

         \[\leadsto x + \color{blue}{\left(-y \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      6. distribute-rgt-neg-in 99.8%

         \[\leadsto x + \color{blue}{y \cdot \left(-\left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      7. remove-double-neg 99.8%

         \[\leadsto x + y \cdot \color{blue}{\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}} \]

      8. fma-define 99.8%

         \[\leadsto x + y \cdot \frac{\color{blue}{\mathsf{fma}\left(z \cdot 0.0692910599291889 + 0.4917317610505968, z, 0.279195317918525\right)}}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

      9. fma-define 99.8%

         \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}, z, 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

      10. fma-define 99.8%

          \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}{\color{blue}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 99.8%

      \[\leadsto x + y \cdot \color{blue}{\left(0.08333333333333323 + z \cdot \left(0.0007936505811533442 \cdot z - 0.00277777777751721\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \lor \neg \left(z \leq 5.1 \cdot 10^{-8}\right):\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.08333333333333323 + z \cdot \left(z \cdot 0.0007936505811533442 - 0.00277777777751721\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.1% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.4) (not (<= z 5.1e-8)))
   (+ x (* y (+ 0.0692910599291889 (/ 0.07512208616047561 z))))
   (+ x (+ (* y 0.08333333333333323) (* z (* y -0.00277777777751721))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.4) || !(z <= 5.1e-8)) {
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)));
	} else {
		tmp = x + ((y * 0.08333333333333323) + (z * (y * -0.00277777777751721)));
	}
	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 <= (-5.4d0)) .or. (.not. (z <= 5.1d-8))) then
        tmp = x + (y * (0.0692910599291889d0 + (0.07512208616047561d0 / z)))
    else
        tmp = x + ((y * 0.08333333333333323d0) + (z * (y * (-0.00277777777751721d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.4) || !(z <= 5.1e-8)) {
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)));
	} else {
		tmp = x + ((y * 0.08333333333333323) + (z * (y * -0.00277777777751721)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.4) or not (z <= 5.1e-8):
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)))
	else:
		tmp = x + ((y * 0.08333333333333323) + (z * (y * -0.00277777777751721)))
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.4], N[Not[LessEqual[z, 5.1e-8]], $MachinePrecision]], N[(x + N[(y * N[(0.0692910599291889 + N[(0.07512208616047561 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * 0.08333333333333323), $MachinePrecision] + N[(z * N[(y * -0.00277777777751721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

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. Step-by-step derivation

      1. remove-double-neg 44.9%

         \[\leadsto x + \color{blue}{\left(-\left(-\frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      2. associate-/l* 54.8%

         \[\leadsto x + \left(-\left(-\color{blue}{y \cdot \frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}}\right)\right) \]

      3. distribute-rgt-neg-in 54.8%

         \[\leadsto x + \left(-\color{blue}{y \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)}\right) \]

      4. distribute-lft-neg-in 54.8%

         \[\leadsto x + \color{blue}{\left(-y\right) \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)} \]

      5. distribute-lft-neg-in 54.8%

         \[\leadsto x + \color{blue}{\left(-y \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      6. distribute-rgt-neg-in 54.8%

         \[\leadsto x + \color{blue}{y \cdot \left(-\left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      7. remove-double-neg 54.8%

         \[\leadsto x + y \cdot \color{blue}{\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}} \]

      8. fma-define 54.8%

         \[\leadsto x + y \cdot \frac{\color{blue}{\mathsf{fma}\left(z \cdot 0.0692910599291889 + 0.4917317610505968, z, 0.279195317918525\right)}}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

      9. fma-define 54.8%

         \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}, z, 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

      10. fma-define 54.8%

          \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}{\color{blue}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}} \]

   3. Simplified 54.8%

      \[\leadsto \color{blue}{x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 99.6%

      \[\leadsto x + y \cdot \color{blue}{\left(0.0692910599291889 + 0.07512208616047561 \cdot \frac{1}{z}\right)} \]
   6. Step-by-step derivation

      1. associate-*r/ 99.6%

         \[\leadsto x + y \cdot \left(0.0692910599291889 + \color{blue}{\frac{0.07512208616047561 \cdot 1}{z}}\right) \]

      2. metadata-eval 99.6%

         \[\leadsto x + y \cdot \left(0.0692910599291889 + \frac{\color{blue}{0.07512208616047561}}{z}\right) \]

   7. Simplified 99.6%

      \[\leadsto x + y \cdot \color{blue}{\left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)} \]

   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. Step-by-step derivation

      1. remove-double-neg 99.6%

         \[\leadsto x + \color{blue}{\left(-\left(-\frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      2. associate-/l* 99.8%

         \[\leadsto x + \left(-\left(-\color{blue}{y \cdot \frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}}\right)\right) \]

      3. distribute-rgt-neg-in 99.8%

         \[\leadsto x + \left(-\color{blue}{y \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)}\right) \]

      4. distribute-lft-neg-in 99.8%

         \[\leadsto x + \color{blue}{\left(-y\right) \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)} \]

      5. distribute-lft-neg-in 99.8%

         \[\leadsto x + \color{blue}{\left(-y \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      6. distribute-rgt-neg-in 99.8%

         \[\leadsto x + \color{blue}{y \cdot \left(-\left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      7. remove-double-neg 99.8%

         \[\leadsto x + y \cdot \color{blue}{\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}} \]

      8. fma-define 99.8%

         \[\leadsto x + y \cdot \frac{\color{blue}{\mathsf{fma}\left(z \cdot 0.0692910599291889 + 0.4917317610505968, z, 0.279195317918525\right)}}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

      9. fma-define 99.8%

         \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}, z, 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

      10. fma-define 99.8%

          \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}{\color{blue}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 99.8%

      \[\leadsto x + \color{blue}{\left(0.08333333333333323 \cdot y + z \cdot \left(0.14677053705526136 \cdot y - 0.14954831483277858 \cdot y\right)\right)} \]

   6. Taylor expanded in y around 0 99.8%

      \[\leadsto x + \left(0.08333333333333323 \cdot y + z \cdot \color{blue}{\left(-0.00277777777751721 \cdot y\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto x + \left(0.08333333333333323 \cdot y + z \cdot \color{blue}{\left(y \cdot -0.00277777777751721\right)}\right) \]

   8. Simplified 99.8%

      \[\leadsto x + \left(0.08333333333333323 \cdot y + z \cdot \color{blue}{\left(y \cdot -0.00277777777751721\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \lor \neg \left(z \leq 5.1 \cdot 10^{-8}\right):\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 0.08333333333333323 + z \cdot \left(y \cdot -0.00277777777751721\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.1% accurate, 1.1× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.4) (not (<= z 5.1e-8)))
   (+ x (* y (+ 0.0692910599291889 (/ 0.07512208616047561 z))))
   (+ x (* y (+ 0.08333333333333323 (* z -0.00277777777751721))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.4) || !(z <= 5.1e-8)) {
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)));
	} else {
		tmp = x + (y * (0.08333333333333323 + (z * -0.00277777777751721)));
	}
	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 <= (-5.4d0)) .or. (.not. (z <= 5.1d-8))) then
        tmp = x + (y * (0.0692910599291889d0 + (0.07512208616047561d0 / z)))
    else
        tmp = x + (y * (0.08333333333333323d0 + (z * (-0.00277777777751721d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.4) || !(z <= 5.1e-8)) {
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)));
	} else {
		tmp = x + (y * (0.08333333333333323 + (z * -0.00277777777751721)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.4) or not (z <= 5.1e-8):
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)))
	else:
		tmp = x + (y * (0.08333333333333323 + (z * -0.00277777777751721)))
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.4], N[Not[LessEqual[z, 5.1e-8]], $MachinePrecision]], N[(x + N[(y * N[(0.0692910599291889 + N[(0.07512208616047561 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(0.08333333333333323 + N[(z * -0.00277777777751721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

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. Step-by-step derivation

      1. remove-double-neg 44.9%

         \[\leadsto x + \color{blue}{\left(-\left(-\frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      2. associate-/l* 54.8%

         \[\leadsto x + \left(-\left(-\color{blue}{y \cdot \frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}}\right)\right) \]

      3. distribute-rgt-neg-in 54.8%

         \[\leadsto x + \left(-\color{blue}{y \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)}\right) \]

      4. distribute-lft-neg-in 54.8%

         \[\leadsto x + \color{blue}{\left(-y\right) \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)} \]

      5. distribute-lft-neg-in 54.8%

         \[\leadsto x + \color{blue}{\left(-y \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      6. distribute-rgt-neg-in 54.8%

         \[\leadsto x + \color{blue}{y \cdot \left(-\left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      7. remove-double-neg 54.8%

         \[\leadsto x + y \cdot \color{blue}{\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}} \]

      8. fma-define 54.8%

         \[\leadsto x + y \cdot \frac{\color{blue}{\mathsf{fma}\left(z \cdot 0.0692910599291889 + 0.4917317610505968, z, 0.279195317918525\right)}}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

      9. fma-define 54.8%

         \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}, z, 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

      10. fma-define 54.8%

          \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}{\color{blue}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}} \]

   3. Simplified 54.8%

      \[\leadsto \color{blue}{x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 99.6%

      \[\leadsto x + y \cdot \color{blue}{\left(0.0692910599291889 + 0.07512208616047561 \cdot \frac{1}{z}\right)} \]
   6. Step-by-step derivation

      1. associate-*r/ 99.6%

         \[\leadsto x + y \cdot \left(0.0692910599291889 + \color{blue}{\frac{0.07512208616047561 \cdot 1}{z}}\right) \]

      2. metadata-eval 99.6%

         \[\leadsto x + y \cdot \left(0.0692910599291889 + \frac{\color{blue}{0.07512208616047561}}{z}\right) \]

   7. Simplified 99.6%

      \[\leadsto x + y \cdot \color{blue}{\left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)} \]

   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. Step-by-step derivation

      1. remove-double-neg 99.6%

         \[\leadsto x + \color{blue}{\left(-\left(-\frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      2. associate-/l* 99.8%

         \[\leadsto x + \left(-\left(-\color{blue}{y \cdot \frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}}\right)\right) \]

      3. distribute-rgt-neg-in 99.8%

         \[\leadsto x + \left(-\color{blue}{y \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)}\right) \]

      4. distribute-lft-neg-in 99.8%

         \[\leadsto x + \color{blue}{\left(-y\right) \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)} \]

      5. distribute-lft-neg-in 99.8%

         \[\leadsto x + \color{blue}{\left(-y \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      6. distribute-rgt-neg-in 99.8%

         \[\leadsto x + \color{blue}{y \cdot \left(-\left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      7. remove-double-neg 99.8%

         \[\leadsto x + y \cdot \color{blue}{\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}} \]

      8. fma-define 99.8%

         \[\leadsto x + y \cdot \frac{\color{blue}{\mathsf{fma}\left(z \cdot 0.0692910599291889 + 0.4917317610505968, z, 0.279195317918525\right)}}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

      9. fma-define 99.8%

         \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}, z, 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

      10. fma-define 99.8%

          \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}{\color{blue}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 99.8%

      \[\leadsto x + y \cdot \color{blue}{\left(0.08333333333333323 + -0.00277777777751721 \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \lor \neg \left(z \leq 5.1 \cdot 10^{-8}\right):\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.08333333333333323 + z \cdot -0.00277777777751721\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.9% accurate, 1.1× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.4) (not (<= z 5.1e-8)))
   (+ x (* y (+ 0.0692910599291889 (/ 0.07512208616047561 z))))
   (+ x (* y 0.08333333333333323))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.4) || !(z <= 5.1e-8)) {
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)));
	} else {
		tmp = x + (y * 0.08333333333333323);
	}
	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 <= (-5.4d0)) .or. (.not. (z <= 5.1d-8))) then
        tmp = x + (y * (0.0692910599291889d0 + (0.07512208616047561d0 / z)))
    else
        tmp = x + (y * 0.08333333333333323d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.4) || !(z <= 5.1e-8)) {
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)));
	} else {
		tmp = x + (y * 0.08333333333333323);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.4) or not (z <= 5.1e-8):
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)))
	else:
		tmp = x + (y * 0.08333333333333323)
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.4], N[Not[LessEqual[z, 5.1e-8]], $MachinePrecision]], N[(x + N[(y * N[(0.0692910599291889 + N[(0.07512208616047561 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 0.08333333333333323), $MachinePrecision]), $MachinePrecision]]

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. Step-by-step derivation

      1. remove-double-neg 44.9%

         \[\leadsto x + \color{blue}{\left(-\left(-\frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      2. associate-/l* 54.8%

         \[\leadsto x + \left(-\left(-\color{blue}{y \cdot \frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}}\right)\right) \]

      3. distribute-rgt-neg-in 54.8%

         \[\leadsto x + \left(-\color{blue}{y \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)}\right) \]

      4. distribute-lft-neg-in 54.8%

         \[\leadsto x + \color{blue}{\left(-y\right) \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)} \]

      5. distribute-lft-neg-in 54.8%

         \[\leadsto x + \color{blue}{\left(-y \cdot \left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      6. distribute-rgt-neg-in 54.8%

         \[\leadsto x + \color{blue}{y \cdot \left(-\left(-\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\right)\right)} \]

      7. remove-double-neg 54.8%

         \[\leadsto x + y \cdot \color{blue}{\frac{\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}} \]

      8. fma-define 54.8%

         \[\leadsto x + y \cdot \frac{\color{blue}{\mathsf{fma}\left(z \cdot 0.0692910599291889 + 0.4917317610505968, z, 0.279195317918525\right)}}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

      9. fma-define 54.8%

         \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}, z, 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

      10. fma-define 54.8%

          \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}{\color{blue}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}} \]

   3. Simplified 54.8%

      \[\leadsto \color{blue}{x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 99.6%

      \[\leadsto x + y \cdot \color{blue}{\left(0.0692910599291889 + 0.07512208616047561 \cdot \frac{1}{z}\right)} \]
   6. Step-by-step derivation

      1. associate-*r/ 99.6%

         \[\leadsto x + y \cdot \left(0.0692910599291889 + \color{blue}{\frac{0.07512208616047561 \cdot 1}{z}}\right) \]

      2. metadata-eval 99.6%

         \[\leadsto x + y \cdot \left(0.0692910599291889 + \frac{\color{blue}{0.07512208616047561}}{z}\right) \]

   7. Simplified 99.6%

      \[\leadsto x + y \cdot \color{blue}{\left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)} \]

   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. Step-by-step derivation

      1. +-commutative 99.6%

         \[\leadsto \color{blue}{\frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} + x} \]

      2. *-commutative 99.6%

         \[\leadsto \frac{\color{blue}{\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right) \cdot y}}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} + x \]

      3. associate-/l* 99.7%

         \[\leadsto \color{blue}{\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right) \cdot \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}} + x \]

      4. fma-define 99.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right)} \]

      5. *-commutative 99.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right)} + 0.279195317918525, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      6. fma-define 99.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z, z \cdot 0.0692910599291889 + 0.4917317610505968, 0.279195317918525\right)}, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      7. fma-define 99.7%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}, 0.279195317918525\right), \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      8. *-commutative 99.7%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\color{blue}{z \cdot \left(z + 6.012459259764103\right)} + 3.350343815022304}, x\right) \]

      9. fma-define 99.7%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\color{blue}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}}, x\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 98.9%

      \[\leadsto \color{blue}{x + 0.08333333333333323 \cdot y} \]
   6. Step-by-step derivation

      1. +-commutative 98.9%

         \[\leadsto \color{blue}{0.08333333333333323 \cdot y + x} \]

   7. Simplified 98.9%

      \[\leadsto \color{blue}{0.08333333333333323 \cdot y + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \lor \neg \left(z \leq 5.1 \cdot 10^{-8}\right):\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.08333333333333323\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 98.7% accurate, 1.4× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.4) (not (<= z 5.1e-8)))
   (+ x (* y 0.0692910599291889))
   (+ x (* y 0.08333333333333323))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.4) || !(z <= 5.1e-8)) {
		tmp = x + (y * 0.0692910599291889);
	} else {
		tmp = x + (y * 0.08333333333333323);
	}
	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 <= (-5.4d0)) .or. (.not. (z <= 5.1d-8))) then
        tmp = x + (y * 0.0692910599291889d0)
    else
        tmp = x + (y * 0.08333333333333323d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.4) || !(z <= 5.1e-8)) {
		tmp = x + (y * 0.0692910599291889);
	} else {
		tmp = x + (y * 0.08333333333333323);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.4) or not (z <= 5.1e-8):
		tmp = x + (y * 0.0692910599291889)
	else:
		tmp = x + (y * 0.08333333333333323)
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.4], N[Not[LessEqual[z, 5.1e-8]], $MachinePrecision]], N[(x + N[(y * 0.0692910599291889), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 0.08333333333333323), $MachinePrecision]), $MachinePrecision]]

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. Step-by-step derivation

      1. +-commutative 44.9%

         \[\leadsto \color{blue}{\frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} + x} \]

      2. *-commutative 44.9%

         \[\leadsto \frac{\color{blue}{\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right) \cdot y}}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} + x \]

      3. associate-/l* 53.3%

         \[\leadsto \color{blue}{\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right) \cdot \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}} + x \]

      4. fma-define 53.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right)} \]

      5. *-commutative 53.3%

         \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right)} + 0.279195317918525, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      6. fma-define 53.3%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z, z \cdot 0.0692910599291889 + 0.4917317610505968, 0.279195317918525\right)}, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      7. fma-define 53.3%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}, 0.279195317918525\right), \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      8. *-commutative 53.3%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\color{blue}{z \cdot \left(z + 6.012459259764103\right)} + 3.350343815022304}, x\right) \]

      9. fma-define 53.3%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\color{blue}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}}, x\right) \]

   3. Simplified 53.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 99.0%

      \[\leadsto \color{blue}{x + 0.0692910599291889 \cdot y} \]
   6. Step-by-step derivation

      1. +-commutative 99.0%

         \[\leadsto \color{blue}{0.0692910599291889 \cdot y + x} \]

   7. Simplified 99.0%

      \[\leadsto \color{blue}{0.0692910599291889 \cdot y + x} \]

   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. Step-by-step derivation

      1. +-commutative 99.6%

         \[\leadsto \color{blue}{\frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} + x} \]

      2. *-commutative 99.6%

         \[\leadsto \frac{\color{blue}{\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right) \cdot y}}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} + x \]

      3. associate-/l* 99.7%

         \[\leadsto \color{blue}{\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right) \cdot \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}} + x \]

      4. fma-define 99.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right)} \]

      5. *-commutative 99.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right)} + 0.279195317918525, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      6. fma-define 99.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z, z \cdot 0.0692910599291889 + 0.4917317610505968, 0.279195317918525\right)}, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      7. fma-define 99.7%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}, 0.279195317918525\right), \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      8. *-commutative 99.7%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\color{blue}{z \cdot \left(z + 6.012459259764103\right)} + 3.350343815022304}, x\right) \]

      9. fma-define 99.7%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\color{blue}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}}, x\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 98.9%

      \[\leadsto \color{blue}{x + 0.08333333333333323 \cdot y} \]
   6. Step-by-step derivation

      1. +-commutative 98.9%

         \[\leadsto \color{blue}{0.08333333333333323 \cdot y + x} \]

   7. Simplified 98.9%

      \[\leadsto \color{blue}{0.08333333333333323 \cdot y + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \lor \neg \left(z \leq 5.1 \cdot 10^{-8}\right):\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.08333333333333323\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-59} \lor \neg \left(z \leq 1.7 \cdot 10^{-239}\right):\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.08333333333333323\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.1e-59) (not (<= z 1.7e-239)))
   (+ x (* y 0.0692910599291889))
   (* y 0.08333333333333323)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.1e-59) || !(z <= 1.7e-239)) {
		tmp = x + (y * 0.0692910599291889);
	} else {
		tmp = y * 0.08333333333333323;
	}
	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 <= (-1.1d-59)) .or. (.not. (z <= 1.7d-239))) then
        tmp = x + (y * 0.0692910599291889d0)
    else
        tmp = y * 0.08333333333333323d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.1e-59) || !(z <= 1.7e-239)) {
		tmp = x + (y * 0.0692910599291889);
	} else {
		tmp = y * 0.08333333333333323;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.1e-59) or not (z <= 1.7e-239):
		tmp = x + (y * 0.0692910599291889)
	else:
		tmp = y * 0.08333333333333323
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.1e-59], N[Not[LessEqual[z, 1.7e-239]], $MachinePrecision]], N[(x + N[(y * 0.0692910599291889), $MachinePrecision]), $MachinePrecision], N[(y * 0.08333333333333323), $MachinePrecision]]

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. Step-by-step derivation

      1. +-commutative 63.1%

         \[\leadsto \color{blue}{\frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} + x} \]

      2. *-commutative 63.1%

         \[\leadsto \frac{\color{blue}{\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right) \cdot y}}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} + x \]

      3. associate-/l* 68.7%

         \[\leadsto \color{blue}{\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right) \cdot \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}} + x \]

      4. fma-define 68.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right)} \]

      5. *-commutative 68.8%

         \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right)} + 0.279195317918525, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      6. fma-define 68.8%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z, z \cdot 0.0692910599291889 + 0.4917317610505968, 0.279195317918525\right)}, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      7. fma-define 68.8%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}, 0.279195317918525\right), \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      8. *-commutative 68.8%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\color{blue}{z \cdot \left(z + 6.012459259764103\right)} + 3.350343815022304}, x\right) \]

      9. fma-define 68.8%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\color{blue}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}}, x\right) \]

   3. Simplified 68.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 88.6%

      \[\leadsto \color{blue}{x + 0.0692910599291889 \cdot y} \]
   6. Step-by-step derivation

      1. +-commutative 88.6%

         \[\leadsto \color{blue}{0.0692910599291889 \cdot y + x} \]

   7. Simplified 88.6%

      \[\leadsto \color{blue}{0.0692910599291889 \cdot y + x} \]

   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. Step-by-step derivation

      1. +-commutative 99.4%

         \[\leadsto \color{blue}{\frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} + x} \]

      2. *-commutative 99.4%

         \[\leadsto \frac{\color{blue}{\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right) \cdot y}}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} + x \]

      3. associate-/l* 99.6%

         \[\leadsto \color{blue}{\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right) \cdot \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}} + x \]

      4. fma-define 99.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right)} \]

      5. *-commutative 99.6%

         \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right)} + 0.279195317918525, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      6. fma-define 99.6%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z, z \cdot 0.0692910599291889 + 0.4917317610505968, 0.279195317918525\right)}, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      7. fma-define 99.6%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}, 0.279195317918525\right), \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      8. *-commutative 99.6%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\color{blue}{z \cdot \left(z + 6.012459259764103\right)} + 3.350343815022304}, x\right) \]

      9. fma-define 99.6%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\color{blue}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}}, x\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 99.8%

      \[\leadsto \color{blue}{x + 0.08333333333333323 \cdot y} \]
   6. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{0.08333333333333323 \cdot y + x} \]

   7. Simplified 99.8%

      \[\leadsto \color{blue}{0.08333333333333323 \cdot y + x} \]

   8. Taylor expanded in y around inf 73.4%

      \[\leadsto \color{blue}{0.08333333333333323 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-59} \lor \neg \left(z \leq 1.7 \cdot 10^{-239}\right):\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.08333333333333323\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+23} \lor \neg \left(y \leq 8200\right):\\ \;\;\;\;y \cdot 0.08333333333333323\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.8e+23) (not (<= y 8200.0))) (* y 0.08333333333333323) x))

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2.8d+23)) .or. (.not. (y <= 8200.0d0))) then
        tmp = y * 0.08333333333333323d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

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

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.8e+23) or not (y <= 8200.0):
		tmp = y * 0.08333333333333323
	else:
		tmp = x
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.8e+23], N[Not[LessEqual[y, 8200.0]], $MachinePrecision]], N[(y * 0.08333333333333323), $MachinePrecision], x]

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. Step-by-step derivation

      1. +-commutative 65.2%

         \[\leadsto \color{blue}{\frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} + x} \]

      2. *-commutative 65.2%

         \[\leadsto \frac{\color{blue}{\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right) \cdot y}}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} + x \]

      3. associate-/l* 75.6%

         \[\leadsto \color{blue}{\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right) \cdot \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}} + x \]

      4. fma-define 75.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right)} \]

      5. *-commutative 75.6%

         \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right)} + 0.279195317918525, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      6. fma-define 75.6%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z, z \cdot 0.0692910599291889 + 0.4917317610505968, 0.279195317918525\right)}, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      7. fma-define 75.6%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}, 0.279195317918525\right), \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      8. *-commutative 75.6%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\color{blue}{z \cdot \left(z + 6.012459259764103\right)} + 3.350343815022304}, x\right) \]

      9. fma-define 75.6%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\color{blue}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}}, x\right) \]

   3. Simplified 75.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 71.2%

      \[\leadsto \color{blue}{x + 0.08333333333333323 \cdot y} \]
   6. Step-by-step derivation

      1. +-commutative 71.2%

         \[\leadsto \color{blue}{0.08333333333333323 \cdot y + x} \]

   7. Simplified 71.2%

      \[\leadsto \color{blue}{0.08333333333333323 \cdot y + x} \]

   8. Taylor expanded in y around inf 52.5%

      \[\leadsto \color{blue}{0.08333333333333323 \cdot y} \]

   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. Step-by-step derivation

      1. +-commutative 77.7%

         \[\leadsto \color{blue}{\frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} + x} \]

      2. *-commutative 77.7%

         \[\leadsto \frac{\color{blue}{\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right) \cdot y}}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} + x \]

      3. associate-/l* 76.3%

         \[\leadsto \color{blue}{\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right) \cdot \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}} + x \]

      4. fma-define 76.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right)} \]

      5. *-commutative 76.4%

         \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right)} + 0.279195317918525, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      6. fma-define 76.4%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z, z \cdot 0.0692910599291889 + 0.4917317610505968, 0.279195317918525\right)}, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      7. fma-define 76.4%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}, 0.279195317918525\right), \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

      8. *-commutative 76.4%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\color{blue}{z \cdot \left(z + 6.012459259764103\right)} + 3.350343815022304}, x\right) \]

      9. fma-define 76.4%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\color{blue}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}}, x\right) \]

   3. Simplified 76.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 79.3%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+23} \lor \neg \left(y \leq 8200\right):\\ \;\;\;\;y \cdot 0.08333333333333323\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 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. Step-by-step derivation

   1. +-commutative 71.6%

      \[\leadsto \color{blue}{\frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} + x} \]

   2. *-commutative 71.6%

      \[\leadsto \frac{\color{blue}{\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right) \cdot y}}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} + x \]

   3. associate-/l* 76.0%

      \[\leadsto \color{blue}{\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right) \cdot \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}} + x \]

   4. fma-define 76.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right)} \]

   5. *-commutative 76.0%

      \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right)} + 0.279195317918525, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

   6. fma-define 76.0%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z, z \cdot 0.0692910599291889 + 0.4917317610505968, 0.279195317918525\right)}, \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

   7. fma-define 76.0%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}, 0.279195317918525\right), \frac{y}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}, x\right) \]

   8. *-commutative 76.0%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\color{blue}{z \cdot \left(z + 6.012459259764103\right)} + 3.350343815022304}, x\right) \]

   9. fma-define 76.0%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\color{blue}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}}, x\right) \]

3. Simplified 76.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right), \frac{y}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}, x\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 51.1%

   \[\leadsto \color{blue}{x} \]
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))))