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

Percentage Accurate: 69.8% → 99.6%

Time: 11.9s

Alternatives: 13

Speedup: 2.1×

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: 69.8% 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

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} \leq 2 \cdot 10^{+303}:\\ \;\;\;\;x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (/
       (*
        y
        (+
         (* z (+ (* z 0.0692910599291889) 0.4917317610505968))
         0.279195317918525))
       (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
      2e+303)
   (+
    x
    (*
     y
     (/
      (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
      (fma (+ z 6.012459259764103) z 3.350343815022304))))
   (+ x (/ y 14.431876219268936))))

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)) <= 2e+303) {
		tmp = x + (y * (fma(fma(z, 0.0692910599291889, 0.4917317610505968), z, 0.279195317918525) / fma((z + 6.012459259764103), z, 3.350343815022304)));
	} else {
		tmp = x + (y / 14.431876219268936);
	}
	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)) <= 2e+303)
		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 / 14.431876219268936));
	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], 2e+303], 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 / 14.431876219268936), $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))) < 2e303

   1. Initial program 96.4%

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

      1. remove-double-neg 96.4%

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

      2. distribute-lft-neg-out 96.4%

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

      3. distribute-neg-frac 96.4%

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

      4. associate-/l* 99.8%

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

      5. distribute-lft-neg-in 99.8%

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

      6. remove-double-neg 99.8%

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

      7. fma-define 99.8%

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

      8. fma-define 99.8%

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

      9. fma-define 99.8%

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

   3. Simplified 99.8%

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

   if 2e303 < (/.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 0.7%

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

      1. remove-double-neg 0.7%

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

      2. distribute-lft-neg-out 0.7%

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

      3. distribute-neg-frac 0.7%

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

      4. associate-/l* 13.8%

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

      5. distribute-lft-neg-in 13.8%

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

      6. remove-double-neg 13.8%

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

      7. fma-define 13.8%

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

      8. fma-define 13.8%

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

      9. fma-define 13.8%

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

   3. Simplified 13.8%

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

      1. fma-define 13.8%

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

      2. clear-num 13.8%

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

      3. un-div-inv 13.9%

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

      4. *-commutative 13.9%

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

      5. fma-undefine 13.9%

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

      6. fma-define 13.9%

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

      7. fma-define 13.9%

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

      8. *-commutative 13.9%

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

      9. fma-undefine 13.9%

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

      10. fma-define 13.9%

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

   6. Applied egg-rr 13.9%

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

   7. Taylor expanded in z around inf 100.0%

      \[\leadsto x + \frac{y}{\color{blue}{14.431876219268936}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} \leq 2 \cdot 10^{+303}:\\ \;\;\;\;x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -125000000000 \lor \neg \left(z \leq 550\right):\\ \;\;\;\;x + \frac{y}{14.431876219268936 - \frac{15.646356830292042}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(0.279195317918525 + \left(z \cdot \left(z \cdot 0.0692910599291889\right) + z \cdot 0.4917317610505968\right)\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -125000000000.0) (not (<= z 550.0)))
   (+ x (/ y (- 14.431876219268936 (/ 15.646356830292042 z))))
   (+
    x
    (/
     (*
      y
      (+
       0.279195317918525
       (+ (* z (* z 0.0692910599291889)) (* z 0.4917317610505968))))
     (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -125000000000.0) || !(z <= 550.0)) {
		tmp = x + (y / (14.431876219268936 - (15.646356830292042 / z)));
	} else {
		tmp = x + ((y * (0.279195317918525 + ((z * (z * 0.0692910599291889)) + (z * 0.4917317610505968)))) / ((z * (z + 6.012459259764103)) + 3.350343815022304));
	}
	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 <= (-125000000000.0d0)) .or. (.not. (z <= 550.0d0))) then
        tmp = x + (y / (14.431876219268936d0 - (15.646356830292042d0 / z)))
    else
        tmp = x + ((y * (0.279195317918525d0 + ((z * (z * 0.0692910599291889d0)) + (z * 0.4917317610505968d0)))) / ((z * (z + 6.012459259764103d0)) + 3.350343815022304d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -125000000000.0) || !(z <= 550.0)) {
		tmp = x + (y / (14.431876219268936 - (15.646356830292042 / z)));
	} else {
		tmp = x + ((y * (0.279195317918525 + ((z * (z * 0.0692910599291889)) + (z * 0.4917317610505968)))) / ((z * (z + 6.012459259764103)) + 3.350343815022304));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -125000000000.0) or not (z <= 550.0):
		tmp = x + (y / (14.431876219268936 - (15.646356830292042 / z)))
	else:
		tmp = x + ((y * (0.279195317918525 + ((z * (z * 0.0692910599291889)) + (z * 0.4917317610505968)))) / ((z * (z + 6.012459259764103)) + 3.350343815022304))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -125000000000.0) || !(z <= 550.0))
		tmp = Float64(x + Float64(y / Float64(14.431876219268936 - Float64(15.646356830292042 / z))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(0.279195317918525 + Float64(Float64(z * Float64(z * 0.0692910599291889)) + Float64(z * 0.4917317610505968)))) / Float64(Float64(z * Float64(z + 6.012459259764103)) + 3.350343815022304)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -125000000000.0) || ~((z <= 550.0)))
		tmp = x + (y / (14.431876219268936 - (15.646356830292042 / z)));
	else
		tmp = x + ((y * (0.279195317918525 + ((z * (z * 0.0692910599291889)) + (z * 0.4917317610505968)))) / ((z * (z + 6.012459259764103)) + 3.350343815022304));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -125000000000.0], N[Not[LessEqual[z, 550.0]], $MachinePrecision]], N[(x + N[(y / N[(14.431876219268936 - N[(15.646356830292042 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(0.279195317918525 + N[(N[(z * N[(z * 0.0692910599291889), $MachinePrecision]), $MachinePrecision] + N[(z * 0.4917317610505968), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(z + 6.012459259764103), $MachinePrecision]), $MachinePrecision] + 3.350343815022304), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25e11 or 550 < z

   1. Initial program 32.5%

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

      1. remove-double-neg 32.5%

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

      2. distribute-lft-neg-out 32.5%

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

      3. distribute-neg-frac 32.5%

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

      4. associate-/l* 45.4%

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

      5. distribute-lft-neg-in 45.4%

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

      6. remove-double-neg 45.4%

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

      7. fma-define 45.4%

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

      8. fma-define 45.4%

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

      9. fma-define 45.4%

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

   3. Simplified 45.4%

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

      1. fma-define 45.4%

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

      2. clear-num 45.4%

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

      3. un-div-inv 45.4%

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

      4. *-commutative 45.4%

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

      5. fma-undefine 45.4%

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

      6. fma-define 45.4%

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

      7. fma-define 45.4%

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

      8. *-commutative 45.4%

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

      9. fma-undefine 45.4%

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

      10. fma-define 45.4%

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

   6. Applied egg-rr 45.4%

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

   7. Taylor expanded in z around inf 100.0%

      \[\leadsto x + \frac{y}{\color{blue}{14.431876219268936 - 15.646356830292042 \cdot \frac{1}{z}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto x + \frac{y}{14.431876219268936 - \color{blue}{\frac{15.646356830292042 \cdot 1}{z}}} \]

      2. metadata-eval 100.0%

         \[\leadsto x + \frac{y}{14.431876219268936 - \frac{\color{blue}{15.646356830292042}}{z}} \]

   9. Simplified 100.0%

      \[\leadsto x + \frac{y}{\color{blue}{14.431876219268936 - \frac{15.646356830292042}{z}}} \]

   if -1.25e11 < z < 550

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. distribute-rgt-in 99.6%

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

   4. Applied egg-rr 99.6%

      \[\leadsto x + \frac{y \cdot \left(\color{blue}{\left(\left(z \cdot 0.0692910599291889\right) \cdot z + 0.4917317610505968 \cdot z\right)} + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -125000000000 \lor \neg \left(z \leq 550\right):\\ \;\;\;\;x + \frac{y}{14.431876219268936 - \frac{15.646356830292042}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(0.279195317918525 + \left(z \cdot \left(z \cdot 0.0692910599291889\right) + z \cdot 0.4917317610505968\right)\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \mathbf{elif}\;z \leq 550:\\ \;\;\;\;\frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{14.431876219268936 - \frac{15.646356830292042}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.05e+16)
   (+ x (/ y 14.431876219268936))
   (if (<= z 550.0)
     (+
      (/
       (*
        y
        (+
         (* z (+ (* z 0.0692910599291889) 0.4917317610505968))
         0.279195317918525))
       (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
      x)
     (+ x (/ y (- 14.431876219268936 (/ 15.646356830292042 z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.05e+16) {
		tmp = x + (y / 14.431876219268936);
	} else if (z <= 550.0) {
		tmp = ((y * ((z * ((z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / ((z * (z + 6.012459259764103)) + 3.350343815022304)) + x;
	} else {
		tmp = x + (y / (14.431876219268936 - (15.646356830292042 / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-3.05d+16)) then
        tmp = x + (y / 14.431876219268936d0)
    else if (z <= 550.0d0) then
        tmp = ((y * ((z * ((z * 0.0692910599291889d0) + 0.4917317610505968d0)) + 0.279195317918525d0)) / ((z * (z + 6.012459259764103d0)) + 3.350343815022304d0)) + x
    else
        tmp = x + (y / (14.431876219268936d0 - (15.646356830292042d0 / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.05e+16) {
		tmp = x + (y / 14.431876219268936);
	} else if (z <= 550.0) {
		tmp = ((y * ((z * ((z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / ((z * (z + 6.012459259764103)) + 3.350343815022304)) + x;
	} else {
		tmp = x + (y / (14.431876219268936 - (15.646356830292042 / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.05e+16:
		tmp = x + (y / 14.431876219268936)
	elif z <= 550.0:
		tmp = ((y * ((z * ((z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / ((z * (z + 6.012459259764103)) + 3.350343815022304)) + x
	else:
		tmp = x + (y / (14.431876219268936 - (15.646356830292042 / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.05e+16)
		tmp = Float64(x + Float64(y / 14.431876219268936));
	elseif (z <= 550.0)
		tmp = Float64(Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / Float64(Float64(z * Float64(z + 6.012459259764103)) + 3.350343815022304)) + x);
	else
		tmp = Float64(x + Float64(y / Float64(14.431876219268936 - Float64(15.646356830292042 / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.05e+16)
		tmp = x + (y / 14.431876219268936);
	elseif (z <= 550.0)
		tmp = ((y * ((z * ((z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / ((z * (z + 6.012459259764103)) + 3.350343815022304)) + x;
	else
		tmp = x + (y / (14.431876219268936 - (15.646356830292042 / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.05e+16], N[(x + N[(y / 14.431876219268936), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 550.0], N[(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] + x), $MachinePrecision], N[(x + N[(y / N[(14.431876219268936 - N[(15.646356830292042 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.05e16

   1. Initial program 31.1%

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

      1. remove-double-neg 31.1%

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

      2. distribute-lft-neg-out 31.1%

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

      3. distribute-neg-frac 31.1%

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

      4. associate-/l* 41.4%

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

      5. distribute-lft-neg-in 41.4%

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

      6. remove-double-neg 41.4%

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

      7. fma-define 41.4%

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

      8. fma-define 41.4%

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

      9. fma-define 41.4%

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

   3. Simplified 41.4%

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

      1. fma-define 41.4%

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

      2. clear-num 41.4%

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

      3. un-div-inv 41.4%

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

      4. *-commutative 41.4%

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

      5. fma-undefine 41.4%

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

      6. fma-define 41.4%

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

      7. fma-define 41.4%

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

      8. *-commutative 41.4%

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

      9. fma-undefine 41.4%

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

      10. fma-define 41.4%

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

   6. Applied egg-rr 41.4%

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

   7. Taylor expanded in z around inf 100.0%

      \[\leadsto x + \frac{y}{\color{blue}{14.431876219268936}} \]

   if -3.05e16 < z < 550

   1. Initial program 99.6%

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

   if 550 < z

   1. Initial program 30.6%

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

      1. remove-double-neg 30.6%

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

      2. distribute-lft-neg-out 30.6%

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

      3. distribute-neg-frac 30.6%

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

      4. associate-/l* 47.2%

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

      5. distribute-lft-neg-in 47.2%

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

      6. remove-double-neg 47.2%

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

      7. fma-define 47.2%

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

      8. fma-define 47.2%

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

      9. fma-define 47.2%

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

   3. Simplified 47.2%

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

      1. fma-define 47.2%

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

      2. clear-num 47.2%

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

      3. un-div-inv 47.2%

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

      4. *-commutative 47.2%

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

      5. fma-undefine 47.2%

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

      6. fma-define 47.2%

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

      7. fma-define 47.2%

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

      8. *-commutative 47.2%

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

      9. fma-undefine 47.2%

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

      10. fma-define 47.2%

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

   6. Applied egg-rr 47.2%

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

   7. Taylor expanded in z around inf 100.0%

      \[\leadsto x + \frac{y}{\color{blue}{14.431876219268936 - 15.646356830292042 \cdot \frac{1}{z}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto x + \frac{y}{14.431876219268936 - \color{blue}{\frac{15.646356830292042 \cdot 1}{z}}} \]

      2. metadata-eval 100.0%

         \[\leadsto x + \frac{y}{14.431876219268936 - \frac{\color{blue}{15.646356830292042}}{z}} \]

   9. Simplified 100.0%

      \[\leadsto x + \frac{y}{\color{blue}{14.431876219268936 - \frac{15.646356830292042}{z}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \mathbf{elif}\;z \leq 550:\\ \;\;\;\;\frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{14.431876219268936 - \frac{15.646356830292042}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 1.65 \cdot 10^{-10}\right):\\ \;\;\;\;x + \frac{y}{14.431876219268936 + \frac{\frac{101.23733352003822 + \frac{-655.3980091051341}{z}}{z} - 15.646356830292042}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{12.000000000000014 + z \cdot \left(0.39999999996247915 + z \cdot -0.10095235035524991\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.5) (not (<= z 1.65e-10)))
   (+
    x
    (/
     y
     (+
      14.431876219268936
      (/
       (-
        (/ (+ 101.23733352003822 (/ -655.3980091051341 z)) z)
        15.646356830292042)
       z))))
   (+
    x
    (/
     y
     (+
      12.000000000000014
      (* z (+ 0.39999999996247915 (* z -0.10095235035524991))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.5) || !(z <= 1.65e-10)) {
		tmp = x + (y / (14.431876219268936 + ((((101.23733352003822 + (-655.3980091051341 / z)) / z) - 15.646356830292042) / z)));
	} else {
		tmp = x + (y / (12.000000000000014 + (z * (0.39999999996247915 + (z * -0.10095235035524991)))));
	}
	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 <= 1.65d-10))) then
        tmp = x + (y / (14.431876219268936d0 + ((((101.23733352003822d0 + ((-655.3980091051341d0) / z)) / z) - 15.646356830292042d0) / z)))
    else
        tmp = x + (y / (12.000000000000014d0 + (z * (0.39999999996247915d0 + (z * (-0.10095235035524991d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.5) || !(z <= 1.65e-10)) {
		tmp = x + (y / (14.431876219268936 + ((((101.23733352003822 + (-655.3980091051341 / z)) / z) - 15.646356830292042) / z)));
	} else {
		tmp = x + (y / (12.000000000000014 + (z * (0.39999999996247915 + (z * -0.10095235035524991)))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.5) or not (z <= 1.65e-10):
		tmp = x + (y / (14.431876219268936 + ((((101.23733352003822 + (-655.3980091051341 / z)) / z) - 15.646356830292042) / z)))
	else:
		tmp = x + (y / (12.000000000000014 + (z * (0.39999999996247915 + (z * -0.10095235035524991)))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.5) || !(z <= 1.65e-10))
		tmp = Float64(x + Float64(y / Float64(14.431876219268936 + Float64(Float64(Float64(Float64(101.23733352003822 + Float64(-655.3980091051341 / z)) / z) - 15.646356830292042) / z))));
	else
		tmp = Float64(x + Float64(y / Float64(12.000000000000014 + Float64(z * Float64(0.39999999996247915 + Float64(z * -0.10095235035524991))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.5) || ~((z <= 1.65e-10)))
		tmp = x + (y / (14.431876219268936 + ((((101.23733352003822 + (-655.3980091051341 / z)) / z) - 15.646356830292042) / z)));
	else
		tmp = x + (y / (12.000000000000014 + (z * (0.39999999996247915 + (z * -0.10095235035524991)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.5], N[Not[LessEqual[z, 1.65e-10]], $MachinePrecision]], N[(x + N[(y / N[(14.431876219268936 + N[(N[(N[(N[(101.23733352003822 + N[(-655.3980091051341 / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - 15.646356830292042), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(12.000000000000014 + N[(z * N[(0.39999999996247915 + N[(z * -0.10095235035524991), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5 or 1.65e-10 < z

   1. Initial program 35.6%

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

      1. remove-double-neg 35.6%

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

      2. distribute-lft-neg-out 35.6%

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

      3. distribute-neg-frac 35.6%

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

      4. associate-/l* 47.9%

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

      5. distribute-lft-neg-in 47.9%

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

      6. remove-double-neg 47.9%

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

      7. fma-define 47.9%

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

      8. fma-define 47.9%

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

      9. fma-define 47.9%

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

   3. Simplified 47.9%

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

      1. fma-define 47.9%

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

      2. clear-num 47.9%

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

      3. un-div-inv 47.9%

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

      4. *-commutative 47.9%

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

      5. fma-undefine 47.9%

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

      6. fma-define 47.9%

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

      7. fma-define 47.9%

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

      8. *-commutative 47.9%

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

      9. fma-undefine 47.9%

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

      10. fma-define 47.9%

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

   6. Applied egg-rr 47.9%

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

   7. Taylor expanded in z around -inf 99.6%

      \[\leadsto x + \frac{y}{\color{blue}{14.431876219268936 + -1 \cdot \frac{15.646356830292042 + -1 \cdot \frac{101.23733352003822 - 655.3980091051341 \cdot \frac{1}{z}}{z}}{z}}} \]
   8. Step-by-step derivation

      1. mul-1-neg 99.6%

         \[\leadsto x + \frac{y}{14.431876219268936 + \color{blue}{\left(-\frac{15.646356830292042 + -1 \cdot \frac{101.23733352003822 - 655.3980091051341 \cdot \frac{1}{z}}{z}}{z}\right)}} \]

      2. unsub-neg 99.6%

         \[\leadsto x + \frac{y}{\color{blue}{14.431876219268936 - \frac{15.646356830292042 + -1 \cdot \frac{101.23733352003822 - 655.3980091051341 \cdot \frac{1}{z}}{z}}{z}}} \]

      3. mul-1-neg 99.6%

         \[\leadsto x + \frac{y}{14.431876219268936 - \frac{15.646356830292042 + \color{blue}{\left(-\frac{101.23733352003822 - 655.3980091051341 \cdot \frac{1}{z}}{z}\right)}}{z}} \]

      4. unsub-neg 99.6%

         \[\leadsto x + \frac{y}{14.431876219268936 - \frac{\color{blue}{15.646356830292042 - \frac{101.23733352003822 - 655.3980091051341 \cdot \frac{1}{z}}{z}}}{z}} \]

      5. sub-neg 99.6%

         \[\leadsto x + \frac{y}{14.431876219268936 - \frac{15.646356830292042 - \frac{\color{blue}{101.23733352003822 + \left(-655.3980091051341 \cdot \frac{1}{z}\right)}}{z}}{z}} \]

      6. associate-*r/ 99.6%

         \[\leadsto x + \frac{y}{14.431876219268936 - \frac{15.646356830292042 - \frac{101.23733352003822 + \left(-\color{blue}{\frac{655.3980091051341 \cdot 1}{z}}\right)}{z}}{z}} \]

      7. metadata-eval 99.6%

         \[\leadsto x + \frac{y}{14.431876219268936 - \frac{15.646356830292042 - \frac{101.23733352003822 + \left(-\frac{\color{blue}{655.3980091051341}}{z}\right)}{z}}{z}} \]

      8. distribute-neg-frac 99.6%

         \[\leadsto x + \frac{y}{14.431876219268936 - \frac{15.646356830292042 - \frac{101.23733352003822 + \color{blue}{\frac{-655.3980091051341}{z}}}{z}}{z}} \]

      9. metadata-eval 99.6%

         \[\leadsto x + \frac{y}{14.431876219268936 - \frac{15.646356830292042 - \frac{101.23733352003822 + \frac{\color{blue}{-655.3980091051341}}{z}}{z}}{z}} \]

   9. Simplified 99.6%

      \[\leadsto x + \frac{y}{\color{blue}{14.431876219268936 - \frac{15.646356830292042 - \frac{101.23733352003822 + \frac{-655.3980091051341}{z}}{z}}{z}}} \]

   if -5.5 < z < 1.65e-10

   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%

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

      2. distribute-lft-neg-out 99.6%

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

      3. distribute-neg-frac 99.6%

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

      4. associate-/l* 99.9%

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

      5. distribute-lft-neg-in 99.9%

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

      6. remove-double-neg 99.9%

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

      7. fma-define 99.9%

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

      8. fma-define 99.9%

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

      9. fma-define 99.9%

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

   3. Simplified 99.9%

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

      1. fma-define 99.9%

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

      2. clear-num 99.0%

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

      3. un-div-inv 99.3%

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

      4. *-commutative 99.3%

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

      5. fma-undefine 99.3%

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

      6. fma-define 99.3%

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

      7. fma-define 99.3%

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

      8. *-commutative 99.3%

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

      9. fma-undefine 99.3%

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

      10. fma-define 99.3%

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

   6. Applied egg-rr 99.3%

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

   7. Taylor expanded in z around 0 100.0%

      \[\leadsto x + \frac{y}{\color{blue}{12.000000000000014 + z \cdot \left(0.39999999996247915 + -0.10095235035524991 \cdot z\right)}} \]
   8. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto x + \frac{y}{12.000000000000014 + z \cdot \left(0.39999999996247915 + \color{blue}{z \cdot -0.10095235035524991}\right)} \]

   9. Simplified 100.0%

      \[\leadsto x + \frac{y}{\color{blue}{12.000000000000014 + z \cdot \left(0.39999999996247915 + z \cdot -0.10095235035524991\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 1.65 \cdot 10^{-10}\right):\\ \;\;\;\;x + \frac{y}{14.431876219268936 + \frac{\frac{101.23733352003822 + \frac{-655.3980091051341}{z}}{z} - 15.646356830292042}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{12.000000000000014 + z \cdot \left(0.39999999996247915 + z \cdot -0.10095235035524991\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 1.65 \cdot 10^{-10}\right):\\ \;\;\;\;x + \frac{y}{14.431876219268936 - \frac{15.646356830292042}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{12.000000000000014 + z \cdot \left(0.39999999996247915 + z \cdot -0.10095235035524991\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.5) (not (<= z 1.65e-10)))
   (+ x (/ y (- 14.431876219268936 (/ 15.646356830292042 z))))
   (+
    x
    (/
     y
     (+
      12.000000000000014
      (* z (+ 0.39999999996247915 (* z -0.10095235035524991))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.5) || !(z <= 1.65e-10)) {
		tmp = x + (y / (14.431876219268936 - (15.646356830292042 / z)));
	} else {
		tmp = x + (y / (12.000000000000014 + (z * (0.39999999996247915 + (z * -0.10095235035524991)))));
	}
	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 <= 1.65d-10))) then
        tmp = x + (y / (14.431876219268936d0 - (15.646356830292042d0 / z)))
    else
        tmp = x + (y / (12.000000000000014d0 + (z * (0.39999999996247915d0 + (z * (-0.10095235035524991d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.5) || !(z <= 1.65e-10)) {
		tmp = x + (y / (14.431876219268936 - (15.646356830292042 / z)));
	} else {
		tmp = x + (y / (12.000000000000014 + (z * (0.39999999996247915 + (z * -0.10095235035524991)))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.5) or not (z <= 1.65e-10):
		tmp = x + (y / (14.431876219268936 - (15.646356830292042 / z)))
	else:
		tmp = x + (y / (12.000000000000014 + (z * (0.39999999996247915 + (z * -0.10095235035524991)))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.5) || !(z <= 1.65e-10))
		tmp = Float64(x + Float64(y / Float64(14.431876219268936 - Float64(15.646356830292042 / z))));
	else
		tmp = Float64(x + Float64(y / Float64(12.000000000000014 + Float64(z * Float64(0.39999999996247915 + Float64(z * -0.10095235035524991))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.5) || ~((z <= 1.65e-10)))
		tmp = x + (y / (14.431876219268936 - (15.646356830292042 / z)));
	else
		tmp = x + (y / (12.000000000000014 + (z * (0.39999999996247915 + (z * -0.10095235035524991)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.5], N[Not[LessEqual[z, 1.65e-10]], $MachinePrecision]], N[(x + N[(y / N[(14.431876219268936 - N[(15.646356830292042 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(12.000000000000014 + N[(z * N[(0.39999999996247915 + N[(z * -0.10095235035524991), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5 or 1.65e-10 < z

   1. Initial program 35.6%

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

      1. remove-double-neg 35.6%

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

      2. distribute-lft-neg-out 35.6%

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

      3. distribute-neg-frac 35.6%

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

      4. associate-/l* 47.9%

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

      5. distribute-lft-neg-in 47.9%

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

      6. remove-double-neg 47.9%

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

      7. fma-define 47.9%

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

      8. fma-define 47.9%

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

      9. fma-define 47.9%

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

   3. Simplified 47.9%

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

      1. fma-define 47.9%

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

      2. clear-num 47.9%

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

      3. un-div-inv 47.9%

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

      4. *-commutative 47.9%

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

      5. fma-undefine 47.9%

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

      6. fma-define 47.9%

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

      7. fma-define 47.9%

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

      8. *-commutative 47.9%

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

      9. fma-undefine 47.9%

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

      10. fma-define 47.9%

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

   6. Applied egg-rr 47.9%

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

   7. Taylor expanded in z around inf 99.2%

      \[\leadsto x + \frac{y}{\color{blue}{14.431876219268936 - 15.646356830292042 \cdot \frac{1}{z}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 99.2%

         \[\leadsto x + \frac{y}{14.431876219268936 - \color{blue}{\frac{15.646356830292042 \cdot 1}{z}}} \]

      2. metadata-eval 99.2%

         \[\leadsto x + \frac{y}{14.431876219268936 - \frac{\color{blue}{15.646356830292042}}{z}} \]

   9. Simplified 99.2%

      \[\leadsto x + \frac{y}{\color{blue}{14.431876219268936 - \frac{15.646356830292042}{z}}} \]

   if -5.5 < z < 1.65e-10

   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%

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

      2. distribute-lft-neg-out 99.6%

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

      3. distribute-neg-frac 99.6%

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

      4. associate-/l* 99.9%

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

      5. distribute-lft-neg-in 99.9%

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

      6. remove-double-neg 99.9%

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

      7. fma-define 99.9%

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

      8. fma-define 99.9%

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

      9. fma-define 99.9%

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

   3. Simplified 99.9%

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

      1. fma-define 99.9%

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

      2. clear-num 99.0%

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

      3. un-div-inv 99.3%

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

      4. *-commutative 99.3%

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

      5. fma-undefine 99.3%

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

      6. fma-define 99.3%

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

      7. fma-define 99.3%

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

      8. *-commutative 99.3%

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

      9. fma-undefine 99.3%

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

      10. fma-define 99.3%

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

   6. Applied egg-rr 99.3%

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

   7. Taylor expanded in z around 0 100.0%

      \[\leadsto x + \frac{y}{\color{blue}{12.000000000000014 + z \cdot \left(0.39999999996247915 + -0.10095235035524991 \cdot z\right)}} \]
   8. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto x + \frac{y}{12.000000000000014 + z \cdot \left(0.39999999996247915 + \color{blue}{z \cdot -0.10095235035524991}\right)} \]

   9. Simplified 100.0%

      \[\leadsto x + \frac{y}{\color{blue}{12.000000000000014 + z \cdot \left(0.39999999996247915 + z \cdot -0.10095235035524991\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 1.65 \cdot 10^{-10}\right):\\ \;\;\;\;x + \frac{y}{14.431876219268936 - \frac{15.646356830292042}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{12.000000000000014 + z \cdot \left(0.39999999996247915 + z \cdot -0.10095235035524991\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 1.65 \cdot 10^{-10}\right):\\ \;\;\;\;x + \frac{y}{14.431876219268936 - \frac{15.646356830292042}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{12.000000000000014 + z \cdot 0.39999999996247915}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.5) (not (<= z 1.65e-10)))
   (+ x (/ y (- 14.431876219268936 (/ 15.646356830292042 z))))
   (+ x (/ y (+ 12.000000000000014 (* z 0.39999999996247915))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.5) || !(z <= 1.65e-10)) {
		tmp = x + (y / (14.431876219268936 - (15.646356830292042 / z)));
	} else {
		tmp = x + (y / (12.000000000000014 + (z * 0.39999999996247915)));
	}
	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 <= 1.65d-10))) then
        tmp = x + (y / (14.431876219268936d0 - (15.646356830292042d0 / z)))
    else
        tmp = x + (y / (12.000000000000014d0 + (z * 0.39999999996247915d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.5) || !(z <= 1.65e-10)) {
		tmp = x + (y / (14.431876219268936 - (15.646356830292042 / z)));
	} else {
		tmp = x + (y / (12.000000000000014 + (z * 0.39999999996247915)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.5) or not (z <= 1.65e-10):
		tmp = x + (y / (14.431876219268936 - (15.646356830292042 / z)))
	else:
		tmp = x + (y / (12.000000000000014 + (z * 0.39999999996247915)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.5) || !(z <= 1.65e-10))
		tmp = Float64(x + Float64(y / Float64(14.431876219268936 - Float64(15.646356830292042 / z))));
	else
		tmp = Float64(x + Float64(y / Float64(12.000000000000014 + Float64(z * 0.39999999996247915))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.5) || ~((z <= 1.65e-10)))
		tmp = x + (y / (14.431876219268936 - (15.646356830292042 / z)));
	else
		tmp = x + (y / (12.000000000000014 + (z * 0.39999999996247915)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.5], N[Not[LessEqual[z, 1.65e-10]], $MachinePrecision]], N[(x + N[(y / N[(14.431876219268936 - N[(15.646356830292042 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(12.000000000000014 + N[(z * 0.39999999996247915), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5 or 1.65e-10 < z

   1. Initial program 35.6%

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

      1. remove-double-neg 35.6%

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

      2. distribute-lft-neg-out 35.6%

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

      3. distribute-neg-frac 35.6%

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

      4. associate-/l* 47.9%

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

      5. distribute-lft-neg-in 47.9%

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

      6. remove-double-neg 47.9%

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

      7. fma-define 47.9%

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

      8. fma-define 47.9%

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

      9. fma-define 47.9%

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

   3. Simplified 47.9%

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

      1. fma-define 47.9%

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

      2. clear-num 47.9%

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

      3. un-div-inv 47.9%

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

      4. *-commutative 47.9%

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

      5. fma-undefine 47.9%

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

      6. fma-define 47.9%

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

      7. fma-define 47.9%

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

      8. *-commutative 47.9%

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

      9. fma-undefine 47.9%

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

      10. fma-define 47.9%

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

   6. Applied egg-rr 47.9%

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

   7. Taylor expanded in z around inf 99.2%

      \[\leadsto x + \frac{y}{\color{blue}{14.431876219268936 - 15.646356830292042 \cdot \frac{1}{z}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 99.2%

         \[\leadsto x + \frac{y}{14.431876219268936 - \color{blue}{\frac{15.646356830292042 \cdot 1}{z}}} \]

      2. metadata-eval 99.2%

         \[\leadsto x + \frac{y}{14.431876219268936 - \frac{\color{blue}{15.646356830292042}}{z}} \]

   9. Simplified 99.2%

      \[\leadsto x + \frac{y}{\color{blue}{14.431876219268936 - \frac{15.646356830292042}{z}}} \]

   if -5.5 < z < 1.65e-10

   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%

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

      2. distribute-lft-neg-out 99.6%

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

      3. distribute-neg-frac 99.6%

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

      4. associate-/l* 99.9%

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

      5. distribute-lft-neg-in 99.9%

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

      6. remove-double-neg 99.9%

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

      7. fma-define 99.9%

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

      8. fma-define 99.9%

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

      9. fma-define 99.9%

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

   3. Simplified 99.9%

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

      1. fma-define 99.9%

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

      2. clear-num 99.0%

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

      3. un-div-inv 99.3%

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

      4. *-commutative 99.3%

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

      5. fma-undefine 99.3%

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

      6. fma-define 99.3%

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

      7. fma-define 99.3%

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

      8. *-commutative 99.3%

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

      9. fma-undefine 99.3%

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

      10. fma-define 99.3%

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

   6. Applied egg-rr 99.3%

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

   7. Taylor expanded in z around 0 99.9%

      \[\leadsto x + \frac{y}{\color{blue}{12.000000000000014 + 0.39999999996247915 \cdot z}} \]
   8. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto x + \frac{y}{12.000000000000014 + \color{blue}{z \cdot 0.39999999996247915}} \]

   9. Simplified 99.9%

      \[\leadsto x + \frac{y}{\color{blue}{12.000000000000014 + z \cdot 0.39999999996247915}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 1.65 \cdot 10^{-10}\right):\\ \;\;\;\;x + \frac{y}{14.431876219268936 - \frac{15.646356830292042}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{12.000000000000014 + z \cdot 0.39999999996247915}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 1.65 \cdot 10^{-10}\right):\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{12.000000000000014 + z \cdot 0.39999999996247915}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.5) (not (<= z 1.65e-10)))
   (+ x (* y (+ 0.0692910599291889 (/ 0.07512208616047561 z))))
   (+ x (/ y (+ 12.000000000000014 (* z 0.39999999996247915))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.5) || !(z <= 1.65e-10)) {
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)));
	} else {
		tmp = x + (y / (12.000000000000014 + (z * 0.39999999996247915)));
	}
	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 <= 1.65d-10))) then
        tmp = x + (y * (0.0692910599291889d0 + (0.07512208616047561d0 / z)))
    else
        tmp = x + (y / (12.000000000000014d0 + (z * 0.39999999996247915d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.5) || !(z <= 1.65e-10)) {
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)));
	} else {
		tmp = x + (y / (12.000000000000014 + (z * 0.39999999996247915)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.5) or not (z <= 1.65e-10):
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)))
	else:
		tmp = x + (y / (12.000000000000014 + (z * 0.39999999996247915)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.5) || !(z <= 1.65e-10))
		tmp = Float64(x + Float64(y * Float64(0.0692910599291889 + Float64(0.07512208616047561 / z))));
	else
		tmp = Float64(x + Float64(y / Float64(12.000000000000014 + Float64(z * 0.39999999996247915))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.5) || ~((z <= 1.65e-10)))
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)));
	else
		tmp = x + (y / (12.000000000000014 + (z * 0.39999999996247915)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.5], N[Not[LessEqual[z, 1.65e-10]], $MachinePrecision]], N[(x + N[(y * N[(0.0692910599291889 + N[(0.07512208616047561 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(12.000000000000014 + N[(z * 0.39999999996247915), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5 or 1.65e-10 < z

   1. Initial program 35.6%

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

      1. remove-double-neg 35.6%

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

      2. distribute-lft-neg-out 35.6%

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

      3. distribute-neg-frac 35.6%

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

      4. associate-/l* 47.9%

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

      5. distribute-lft-neg-in 47.9%

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

      6. remove-double-neg 47.9%

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

      7. fma-define 47.9%

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

      8. fma-define 47.9%

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

      9. fma-define 47.9%

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

   3. Simplified 47.9%

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

   5. Taylor expanded in z around inf 98.9%

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

      1. associate-*r/ 98.9%

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

      2. metadata-eval 98.9%

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

   7. Simplified 98.9%

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

   if -5.5 < z < 1.65e-10

   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%

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

      2. distribute-lft-neg-out 99.6%

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

      3. distribute-neg-frac 99.6%

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

      4. associate-/l* 99.9%

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

      5. distribute-lft-neg-in 99.9%

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

      6. remove-double-neg 99.9%

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

      7. fma-define 99.9%

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

      8. fma-define 99.9%

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

      9. fma-define 99.9%

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

   3. Simplified 99.9%

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

      1. fma-define 99.9%

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

      2. clear-num 99.0%

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

      3. un-div-inv 99.3%

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

      4. *-commutative 99.3%

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

      5. fma-undefine 99.3%

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

      6. fma-define 99.3%

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

      7. fma-define 99.3%

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

      8. *-commutative 99.3%

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

      9. fma-undefine 99.3%

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

      10. fma-define 99.3%

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

   6. Applied egg-rr 99.3%

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

   7. Taylor expanded in z around 0 99.9%

      \[\leadsto x + \frac{y}{\color{blue}{12.000000000000014 + 0.39999999996247915 \cdot z}} \]
   8. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto x + \frac{y}{12.000000000000014 + \color{blue}{z \cdot 0.39999999996247915}} \]

   9. Simplified 99.9%

      \[\leadsto x + \frac{y}{\color{blue}{12.000000000000014 + z \cdot 0.39999999996247915}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 1.65 \cdot 10^{-10}\right):\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{12.000000000000014 + z \cdot 0.39999999996247915}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 1.65 \cdot 10^{-10}\right):\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.08333333333333323 + z \cdot -0.00277777777751721\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.5) (not (<= z 1.65e-10)))
   (+ 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 <= 1.65e-10)) {
		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 <= 1.65d-10))) 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 <= 1.65e-10)) {
		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 <= 1.65e-10):
		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 <= 1.65e-10))
		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 <= 1.65e-10)))
		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, 1.65e-10]], $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 1.65e-10 < z

   1. Initial program 35.6%

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

      1. remove-double-neg 35.6%

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

      2. distribute-lft-neg-out 35.6%

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

      3. distribute-neg-frac 35.6%

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

      4. associate-/l* 47.9%

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

      5. distribute-lft-neg-in 47.9%

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

      6. remove-double-neg 47.9%

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

      7. fma-define 47.9%

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

      8. fma-define 47.9%

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

      9. fma-define 47.9%

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

   3. Simplified 47.9%

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

   5. Taylor expanded in z around inf 98.9%

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

      1. associate-*r/ 98.9%

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

      2. metadata-eval 98.9%

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

   7. Simplified 98.9%

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

   if -5.5 < z < 1.65e-10

   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%

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

      2. distribute-lft-neg-out 99.6%

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

      3. distribute-neg-frac 99.6%

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

      4. associate-/l* 99.9%

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

      5. distribute-lft-neg-in 99.9%

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

      6. remove-double-neg 99.9%

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

      7. fma-define 99.9%

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

      8. fma-define 99.9%

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

      9. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 99.9%

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

      1. *-commutative 99.9%

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

   7. Simplified 99.9%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 1.65 \cdot 10^{-10}\right):\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.08333333333333323 + z \cdot -0.00277777777751721\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 1.65 \cdot 10^{-10}\right):\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{12.000000000000014}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.5) (not (<= z 1.65e-10)))
   (+ x (* y (+ 0.0692910599291889 (/ 0.07512208616047561 z))))
   (+ x (/ y 12.000000000000014))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.5) || !(z <= 1.65e-10)) {
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)));
	} else {
		tmp = x + (y / 12.000000000000014);
	}
	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 <= 1.65d-10))) then
        tmp = x + (y * (0.0692910599291889d0 + (0.07512208616047561d0 / z)))
    else
        tmp = x + (y / 12.000000000000014d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.5) || !(z <= 1.65e-10)) {
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)));
	} else {
		tmp = x + (y / 12.000000000000014);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.5) or not (z <= 1.65e-10):
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)))
	else:
		tmp = x + (y / 12.000000000000014)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.5) || !(z <= 1.65e-10))
		tmp = Float64(x + Float64(y * Float64(0.0692910599291889 + Float64(0.07512208616047561 / z))));
	else
		tmp = Float64(x + Float64(y / 12.000000000000014));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.5) || ~((z <= 1.65e-10)))
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)));
	else
		tmp = x + (y / 12.000000000000014);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.5], N[Not[LessEqual[z, 1.65e-10]], $MachinePrecision]], N[(x + N[(y * N[(0.0692910599291889 + N[(0.07512208616047561 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / 12.000000000000014), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5 or 1.65e-10 < z

   1. Initial program 35.6%

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

      1. remove-double-neg 35.6%

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

      2. distribute-lft-neg-out 35.6%

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

      3. distribute-neg-frac 35.6%

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

      4. associate-/l* 47.9%

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

      5. distribute-lft-neg-in 47.9%

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

      6. remove-double-neg 47.9%

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

      7. fma-define 47.9%

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

      8. fma-define 47.9%

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

      9. fma-define 47.9%

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

   3. Simplified 47.9%

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

   5. Taylor expanded in z around inf 98.9%

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

      1. associate-*r/ 98.9%

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

      2. metadata-eval 98.9%

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

   7. Simplified 98.9%

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

   if -5.5 < z < 1.65e-10

   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%

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

      2. distribute-lft-neg-out 99.6%

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

      3. distribute-neg-frac 99.6%

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

      4. associate-/l* 99.9%

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

      5. distribute-lft-neg-in 99.9%

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

      6. remove-double-neg 99.9%

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

      7. fma-define 99.9%

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

      8. fma-define 99.9%

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

      9. fma-define 99.9%

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

   3. Simplified 99.9%

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

      1. fma-define 99.9%

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

      2. clear-num 99.0%

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

      3. un-div-inv 99.3%

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

      4. *-commutative 99.3%

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

      5. fma-undefine 99.3%

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

      6. fma-define 99.3%

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

      7. fma-define 99.3%

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

      8. *-commutative 99.3%

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

      9. fma-undefine 99.3%

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

      10. fma-define 99.3%

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

   6. Applied egg-rr 99.3%

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

   7. Taylor expanded in z around 0 99.5%

      \[\leadsto x + \frac{y}{\color{blue}{12.000000000000014}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 1.65 \cdot 10^{-10}\right):\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{12.000000000000014}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 98.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 1.65 \cdot 10^{-10}\right):\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{12.000000000000014}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.5) (not (<= z 1.65e-10)))
   (+ x (/ y 14.431876219268936))
   (+ x (/ y 12.000000000000014))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.5) || !(z <= 1.65e-10)) {
		tmp = x + (y / 14.431876219268936);
	} else {
		tmp = x + (y / 12.000000000000014);
	}
	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 <= 1.65d-10))) then
        tmp = x + (y / 14.431876219268936d0)
    else
        tmp = x + (y / 12.000000000000014d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.5) || !(z <= 1.65e-10)) {
		tmp = x + (y / 14.431876219268936);
	} else {
		tmp = x + (y / 12.000000000000014);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.5) or not (z <= 1.65e-10):
		tmp = x + (y / 14.431876219268936)
	else:
		tmp = x + (y / 12.000000000000014)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.5) || !(z <= 1.65e-10))
		tmp = Float64(x + Float64(y / 14.431876219268936));
	else
		tmp = Float64(x + Float64(y / 12.000000000000014));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.5) || ~((z <= 1.65e-10)))
		tmp = x + (y / 14.431876219268936);
	else
		tmp = x + (y / 12.000000000000014);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.5], N[Not[LessEqual[z, 1.65e-10]], $MachinePrecision]], N[(x + N[(y / 14.431876219268936), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / 12.000000000000014), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5 or 1.65e-10 < z

   1. Initial program 35.6%

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

      1. remove-double-neg 35.6%

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

      2. distribute-lft-neg-out 35.6%

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

      3. distribute-neg-frac 35.6%

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

      4. associate-/l* 47.9%

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

      5. distribute-lft-neg-in 47.9%

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

      6. remove-double-neg 47.9%

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

      7. fma-define 47.9%

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

      8. fma-define 47.9%

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

      9. fma-define 47.9%

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

   3. Simplified 47.9%

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

      1. fma-define 47.9%

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

      2. clear-num 47.9%

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

      3. un-div-inv 47.9%

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

      4. *-commutative 47.9%

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

      5. fma-undefine 47.9%

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

      6. fma-define 47.9%

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

      7. fma-define 47.9%

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

      8. *-commutative 47.9%

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

      9. fma-undefine 47.9%

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

      10. fma-define 47.9%

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

   6. Applied egg-rr 47.9%

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

   7. Taylor expanded in z around inf 98.2%

      \[\leadsto x + \frac{y}{\color{blue}{14.431876219268936}} \]

   if -5.5 < z < 1.65e-10

   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%

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

      2. distribute-lft-neg-out 99.6%

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

      3. distribute-neg-frac 99.6%

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

      4. associate-/l* 99.9%

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

      5. distribute-lft-neg-in 99.9%

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

      6. remove-double-neg 99.9%

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

      7. fma-define 99.9%

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

      8. fma-define 99.9%

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

      9. fma-define 99.9%

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

   3. Simplified 99.9%

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

      1. fma-define 99.9%

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

      2. clear-num 99.0%

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

      3. un-div-inv 99.3%

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

      4. *-commutative 99.3%

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

      5. fma-undefine 99.3%

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

      6. fma-define 99.3%

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

      7. fma-define 99.3%

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

      8. *-commutative 99.3%

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

      9. fma-undefine 99.3%

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

      10. fma-define 99.3%

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

   6. Applied egg-rr 99.3%

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

   7. Taylor expanded in z around 0 99.5%

      \[\leadsto x + \frac{y}{\color{blue}{12.000000000000014}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 1.65 \cdot 10^{-10}\right):\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{12.000000000000014}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-190}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-28}:\\ \;\;\;\;\frac{y}{14.431876219268936}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.8e-190) x (if (<= x 3.2e-28) (/ y 14.431876219268936) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.8e-190) {
		tmp = x;
	} else if (x <= 3.2e-28) {
		tmp = y / 14.431876219268936;
	} 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 <= (-1.8d-190)) then
        tmp = x
    else if (x <= 3.2d-28) then
        tmp = y / 14.431876219268936d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.8e-190) {
		tmp = x;
	} else if (x <= 3.2e-28) {
		tmp = y / 14.431876219268936;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.8e-190:
		tmp = x
	elif x <= 3.2e-28:
		tmp = y / 14.431876219268936
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.8e-190)
		tmp = x;
	elseif (x <= 3.2e-28)
		tmp = Float64(y / 14.431876219268936);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.8e-190)
		tmp = x;
	elseif (x <= 3.2e-28)
		tmp = y / 14.431876219268936;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.8e-190], x, If[LessEqual[x, 3.2e-28], N[(y / 14.431876219268936), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.80000000000000003e-190 or 3.19999999999999982e-28 < x

   1. Initial program 66.0%

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

      1. +-commutative 66.0%

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

      2. *-commutative 66.0%

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

      3. associate-/l* 72.1%

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

      4. fma-define 72.1%

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

      5. *-commutative 72.1%

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

      6. fma-define 72.1%

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

      7. fma-define 72.1%

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

      8. *-commutative 72.1%

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

      9. fma-define 72.1%

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

   3. Simplified 72.1%

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

   5. Taylor expanded in y around 0 66.8%

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

   if -1.80000000000000003e-190 < x < 3.19999999999999982e-28

   1. Initial program 68.6%

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

      1. remove-double-neg 68.6%

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

      2. distribute-lft-neg-out 68.6%

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

      3. distribute-neg-frac 68.6%

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

      4. associate-/l* 75.6%

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

      5. distribute-lft-neg-in 75.6%

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

      6. remove-double-neg 75.6%

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

      7. fma-define 75.6%

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

      8. fma-define 75.6%

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

      9. fma-define 75.6%

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

   3. Simplified 75.6%

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

      1. fma-define 75.6%

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

      2. clear-num 74.9%

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

      3. un-div-inv 75.1%

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

      4. *-commutative 75.1%

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

      5. fma-undefine 75.1%

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

      6. fma-define 75.1%

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

      7. fma-define 75.1%

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

      8. *-commutative 75.1%

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

      9. fma-undefine 75.1%

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

      10. fma-define 75.1%

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

   6. Applied egg-rr 75.1%

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

   7. Taylor expanded in z around inf 54.4%

      \[\leadsto x + \frac{y}{\color{blue}{14.431876219268936 - 15.646356830292042 \cdot \frac{1}{z}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 54.4%

         \[\leadsto x + \frac{y}{14.431876219268936 - \color{blue}{\frac{15.646356830292042 \cdot 1}{z}}} \]

      2. metadata-eval 54.4%

         \[\leadsto x + \frac{y}{14.431876219268936 - \frac{\color{blue}{15.646356830292042}}{z}} \]

   9. Simplified 54.4%

      \[\leadsto x + \frac{y}{\color{blue}{14.431876219268936 - \frac{15.646356830292042}{z}}} \]

   10. Taylor expanded in x around 0 45.8%

       \[\leadsto \color{blue}{\frac{y}{14.431876219268936 - 15.646356830292042 \cdot \frac{1}{z}}} \]
   11. Step-by-step derivation

       1. associate-*r/ 45.8%

          \[\leadsto \frac{y}{14.431876219268936 - \color{blue}{\frac{15.646356830292042 \cdot 1}{z}}} \]

       2. metadata-eval 45.8%

          \[\leadsto \frac{y}{14.431876219268936 - \frac{\color{blue}{15.646356830292042}}{z}} \]

   12. Simplified 45.8%

       \[\leadsto \color{blue}{\frac{y}{14.431876219268936 - \frac{15.646356830292042}{z}}} \]

   13. Taylor expanded in z around inf 52.7%

       \[\leadsto \frac{y}{\color{blue}{14.431876219268936}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 77.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+83}:\\ \;\;\;\;\frac{y}{14.431876219268936}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{12.000000000000014}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.3e+83) (/ y 14.431876219268936) (+ x (/ y 12.000000000000014))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.3e+83) {
		tmp = y / 14.431876219268936;
	} else {
		tmp = x + (y / 12.000000000000014);
	}
	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 <= (-2.3d+83)) then
        tmp = y / 14.431876219268936d0
    else
        tmp = x + (y / 12.000000000000014d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.3e+83) {
		tmp = y / 14.431876219268936;
	} else {
		tmp = x + (y / 12.000000000000014);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.3e+83:
		tmp = y / 14.431876219268936
	else:
		tmp = x + (y / 12.000000000000014)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.3e+83)
		tmp = Float64(y / 14.431876219268936);
	else
		tmp = Float64(x + Float64(y / 12.000000000000014));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.3e+83)
		tmp = y / 14.431876219268936;
	else
		tmp = x + (y / 12.000000000000014);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.3e+83], N[(y / 14.431876219268936), $MachinePrecision], N[(x + N[(y / 12.000000000000014), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.29999999999999995e83

   1. Initial program 15.8%

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

      1. remove-double-neg 15.8%

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

      2. distribute-lft-neg-out 15.8%

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

      3. distribute-neg-frac 15.8%

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

      4. associate-/l* 26.8%

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

      5. distribute-lft-neg-in 26.8%

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

      6. remove-double-neg 26.8%

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

      7. fma-define 26.8%

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

      8. fma-define 26.8%

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

      9. fma-define 26.8%

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

   3. Simplified 26.8%

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

      1. fma-define 26.8%

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

      2. clear-num 26.8%

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

      3. un-div-inv 26.7%

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

      4. *-commutative 26.7%

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

      5. fma-undefine 26.7%

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

      6. fma-define 26.7%

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

      7. fma-define 26.7%

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

      8. *-commutative 26.7%

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

      9. fma-undefine 26.7%

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

      10. fma-define 26.7%

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

   6. Applied egg-rr 26.7%

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

   7. Taylor expanded in z around inf 100.0%

      \[\leadsto x + \frac{y}{\color{blue}{14.431876219268936 - 15.646356830292042 \cdot \frac{1}{z}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto x + \frac{y}{14.431876219268936 - \color{blue}{\frac{15.646356830292042 \cdot 1}{z}}} \]

      2. metadata-eval 100.0%

         \[\leadsto x + \frac{y}{14.431876219268936 - \frac{\color{blue}{15.646356830292042}}{z}} \]

   9. Simplified 100.0%

      \[\leadsto x + \frac{y}{\color{blue}{14.431876219268936 - \frac{15.646356830292042}{z}}} \]

   10. Taylor expanded in x around 0 60.8%

       \[\leadsto \color{blue}{\frac{y}{14.431876219268936 - 15.646356830292042 \cdot \frac{1}{z}}} \]
   11. Step-by-step derivation

       1. associate-*r/ 60.8%

          \[\leadsto \frac{y}{14.431876219268936 - \color{blue}{\frac{15.646356830292042 \cdot 1}{z}}} \]

       2. metadata-eval 60.8%

          \[\leadsto \frac{y}{14.431876219268936 - \frac{\color{blue}{15.646356830292042}}{z}} \]

   12. Simplified 60.8%

       \[\leadsto \color{blue}{\frac{y}{14.431876219268936 - \frac{15.646356830292042}{z}}} \]

   13. Taylor expanded in z around inf 60.8%

       \[\leadsto \frac{y}{\color{blue}{14.431876219268936}} \]

   if -2.29999999999999995e83 < z

   1. Initial program 79.9%

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

      1. remove-double-neg 79.9%

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

      2. distribute-lft-neg-out 79.9%

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

      3. distribute-neg-frac 79.9%

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

      4. associate-/l* 85.1%

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

      5. distribute-lft-neg-in 85.1%

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

      6. remove-double-neg 85.1%

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

      7. fma-define 85.1%

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

      8. fma-define 85.1%

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

      9. fma-define 85.1%

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

   3. Simplified 85.1%

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

      1. fma-define 85.1%

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

      2. clear-num 84.6%

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

      3. un-div-inv 84.8%

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

      4. *-commutative 84.8%

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

      5. fma-undefine 84.8%

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

      6. fma-define 84.8%

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

      7. fma-define 84.8%

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

      8. *-commutative 84.8%

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

      9. fma-undefine 84.8%

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

      10. fma-define 84.8%

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

   6. Applied egg-rr 84.8%

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

   7. Taylor expanded in z around 0 86.8%

      \[\leadsto x + \frac{y}{\color{blue}{12.000000000000014}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 50.2% 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 66.9%

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

   1. +-commutative 66.9%

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

   2. *-commutative 66.9%

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

   3. associate-/l* 72.8%

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

   4. fma-define 72.8%

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

   5. *-commutative 72.8%

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

   6. fma-define 72.8%

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

   7. fma-define 72.8%

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

   8. *-commutative 72.8%

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

   9. fma-define 72.8%

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

3. Simplified 72.8%

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

5. Taylor expanded in y around 0 49.1%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 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 2024181 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -324806146098267/40000000) (- (* (+ (/ 7512208616047561/100000000000000000 z) 692910599291889/10000000000000000) y) (- (/ (* 323697630959937/800000000000000 y) (* z z)) x)) (if (< z 657611897278737700000) (+ x (* (* y (+ (* (+ (* z 692910599291889/10000000000000000) 307332350656623/625000000000000) z) 11167812716741/40000000000000)) (/ 1 (+ (* (+ z 6012459259764103/1000000000000000) z) 104698244219447/31250000000000)))) (- (* (+ (/ 7512208616047561/100000000000000000 z) 692910599291889/10000000000000000) y) (- (/ (* 323697630959937/800000000000000 y) (* z z)) x)))))

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