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

Percentage Accurate: 69.6% → 99.6%

Time: 13.2s

Alternatives: 14

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: 69.6% 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

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} \leq \infty:\\ \;\;\;\;x + y \cdot \frac{\mathsf{fma}\left(\frac{0.24180012482592123 - {z}^{2} \cdot 0.004801250986110448}{0.4917317610505968 - z \cdot 0.0692910599291889}, z, 0.279195317918525\right)}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{{\left(\frac{0.07512208616047561}{z}\right)}^{2} - 0.004801250986110448}{\frac{0.07512208616047561}{z} - 0.0692910599291889}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (/
       (*
        y
        (+
         (* z (+ (* z 0.0692910599291889) 0.4917317610505968))
         0.279195317918525))
       (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
      INFINITY)
   (+
    x
    (*
     y
     (/
      (fma
       (/
        (- 0.24180012482592123 (* (pow z 2.0) 0.004801250986110448))
        (- 0.4917317610505968 (* z 0.0692910599291889)))
       z
       0.279195317918525)
      (fma (+ z 6.012459259764103) z 3.350343815022304))))
   (+
    x
    (*
     y
     (/
      (- (pow (/ 0.07512208616047561 z) 2.0) 0.004801250986110448)
      (- (/ 0.07512208616047561 z) 0.0692910599291889))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((y * ((z * ((z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / ((z * (z + 6.012459259764103)) + 3.350343815022304)) <= ((double) INFINITY)) {
		tmp = x + (y * (fma(((0.24180012482592123 - (pow(z, 2.0) * 0.004801250986110448)) / (0.4917317610505968 - (z * 0.0692910599291889))), z, 0.279195317918525) / fma((z + 6.012459259764103), z, 3.350343815022304)));
	} else {
		tmp = x + (y * ((pow((0.07512208616047561 / z), 2.0) - 0.004801250986110448) / ((0.07512208616047561 / z) - 0.0692910599291889)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / Float64(Float64(z * Float64(z + 6.012459259764103)) + 3.350343815022304)) <= Inf)
		tmp = Float64(x + Float64(y * Float64(fma(Float64(Float64(0.24180012482592123 - Float64((z ^ 2.0) * 0.004801250986110448)) / Float64(0.4917317610505968 - Float64(z * 0.0692910599291889))), z, 0.279195317918525) / fma(Float64(z + 6.012459259764103), z, 3.350343815022304))));
	else
		tmp = Float64(x + Float64(y * Float64(Float64((Float64(0.07512208616047561 / z) ^ 2.0) - 0.004801250986110448) / Float64(Float64(0.07512208616047561 / z) - 0.0692910599291889))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(y * N[(N[(z * N[(N[(z * 0.0692910599291889), $MachinePrecision] + 0.4917317610505968), $MachinePrecision]), $MachinePrecision] + 0.279195317918525), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(z + 6.012459259764103), $MachinePrecision]), $MachinePrecision] + 3.350343815022304), $MachinePrecision]), $MachinePrecision], Infinity], N[(x + N[(y * N[(N[(N[(N[(0.24180012482592123 - N[(N[Power[z, 2.0], $MachinePrecision] * 0.004801250986110448), $MachinePrecision]), $MachinePrecision] / N[(0.4917317610505968 - N[(z * 0.0692910599291889), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z + 0.279195317918525), $MachinePrecision] / N[(N[(z + 6.012459259764103), $MachinePrecision] * z + 3.350343815022304), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(N[Power[N[(0.07512208616047561 / z), $MachinePrecision], 2.0], $MachinePrecision] - 0.004801250986110448), $MachinePrecision] / N[(N[(0.07512208616047561 / z), $MachinePrecision] - 0.0692910599291889), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 692910599291889/10000000000000000) 307332350656623/625000000000000) z) 11167812716741/40000000000000)) (+.f64 (*.f64 (+.f64 z 6012459259764103/1000000000000000) z) 104698244219447/31250000000000)) < +inf.0

   1. Initial program 96.1%

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

      1. remove-double-neg 96.1%

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

      2. distribute-lft-neg-out 96.1%

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

      3. distribute-neg-frac 96.1%

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

      4. associate-/l* 99.7%

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

      5. distribute-lft-neg-in 99.7%

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

      6. remove-double-neg 99.7%

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

      7. fma-define 99.7%

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

      8. fma-define 99.7%

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

      9. fma-define 99.7%

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

   3. Simplified 99.7%

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

      1. fma-define 99.7%

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

      2. +-commutative 99.7%

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

      3. flip-+ 99.7%

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

      4. metadata-eval 99.7%

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

      5. swap-sqr 99.7%

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

      6. pow2 99.7%

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

      7. metadata-eval 99.7%

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

   6. Applied egg-rr 99.7%

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

   if +inf.0 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 692910599291889/10000000000000000) 307332350656623/625000000000000) z) 11167812716741/40000000000000)) (+.f64 (*.f64 (+.f64 z 6012459259764103/1000000000000000) z) 104698244219447/31250000000000))

   1. Initial program 0.0%

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

      1. remove-double-neg 0.0%

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

      2. distribute-lft-neg-out 0.0%

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

      3. distribute-neg-frac 0.0%

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

      4. associate-/l* 0.0%

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

      5. distribute-lft-neg-in 0.0%

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

      6. remove-double-neg 0.0%

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

      7. fma-define 0.0%

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

      8. fma-define 0.0%

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

      9. fma-define 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around inf 99.5%

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

      1. associate-*r/ 99.5%

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

      2. metadata-eval 99.5%

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

   7. Simplified 99.5%

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

      1. +-commutative 99.5%

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

      2. flip-+ 99.5%

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

      3. pow2 99.5%

         \[\leadsto x + y \cdot \frac{\color{blue}{{\left(\frac{0.07512208616047561}{z}\right)}^{2}} - 0.0692910599291889 \cdot 0.0692910599291889}{\frac{0.07512208616047561}{z} - 0.0692910599291889} \]

      4. metadata-eval 99.5%

         \[\leadsto x + y \cdot \frac{{\left(\frac{0.07512208616047561}{z}\right)}^{2} - \color{blue}{0.004801250986110448}}{\frac{0.07512208616047561}{z} - 0.0692910599291889} \]

   9. Applied egg-rr 99.5%

      \[\leadsto x + y \cdot \color{blue}{\frac{{\left(\frac{0.07512208616047561}{z}\right)}^{2} - 0.004801250986110448}{\frac{0.07512208616047561}{z} - 0.0692910599291889}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} \leq \infty:\\ \;\;\;\;x + y \cdot \frac{\mathsf{fma}\left(\frac{0.24180012482592123 - {z}^{2} \cdot 0.004801250986110448}{0.4917317610505968 - z \cdot 0.0692910599291889}, z, 0.279195317918525\right)}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{{\left(\frac{0.07512208616047561}{z}\right)}^{2} - 0.004801250986110448}{\frac{0.07512208616047561}{z} - 0.0692910599291889}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} \leq \infty:\\ \;\;\;\;x + y \cdot \frac{0.279195317918525 + z \cdot \frac{0.24180012482592123 + {z}^{2} \cdot -0.004801250986110448}{0.4917317610505968 + z \cdot -0.0692910599291889}}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{{\left(\frac{0.07512208616047561}{z}\right)}^{2} - 0.004801250986110448}{\frac{0.07512208616047561}{z} - 0.0692910599291889}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (/
       (*
        y
        (+
         (* z (+ (* z 0.0692910599291889) 0.4917317610505968))
         0.279195317918525))
       (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
      INFINITY)
   (+
    x
    (*
     y
     (/
      (+
       0.279195317918525
       (*
        z
        (/
         (+ 0.24180012482592123 (* (pow z 2.0) -0.004801250986110448))
         (+ 0.4917317610505968 (* z -0.0692910599291889)))))
      (fma z (+ z 6.012459259764103) 3.350343815022304))))
   (+
    x
    (*
     y
     (/
      (- (pow (/ 0.07512208616047561 z) 2.0) 0.004801250986110448)
      (- (/ 0.07512208616047561 z) 0.0692910599291889))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((y * ((z * ((z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / ((z * (z + 6.012459259764103)) + 3.350343815022304)) <= ((double) INFINITY)) {
		tmp = x + (y * ((0.279195317918525 + (z * ((0.24180012482592123 + (pow(z, 2.0) * -0.004801250986110448)) / (0.4917317610505968 + (z * -0.0692910599291889))))) / fma(z, (z + 6.012459259764103), 3.350343815022304)));
	} else {
		tmp = x + (y * ((pow((0.07512208616047561 / z), 2.0) - 0.004801250986110448) / ((0.07512208616047561 / z) - 0.0692910599291889)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / Float64(Float64(z * Float64(z + 6.012459259764103)) + 3.350343815022304)) <= Inf)
		tmp = Float64(x + Float64(y * Float64(Float64(0.279195317918525 + Float64(z * Float64(Float64(0.24180012482592123 + Float64((z ^ 2.0) * -0.004801250986110448)) / Float64(0.4917317610505968 + Float64(z * -0.0692910599291889))))) / fma(z, Float64(z + 6.012459259764103), 3.350343815022304))));
	else
		tmp = Float64(x + Float64(y * Float64(Float64((Float64(0.07512208616047561 / z) ^ 2.0) - 0.004801250986110448) / Float64(Float64(0.07512208616047561 / z) - 0.0692910599291889))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(y * N[(N[(z * N[(N[(z * 0.0692910599291889), $MachinePrecision] + 0.4917317610505968), $MachinePrecision]), $MachinePrecision] + 0.279195317918525), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(z + 6.012459259764103), $MachinePrecision]), $MachinePrecision] + 3.350343815022304), $MachinePrecision]), $MachinePrecision], Infinity], N[(x + N[(y * N[(N[(0.279195317918525 + N[(z * N[(N[(0.24180012482592123 + N[(N[Power[z, 2.0], $MachinePrecision] * -0.004801250986110448), $MachinePrecision]), $MachinePrecision] / N[(0.4917317610505968 + N[(z * -0.0692910599291889), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * N[(z + 6.012459259764103), $MachinePrecision] + 3.350343815022304), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(N[Power[N[(0.07512208616047561 / z), $MachinePrecision], 2.0], $MachinePrecision] - 0.004801250986110448), $MachinePrecision] / N[(N[(0.07512208616047561 / z), $MachinePrecision] - 0.0692910599291889), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 692910599291889/10000000000000000) 307332350656623/625000000000000) z) 11167812716741/40000000000000)) (+.f64 (*.f64 (+.f64 z 6012459259764103/1000000000000000) z) 104698244219447/31250000000000)) < +inf.0

   1. Initial program 96.1%

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

      1. remove-double-neg 96.1%

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

      2. distribute-lft-neg-out 96.1%

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

      3. distribute-neg-frac 96.1%

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

      4. associate-/l* 99.7%

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

      5. distribute-lft-neg-in 99.7%

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

      6. remove-double-neg 99.7%

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

      7. fma-define 99.7%

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

      8. fma-define 99.7%

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

      9. fma-define 99.7%

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

   3. Simplified 99.7%

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

      1. fma-define 99.7%

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

      2. +-commutative 99.7%

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

      3. flip-+ 99.7%

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

      4. metadata-eval 99.7%

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

      5. swap-sqr 99.7%

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

      6. pow2 99.7%

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

      7. metadata-eval 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around 0 89.9%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(0.279195317918525 + \frac{z \cdot \left(0.24180012482592123 - 0.004801250986110448 \cdot {z}^{2}\right)}{0.4917317610505968 - 0.0692910599291889 \cdot z}\right)}{3.350343815022304 + z \cdot \left(6.012459259764103 + z\right)}} \]
   8. Step-by-step derivation

      1. associate-/l* 92.4%

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

      2. associate-/l* 99.7%

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

      3. cancel-sign-sub-inv 99.7%

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

      4. metadata-eval 99.7%

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

      5. *-commutative 99.7%

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

      6. cancel-sign-sub-inv 99.7%

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

      7. metadata-eval 99.7%

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

      8. *-commutative 99.7%

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

      9. +-commutative 99.7%

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

      10. +-commutative 99.7%

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

      11. fma-undefine 99.7%

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

   9. Simplified 99.7%

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

   if +inf.0 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 692910599291889/10000000000000000) 307332350656623/625000000000000) z) 11167812716741/40000000000000)) (+.f64 (*.f64 (+.f64 z 6012459259764103/1000000000000000) z) 104698244219447/31250000000000))

   1. Initial program 0.0%

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

      1. remove-double-neg 0.0%

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

      2. distribute-lft-neg-out 0.0%

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

      3. distribute-neg-frac 0.0%

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

      4. associate-/l* 0.0%

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

      5. distribute-lft-neg-in 0.0%

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

      6. remove-double-neg 0.0%

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

      7. fma-define 0.0%

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

      8. fma-define 0.0%

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

      9. fma-define 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around inf 99.5%

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

      1. associate-*r/ 99.5%

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

      2. metadata-eval 99.5%

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

   7. Simplified 99.5%

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

      1. +-commutative 99.5%

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

      2. flip-+ 99.5%

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

      3. pow2 99.5%

         \[\leadsto x + y \cdot \frac{\color{blue}{{\left(\frac{0.07512208616047561}{z}\right)}^{2}} - 0.0692910599291889 \cdot 0.0692910599291889}{\frac{0.07512208616047561}{z} - 0.0692910599291889} \]

      4. metadata-eval 99.5%

         \[\leadsto x + y \cdot \frac{{\left(\frac{0.07512208616047561}{z}\right)}^{2} - \color{blue}{0.004801250986110448}}{\frac{0.07512208616047561}{z} - 0.0692910599291889} \]

   9. Applied egg-rr 99.5%

      \[\leadsto x + y \cdot \color{blue}{\frac{{\left(\frac{0.07512208616047561}{z}\right)}^{2} - 0.004801250986110448}{\frac{0.07512208616047561}{z} - 0.0692910599291889}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} \leq \infty:\\ \;\;\;\;x + y \cdot \frac{0.279195317918525 + z \cdot \frac{0.24180012482592123 + {z}^{2} \cdot -0.004801250986110448}{0.4917317610505968 + z \cdot -0.0692910599291889}}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{{\left(\frac{0.07512208616047561}{z}\right)}^{2} - 0.004801250986110448}{\frac{0.07512208616047561}{z} - 0.0692910599291889}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304\\ \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{t\_0} \leq 2 \cdot 10^{+304}:\\ \;\;\;\;x + \frac{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right) \cdot \left(y \cdot z\right) + y \cdot 0.279195317918525}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{{\left(\frac{0.07512208616047561}{z}\right)}^{2} - 0.004801250986110448}{\frac{0.07512208616047561}{z} - 0.0692910599291889}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))
   (if (<=
        (/
         (*
          y
          (+
           (* z (+ (* z 0.0692910599291889) 0.4917317610505968))
           0.279195317918525))
         t_0)
        2e+304)
     (+
      x
      (/
       (+
        (* (fma z 0.0692910599291889 0.4917317610505968) (* y z))
        (* y 0.279195317918525))
       t_0))
     (+
      x
      (*
       y
       (/
        (- (pow (/ 0.07512208616047561 z) 2.0) 0.004801250986110448)
        (- (/ 0.07512208616047561 z) 0.0692910599291889)))))))

C

double code(double x, double y, double z) {
	double t_0 = (z * (z + 6.012459259764103)) + 3.350343815022304;
	double tmp;
	if (((y * ((z * ((z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / t_0) <= 2e+304) {
		tmp = x + (((fma(z, 0.0692910599291889, 0.4917317610505968) * (y * z)) + (y * 0.279195317918525)) / t_0);
	} else {
		tmp = x + (y * ((pow((0.07512208616047561 / z), 2.0) - 0.004801250986110448) / ((0.07512208616047561 / z) - 0.0692910599291889)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * Float64(z + 6.012459259764103)) + 3.350343815022304)
	tmp = 0.0
	if (Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / t_0) <= 2e+304)
		tmp = Float64(x + Float64(Float64(Float64(fma(z, 0.0692910599291889, 0.4917317610505968) * Float64(y * z)) + Float64(y * 0.279195317918525)) / t_0));
	else
		tmp = Float64(x + Float64(y * Float64(Float64((Float64(0.07512208616047561 / z) ^ 2.0) - 0.004801250986110448) / Float64(Float64(0.07512208616047561 / z) - 0.0692910599291889))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * N[(z + 6.012459259764103), $MachinePrecision]), $MachinePrecision] + 3.350343815022304), $MachinePrecision]}, If[LessEqual[N[(N[(y * N[(N[(z * N[(N[(z * 0.0692910599291889), $MachinePrecision] + 0.4917317610505968), $MachinePrecision]), $MachinePrecision] + 0.279195317918525), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision], 2e+304], N[(x + N[(N[(N[(N[(z * 0.0692910599291889 + 0.4917317610505968), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(y * 0.279195317918525), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(N[Power[N[(0.07512208616047561 / z), $MachinePrecision], 2.0], $MachinePrecision] - 0.004801250986110448), $MachinePrecision] / N[(N[(0.07512208616047561 / z), $MachinePrecision] - 0.0692910599291889), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 692910599291889/10000000000000000) 307332350656623/625000000000000) z) 11167812716741/40000000000000)) (+.f64 (*.f64 (+.f64 z 6012459259764103/1000000000000000) z) 104698244219447/31250000000000)) < 1.9999999999999999e304

   1. Initial program 97.6%

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

      1. distribute-rgt-in 97.6%

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

      2. fma-define 97.6%

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

      3. associate-*l* 97.6%

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

   4. Applied egg-rr 97.6%

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

   if 1.9999999999999999e304 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 692910599291889/10000000000000000) 307332350656623/625000000000000) z) 11167812716741/40000000000000)) (+.f64 (*.f64 (+.f64 z 6012459259764103/1000000000000000) z) 104698244219447/31250000000000))

   1. Initial program 0.2%

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

      1. remove-double-neg 0.2%

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

      2. distribute-lft-neg-out 0.2%

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

      3. distribute-neg-frac 0.2%

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

      4. associate-/l* 4.1%

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

      5. distribute-lft-neg-in 4.1%

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

      6. remove-double-neg 4.1%

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

      7. fma-define 4.1%

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

      8. fma-define 4.1%

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

      9. fma-define 4.1%

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

   3. Simplified 4.1%

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

   5. Taylor expanded in z around inf 99.5%

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

      1. associate-*r/ 99.5%

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

      2. metadata-eval 99.5%

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

   7. Simplified 99.5%

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

      1. +-commutative 99.5%

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

      2. flip-+ 99.5%

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

      3. pow2 99.5%

         \[\leadsto x + y \cdot \frac{\color{blue}{{\left(\frac{0.07512208616047561}{z}\right)}^{2}} - 0.0692910599291889 \cdot 0.0692910599291889}{\frac{0.07512208616047561}{z} - 0.0692910599291889} \]

      4. metadata-eval 99.5%

         \[\leadsto x + y \cdot \frac{{\left(\frac{0.07512208616047561}{z}\right)}^{2} - \color{blue}{0.004801250986110448}}{\frac{0.07512208616047561}{z} - 0.0692910599291889} \]

   9. Applied egg-rr 99.5%

      \[\leadsto x + y \cdot \color{blue}{\frac{{\left(\frac{0.07512208616047561}{z}\right)}^{2} - 0.004801250986110448}{\frac{0.07512208616047561}{z} - 0.0692910599291889}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} \leq 2 \cdot 10^{+304}:\\ \;\;\;\;x + \frac{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right) \cdot \left(y \cdot z\right) + y \cdot 0.279195317918525}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{{\left(\frac{0.07512208616047561}{z}\right)}^{2} - 0.004801250986110448}{\frac{0.07512208616047561}{z} - 0.0692910599291889}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304}\\ \mathbf{if}\;t\_0 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t\_0 + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{{\left(\frac{0.07512208616047561}{z}\right)}^{2} - 0.004801250986110448}{\frac{0.07512208616047561}{z} - 0.0692910599291889}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (/
          (*
           y
           (+
            (* z (+ (* z 0.0692910599291889) 0.4917317610505968))
            0.279195317918525))
          (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
   (if (<= t_0 2e+304)
     (+ t_0 x)
     (+
      x
      (*
       y
       (/
        (- (pow (/ 0.07512208616047561 z) 2.0) 0.004801250986110448)
        (- (/ 0.07512208616047561 z) 0.0692910599291889)))))))

C

double code(double x, double y, double z) {
	double t_0 = (y * ((z * ((z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / ((z * (z + 6.012459259764103)) + 3.350343815022304);
	double tmp;
	if (t_0 <= 2e+304) {
		tmp = t_0 + x;
	} else {
		tmp = x + (y * ((pow((0.07512208616047561 / z), 2.0) - 0.004801250986110448) / ((0.07512208616047561 / z) - 0.0692910599291889)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (y * ((z * ((z * 0.0692910599291889d0) + 0.4917317610505968d0)) + 0.279195317918525d0)) / ((z * (z + 6.012459259764103d0)) + 3.350343815022304d0)
    if (t_0 <= 2d+304) then
        tmp = t_0 + x
    else
        tmp = x + (y * ((((0.07512208616047561d0 / z) ** 2.0d0) - 0.004801250986110448d0) / ((0.07512208616047561d0 / z) - 0.0692910599291889d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y * ((z * ((z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / ((z * (z + 6.012459259764103)) + 3.350343815022304);
	double tmp;
	if (t_0 <= 2e+304) {
		tmp = t_0 + x;
	} else {
		tmp = x + (y * ((Math.pow((0.07512208616047561 / z), 2.0) - 0.004801250986110448) / ((0.07512208616047561 / z) - 0.0692910599291889)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y * ((z * ((z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / ((z * (z + 6.012459259764103)) + 3.350343815022304)
	tmp = 0
	if t_0 <= 2e+304:
		tmp = t_0 + x
	else:
		tmp = x + (y * ((math.pow((0.07512208616047561 / z), 2.0) - 0.004801250986110448) / ((0.07512208616047561 / z) - 0.0692910599291889)))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / Float64(Float64(z * Float64(z + 6.012459259764103)) + 3.350343815022304))
	tmp = 0.0
	if (t_0 <= 2e+304)
		tmp = Float64(t_0 + x);
	else
		tmp = Float64(x + Float64(y * Float64(Float64((Float64(0.07512208616047561 / z) ^ 2.0) - 0.004801250986110448) / Float64(Float64(0.07512208616047561 / z) - 0.0692910599291889))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y * ((z * ((z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / ((z * (z + 6.012459259764103)) + 3.350343815022304);
	tmp = 0.0;
	if (t_0 <= 2e+304)
		tmp = t_0 + x;
	else
		tmp = x + (y * ((((0.07512208616047561 / z) ^ 2.0) - 0.004801250986110448) / ((0.07512208616047561 / z) - 0.0692910599291889)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * N[(N[(z * N[(N[(z * 0.0692910599291889), $MachinePrecision] + 0.4917317610505968), $MachinePrecision]), $MachinePrecision] + 0.279195317918525), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(z + 6.012459259764103), $MachinePrecision]), $MachinePrecision] + 3.350343815022304), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 2e+304], N[(t$95$0 + x), $MachinePrecision], N[(x + N[(y * N[(N[(N[Power[N[(0.07512208616047561 / z), $MachinePrecision], 2.0], $MachinePrecision] - 0.004801250986110448), $MachinePrecision] / N[(N[(0.07512208616047561 / z), $MachinePrecision] - 0.0692910599291889), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 692910599291889/10000000000000000) 307332350656623/625000000000000) z) 11167812716741/40000000000000)) (+.f64 (*.f64 (+.f64 z 6012459259764103/1000000000000000) z) 104698244219447/31250000000000)) < 1.9999999999999999e304

   1. Initial program 97.6%

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

   if 1.9999999999999999e304 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 692910599291889/10000000000000000) 307332350656623/625000000000000) z) 11167812716741/40000000000000)) (+.f64 (*.f64 (+.f64 z 6012459259764103/1000000000000000) z) 104698244219447/31250000000000))

   1. Initial program 0.2%

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

      1. remove-double-neg 0.2%

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

      2. distribute-lft-neg-out 0.2%

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

      3. distribute-neg-frac 0.2%

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

      4. associate-/l* 4.1%

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

      5. distribute-lft-neg-in 4.1%

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

      6. remove-double-neg 4.1%

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

      7. fma-define 4.1%

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

      8. fma-define 4.1%

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

      9. fma-define 4.1%

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

   3. Simplified 4.1%

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

   5. Taylor expanded in z around inf 99.5%

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

      1. associate-*r/ 99.5%

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

      2. metadata-eval 99.5%

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

   7. Simplified 99.5%

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

      1. +-commutative 99.5%

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

      2. flip-+ 99.5%

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

      3. pow2 99.5%

         \[\leadsto x + y \cdot \frac{\color{blue}{{\left(\frac{0.07512208616047561}{z}\right)}^{2}} - 0.0692910599291889 \cdot 0.0692910599291889}{\frac{0.07512208616047561}{z} - 0.0692910599291889} \]

      4. metadata-eval 99.5%

         \[\leadsto x + y \cdot \frac{{\left(\frac{0.07512208616047561}{z}\right)}^{2} - \color{blue}{0.004801250986110448}}{\frac{0.07512208616047561}{z} - 0.0692910599291889} \]

   9. Applied egg-rr 99.5%

      \[\leadsto x + y \cdot \color{blue}{\frac{{\left(\frac{0.07512208616047561}{z}\right)}^{2} - 0.004801250986110448}{\frac{0.07512208616047561}{z} - 0.0692910599291889}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{{\left(\frac{0.07512208616047561}{z}\right)}^{2} - 0.004801250986110448}{\frac{0.07512208616047561}{z} - 0.0692910599291889}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 96.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304}\\ \mathbf{if}\;t\_0 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t\_0 + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (/
          (*
           y
           (+
            (* z (+ (* z 0.0692910599291889) 0.4917317610505968))
            0.279195317918525))
          (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
   (if (<= t_0 2e+304) (+ t_0 x) (+ x (* y 0.0692910599291889)))))

C

double code(double x, double y, double z) {
	double t_0 = (y * ((z * ((z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / ((z * (z + 6.012459259764103)) + 3.350343815022304);
	double tmp;
	if (t_0 <= 2e+304) {
		tmp = t_0 + x;
	} else {
		tmp = x + (y * 0.0692910599291889);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (y * ((z * ((z * 0.0692910599291889d0) + 0.4917317610505968d0)) + 0.279195317918525d0)) / ((z * (z + 6.012459259764103d0)) + 3.350343815022304d0)
    if (t_0 <= 2d+304) then
        tmp = t_0 + x
    else
        tmp = x + (y * 0.0692910599291889d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y * ((z * ((z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / ((z * (z + 6.012459259764103)) + 3.350343815022304);
	double tmp;
	if (t_0 <= 2e+304) {
		tmp = t_0 + x;
	} else {
		tmp = x + (y * 0.0692910599291889);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y * ((z * ((z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / ((z * (z + 6.012459259764103)) + 3.350343815022304)
	tmp = 0
	if t_0 <= 2e+304:
		tmp = t_0 + x
	else:
		tmp = x + (y * 0.0692910599291889)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / Float64(Float64(z * Float64(z + 6.012459259764103)) + 3.350343815022304))
	tmp = 0.0
	if (t_0 <= 2e+304)
		tmp = Float64(t_0 + x);
	else
		tmp = Float64(x + Float64(y * 0.0692910599291889));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y * ((z * ((z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / ((z * (z + 6.012459259764103)) + 3.350343815022304);
	tmp = 0.0;
	if (t_0 <= 2e+304)
		tmp = t_0 + x;
	else
		tmp = x + (y * 0.0692910599291889);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * N[(N[(z * N[(N[(z * 0.0692910599291889), $MachinePrecision] + 0.4917317610505968), $MachinePrecision]), $MachinePrecision] + 0.279195317918525), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(z + 6.012459259764103), $MachinePrecision]), $MachinePrecision] + 3.350343815022304), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 2e+304], N[(t$95$0 + x), $MachinePrecision], N[(x + N[(y * 0.0692910599291889), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 692910599291889/10000000000000000) 307332350656623/625000000000000) z) 11167812716741/40000000000000)) (+.f64 (*.f64 (+.f64 z 6012459259764103/1000000000000000) z) 104698244219447/31250000000000)) < 1.9999999999999999e304

   1. Initial program 97.6%

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

   if 1.9999999999999999e304 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 692910599291889/10000000000000000) 307332350656623/625000000000000) z) 11167812716741/40000000000000)) (+.f64 (*.f64 (+.f64 z 6012459259764103/1000000000000000) z) 104698244219447/31250000000000))

   1. Initial program 0.2%

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

      1. +-commutative 0.2%

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

      2. *-commutative 0.2%

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

      3. associate-/l* 4.1%

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

      4. fma-define 4.1%

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

      5. *-commutative 4.1%

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

      6. fma-define 4.1%

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

      7. fma-define 4.1%

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

      8. *-commutative 4.1%

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

      9. fma-define 4.1%

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

   3. Simplified 4.1%

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

   5. Taylor expanded in z around inf 99.5%

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

      1. +-commutative 99.5%

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

   7. Simplified 99.5%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+29}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-11}:\\ \;\;\;\;x + \left(y \cdot 0.08333333333333323 + z \cdot \left(y \cdot -0.00277777777751721\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3e+29)
   (+ x (* y 0.0692910599291889))
   (if (<= z 2.25e-11)
     (+ x (+ (* y 0.08333333333333323) (* z (* y -0.00277777777751721))))
     (+ x (* y (+ 0.0692910599291889 (/ 0.07512208616047561 z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3e+29) {
		tmp = x + (y * 0.0692910599291889);
	} else if (z <= 2.25e-11) {
		tmp = x + ((y * 0.08333333333333323) + (z * (y * -0.00277777777751721)));
	} else {
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / 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 <= (-3d+29)) then
        tmp = x + (y * 0.0692910599291889d0)
    else if (z <= 2.25d-11) then
        tmp = x + ((y * 0.08333333333333323d0) + (z * (y * (-0.00277777777751721d0))))
    else
        tmp = x + (y * (0.0692910599291889d0 + (0.07512208616047561d0 / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3e+29) {
		tmp = x + (y * 0.0692910599291889);
	} else if (z <= 2.25e-11) {
		tmp = x + ((y * 0.08333333333333323) + (z * (y * -0.00277777777751721)));
	} else {
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3e+29:
		tmp = x + (y * 0.0692910599291889)
	elif z <= 2.25e-11:
		tmp = x + ((y * 0.08333333333333323) + (z * (y * -0.00277777777751721)))
	else:
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3e+29)
		tmp = Float64(x + Float64(y * 0.0692910599291889));
	elseif (z <= 2.25e-11)
		tmp = Float64(x + Float64(Float64(y * 0.08333333333333323) + Float64(z * Float64(y * -0.00277777777751721))));
	else
		tmp = Float64(x + Float64(y * Float64(0.0692910599291889 + Float64(0.07512208616047561 / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3e+29)
		tmp = x + (y * 0.0692910599291889);
	elseif (z <= 2.25e-11)
		tmp = x + ((y * 0.08333333333333323) + (z * (y * -0.00277777777751721)));
	else
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3e+29], N[(x + N[(y * 0.0692910599291889), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.25e-11], N[(x + N[(N[(y * 0.08333333333333323), $MachinePrecision] + N[(z * N[(y * -0.00277777777751721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(0.0692910599291889 + N[(0.07512208616047561 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9999999999999999e29

   1. Initial program 31.9%

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

      1. +-commutative 31.9%

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

      2. *-commutative 31.9%

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

      3. associate-/l* 32.8%

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

      4. fma-define 32.8%

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

      5. *-commutative 32.8%

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

      6. fma-define 32.8%

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

      7. fma-define 32.8%

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

      8. *-commutative 32.8%

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

      9. fma-define 32.8%

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

   3. Simplified 32.8%

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

   5. Taylor expanded in z around inf 99.5%

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

      1. +-commutative 99.5%

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

   7. Simplified 99.5%

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

   if -2.9999999999999999e29 < z < 2.25e-11

   1. Initial program 99.7%

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

      1. remove-double-neg 99.7%

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

      2. distribute-lft-neg-out 99.7%

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

      3. distribute-neg-frac 99.7%

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

      4. associate-/l* 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 99.9%

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

      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 99.3%

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

   6. Taylor expanded in y around 0 99.3%

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

      1. *-commutative 99.3%

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

   8. Simplified 99.3%

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

   if 2.25e-11 < z

   1. Initial program 38.4%

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

      1. remove-double-neg 38.4%

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

      2. distribute-lft-neg-out 38.4%

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

      3. distribute-neg-frac 38.4%

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

      4. associate-/l* 44.5%

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

      5. distribute-lft-neg-in 44.5%

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

      6. remove-double-neg 44.5%

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

      7. fma-define 44.5%

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

      8. fma-define 44.5%

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

      9. fma-define 44.5%

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

   3. Simplified 44.5%

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

   5. Taylor expanded in z around inf 99.5%

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

      1. associate-*r/ 99.5%

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

      2. metadata-eval 99.5%

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

   7. Simplified 99.5%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+29}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-11}:\\ \;\;\;\;x + \left(y \cdot 0.08333333333333323 + z \cdot \left(y \cdot -0.00277777777751721\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+29}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-11}:\\ \;\;\;\;x + \left(y \cdot 0.08333333333333323 + z \cdot \left(y \cdot -0.00277777777751721\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 0.0692910599291889 - y \cdot \frac{-0.07512208616047561}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3e+29)
   (+ x (* y 0.0692910599291889))
   (if (<= z 2.25e-11)
     (+ x (+ (* y 0.08333333333333323) (* z (* y -0.00277777777751721))))
     (+ x (- (* y 0.0692910599291889) (* y (/ -0.07512208616047561 z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3e+29) {
		tmp = x + (y * 0.0692910599291889);
	} else if (z <= 2.25e-11) {
		tmp = x + ((y * 0.08333333333333323) + (z * (y * -0.00277777777751721)));
	} else {
		tmp = x + ((y * 0.0692910599291889) - (y * (-0.07512208616047561 / 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 <= (-3d+29)) then
        tmp = x + (y * 0.0692910599291889d0)
    else if (z <= 2.25d-11) then
        tmp = x + ((y * 0.08333333333333323d0) + (z * (y * (-0.00277777777751721d0))))
    else
        tmp = x + ((y * 0.0692910599291889d0) - (y * ((-0.07512208616047561d0) / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3e+29) {
		tmp = x + (y * 0.0692910599291889);
	} else if (z <= 2.25e-11) {
		tmp = x + ((y * 0.08333333333333323) + (z * (y * -0.00277777777751721)));
	} else {
		tmp = x + ((y * 0.0692910599291889) - (y * (-0.07512208616047561 / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3e+29:
		tmp = x + (y * 0.0692910599291889)
	elif z <= 2.25e-11:
		tmp = x + ((y * 0.08333333333333323) + (z * (y * -0.00277777777751721)))
	else:
		tmp = x + ((y * 0.0692910599291889) - (y * (-0.07512208616047561 / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3e+29)
		tmp = Float64(x + Float64(y * 0.0692910599291889));
	elseif (z <= 2.25e-11)
		tmp = Float64(x + Float64(Float64(y * 0.08333333333333323) + Float64(z * Float64(y * -0.00277777777751721))));
	else
		tmp = Float64(x + Float64(Float64(y * 0.0692910599291889) - Float64(y * Float64(-0.07512208616047561 / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3e+29)
		tmp = x + (y * 0.0692910599291889);
	elseif (z <= 2.25e-11)
		tmp = x + ((y * 0.08333333333333323) + (z * (y * -0.00277777777751721)));
	else
		tmp = x + ((y * 0.0692910599291889) - (y * (-0.07512208616047561 / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3e+29], N[(x + N[(y * 0.0692910599291889), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.25e-11], N[(x + N[(N[(y * 0.08333333333333323), $MachinePrecision] + N[(z * N[(y * -0.00277777777751721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * 0.0692910599291889), $MachinePrecision] - N[(y * N[(-0.07512208616047561 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9999999999999999e29

   1. Initial program 31.9%

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

      1. +-commutative 31.9%

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

      2. *-commutative 31.9%

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

      3. associate-/l* 32.8%

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

      4. fma-define 32.8%

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

      5. *-commutative 32.8%

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

      6. fma-define 32.8%

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

      7. fma-define 32.8%

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

      8. *-commutative 32.8%

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

      9. fma-define 32.8%

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

   3. Simplified 32.8%

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

   5. Taylor expanded in z around inf 99.5%

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

      1. +-commutative 99.5%

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

   7. Simplified 99.5%

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

   if -2.9999999999999999e29 < z < 2.25e-11

   1. Initial program 99.7%

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

      1. remove-double-neg 99.7%

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

      2. distribute-lft-neg-out 99.7%

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

      3. distribute-neg-frac 99.7%

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

      4. associate-/l* 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 99.9%

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

      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 99.3%

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

   6. Taylor expanded in y around 0 99.3%

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

      1. *-commutative 99.3%

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

   8. Simplified 99.3%

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

   if 2.25e-11 < z

   1. Initial program 38.4%

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

      1. remove-double-neg 38.4%

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

      2. distribute-lft-neg-out 38.4%

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

      3. distribute-neg-frac 38.4%

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

      4. associate-/l* 44.5%

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

      5. distribute-lft-neg-in 44.5%

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

      6. remove-double-neg 44.5%

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

      7. fma-define 44.5%

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

      8. fma-define 44.5%

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

      9. fma-define 44.5%

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

   3. Simplified 44.5%

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

   5. Taylor expanded in z around -inf 99.5%

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{-0.4917317610505968 \cdot y - -0.4166096748901212 \cdot y}{z} + 0.0692910599291889 \cdot y\right)} \]
   6. Step-by-step derivation

      1. +-commutative 99.5%

         \[\leadsto x + \color{blue}{\left(0.0692910599291889 \cdot y + -1 \cdot \frac{-0.4917317610505968 \cdot y - -0.4166096748901212 \cdot y}{z}\right)} \]

      2. mul-1-neg 99.5%

         \[\leadsto x + \left(0.0692910599291889 \cdot y + \color{blue}{\left(-\frac{-0.4917317610505968 \cdot y - -0.4166096748901212 \cdot y}{z}\right)}\right) \]

      3. unsub-neg 99.5%

         \[\leadsto x + \color{blue}{\left(0.0692910599291889 \cdot y - \frac{-0.4917317610505968 \cdot y - -0.4166096748901212 \cdot y}{z}\right)} \]

      4. distribute-rgt-out-- 99.5%

         \[\leadsto x + \left(0.0692910599291889 \cdot y - \frac{\color{blue}{y \cdot \left(-0.4917317610505968 - -0.4166096748901212\right)}}{z}\right) \]

      5. associate-/l* 99.5%

         \[\leadsto x + \left(0.0692910599291889 \cdot y - \color{blue}{y \cdot \frac{-0.4917317610505968 - -0.4166096748901212}{z}}\right) \]

      6. metadata-eval 99.5%

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

   7. Simplified 99.5%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+29}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-11}:\\ \;\;\;\;x + \left(y \cdot 0.08333333333333323 + z \cdot \left(y \cdot -0.00277777777751721\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 0.0692910599291889 - y \cdot \frac{-0.07512208616047561}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+29}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-11}:\\ \;\;\;\;x + y \cdot 0.08333333333333323\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3e+29)
   (+ x (* y 0.0692910599291889))
   (if (<= z 2.25e-11)
     (+ x (* y 0.08333333333333323))
     (+ x (* y (+ 0.0692910599291889 (/ 0.07512208616047561 z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3e+29) {
		tmp = x + (y * 0.0692910599291889);
	} else if (z <= 2.25e-11) {
		tmp = x + (y * 0.08333333333333323);
	} else {
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / 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 <= (-3d+29)) then
        tmp = x + (y * 0.0692910599291889d0)
    else if (z <= 2.25d-11) then
        tmp = x + (y * 0.08333333333333323d0)
    else
        tmp = x + (y * (0.0692910599291889d0 + (0.07512208616047561d0 / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3e+29) {
		tmp = x + (y * 0.0692910599291889);
	} else if (z <= 2.25e-11) {
		tmp = x + (y * 0.08333333333333323);
	} else {
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3e+29:
		tmp = x + (y * 0.0692910599291889)
	elif z <= 2.25e-11:
		tmp = x + (y * 0.08333333333333323)
	else:
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3e+29)
		tmp = Float64(x + Float64(y * 0.0692910599291889));
	elseif (z <= 2.25e-11)
		tmp = Float64(x + Float64(y * 0.08333333333333323));
	else
		tmp = Float64(x + Float64(y * Float64(0.0692910599291889 + Float64(0.07512208616047561 / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3e+29)
		tmp = x + (y * 0.0692910599291889);
	elseif (z <= 2.25e-11)
		tmp = x + (y * 0.08333333333333323);
	else
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3e+29], N[(x + N[(y * 0.0692910599291889), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.25e-11], N[(x + N[(y * 0.08333333333333323), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(0.0692910599291889 + N[(0.07512208616047561 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9999999999999999e29

   1. Initial program 31.9%

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

      1. +-commutative 31.9%

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

      2. *-commutative 31.9%

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

      3. associate-/l* 32.8%

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

      4. fma-define 32.8%

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

      5. *-commutative 32.8%

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

      6. fma-define 32.8%

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

      7. fma-define 32.8%

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

      8. *-commutative 32.8%

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

      9. fma-define 32.8%

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

   3. Simplified 32.8%

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

   5. Taylor expanded in z around inf 99.5%

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

      1. +-commutative 99.5%

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

   7. Simplified 99.5%

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

   if -2.9999999999999999e29 < z < 2.25e-11

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-/l* 99.7%

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

      4. fma-define 99.7%

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

      5. *-commutative 99.7%

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

      6. fma-define 99.7%

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

      7. fma-define 99.7%

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

      8. *-commutative 99.7%

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

      9. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 98.5%

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

      1. +-commutative 98.5%

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

   7. Simplified 98.5%

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

   if 2.25e-11 < z

   1. Initial program 38.4%

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

      1. remove-double-neg 38.4%

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

      2. distribute-lft-neg-out 38.4%

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

      3. distribute-neg-frac 38.4%

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

      4. associate-/l* 44.5%

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

      5. distribute-lft-neg-in 44.5%

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

      6. remove-double-neg 44.5%

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

      7. fma-define 44.5%

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

      8. fma-define 44.5%

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

      9. fma-define 44.5%

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

   3. Simplified 44.5%

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

   5. Taylor expanded in z around inf 99.5%

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

      1. associate-*r/ 99.5%

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

      2. metadata-eval 99.5%

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

   7. Simplified 99.5%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+29}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-11}:\\ \;\;\;\;x + y \cdot 0.08333333333333323\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+29}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-11}:\\ \;\;\;\;x + y \cdot \left(0.08333333333333323 + z \cdot -0.00277777777751721\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3e+29)
   (+ x (* y 0.0692910599291889))
   (if (<= z 2.25e-11)
     (+ x (* y (+ 0.08333333333333323 (* z -0.00277777777751721))))
     (+ x (* y (+ 0.0692910599291889 (/ 0.07512208616047561 z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3e+29) {
		tmp = x + (y * 0.0692910599291889);
	} else if (z <= 2.25e-11) {
		tmp = x + (y * (0.08333333333333323 + (z * -0.00277777777751721)));
	} else {
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / 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 <= (-3d+29)) then
        tmp = x + (y * 0.0692910599291889d0)
    else if (z <= 2.25d-11) then
        tmp = x + (y * (0.08333333333333323d0 + (z * (-0.00277777777751721d0))))
    else
        tmp = x + (y * (0.0692910599291889d0 + (0.07512208616047561d0 / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3e+29) {
		tmp = x + (y * 0.0692910599291889);
	} else if (z <= 2.25e-11) {
		tmp = x + (y * (0.08333333333333323 + (z * -0.00277777777751721)));
	} else {
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3e+29:
		tmp = x + (y * 0.0692910599291889)
	elif z <= 2.25e-11:
		tmp = x + (y * (0.08333333333333323 + (z * -0.00277777777751721)))
	else:
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3e+29)
		tmp = Float64(x + Float64(y * 0.0692910599291889));
	elseif (z <= 2.25e-11)
		tmp = Float64(x + Float64(y * Float64(0.08333333333333323 + Float64(z * -0.00277777777751721))));
	else
		tmp = Float64(x + Float64(y * Float64(0.0692910599291889 + Float64(0.07512208616047561 / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3e+29)
		tmp = x + (y * 0.0692910599291889);
	elseif (z <= 2.25e-11)
		tmp = x + (y * (0.08333333333333323 + (z * -0.00277777777751721)));
	else
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3e+29], N[(x + N[(y * 0.0692910599291889), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.25e-11], N[(x + N[(y * N[(0.08333333333333323 + N[(z * -0.00277777777751721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(0.0692910599291889 + N[(0.07512208616047561 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9999999999999999e29

   1. Initial program 31.9%

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

      1. +-commutative 31.9%

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

      2. *-commutative 31.9%

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

      3. associate-/l* 32.8%

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

      4. fma-define 32.8%

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

      5. *-commutative 32.8%

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

      6. fma-define 32.8%

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

      7. fma-define 32.8%

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

      8. *-commutative 32.8%

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

      9. fma-define 32.8%

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

   3. Simplified 32.8%

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

   5. Taylor expanded in z around inf 99.5%

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

      1. +-commutative 99.5%

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

   7. Simplified 99.5%

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

   if -2.9999999999999999e29 < z < 2.25e-11

   1. Initial program 99.7%

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

      1. remove-double-neg 99.7%

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

      2. distribute-lft-neg-out 99.7%

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

      3. distribute-neg-frac 99.7%

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

      4. associate-/l* 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 99.9%

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

      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 99.3%

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

   if 2.25e-11 < z

   1. Initial program 38.4%

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

      1. remove-double-neg 38.4%

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

      2. distribute-lft-neg-out 38.4%

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

      3. distribute-neg-frac 38.4%

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

      4. associate-/l* 44.5%

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

      5. distribute-lft-neg-in 44.5%

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

      6. remove-double-neg 44.5%

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

      7. fma-define 44.5%

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

      8. fma-define 44.5%

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

      9. fma-define 44.5%

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

   3. Simplified 44.5%

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

   5. Taylor expanded in z around inf 99.5%

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

      1. associate-*r/ 99.5%

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

      2. metadata-eval 99.5%

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

   7. Simplified 99.5%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+29}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-11}:\\ \;\;\;\;x + y \cdot \left(0.08333333333333323 + z \cdot -0.00277777777751721\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 98.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+29} \lor \neg \left(z \leq 2.25 \cdot 10^{-11}\right):\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.08333333333333323\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3e+29) (not (<= z 2.25e-11)))
   (+ x (* y 0.0692910599291889))
   (+ x (* y 0.08333333333333323))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3e+29) || !(z <= 2.25e-11)) {
		tmp = x + (y * 0.0692910599291889);
	} else {
		tmp = x + (y * 0.08333333333333323);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-3d+29)) .or. (.not. (z <= 2.25d-11))) then
        tmp = x + (y * 0.0692910599291889d0)
    else
        tmp = x + (y * 0.08333333333333323d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3e+29) || !(z <= 2.25e-11)) {
		tmp = x + (y * 0.0692910599291889);
	} else {
		tmp = x + (y * 0.08333333333333323);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3e+29) or not (z <= 2.25e-11):
		tmp = x + (y * 0.0692910599291889)
	else:
		tmp = x + (y * 0.08333333333333323)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3e+29) || !(z <= 2.25e-11))
		tmp = Float64(x + Float64(y * 0.0692910599291889));
	else
		tmp = Float64(x + Float64(y * 0.08333333333333323));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3e+29) || ~((z <= 2.25e-11)))
		tmp = x + (y * 0.0692910599291889);
	else
		tmp = x + (y * 0.08333333333333323);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3e+29], N[Not[LessEqual[z, 2.25e-11]], $MachinePrecision]], N[(x + N[(y * 0.0692910599291889), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 0.08333333333333323), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9999999999999999e29 or 2.25e-11 < z

   1. Initial program 36.0%

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

      1. +-commutative 36.0%

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

      2. *-commutative 36.0%

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

      3. associate-/l* 37.9%

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

      4. fma-define 37.8%

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

      5. *-commutative 37.8%

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

      6. fma-define 37.8%

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

      7. fma-define 37.8%

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

      8. *-commutative 37.8%

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

      9. fma-define 37.8%

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

   3. Simplified 37.8%

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

   5. Taylor expanded in z around inf 99.3%

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

      1. +-commutative 99.3%

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

   7. Simplified 99.3%

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

   if -2.9999999999999999e29 < z < 2.25e-11

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-/l* 99.7%

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

      4. fma-define 99.7%

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

      5. *-commutative 99.7%

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

      6. fma-define 99.7%

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

      7. fma-define 99.7%

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

      8. *-commutative 99.7%

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

      9. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 98.5%

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

      1. +-commutative 98.5%

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

   7. Simplified 98.5%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+29} \lor \neg \left(z \leq 2.25 \cdot 10^{-11}\right):\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.08333333333333323\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.62 \cdot 10^{+47} \lor \neg \left(y \leq 2.3 \cdot 10^{+20}\right):\\ \;\;\;\;y \cdot 0.08333333333333323\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.62e+47) (not (<= y 2.3e+20))) (* y 0.08333333333333323) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.62e+47) || !(y <= 2.3e+20)) {
		tmp = y * 0.08333333333333323;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.62d+47)) .or. (.not. (y <= 2.3d+20))) then
        tmp = y * 0.08333333333333323d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.62e+47) || !(y <= 2.3e+20)) {
		tmp = y * 0.08333333333333323;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.62e+47) or not (y <= 2.3e+20):
		tmp = y * 0.08333333333333323
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.62e+47) || !(y <= 2.3e+20))
		tmp = Float64(y * 0.08333333333333323);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.62e+47) || ~((y <= 2.3e+20)))
		tmp = y * 0.08333333333333323;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.62e+47], N[Not[LessEqual[y, 2.3e+20]], $MachinePrecision]], N[(y * 0.08333333333333323), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.6200000000000001e47 or 2.3e20 < y

   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. +-commutative 68.6%

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

      2. *-commutative 68.6%

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

      3. associate-/l* 74.8%

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

      4. fma-define 74.8%

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

      5. *-commutative 74.8%

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

      6. fma-define 74.8%

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

      7. fma-define 74.8%

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

      8. *-commutative 74.8%

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

      9. fma-define 74.8%

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

   3. Simplified 74.8%

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

   5. Taylor expanded in z around 0 75.2%

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

      1. +-commutative 75.2%

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

      2. fma-define 75.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(0.08333333333333323, y, x\right)} \]

   7. Simplified 75.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.08333333333333323, y, x\right)} \]

   8. Taylor expanded in y around inf 56.2%

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

   if -1.6200000000000001e47 < y < 2.3e20

   1. Initial program 70.7%

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

      1. +-commutative 70.7%

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

      2. *-commutative 70.7%

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

      3. associate-/l* 67.8%

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

      4. fma-define 67.8%

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

      5. *-commutative 67.8%

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

      6. fma-define 67.8%

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

      7. fma-define 67.8%

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

      8. *-commutative 67.8%

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

      9. fma-define 67.8%

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

   3. Simplified 67.8%

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

   5. Taylor expanded in y around 0 73.7%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.62 \cdot 10^{+47} \lor \neg \left(y \leq 2.3 \cdot 10^{+20}\right):\\ \;\;\;\;y \cdot 0.08333333333333323\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.42 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-170}:\\ \;\;\;\;y \cdot 0.0692910599291889\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.42e-5) x (if (<= x 5.5e-170) (* y 0.0692910599291889) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.42e-5) {
		tmp = x;
	} else if (x <= 5.5e-170) {
		tmp = y * 0.0692910599291889;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.42d-5)) then
        tmp = x
    else if (x <= 5.5d-170) then
        tmp = y * 0.0692910599291889d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.42e-5) {
		tmp = x;
	} else if (x <= 5.5e-170) {
		tmp = y * 0.0692910599291889;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.42e-5:
		tmp = x
	elif x <= 5.5e-170:
		tmp = y * 0.0692910599291889
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.42e-5)
		tmp = x;
	elseif (x <= 5.5e-170)
		tmp = Float64(y * 0.0692910599291889);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.42e-5)
		tmp = x;
	elseif (x <= 5.5e-170)
		tmp = y * 0.0692910599291889;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.42e-5], x, If[LessEqual[x, 5.5e-170], N[(y * 0.0692910599291889), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.42e-5 or 5.50000000000000018e-170 < x

   1. Initial program 72.2%

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

      1. +-commutative 72.2%

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

      2. *-commutative 72.2%

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

      3. associate-/l* 75.0%

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

      4. fma-define 75.0%

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

      5. *-commutative 75.0%

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

      6. fma-define 75.0%

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

      7. fma-define 75.0%

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

      8. *-commutative 75.0%

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

      9. fma-define 75.0%

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

   3. Simplified 75.0%

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

   5. Taylor expanded in y around 0 70.6%

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

   if -1.42e-5 < x < 5.50000000000000018e-170

   1. Initial program 65.7%

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

      1. +-commutative 65.7%

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

      2. *-commutative 65.7%

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

      3. associate-/l* 62.9%

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

      4. fma-define 62.9%

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

      5. *-commutative 62.9%

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

      6. fma-define 62.9%

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

      7. fma-define 62.9%

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

      8. *-commutative 62.9%

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

      9. fma-define 62.9%

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

   3. Simplified 62.9%

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

   5. Taylor expanded in z around inf 67.5%

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

      1. +-commutative 67.5%

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

   7. Simplified 67.5%

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

   8. Taylor expanded in y around inf 51.2%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.42 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-170}:\\ \;\;\;\;y \cdot 0.0692910599291889\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 77.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.05 \cdot 10^{+147}:\\ \;\;\;\;y \cdot 0.08333333333333323\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.05e+147)
   (* y 0.08333333333333323)
   (+ x (* y 0.0692910599291889))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.05e+147) {
		tmp = y * 0.08333333333333323;
	} else {
		tmp = x + (y * 0.0692910599291889);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3.05d+147)) then
        tmp = y * 0.08333333333333323d0
    else
        tmp = x + (y * 0.0692910599291889d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.05e+147) {
		tmp = y * 0.08333333333333323;
	} else {
		tmp = x + (y * 0.0692910599291889);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.05e+147:
		tmp = y * 0.08333333333333323
	else:
		tmp = x + (y * 0.0692910599291889)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.05e+147)
		tmp = Float64(y * 0.08333333333333323);
	else
		tmp = Float64(x + Float64(y * 0.0692910599291889));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.05e+147)
		tmp = y * 0.08333333333333323;
	else
		tmp = x + (y * 0.0692910599291889);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.05e+147], N[(y * 0.08333333333333323), $MachinePrecision], N[(x + N[(y * 0.0692910599291889), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.05000000000000016e147

   1. Initial program 78.6%

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

      1. +-commutative 78.6%

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

      2. *-commutative 78.6%

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

      3. associate-/l* 90.0%

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

      4. fma-define 90.1%

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

      5. *-commutative 90.1%

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

      6. fma-define 90.1%

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

      7. fma-define 90.1%

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

      8. *-commutative 90.1%

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

      9. fma-define 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in z around 0 81.1%

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

      1. +-commutative 81.1%

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

      2. fma-define 81.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(0.08333333333333323, y, x\right)} \]

   7. Simplified 81.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.08333333333333323, y, x\right)} \]

   8. Taylor expanded in y around inf 69.7%

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

   if -3.05000000000000016e147 < y

   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. +-commutative 68.6%

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

      2. *-commutative 68.6%

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

      3. associate-/l* 67.9%

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

      4. fma-define 67.9%

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

      5. *-commutative 67.9%

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

      6. fma-define 67.9%

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

      7. fma-define 67.9%

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

      8. *-commutative 67.9%

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

      9. fma-define 67.9%

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

   3. Simplified 67.9%

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

   5. Taylor expanded in z around inf 82.6%

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

      1. +-commutative 82.6%

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

   7. Simplified 82.6%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.05 \cdot 10^{+147}:\\ \;\;\;\;y \cdot 0.08333333333333323\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.8% 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 69.8%

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

   1. +-commutative 69.8%

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

   2. *-commutative 69.8%

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

   3. associate-/l* 70.7%

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

   4. fma-define 70.7%

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

   5. *-commutative 70.7%

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

   6. fma-define 70.7%

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

   7. fma-define 70.7%

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

   8. *-commutative 70.7%

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

   9. fma-define 70.7%

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

3. Simplified 70.7%

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

5. Taylor expanded in y around 0 52.2%

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

6. Final simplification 52.2%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.4% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (((0.07512208616047561d0 / z) + 0.0692910599291889d0) * y) - (((0.40462203869992125d0 * y) / (z * z)) - x)
    if (z < (-8120153.652456675d0)) then
        tmp = t_0
    else if (z < 6.576118972787377d+20) then
        tmp = x + ((y * ((((z * 0.0692910599291889d0) + 0.4917317610505968d0) * z) + 0.279195317918525d0)) * (1.0d0 / (((z + 6.012459259764103d0) * z) + 3.350343815022304d0)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024043 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, B"
  :precision binary64

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

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