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

Percentage Accurate: 69.4% → 99.6%

Time: 11.2s

Alternatives: 15

Speedup: 4.2×

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: 69.4% 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: 99.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} \leq 5 \cdot 10^{+304}:\\ \;\;\;\;x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{\mathsf{fma}\left(0.0692910599291889, z, 0.07512208616047561\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (/
       (*
        y
        (+
         (* z (+ (* z 0.0692910599291889) 0.4917317610505968))
         0.279195317918525))
       (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
      5e+304)
   (+
    x
    (*
     y
     (/
      (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
      (fma (+ z 6.012459259764103) z 3.350343815022304))))
   (+ x (/ y (/ z (fma 0.0692910599291889 z 0.07512208616047561))))))

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+304) {
		tmp = x + (y * (fma(fma(z, 0.0692910599291889, 0.4917317610505968), z, 0.279195317918525) / fma((z + 6.012459259764103), z, 3.350343815022304)));
	} else {
		tmp = x + (y / (z / fma(0.0692910599291889, z, 0.07512208616047561)));
	}
	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+304)
		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 / Float64(z / fma(0.0692910599291889, z, 0.07512208616047561))));
	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+304], 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 / N[(z / N[(0.0692910599291889 * z + 0.07512208616047561), $MachinePrecision]), $MachinePrecision]), $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))) < 4.9999999999999997e304

   1. Initial program 97.4%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Step-by-step derivation

      1. remove-double-neg 97.4%

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

      2. associate-/l* 99.7%

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

      3. distribute-rgt-neg-in 99.7%

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

      4. distribute-lft-neg-in 99.7%

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

      5. distribute-lft-neg-in 99.7%

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

      6. distribute-rgt-neg-in 99.7%

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

      7. remove-double-neg 99.7%

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

      8. fma-define 99.7%

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

      9. fma-define 99.7%

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

      10. fma-define 99.7%

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

   3. Simplified 99.7%

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

   if 4.9999999999999997e304 < (/.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. remove-double-neg 0.9%

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

      2. associate-/l* 14.8%

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

      3. distribute-rgt-neg-in 14.8%

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

      4. distribute-lft-neg-in 14.8%

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

      5. distribute-lft-neg-in 14.8%

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

      6. distribute-rgt-neg-in 14.8%

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

      7. remove-double-neg 14.8%

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

      8. fma-define 14.8%

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

      9. fma-define 14.8%

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

      10. fma-define 14.8%

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

   3. Simplified 14.8%

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

   5. Taylor expanded in z around -inf 99.5%

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

      1. mul-1-neg 99.5%

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

      2. unsub-neg 99.5%

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

      3. sub-neg 99.5%

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

      4. associate-*r/ 99.5%

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

      5. metadata-eval 99.5%

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

      6. metadata-eval 99.5%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in z around inf 99.5%

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

   9. Taylor expanded in z around 0 99.5%

      \[\leadsto x + y \cdot \color{blue}{\frac{0.07512208616047561 + 0.0692910599291889 \cdot z}{z}} \]
   10. Step-by-step derivation

       1. clear-num 99.5%

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

       2. un-div-inv 99.6%

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

       3. +-commutative 99.6%

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

       4. fma-define 99.6%

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

   11. Applied egg-rr 99.6%

       \[\leadsto x + \color{blue}{\frac{y}{\frac{z}{\mathsf{fma}\left(0.0692910599291889, z, 0.07512208616047561\right)}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} \leq 5 \cdot 10^{+304}:\\ \;\;\;\;x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{\mathsf{fma}\left(0.0692910599291889, z, 0.07512208616047561\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304\\ \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{t\_0} \leq 5 \cdot 10^{+304}:\\ \;\;\;\;x + \frac{y \cdot 0.279195317918525 + z \cdot \left(0.0692910599291889 \cdot \left(y \cdot z\right) + y \cdot 0.4917317610505968\right)}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{\mathsf{fma}\left(0.0692910599291889, z, 0.07512208616047561\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))
   (if (<=
        (/
         (*
          y
          (+
           (* z (+ (* z 0.0692910599291889) 0.4917317610505968))
           0.279195317918525))
         t_0)
        5e+304)
     (+
      x
      (/
       (+
        (* y 0.279195317918525)
        (* z (+ (* 0.0692910599291889 (* y z)) (* y 0.4917317610505968))))
       t_0))
     (+ x (/ y (/ z (fma 0.0692910599291889 z 0.07512208616047561)))))))

C

double code(double x, double y, double z) {
	double t_0 = (z * (z + 6.012459259764103)) + 3.350343815022304;
	double tmp;
	if (((y * ((z * ((z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / t_0) <= 5e+304) {
		tmp = x + (((y * 0.279195317918525) + (z * ((0.0692910599291889 * (y * z)) + (y * 0.4917317610505968)))) / t_0);
	} else {
		tmp = x + (y / (z / fma(0.0692910599291889, z, 0.07512208616047561)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * Float64(z + 6.012459259764103)) + 3.350343815022304)
	tmp = 0.0
	if (Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / t_0) <= 5e+304)
		tmp = Float64(x + Float64(Float64(Float64(y * 0.279195317918525) + Float64(z * Float64(Float64(0.0692910599291889 * Float64(y * z)) + Float64(y * 0.4917317610505968)))) / t_0));
	else
		tmp = Float64(x + Float64(y / Float64(z / fma(0.0692910599291889, z, 0.07512208616047561))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * N[(z + 6.012459259764103), $MachinePrecision]), $MachinePrecision] + 3.350343815022304), $MachinePrecision]}, If[LessEqual[N[(N[(y * N[(N[(z * N[(N[(z * 0.0692910599291889), $MachinePrecision] + 0.4917317610505968), $MachinePrecision]), $MachinePrecision] + 0.279195317918525), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision], 5e+304], N[(x + N[(N[(N[(y * 0.279195317918525), $MachinePrecision] + N[(z * N[(N[(0.0692910599291889 * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(y * 0.4917317610505968), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(z / N[(0.0692910599291889 * z + 0.07512208616047561), $MachinePrecision]), $MachinePrecision]), $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))) < 4.9999999999999997e304

   1. Initial program 97.4%

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

   3. Taylor expanded in z around 0 97.4%

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

   if 4.9999999999999997e304 < (/.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. remove-double-neg 0.9%

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

      2. associate-/l* 14.8%

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

      3. distribute-rgt-neg-in 14.8%

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

      4. distribute-lft-neg-in 14.8%

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

      5. distribute-lft-neg-in 14.8%

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

      6. distribute-rgt-neg-in 14.8%

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

      7. remove-double-neg 14.8%

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

      8. fma-define 14.8%

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

      9. fma-define 14.8%

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

      10. fma-define 14.8%

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

   3. Simplified 14.8%

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

   5. Taylor expanded in z around -inf 99.5%

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

      1. mul-1-neg 99.5%

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

      2. unsub-neg 99.5%

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

      3. sub-neg 99.5%

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

      4. associate-*r/ 99.5%

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

      5. metadata-eval 99.5%

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

      6. metadata-eval 99.5%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in z around inf 99.5%

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

   9. Taylor expanded in z around 0 99.5%

      \[\leadsto x + y \cdot \color{blue}{\frac{0.07512208616047561 + 0.0692910599291889 \cdot z}{z}} \]
   10. Step-by-step derivation

       1. clear-num 99.5%

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

       2. un-div-inv 99.6%

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

       3. +-commutative 99.6%

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

       4. fma-define 99.6%

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

   11. Applied egg-rr 99.6%

       \[\leadsto x + \color{blue}{\frac{y}{\frac{z}{\mathsf{fma}\left(0.0692910599291889, z, 0.07512208616047561\right)}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} \leq 5 \cdot 10^{+304}:\\ \;\;\;\;x + \frac{y \cdot 0.279195317918525 + z \cdot \left(0.0692910599291889 \cdot \left(y \cdot z\right) + y \cdot 0.4917317610505968\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{\mathsf{fma}\left(0.0692910599291889, z, 0.07512208616047561\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304\\ \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{t\_0} \leq 5 \cdot 10^{+304}:\\ \;\;\;\;x + \frac{y \cdot 0.279195317918525 + z \cdot \left(0.0692910599291889 \cdot \left(y \cdot z\right) + y \cdot 0.4917317610505968\right)}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))
   (if (<=
        (/
         (*
          y
          (+
           (* z (+ (* z 0.0692910599291889) 0.4917317610505968))
           0.279195317918525))
         t_0)
        5e+304)
     (+
      x
      (/
       (+
        (* y 0.279195317918525)
        (* z (+ (* 0.0692910599291889 (* y z)) (* y 0.4917317610505968))))
       t_0))
     (+ x (* y 0.0692910599291889)))))

C

double code(double x, double y, double z) {
	double t_0 = (z * (z + 6.012459259764103)) + 3.350343815022304;
	double tmp;
	if (((y * ((z * ((z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / t_0) <= 5e+304) {
		tmp = x + (((y * 0.279195317918525) + (z * ((0.0692910599291889 * (y * z)) + (y * 0.4917317610505968)))) / t_0);
	} 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 = (z * (z + 6.012459259764103d0)) + 3.350343815022304d0
    if (((y * ((z * ((z * 0.0692910599291889d0) + 0.4917317610505968d0)) + 0.279195317918525d0)) / t_0) <= 5d+304) then
        tmp = x + (((y * 0.279195317918525d0) + (z * ((0.0692910599291889d0 * (y * z)) + (y * 0.4917317610505968d0)))) / t_0)
    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 = (z * (z + 6.012459259764103)) + 3.350343815022304;
	double tmp;
	if (((y * ((z * ((z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / t_0) <= 5e+304) {
		tmp = x + (((y * 0.279195317918525) + (z * ((0.0692910599291889 * (y * z)) + (y * 0.4917317610505968)))) / t_0);
	} else {
		tmp = x + (y * 0.0692910599291889);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z * (z + 6.012459259764103)) + 3.350343815022304
	tmp = 0
	if ((y * ((z * ((z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / t_0) <= 5e+304:
		tmp = x + (((y * 0.279195317918525) + (z * ((0.0692910599291889 * (y * z)) + (y * 0.4917317610505968)))) / t_0)
	else:
		tmp = x + (y * 0.0692910599291889)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * Float64(z + 6.012459259764103)) + 3.350343815022304)
	tmp = 0.0
	if (Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / t_0) <= 5e+304)
		tmp = Float64(x + Float64(Float64(Float64(y * 0.279195317918525) + Float64(z * Float64(Float64(0.0692910599291889 * Float64(y * z)) + Float64(y * 0.4917317610505968)))) / t_0));
	else
		tmp = Float64(x + Float64(y * 0.0692910599291889));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z * (z + 6.012459259764103)) + 3.350343815022304;
	tmp = 0.0;
	if (((y * ((z * ((z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / t_0) <= 5e+304)
		tmp = x + (((y * 0.279195317918525) + (z * ((0.0692910599291889 * (y * z)) + (y * 0.4917317610505968)))) / t_0);
	else
		tmp = x + (y * 0.0692910599291889);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * N[(z + 6.012459259764103), $MachinePrecision]), $MachinePrecision] + 3.350343815022304), $MachinePrecision]}, If[LessEqual[N[(N[(y * N[(N[(z * N[(N[(z * 0.0692910599291889), $MachinePrecision] + 0.4917317610505968), $MachinePrecision]), $MachinePrecision] + 0.279195317918525), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision], 5e+304], N[(x + N[(N[(N[(y * 0.279195317918525), $MachinePrecision] + N[(z * N[(N[(0.0692910599291889 * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(y * 0.4917317610505968), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $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))) < 4.9999999999999997e304

   1. Initial program 97.4%

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

   3. Taylor expanded in z around 0 97.4%

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

   if 4.9999999999999997e304 < (/.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* 14.8%

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

      4. fma-define 14.8%

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

      5. *-commutative 14.8%

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

      6. fma-define 14.8%

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

      7. fma-define 14.8%

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

      8. *-commutative 14.8%

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

      9. fma-define 14.8%

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

   3. Simplified 14.8%

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

   5. Taylor expanded in z around inf 99.5%

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

      1. +-commutative 99.5%

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

   7. Simplified 99.5%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} \leq 5 \cdot 10^{+304}:\\ \;\;\;\;x + \frac{y \cdot 0.279195317918525 + z \cdot \left(0.0692910599291889 \cdot \left(y \cdot z\right) + y \cdot 0.4917317610505968\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304}\\ \mathbf{if}\;t\_0 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;t\_0 + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \end{array} \end{array} \]

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+304) (+ 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+304) {
		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+304) 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+304) {
		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+304:
		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+304)
		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+304)
		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+304], 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))) < 4.9999999999999997e304

   1. Initial program 97.4%

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

   if 4.9999999999999997e304 < (/.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* 14.8%

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

      4. fma-define 14.8%

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

      5. *-commutative 14.8%

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

      6. fma-define 14.8%

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

      7. fma-define 14.8%

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

      8. *-commutative 14.8%

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

      9. fma-define 14.8%

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

   3. Simplified 14.8%

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

   5. Taylor expanded in z around inf 99.5%

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

      1. +-commutative 99.5%

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

   7. Simplified 99.5%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} \leq 5 \cdot 10^{+304}:\\ \;\;\;\;\frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 3.5\right):\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 - \frac{\frac{0.4046220386999212}{z} + -0.07512208616047561}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.08333333333333323 + z \cdot \left(z \cdot \left(0.0007936505811533442 + z \cdot -0.0005951669793454025\right) - 0.00277777777751721\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.5) (not (<= z 3.5)))
   (+
    x
    (*
     y
     (-
      0.0692910599291889
      (/ (+ (/ 0.4046220386999212 z) -0.07512208616047561) z))))
   (+
    x
    (*
     y
     (+
      0.08333333333333323
      (*
       z
       (-
        (* z (+ 0.0007936505811533442 (* z -0.0005951669793454025)))
        0.00277777777751721)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.5) || !(z <= 3.5)) {
		tmp = x + (y * (0.0692910599291889 - (((0.4046220386999212 / z) + -0.07512208616047561) / z)));
	} else {
		tmp = x + (y * (0.08333333333333323 + (z * ((z * (0.0007936505811533442 + (z * -0.0005951669793454025))) - 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 <= (-5.5d0)) .or. (.not. (z <= 3.5d0))) then
        tmp = x + (y * (0.0692910599291889d0 - (((0.4046220386999212d0 / z) + (-0.07512208616047561d0)) / z)))
    else
        tmp = x + (y * (0.08333333333333323d0 + (z * ((z * (0.0007936505811533442d0 + (z * (-0.0005951669793454025d0)))) - 0.00277777777751721d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.5) || !(z <= 3.5)) {
		tmp = x + (y * (0.0692910599291889 - (((0.4046220386999212 / z) + -0.07512208616047561) / z)));
	} else {
		tmp = x + (y * (0.08333333333333323 + (z * ((z * (0.0007936505811533442 + (z * -0.0005951669793454025))) - 0.00277777777751721))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.5) or not (z <= 3.5):
		tmp = x + (y * (0.0692910599291889 - (((0.4046220386999212 / z) + -0.07512208616047561) / z)))
	else:
		tmp = x + (y * (0.08333333333333323 + (z * ((z * (0.0007936505811533442 + (z * -0.0005951669793454025))) - 0.00277777777751721))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.5) || !(z <= 3.5))
		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 * Float64(0.0007936505811533442 + Float64(z * -0.0005951669793454025))) - 0.00277777777751721)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.5) || ~((z <= 3.5)))
		tmp = x + (y * (0.0692910599291889 - (((0.4046220386999212 / z) + -0.07512208616047561) / z)));
	else
		tmp = x + (y * (0.08333333333333323 + (z * ((z * (0.0007936505811533442 + (z * -0.0005951669793454025))) - 0.00277777777751721))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.5], N[Not[LessEqual[z, 3.5]], $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 * N[(0.0007936505811533442 + N[(z * -0.0005951669793454025), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 0.00277777777751721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5 or 3.5 < z

   1. Initial program 34.2%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Step-by-step derivation

      1. remove-double-neg 34.2%

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

      2. associate-/l* 45.7%

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

      3. distribute-rgt-neg-in 45.7%

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

      4. distribute-lft-neg-in 45.7%

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

      5. distribute-lft-neg-in 45.7%

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

      6. distribute-rgt-neg-in 45.7%

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

      7. remove-double-neg 45.7%

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

      8. fma-define 45.7%

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

      9. fma-define 45.7%

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

      10. fma-define 45.7%

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

   3. Simplified 45.7%

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

   5. Taylor expanded in z around -inf 99.1%

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

      1. mul-1-neg 99.1%

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

      2. unsub-neg 99.1%

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

      3. sub-neg 99.1%

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

      4. associate-*r/ 99.1%

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

      5. metadata-eval 99.1%

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

      6. metadata-eval 99.1%

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

   7. Simplified 99.1%

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

   if -5.5 < z < 3.5

   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%

      \[\leadsto x + y \cdot \color{blue}{\left(0.08333333333333323 + z \cdot \left(z \cdot \left(0.0007936505811533442 + -0.0005951669793454025 \cdot z\right) - 0.00277777777751721\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 3.5\right):\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 - \frac{\frac{0.4046220386999212}{z} + -0.07512208616047561}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.08333333333333323 + z \cdot \left(z \cdot \left(0.0007936505811533442 + z \cdot -0.0005951669793454025\right) - 0.00277777777751721\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 4.8\right):\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 - \frac{\frac{0.4046220386999212}{z} + -0.07512208616047561}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.08333333333333323 + z \cdot \left(z \cdot 0.0007936505811533442 - 0.00277777777751721\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.5) (not (<= z 4.8)))
   (+
    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 <= -5.5) || !(z <= 4.8)) {
		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 <= (-5.5d0)) .or. (.not. (z <= 4.8d0))) 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 <= -5.5) || !(z <= 4.8)) {
		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 <= -5.5) or not (z <= 4.8):
		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 <= -5.5) || !(z <= 4.8))
		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 <= -5.5) || ~((z <= 4.8)))
		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, -5.5], N[Not[LessEqual[z, 4.8]], $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 < -5.5 or 4.79999999999999982 < z

   1. Initial program 34.2%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Step-by-step derivation

      1. remove-double-neg 34.2%

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

      2. associate-/l* 45.7%

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

      3. distribute-rgt-neg-in 45.7%

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

      4. distribute-lft-neg-in 45.7%

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

      5. distribute-lft-neg-in 45.7%

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

      6. distribute-rgt-neg-in 45.7%

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

      7. remove-double-neg 45.7%

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

      8. fma-define 45.7%

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

      9. fma-define 45.7%

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

      10. fma-define 45.7%

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

   3. Simplified 45.7%

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

   5. Taylor expanded in z around -inf 99.1%

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

      1. mul-1-neg 99.1%

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

      2. unsub-neg 99.1%

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

      3. sub-neg 99.1%

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

      4. associate-*r/ 99.1%

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

      5. metadata-eval 99.1%

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

      6. metadata-eval 99.1%

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

   7. Simplified 99.1%

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

   if -5.5 < z < 4.79999999999999982

   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 99.7%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 4.8\right):\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 - \frac{\frac{0.4046220386999212}{z} + -0.07512208616047561}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.08333333333333323 + z \cdot \left(z \cdot 0.0007936505811533442 - 0.00277777777751721\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 4.4\right):\\ \;\;\;\;x + y \cdot \frac{z \cdot 0.0692910599291889 + 0.07512208616047561}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.08333333333333323 + z \cdot \left(z \cdot 0.0007936505811533442 - 0.00277777777751721\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.5) (not (<= z 4.4)))
   (+ x (* y (/ (+ (* z 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 <= -5.5) || !(z <= 4.4)) {
		tmp = x + (y * (((z * 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 <= (-5.5d0)) .or. (.not. (z <= 4.4d0))) then
        tmp = x + (y * (((z * 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 <= -5.5) || !(z <= 4.4)) {
		tmp = x + (y * (((z * 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 <= -5.5) or not (z <= 4.4):
		tmp = x + (y * (((z * 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 <= -5.5) || !(z <= 4.4))
		tmp = Float64(x + Float64(y * Float64(Float64(Float64(z * 0.0692910599291889) + 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 <= -5.5) || ~((z <= 4.4)))
		tmp = x + (y * (((z * 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, -5.5], N[Not[LessEqual[z, 4.4]], $MachinePrecision]], N[(x + N[(y * N[(N[(N[(z * 0.0692910599291889), $MachinePrecision] + 0.07512208616047561), $MachinePrecision] / z), $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 < -5.5 or 4.4000000000000004 < z

   1. Initial program 34.2%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Step-by-step derivation

      1. remove-double-neg 34.2%

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

      2. associate-/l* 45.7%

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

      3. distribute-rgt-neg-in 45.7%

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

      4. distribute-lft-neg-in 45.7%

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

      5. distribute-lft-neg-in 45.7%

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

      6. distribute-rgt-neg-in 45.7%

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

      7. remove-double-neg 45.7%

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

      8. fma-define 45.7%

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

      9. fma-define 45.7%

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

      10. fma-define 45.7%

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

   3. Simplified 45.7%

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

   5. Taylor expanded in z around -inf 99.1%

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

      1. mul-1-neg 99.1%

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

      2. unsub-neg 99.1%

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

      3. sub-neg 99.1%

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

      4. associate-*r/ 99.1%

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

      5. metadata-eval 99.1%

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

      6. metadata-eval 99.1%

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

   7. Simplified 99.1%

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

   8. Taylor expanded in z around inf 98.8%

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

   9. Taylor expanded in z around 0 98.8%

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

   if -5.5 < z < 4.4000000000000004

   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 99.7%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 4.4\right):\\ \;\;\;\;x + y \cdot \frac{z \cdot 0.0692910599291889 + 0.07512208616047561}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.08333333333333323 + z \cdot \left(z \cdot 0.0007936505811533442 - 0.00277777777751721\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 5\right):\\ \;\;\;\;x + y \cdot \frac{z \cdot 0.0692910599291889 + 0.07512208616047561}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.08333333333333323 + z \cdot -0.00277777777751721\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.5) (not (<= z 5.0)))
   (+ x (* y (/ (+ (* z 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 <= -5.5) || !(z <= 5.0)) {
		tmp = x + (y * (((z * 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 <= (-5.5d0)) .or. (.not. (z <= 5.0d0))) then
        tmp = x + (y * (((z * 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 <= -5.5) || !(z <= 5.0)) {
		tmp = x + (y * (((z * 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 <= -5.5) or not (z <= 5.0):
		tmp = x + (y * (((z * 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 <= -5.5) || !(z <= 5.0))
		tmp = Float64(x + Float64(y * Float64(Float64(Float64(z * 0.0692910599291889) + 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 <= -5.5) || ~((z <= 5.0)))
		tmp = x + (y * (((z * 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, -5.5], N[Not[LessEqual[z, 5.0]], $MachinePrecision]], N[(x + N[(y * N[(N[(N[(z * 0.0692910599291889), $MachinePrecision] + 0.07512208616047561), $MachinePrecision] / z), $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 < -5.5 or 5 < z

   1. Initial program 34.2%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Step-by-step derivation

      1. remove-double-neg 34.2%

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

      2. associate-/l* 45.7%

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

      3. distribute-rgt-neg-in 45.7%

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

      4. distribute-lft-neg-in 45.7%

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

      5. distribute-lft-neg-in 45.7%

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

      6. distribute-rgt-neg-in 45.7%

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

      7. remove-double-neg 45.7%

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

      8. fma-define 45.7%

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

      9. fma-define 45.7%

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

      10. fma-define 45.7%

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

   3. Simplified 45.7%

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

   5. Taylor expanded in z around -inf 99.1%

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

      1. mul-1-neg 99.1%

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

      2. unsub-neg 99.1%

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

      3. sub-neg 99.1%

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

      4. associate-*r/ 99.1%

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

      5. metadata-eval 99.1%

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

      6. metadata-eval 99.1%

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

   7. Simplified 99.1%

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

   8. Taylor expanded in z around inf 98.8%

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

   9. Taylor expanded in z around 0 98.8%

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

   if -5.5 < z < 5

   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 99.5%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 5\right):\\ \;\;\;\;x + y \cdot \frac{z \cdot 0.0692910599291889 + 0.07512208616047561}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.08333333333333323 + z \cdot -0.00277777777751721\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 99.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 5.2\right):\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.08333333333333323 + z \cdot -0.00277777777751721\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.5) (not (<= z 5.2)))
   (+ 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 <= -5.5) || !(z <= 5.2)) {
		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 <= (-5.5d0)) .or. (.not. (z <= 5.2d0))) 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 <= -5.5) || !(z <= 5.2)) {
		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 <= -5.5) or not (z <= 5.2):
		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 <= -5.5) || !(z <= 5.2))
		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 <= -5.5) || ~((z <= 5.2)))
		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, -5.5], N[Not[LessEqual[z, 5.2]], $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 < -5.5 or 5.20000000000000018 < z

   1. Initial program 34.2%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Step-by-step derivation

      1. remove-double-neg 34.2%

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

      2. associate-/l* 45.7%

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

      3. distribute-rgt-neg-in 45.7%

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

      4. distribute-lft-neg-in 45.7%

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

      5. distribute-lft-neg-in 45.7%

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

      6. distribute-rgt-neg-in 45.7%

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

      7. remove-double-neg 45.7%

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

      8. fma-define 45.7%

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

      9. fma-define 45.7%

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

      10. fma-define 45.7%

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

   3. Simplified 45.7%

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

   5. Taylor expanded in z around inf 98.8%

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

      1. associate-*r/ 98.8%

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

      2. metadata-eval 98.8%

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

   7. Simplified 98.8%

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

   if -5.5 < z < 5.20000000000000018

   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 99.5%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 5.2\right):\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.08333333333333323 + z \cdot -0.00277777777751721\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 5.4\right):\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.08333333333333323\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.5) (not (<= z 5.4)))
   (+ x (* y (+ 0.0692910599291889 (/ 0.07512208616047561 z))))
   (+ x (* y 0.08333333333333323))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.5) || !(z <= 5.4)) {
		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 <= (-5.5d0)) .or. (.not. (z <= 5.4d0))) 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 <= -5.5) || !(z <= 5.4)) {
		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 <= -5.5) or not (z <= 5.4):
		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 <= -5.5) || !(z <= 5.4))
		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 <= -5.5) || ~((z <= 5.4)))
		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, -5.5], N[Not[LessEqual[z, 5.4]], $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 < -5.5 or 5.4000000000000004 < z

   1. Initial program 34.2%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Step-by-step derivation

      1. remove-double-neg 34.2%

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

      2. associate-/l* 45.7%

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

      3. distribute-rgt-neg-in 45.7%

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

      4. distribute-lft-neg-in 45.7%

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

      5. distribute-lft-neg-in 45.7%

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

      6. distribute-rgt-neg-in 45.7%

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

      7. remove-double-neg 45.7%

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

      8. fma-define 45.7%

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

      9. fma-define 45.7%

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

      10. fma-define 45.7%

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

   3. Simplified 45.7%

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

   5. Taylor expanded in z around inf 98.8%

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

      1. associate-*r/ 98.8%

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

      2. metadata-eval 98.8%

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

   7. Simplified 98.8%

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

   if -5.5 < z < 5.4000000000000004

   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* 99.6%

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

      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 98.8%

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

      1. +-commutative 98.8%

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

   7. Simplified 98.8%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 5.4\right):\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.08333333333333323\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -48000000:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-250}:\\ \;\;\;\;y \cdot 0.08333333333333323\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-23}:\\ \;\;\;\;y \cdot 0.0692910599291889\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -48000000.0)
   x
   (if (<= x -5.4e-250)
     (* y 0.08333333333333323)
     (if (<= x 7e-23) (* y 0.0692910599291889) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -48000000.0) {
		tmp = x;
	} else if (x <= -5.4e-250) {
		tmp = y * 0.08333333333333323;
	} else if (x <= 7e-23) {
		tmp = y * 0.0692910599291889;
	} 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 (x <= (-48000000.0d0)) then
        tmp = x
    else if (x <= (-5.4d-250)) then
        tmp = y * 0.08333333333333323d0
    else if (x <= 7d-23) then
        tmp = y * 0.0692910599291889d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -48000000.0) {
		tmp = x;
	} else if (x <= -5.4e-250) {
		tmp = y * 0.08333333333333323;
	} else if (x <= 7e-23) {
		tmp = y * 0.0692910599291889;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -48000000.0:
		tmp = x
	elif x <= -5.4e-250:
		tmp = y * 0.08333333333333323
	elif x <= 7e-23:
		tmp = y * 0.0692910599291889
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -48000000.0)
		tmp = x;
	elseif (x <= -5.4e-250)
		tmp = Float64(y * 0.08333333333333323);
	elseif (x <= 7e-23)
		tmp = Float64(y * 0.0692910599291889);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -48000000.0)
		tmp = x;
	elseif (x <= -5.4e-250)
		tmp = y * 0.08333333333333323;
	elseif (x <= 7e-23)
		tmp = y * 0.0692910599291889;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -48000000.0], x, If[LessEqual[x, -5.4e-250], N[(y * 0.08333333333333323), $MachinePrecision], If[LessEqual[x, 7e-23], N[(y * 0.0692910599291889), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.8e7 or 6.99999999999999987e-23 < x

   1. Initial program 61.6%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Step-by-step derivation

      1. +-commutative 61.6%

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

      2. *-commutative 61.6%

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

      3. associate-/l* 68.5%

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

      4. fma-define 68.5%

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

      5. *-commutative 68.5%

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

      6. fma-define 68.5%

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

      7. fma-define 68.5%

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

      8. *-commutative 68.5%

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

      9. fma-define 68.5%

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

   3. Simplified 68.5%

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

   5. Taylor expanded in y around 0 77.9%

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

   if -4.8e7 < x < -5.40000000000000004e-250

   1. Initial program 70.4%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Step-by-step derivation

      1. +-commutative 70.4%

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

      2. *-commutative 70.4%

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

      3. associate-/l* 75.4%

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

      4. fma-define 75.4%

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

      5. *-commutative 75.4%

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

      6. fma-define 75.4%

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

      7. fma-define 75.4%

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

      8. *-commutative 75.4%

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

      9. fma-define 75.4%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in x around inf 52.8%

      \[\leadsto \color{blue}{x \cdot \left(1 + \frac{y \cdot \left(0.279195317918525 + z \cdot \left(0.4917317610505968 + 0.0692910599291889 \cdot z\right)\right)}{x \cdot \left(3.350343815022304 + z \cdot \left(6.012459259764103 + z\right)\right)}\right)} \]
   6. Step-by-step derivation

      1. +-commutative 52.8%

         \[\leadsto x \cdot \color{blue}{\left(\frac{y \cdot \left(0.279195317918525 + z \cdot \left(0.4917317610505968 + 0.0692910599291889 \cdot z\right)\right)}{x \cdot \left(3.350343815022304 + z \cdot \left(6.012459259764103 + z\right)\right)} + 1\right)} \]

      2. times-frac 52.9%

         \[\leadsto x \cdot \left(\color{blue}{\frac{y}{x} \cdot \frac{0.279195317918525 + z \cdot \left(0.4917317610505968 + 0.0692910599291889 \cdot z\right)}{3.350343815022304 + z \cdot \left(6.012459259764103 + z\right)}} + 1\right) \]

      3. +-commutative 52.9%

         \[\leadsto x \cdot \left(\frac{y}{x} \cdot \frac{\color{blue}{z \cdot \left(0.4917317610505968 + 0.0692910599291889 \cdot z\right) + 0.279195317918525}}{3.350343815022304 + z \cdot \left(6.012459259764103 + z\right)} + 1\right) \]

      4. +-commutative 52.9%

         \[\leadsto x \cdot \left(\frac{y}{x} \cdot \frac{z \cdot \color{blue}{\left(0.0692910599291889 \cdot z + 0.4917317610505968\right)} + 0.279195317918525}{3.350343815022304 + z \cdot \left(6.012459259764103 + z\right)} + 1\right) \]

      5. *-commutative 52.9%

         \[\leadsto x \cdot \left(\frac{y}{x} \cdot \frac{z \cdot \left(\color{blue}{z \cdot 0.0692910599291889} + 0.4917317610505968\right) + 0.279195317918525}{3.350343815022304 + z \cdot \left(6.012459259764103 + z\right)} + 1\right) \]

      6. fma-define 52.9%

         \[\leadsto x \cdot \left(\frac{y}{x} \cdot \frac{z \cdot \color{blue}{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)} + 0.279195317918525}{3.350343815022304 + z \cdot \left(6.012459259764103 + z\right)} + 1\right) \]

      7. fma-define 52.9%

         \[\leadsto x \cdot \left(\frac{y}{x} \cdot \frac{\color{blue}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right)}}{3.350343815022304 + z \cdot \left(6.012459259764103 + z\right)} + 1\right) \]

      8. +-commutative 52.9%

         \[\leadsto x \cdot \left(\frac{y}{x} \cdot \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right)}{3.350343815022304 + z \cdot \color{blue}{\left(z + 6.012459259764103\right)}} + 1\right) \]

      9. +-commutative 52.9%

         \[\leadsto x \cdot \left(\frac{y}{x} \cdot \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right)}{\color{blue}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304}} + 1\right) \]

      10. fma-undefine 52.9%

          \[\leadsto x \cdot \left(\frac{y}{x} \cdot \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right)}{\color{blue}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}} + 1\right) \]

      11. fma-define 52.9%

          \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(\frac{y}{x}, \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right)}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}, 1\right)} \]

   7. Simplified 52.9%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(\frac{y}{x}, \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right)}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}, 1\right)} \]

   8. Taylor expanded in x around 0 57.4%

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

   9. Taylor expanded in z around 0 56.8%

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

       1. *-commutative 56.8%

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

   11. Simplified 56.8%

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

   if -5.40000000000000004e-250 < x < 6.99999999999999987e-23

   1. Initial program 65.6%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Step-by-step derivation

      1. +-commutative 65.6%

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

      2. *-commutative 65.6%

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

      3. associate-/l* 69.0%

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

      4. fma-define 69.0%

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

      5. *-commutative 69.0%

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

      6. fma-define 69.0%

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

      7. fma-define 69.1%

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

      8. *-commutative 69.1%

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

      9. fma-define 69.1%

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

   3. Simplified 69.1%

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

   5. Taylor expanded in z around inf 75.6%

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

      1. +-commutative 75.6%

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

   7. Simplified 75.6%

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

   8. Taylor expanded in y around inf 59.0%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -48000000:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-250}:\\ \;\;\;\;y \cdot 0.08333333333333323\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-23}:\\ \;\;\;\;y \cdot 0.0692910599291889\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 98.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 6.2\right):\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.08333333333333323\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.5) (not (<= z 6.2)))
   (+ x (* y 0.0692910599291889))
   (+ x (* y 0.08333333333333323))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.5) || !(z <= 6.2)) {
		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 <= (-5.5d0)) .or. (.not. (z <= 6.2d0))) 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 <= -5.5) || !(z <= 6.2)) {
		tmp = x + (y * 0.0692910599291889);
	} else {
		tmp = x + (y * 0.08333333333333323);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.5) or not (z <= 6.2):
		tmp = x + (y * 0.0692910599291889)
	else:
		tmp = x + (y * 0.08333333333333323)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.5) || !(z <= 6.2))
		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 <= -5.5) || ~((z <= 6.2)))
		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, -5.5], N[Not[LessEqual[z, 6.2]], $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 < -5.5 or 6.20000000000000018 < z

   1. Initial program 34.2%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Step-by-step derivation

      1. +-commutative 34.2%

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

      2. *-commutative 34.2%

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

      3. associate-/l* 44.7%

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

      4. fma-define 44.7%

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

      5. *-commutative 44.7%

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

      6. fma-define 44.7%

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

      7. fma-define 44.7%

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

      8. *-commutative 44.7%

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

      9. fma-define 44.7%

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

   3. Simplified 44.7%

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

   5. Taylor expanded in z around inf 98.1%

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

      1. +-commutative 98.1%

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

   7. Simplified 98.1%

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

   if -5.5 < z < 6.20000000000000018

   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* 99.6%

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

      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 98.8%

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

      1. +-commutative 98.8%

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

   7. Simplified 98.8%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 6.2\right):\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.08333333333333323\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 60.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+58} \lor \neg \left(y \leq 2.8 \cdot 10^{+34}\right):\\ \;\;\;\;y \cdot 0.0692910599291889\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.12e+58) (not (<= y 2.8e+34))) (* y 0.0692910599291889) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.12e+58) || !(y <= 2.8e+34)) {
		tmp = y * 0.0692910599291889;
	} 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 <= (-1.12d+58)) .or. (.not. (y <= 2.8d+34))) then
        tmp = y * 0.0692910599291889d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.12e+58) || !(y <= 2.8e+34)) {
		tmp = y * 0.0692910599291889;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.12e+58) or not (y <= 2.8e+34):
		tmp = y * 0.0692910599291889
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.12e+58) || !(y <= 2.8e+34))
		tmp = Float64(y * 0.0692910599291889);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.12e+58) || ~((y <= 2.8e+34)))
		tmp = y * 0.0692910599291889;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.12e+58], N[Not[LessEqual[y, 2.8e+34]], $MachinePrecision]], N[(y * 0.0692910599291889), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.12e58 or 2.80000000000000008e34 < y

   1. Initial program 59.3%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Step-by-step derivation

      1. +-commutative 59.3%

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

      2. *-commutative 59.3%

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

      3. associate-/l* 72.9%

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

      4. fma-define 72.9%

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

      5. *-commutative 72.9%

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

      6. fma-define 72.9%

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

      7. fma-define 72.9%

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

      8. *-commutative 72.9%

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

      9. fma-define 72.9%

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

   3. Simplified 72.9%

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

   5. Taylor expanded in z around inf 70.2%

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

      1. +-commutative 70.2%

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

   7. Simplified 70.2%

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

   8. Taylor expanded in y around inf 52.4%

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

   if -1.12e58 < y < 2.80000000000000008e34

   1. Initial program 68.5%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Step-by-step derivation

      1. +-commutative 68.5%

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

      2. *-commutative 68.5%

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

      3. associate-/l* 68.2%

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

      4. fma-define 68.2%

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

      5. *-commutative 68.2%

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

      6. fma-define 68.2%

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

      7. fma-define 68.2%

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

      8. *-commutative 68.2%

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

      9. fma-define 68.2%

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

   3. Simplified 68.2%

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

   5. Taylor expanded in y around 0 73.4%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+58} \lor \neg \left(y \leq 2.8 \cdot 10^{+34}\right):\\ \;\;\;\;y \cdot 0.0692910599291889\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 79.2% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ x + y \cdot 0.0692910599291889 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* y 0.0692910599291889)))

C

double code(double x, double y, double z) {
	return x + (y * 0.0692910599291889);
}

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 * 0.0692910599291889d0)
end function

Java

public static double code(double x, double y, double z) {
	return x + (y * 0.0692910599291889);
}

Python

def code(x, y, z):
	return x + (y * 0.0692910599291889)

Julia

function code(x, y, z)
	return Float64(x + Float64(y * 0.0692910599291889))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (y * 0.0692910599291889);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(y * 0.0692910599291889), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 64.6%

   \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
2. Step-by-step derivation

   1. +-commutative 64.6%

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

   2. *-commutative 64.6%

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

   3. associate-/l* 70.2%

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

   4. fma-define 70.2%

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

   5. *-commutative 70.2%

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

   6. fma-define 70.2%

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

   7. fma-define 70.2%

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

   8. *-commutative 70.2%

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

   9. fma-define 70.2%

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

3. Simplified 70.2%

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

5. Taylor expanded in z around inf 80.0%

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

   1. +-commutative 80.0%

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

7. Simplified 80.0%

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

8. Final simplification 80.0%

   \[\leadsto x + y \cdot 0.0692910599291889 \]
9. Add Preprocessing

Alternative 15: 50.5% 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 64.6%

   \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
2. Step-by-step derivation

   1. +-commutative 64.6%

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

   2. *-commutative 64.6%

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

   3. associate-/l* 70.2%

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

   4. fma-define 70.2%

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

   5. *-commutative 70.2%

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

   6. fma-define 70.2%

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

   7. fma-define 70.2%

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

   8. *-commutative 70.2%

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

   9. fma-define 70.2%

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

3. Simplified 70.2%

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

5. Taylor expanded in y around 0 50.6%

   \[\leadsto \color{blue}{x} \]
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 2024086 
(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))))