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

Percentage Accurate: 69.0% → 99.7%

Time: 9.5s

Alternatives: 13

Speedup: 2.3×

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: 69.0% 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: 99.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \mathbf{elif}\;z \leq 48:\\ \;\;\;\;\frac{y \cdot \left(z \cdot \left(0.4917317610505968 + z \cdot 0.0692910599291889\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{14.431876219268936 - \frac{15.646356830292042}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.1e+16)
   (+ x (/ y 14.431876219268936))
   (if (<= z 48.0)
     (+
      (/
       (*
        y
        (+
         (* z (+ 0.4917317610505968 (* z 0.0692910599291889)))
         0.279195317918525))
       (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
      x)
     (+ x (/ y (- 14.431876219268936 (/ 15.646356830292042 z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.1e+16) {
		tmp = x + (y / 14.431876219268936);
	} else if (z <= 48.0) {
		tmp = ((y * ((z * (0.4917317610505968 + (z * 0.0692910599291889))) + 0.279195317918525)) / ((z * (z + 6.012459259764103)) + 3.350343815022304)) + x;
	} else {
		tmp = x + (y / (14.431876219268936 - (15.646356830292042 / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.1d+16)) then
        tmp = x + (y / 14.431876219268936d0)
    else if (z <= 48.0d0) then
        tmp = ((y * ((z * (0.4917317610505968d0 + (z * 0.0692910599291889d0))) + 0.279195317918525d0)) / ((z * (z + 6.012459259764103d0)) + 3.350343815022304d0)) + x
    else
        tmp = x + (y / (14.431876219268936d0 - (15.646356830292042d0 / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.1e+16) {
		tmp = x + (y / 14.431876219268936);
	} else if (z <= 48.0) {
		tmp = ((y * ((z * (0.4917317610505968 + (z * 0.0692910599291889))) + 0.279195317918525)) / ((z * (z + 6.012459259764103)) + 3.350343815022304)) + x;
	} else {
		tmp = x + (y / (14.431876219268936 - (15.646356830292042 / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.1e+16:
		tmp = x + (y / 14.431876219268936)
	elif z <= 48.0:
		tmp = ((y * ((z * (0.4917317610505968 + (z * 0.0692910599291889))) + 0.279195317918525)) / ((z * (z + 6.012459259764103)) + 3.350343815022304)) + x
	else:
		tmp = x + (y / (14.431876219268936 - (15.646356830292042 / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.1e+16)
		tmp = Float64(x + Float64(y / 14.431876219268936));
	elseif (z <= 48.0)
		tmp = Float64(Float64(Float64(y * Float64(Float64(z * Float64(0.4917317610505968 + Float64(z * 0.0692910599291889))) + 0.279195317918525)) / Float64(Float64(z * Float64(z + 6.012459259764103)) + 3.350343815022304)) + x);
	else
		tmp = Float64(x + Float64(y / Float64(14.431876219268936 - Float64(15.646356830292042 / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.1e+16)
		tmp = x + (y / 14.431876219268936);
	elseif (z <= 48.0)
		tmp = ((y * ((z * (0.4917317610505968 + (z * 0.0692910599291889))) + 0.279195317918525)) / ((z * (z + 6.012459259764103)) + 3.350343815022304)) + x;
	else
		tmp = x + (y / (14.431876219268936 - (15.646356830292042 / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.1e+16], N[(x + N[(y / 14.431876219268936), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 48.0], N[(N[(N[(y * N[(N[(z * N[(0.4917317610505968 + N[(z * 0.0692910599291889), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 0.279195317918525), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(z + 6.012459259764103), $MachinePrecision]), $MachinePrecision] + 3.350343815022304), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(y / N[(14.431876219268936 - N[(15.646356830292042 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1e16

   1. Initial program 33.8%

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

      1. associate-/l* 43.6%

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

      2. fma-def 43.6%

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

      3. fma-def 43.6%

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

      4. fma-def 43.6%

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

   3. Simplified 43.6%

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

   4. Taylor expanded in z around inf 99.9%

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

   if -1.1e16 < z < 48

   1. Initial program 99.6%

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

   if 48 < z

   1. Initial program 40.8%

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

      1. associate-/l* 49.0%

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

      2. fma-def 49.0%

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

      3. fma-def 49.0%

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

      4. fma-def 49.0%

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

   3. Simplified 49.0%

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

   4. Taylor expanded in z around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. metadata-eval 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \mathbf{elif}\;z \leq 48:\\ \;\;\;\;\frac{y \cdot \left(z \cdot \left(0.4917317610505968 + z \cdot 0.0692910599291889\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{14.431876219268936 - \frac{15.646356830292042}{z}}\\ \end{array} \]

Alternative 2: 99.3% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(0.4917317610505968 + z \cdot 0.0692910599291889\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} \leq 5 \cdot 10^{+290}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right)}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (/
       (*
        y
        (+
         (* z (+ 0.4917317610505968 (* z 0.0692910599291889)))
         0.279195317918525))
       (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
      5e+290)
   (fma
    y
    (/
     (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525)
     (fma z (+ z 6.012459259764103) 3.350343815022304))
    x)
   (+ x (/ y 14.431876219268936))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((y * ((z * (0.4917317610505968 + (z * 0.0692910599291889))) + 0.279195317918525)) / ((z * (z + 6.012459259764103)) + 3.350343815022304)) <= 5e+290) {
		tmp = fma(y, (fma(z, fma(z, 0.0692910599291889, 0.4917317610505968), 0.279195317918525) / fma(z, (z + 6.012459259764103), 3.350343815022304)), x);
	} else {
		tmp = x + (y / 14.431876219268936);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(y * Float64(Float64(z * Float64(0.4917317610505968 + Float64(z * 0.0692910599291889))) + 0.279195317918525)) / Float64(Float64(z * Float64(z + 6.012459259764103)) + 3.350343815022304)) <= 5e+290)
		tmp = fma(y, Float64(fma(z, fma(z, 0.0692910599291889, 0.4917317610505968), 0.279195317918525) / fma(z, Float64(z + 6.012459259764103), 3.350343815022304)), x);
	else
		tmp = Float64(x + Float64(y / 14.431876219268936));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(y * N[(N[(z * N[(0.4917317610505968 + N[(z * 0.0692910599291889), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 0.279195317918525), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(z + 6.012459259764103), $MachinePrecision]), $MachinePrecision] + 3.350343815022304), $MachinePrecision]), $MachinePrecision], 5e+290], N[(y * N[(N[(z * N[(z * 0.0692910599291889 + 0.4917317610505968), $MachinePrecision] + 0.279195317918525), $MachinePrecision] / N[(z * N[(z + 6.012459259764103), $MachinePrecision] + 3.350343815022304), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(y / 14.431876219268936), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 692910599291889/10000000000000000) 307332350656623/625000000000000) z) 11167812716741/40000000000000)) (+.f64 (*.f64 (+.f64 z 6012459259764103/1000000000000000) z) 104698244219447/31250000000000)) < 4.9999999999999998e290

   1. Initial program 94.9%

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

      1. +-commutative 94.9%

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

      2. associate-*r/ 99.4%

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

      3. fma-def 99.4%

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

      4. *-commutative 99.4%

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

      5. fma-def 99.4%

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

      6. fma-def 99.4%

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

      7. *-commutative 99.4%

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

      8. fma-def 99.4%

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

   3. Simplified 99.4%

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

   if 4.9999999999999998e290 < (/.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. associate-/l* 4.3%

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

      2. fma-def 4.3%

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

      3. fma-def 4.3%

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

      4. fma-def 4.3%

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

   3. Simplified 4.3%

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

   4. Taylor expanded in z around inf 99.9%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(0.4917317610505968 + z \cdot 0.0692910599291889\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} \leq 5 \cdot 10^{+290}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), 0.279195317918525\right)}{\mathsf{fma}\left(z, z + 6.012459259764103, 3.350343815022304\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \end{array} \]

Alternative 3: 99.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(0.4917317610505968 + z \cdot 0.0692910599291889\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} \leq 5 \cdot 10^{+290}:\\ \;\;\;\;x + \frac{y}{\frac{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (/
       (*
        y
        (+
         (* z (+ 0.4917317610505968 (* z 0.0692910599291889)))
         0.279195317918525))
       (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
      5e+290)
   (+
    x
    (/
     y
     (/
      (fma (+ z 6.012459259764103) z 3.350343815022304)
      (fma
       (fma z 0.0692910599291889 0.4917317610505968)
       z
       0.279195317918525))))
   (+ x (/ y 14.431876219268936))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((y * ((z * (0.4917317610505968 + (z * 0.0692910599291889))) + 0.279195317918525)) / ((z * (z + 6.012459259764103)) + 3.350343815022304)) <= 5e+290) {
		tmp = x + (y / (fma((z + 6.012459259764103), z, 3.350343815022304) / fma(fma(z, 0.0692910599291889, 0.4917317610505968), z, 0.279195317918525)));
	} else {
		tmp = x + (y / 14.431876219268936);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(y * Float64(Float64(z * Float64(0.4917317610505968 + Float64(z * 0.0692910599291889))) + 0.279195317918525)) / Float64(Float64(z * Float64(z + 6.012459259764103)) + 3.350343815022304)) <= 5e+290)
		tmp = Float64(x + Float64(y / Float64(fma(Float64(z + 6.012459259764103), z, 3.350343815022304) / fma(fma(z, 0.0692910599291889, 0.4917317610505968), z, 0.279195317918525))));
	else
		tmp = Float64(x + Float64(y / 14.431876219268936));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(y * N[(N[(z * N[(0.4917317610505968 + N[(z * 0.0692910599291889), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 0.279195317918525), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(z + 6.012459259764103), $MachinePrecision]), $MachinePrecision] + 3.350343815022304), $MachinePrecision]), $MachinePrecision], 5e+290], N[(x + N[(y / N[(N[(N[(z + 6.012459259764103), $MachinePrecision] * z + 3.350343815022304), $MachinePrecision] / N[(N[(z * 0.0692910599291889 + 0.4917317610505968), $MachinePrecision] * z + 0.279195317918525), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / 14.431876219268936), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 692910599291889/10000000000000000) 307332350656623/625000000000000) z) 11167812716741/40000000000000)) (+.f64 (*.f64 (+.f64 z 6012459259764103/1000000000000000) z) 104698244219447/31250000000000)) < 4.9999999999999998e290

   1. Initial program 94.9%

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

      1. associate-/l* 99.1%

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

      2. fma-def 99.1%

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

      3. fma-def 99.1%

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

      4. fma-def 99.1%

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

   3. Simplified 99.1%

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

   if 4.9999999999999998e290 < (/.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. associate-/l* 4.3%

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

      2. fma-def 4.3%

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

      3. fma-def 4.3%

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

      4. fma-def 4.3%

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

   3. Simplified 4.3%

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

   4. Taylor expanded in z around inf 99.9%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(0.4917317610505968 + z \cdot 0.0692910599291889\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} \leq 5 \cdot 10^{+290}:\\ \;\;\;\;x + \frac{y}{\frac{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \end{array} \]

Alternative 4: 98.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304\\ t_1 := z \cdot \left(0.4917317610505968 + z \cdot 0.0692910599291889\right)\\ \mathbf{if}\;\frac{y \cdot \left(t_1 + 0.279195317918525\right)}{t_0} \leq 5 \cdot 10^{+290}:\\ \;\;\;\;x + y \cdot \left(\frac{t_1}{t_0} + 0.279195317918525 \cdot \frac{1}{t_0}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
        (t_1 (* z (+ 0.4917317610505968 (* z 0.0692910599291889)))))
   (if (<= (/ (* y (+ t_1 0.279195317918525)) t_0) 5e+290)
     (+ x (* y (+ (/ t_1 t_0) (* 0.279195317918525 (/ 1.0 t_0)))))
     (+ x (/ y 14.431876219268936)))))

C

double code(double x, double y, double z) {
	double t_0 = (z * (z + 6.012459259764103)) + 3.350343815022304;
	double t_1 = z * (0.4917317610505968 + (z * 0.0692910599291889));
	double tmp;
	if (((y * (t_1 + 0.279195317918525)) / t_0) <= 5e+290) {
		tmp = x + (y * ((t_1 / t_0) + (0.279195317918525 * (1.0 / t_0))));
	} else {
		tmp = x + (y / 14.431876219268936);
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = (z * (z + 6.012459259764103d0)) + 3.350343815022304d0
    t_1 = z * (0.4917317610505968d0 + (z * 0.0692910599291889d0))
    if (((y * (t_1 + 0.279195317918525d0)) / t_0) <= 5d+290) then
        tmp = x + (y * ((t_1 / t_0) + (0.279195317918525d0 * (1.0d0 / t_0))))
    else
        tmp = x + (y / 14.431876219268936d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z * (z + 6.012459259764103)) + 3.350343815022304;
	double t_1 = z * (0.4917317610505968 + (z * 0.0692910599291889));
	double tmp;
	if (((y * (t_1 + 0.279195317918525)) / t_0) <= 5e+290) {
		tmp = x + (y * ((t_1 / t_0) + (0.279195317918525 * (1.0 / t_0))));
	} else {
		tmp = x + (y / 14.431876219268936);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z * (z + 6.012459259764103)) + 3.350343815022304
	t_1 = z * (0.4917317610505968 + (z * 0.0692910599291889))
	tmp = 0
	if ((y * (t_1 + 0.279195317918525)) / t_0) <= 5e+290:
		tmp = x + (y * ((t_1 / t_0) + (0.279195317918525 * (1.0 / t_0))))
	else:
		tmp = x + (y / 14.431876219268936)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * Float64(z + 6.012459259764103)) + 3.350343815022304)
	t_1 = Float64(z * Float64(0.4917317610505968 + Float64(z * 0.0692910599291889)))
	tmp = 0.0
	if (Float64(Float64(y * Float64(t_1 + 0.279195317918525)) / t_0) <= 5e+290)
		tmp = Float64(x + Float64(y * Float64(Float64(t_1 / t_0) + Float64(0.279195317918525 * Float64(1.0 / t_0)))));
	else
		tmp = Float64(x + Float64(y / 14.431876219268936));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z * (z + 6.012459259764103)) + 3.350343815022304;
	t_1 = z * (0.4917317610505968 + (z * 0.0692910599291889));
	tmp = 0.0;
	if (((y * (t_1 + 0.279195317918525)) / t_0) <= 5e+290)
		tmp = x + (y * ((t_1 / t_0) + (0.279195317918525 * (1.0 / t_0))));
	else
		tmp = x + (y / 14.431876219268936);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * N[(z + 6.012459259764103), $MachinePrecision]), $MachinePrecision] + 3.350343815022304), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(0.4917317610505968 + N[(z * 0.0692910599291889), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(y * N[(t$95$1 + 0.279195317918525), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision], 5e+290], N[(x + N[(y * N[(N[(t$95$1 / t$95$0), $MachinePrecision] + N[(0.279195317918525 * N[(1.0 / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / 14.431876219268936), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 692910599291889/10000000000000000) 307332350656623/625000000000000) z) 11167812716741/40000000000000)) (+.f64 (*.f64 (+.f64 z 6012459259764103/1000000000000000) z) 104698244219447/31250000000000)) < 4.9999999999999998e290

   1. Initial program 94.9%

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

      1. +-commutative 94.9%

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

      2. associate-*r/ 99.4%

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

      3. fma-def 99.4%

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

      4. *-commutative 99.4%

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

      5. fma-def 99.4%

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

      6. fma-def 99.4%

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

      7. *-commutative 99.4%

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

      8. fma-def 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in y around 0 99.0%

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

   if 4.9999999999999998e290 < (/.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. associate-/l* 4.3%

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

      2. fma-def 4.3%

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

      3. fma-def 4.3%

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

      4. fma-def 4.3%

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

   3. Simplified 4.3%

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

   4. Taylor expanded in z around inf 99.9%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(0.4917317610505968 + z \cdot 0.0692910599291889\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} \leq 5 \cdot 10^{+290}:\\ \;\;\;\;x + y \cdot \left(\frac{z \cdot \left(0.4917317610505968 + z \cdot 0.0692910599291889\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} + 0.279195317918525 \cdot \frac{1}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \end{array} \]

Alternative 5: 99.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5:\\ \;\;\;\;x + \frac{y}{14.431876219268936 + \frac{\frac{101.23733352003822}{z} - 15.646356830292042}{z}}\\ \mathbf{elif}\;z \leq 6.3:\\ \;\;\;\;x + \frac{y}{z \cdot 0.39999999996247915 + 12.000000000000014}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{14.431876219268936 - \frac{15.646356830292042}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.5)
   (+
    x
    (/
     y
     (+
      14.431876219268936
      (/ (- (/ 101.23733352003822 z) 15.646356830292042) z))))
   (if (<= z 6.3)
     (+ x (/ y (+ (* z 0.39999999996247915) 12.000000000000014)))
     (+ x (/ y (- 14.431876219268936 (/ 15.646356830292042 z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.5) {
		tmp = x + (y / (14.431876219268936 + (((101.23733352003822 / z) - 15.646356830292042) / z)));
	} else if (z <= 6.3) {
		tmp = x + (y / ((z * 0.39999999996247915) + 12.000000000000014));
	} else {
		tmp = x + (y / (14.431876219268936 - (15.646356830292042 / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-5.5d0)) then
        tmp = x + (y / (14.431876219268936d0 + (((101.23733352003822d0 / z) - 15.646356830292042d0) / z)))
    else if (z <= 6.3d0) then
        tmp = x + (y / ((z * 0.39999999996247915d0) + 12.000000000000014d0))
    else
        tmp = x + (y / (14.431876219268936d0 - (15.646356830292042d0 / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.5) {
		tmp = x + (y / (14.431876219268936 + (((101.23733352003822 / z) - 15.646356830292042) / z)));
	} else if (z <= 6.3) {
		tmp = x + (y / ((z * 0.39999999996247915) + 12.000000000000014));
	} else {
		tmp = x + (y / (14.431876219268936 - (15.646356830292042 / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.5:
		tmp = x + (y / (14.431876219268936 + (((101.23733352003822 / z) - 15.646356830292042) / z)))
	elif z <= 6.3:
		tmp = x + (y / ((z * 0.39999999996247915) + 12.000000000000014))
	else:
		tmp = x + (y / (14.431876219268936 - (15.646356830292042 / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.5)
		tmp = Float64(x + Float64(y / Float64(14.431876219268936 + Float64(Float64(Float64(101.23733352003822 / z) - 15.646356830292042) / z))));
	elseif (z <= 6.3)
		tmp = Float64(x + Float64(y / Float64(Float64(z * 0.39999999996247915) + 12.000000000000014)));
	else
		tmp = Float64(x + Float64(y / Float64(14.431876219268936 - Float64(15.646356830292042 / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.5)
		tmp = x + (y / (14.431876219268936 + (((101.23733352003822 / z) - 15.646356830292042) / z)));
	elseif (z <= 6.3)
		tmp = x + (y / ((z * 0.39999999996247915) + 12.000000000000014));
	else
		tmp = x + (y / (14.431876219268936 - (15.646356830292042 / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.5], N[(x + N[(y / N[(14.431876219268936 + N[(N[(N[(101.23733352003822 / z), $MachinePrecision] - 15.646356830292042), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.3], N[(x + N[(y / N[(N[(z * 0.39999999996247915), $MachinePrecision] + 12.000000000000014), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(14.431876219268936 - N[(15.646356830292042 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.5

   1. Initial program 35.0%

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

      1. associate-/l* 44.6%

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

      2. fma-def 44.6%

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

      3. fma-def 44.6%

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

      4. fma-def 44.6%

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

   3. Simplified 44.6%

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

   4. Taylor expanded in z around inf 99.6%

      \[\leadsto x + \frac{y}{\color{blue}{\left(14.431876219268936 + 101.23733352003822 \cdot \frac{1}{{z}^{2}}\right) - 15.646356830292042 \cdot \frac{1}{z}}} \]
   5. Step-by-step derivation

      1. associate-*r/ 99.6%

         \[\leadsto x + \frac{y}{\left(14.431876219268936 + \color{blue}{\frac{101.23733352003822 \cdot 1}{{z}^{2}}}\right) - 15.646356830292042 \cdot \frac{1}{z}} \]

      2. metadata-eval 99.6%

         \[\leadsto x + \frac{y}{\left(14.431876219268936 + \frac{\color{blue}{101.23733352003822}}{{z}^{2}}\right) - 15.646356830292042 \cdot \frac{1}{z}} \]

      3. unpow2 99.6%

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

      4. associate-*r/ 99.6%

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

      5. metadata-eval 99.6%

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

   6. Simplified 99.6%

      \[\leadsto x + \frac{y}{\color{blue}{\left(14.431876219268936 + \frac{101.23733352003822}{z \cdot z}\right) - \frac{15.646356830292042}{z}}} \]
   7. Step-by-step derivation

      1. associate--l+ 99.6%

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

      2. +-commutative 99.6%

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

      3. associate-/r* 99.6%

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

      4. sub-div 99.6%

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

   8. Applied egg-rr 99.6%

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

   if -5.5 < z < 6.29999999999999982

   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. associate-/l* 99.3%

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

      2. fma-def 99.3%

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

      3. fma-def 99.3%

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

      4. fma-def 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in z around 0 99.2%

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

   if 6.29999999999999982 < z

   1. Initial program 40.8%

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

      1. associate-/l* 49.0%

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

      2. fma-def 49.0%

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

      3. fma-def 49.0%

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

      4. fma-def 49.0%

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

   3. Simplified 49.0%

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

   4. Taylor expanded in z around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. metadata-eval 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5:\\ \;\;\;\;x + \frac{y}{14.431876219268936 + \frac{\frac{101.23733352003822}{z} - 15.646356830292042}{z}}\\ \mathbf{elif}\;z \leq 6.3:\\ \;\;\;\;x + \frac{y}{z \cdot 0.39999999996247915 + 12.000000000000014}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{14.431876219268936 - \frac{15.646356830292042}{z}}\\ \end{array} \]

Alternative 6: 99.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 6.2\right):\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot 0.39999999996247915 + 12.000000000000014}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.5) (not (<= z 6.2)))
   (+ x (/ y 14.431876219268936))
   (+ x (/ y (+ (* z 0.39999999996247915) 12.000000000000014)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.5) || !(z <= 6.2)) {
		tmp = x + (y / 14.431876219268936);
	} else {
		tmp = x + (y / ((z * 0.39999999996247915) + 12.000000000000014));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-5.5d0)) .or. (.not. (z <= 6.2d0))) then
        tmp = x + (y / 14.431876219268936d0)
    else
        tmp = x + (y / ((z * 0.39999999996247915d0) + 12.000000000000014d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.5) || !(z <= 6.2)) {
		tmp = x + (y / 14.431876219268936);
	} else {
		tmp = x + (y / ((z * 0.39999999996247915) + 12.000000000000014));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.5) or not (z <= 6.2):
		tmp = x + (y / 14.431876219268936)
	else:
		tmp = x + (y / ((z * 0.39999999996247915) + 12.000000000000014))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.5) || !(z <= 6.2))
		tmp = Float64(x + Float64(y / 14.431876219268936));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(z * 0.39999999996247915) + 12.000000000000014)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.5) || ~((z <= 6.2)))
		tmp = x + (y / 14.431876219268936);
	else
		tmp = x + (y / ((z * 0.39999999996247915) + 12.000000000000014));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.5], N[Not[LessEqual[z, 6.2]], $MachinePrecision]], N[(x + N[(y / 14.431876219268936), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(z * 0.39999999996247915), $MachinePrecision] + 12.000000000000014), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5 or 6.20000000000000018 < z

   1. Initial program 38.1%

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

      1. associate-/l* 47.0%

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

      2. fma-def 47.0%

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

      3. fma-def 47.0%

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

      4. fma-def 47.0%

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

   3. Simplified 47.0%

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

   4. Taylor expanded in z around inf 99.1%

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

   if -5.5 < z < 6.20000000000000018

   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. associate-/l* 99.3%

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

      2. fma-def 99.3%

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

      3. fma-def 99.3%

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

      4. fma-def 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in z around 0 99.2%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 6.2\right):\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot 0.39999999996247915 + 12.000000000000014}\\ \end{array} \]

Alternative 7: 99.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 6.2\right):\\ \;\;\;\;x + \frac{y}{14.431876219268936 - \frac{15.646356830292042}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot 0.39999999996247915 + 12.000000000000014}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.5) (not (<= z 6.2)))
   (+ x (/ y (- 14.431876219268936 (/ 15.646356830292042 z))))
   (+ x (/ y (+ (* z 0.39999999996247915) 12.000000000000014)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.5) || !(z <= 6.2)) {
		tmp = x + (y / (14.431876219268936 - (15.646356830292042 / z)));
	} else {
		tmp = x + (y / ((z * 0.39999999996247915) + 12.000000000000014));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-5.5d0)) .or. (.not. (z <= 6.2d0))) then
        tmp = x + (y / (14.431876219268936d0 - (15.646356830292042d0 / z)))
    else
        tmp = x + (y / ((z * 0.39999999996247915d0) + 12.000000000000014d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.5) || !(z <= 6.2)) {
		tmp = x + (y / (14.431876219268936 - (15.646356830292042 / z)));
	} else {
		tmp = x + (y / ((z * 0.39999999996247915) + 12.000000000000014));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.5) or not (z <= 6.2):
		tmp = x + (y / (14.431876219268936 - (15.646356830292042 / z)))
	else:
		tmp = x + (y / ((z * 0.39999999996247915) + 12.000000000000014))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.5) || !(z <= 6.2))
		tmp = Float64(x + Float64(y / Float64(14.431876219268936 - Float64(15.646356830292042 / z))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(z * 0.39999999996247915) + 12.000000000000014)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.5) || ~((z <= 6.2)))
		tmp = x + (y / (14.431876219268936 - (15.646356830292042 / z)));
	else
		tmp = x + (y / ((z * 0.39999999996247915) + 12.000000000000014));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.5], N[Not[LessEqual[z, 6.2]], $MachinePrecision]], N[(x + N[(y / N[(14.431876219268936 - N[(15.646356830292042 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(z * 0.39999999996247915), $MachinePrecision] + 12.000000000000014), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5 or 6.20000000000000018 < z

   1. Initial program 38.1%

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

      1. associate-/l* 47.0%

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

      2. fma-def 47.0%

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

      3. fma-def 47.0%

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

      4. fma-def 47.0%

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

   3. Simplified 47.0%

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

   4. Taylor expanded in z around inf 99.6%

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

      1. associate-*r/ 99.6%

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

      2. metadata-eval 99.6%

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

   6. Simplified 99.6%

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

   if -5.5 < z < 6.20000000000000018

   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. associate-/l* 99.3%

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

      2. fma-def 99.3%

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

      3. fma-def 99.3%

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

      4. fma-def 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in z around 0 99.2%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 6.2\right):\\ \;\;\;\;x + \frac{y}{14.431876219268936 - \frac{15.646356830292042}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot 0.39999999996247915 + 12.000000000000014}\\ \end{array} \]

Alternative 8: 60.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+234}:\\ \;\;\;\;y \cdot 0.08333333333333323\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-29}:\\ \;\;\;\;y \cdot 0.0692910599291889\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+72}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.08333333333333323\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.7e+234)
   (* y 0.08333333333333323)
   (if (<= y -1.05e-29)
     (* y 0.0692910599291889)
     (if (<= y 1.45e+72) x (* y 0.08333333333333323)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.7e+234) {
		tmp = y * 0.08333333333333323;
	} else if (y <= -1.05e-29) {
		tmp = y * 0.0692910599291889;
	} else if (y <= 1.45e+72) {
		tmp = x;
	} else {
		tmp = y * 0.08333333333333323;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.7d+234)) then
        tmp = y * 0.08333333333333323d0
    else if (y <= (-1.05d-29)) then
        tmp = y * 0.0692910599291889d0
    else if (y <= 1.45d+72) then
        tmp = x
    else
        tmp = y * 0.08333333333333323d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.7e+234) {
		tmp = y * 0.08333333333333323;
	} else if (y <= -1.05e-29) {
		tmp = y * 0.0692910599291889;
	} else if (y <= 1.45e+72) {
		tmp = x;
	} else {
		tmp = y * 0.08333333333333323;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.7e+234:
		tmp = y * 0.08333333333333323
	elif y <= -1.05e-29:
		tmp = y * 0.0692910599291889
	elif y <= 1.45e+72:
		tmp = x
	else:
		tmp = y * 0.08333333333333323
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.7e+234)
		tmp = Float64(y * 0.08333333333333323);
	elseif (y <= -1.05e-29)
		tmp = Float64(y * 0.0692910599291889);
	elseif (y <= 1.45e+72)
		tmp = x;
	else
		tmp = Float64(y * 0.08333333333333323);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.7e+234)
		tmp = y * 0.08333333333333323;
	elseif (y <= -1.05e-29)
		tmp = y * 0.0692910599291889;
	elseif (y <= 1.45e+72)
		tmp = x;
	else
		tmp = y * 0.08333333333333323;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.7e+234], N[(y * 0.08333333333333323), $MachinePrecision], If[LessEqual[y, -1.05e-29], N[(y * 0.0692910599291889), $MachinePrecision], If[LessEqual[y, 1.45e+72], x, N[(y * 0.08333333333333323), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7e234 or 1.45000000000000009e72 < y

   1. Initial program 68.2%

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

      1. associate-/l* 73.4%

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

      2. fma-def 73.4%

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

      3. fma-def 73.4%

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

      4. fma-def 73.4%

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

   3. Simplified 73.4%

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

   4. Taylor expanded in z around 0 67.8%

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

   5. Taylor expanded in x around 0 57.1%

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

   6. Taylor expanded in z around 0 62.3%

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

      1. *-commutative 62.3%

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

   8. Simplified 62.3%

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

   if -1.7e234 < y < -1.04999999999999995e-29

   1. Initial program 54.2%

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

      1. +-commutative 54.2%

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

      2. associate-*r/ 68.1%

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

      3. fma-def 68.1%

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

      4. *-commutative 68.1%

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

      5. fma-def 68.1%

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

      6. fma-def 68.2%

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

      7. *-commutative 68.2%

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

      8. fma-def 68.2%

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

   3. Simplified 68.2%

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

   4. Taylor expanded in z around inf 76.9%

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

   5. Taylor expanded in y around inf 56.4%

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

   if -1.04999999999999995e-29 < y < 1.45000000000000009e72

   1. Initial program 75.9%

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

      1. +-commutative 75.9%

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

      2. associate-*r/ 75.9%

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

      3. fma-def 75.9%

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

      4. *-commutative 75.9%

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

      5. fma-def 75.9%

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

      6. fma-def 75.9%

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

      7. *-commutative 75.9%

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

      8. fma-def 75.9%

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

   3. Simplified 75.9%

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

   4. Taylor expanded in y around 0 75.9%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+234}:\\ \;\;\;\;y \cdot 0.08333333333333323\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-29}:\\ \;\;\;\;y \cdot 0.0692910599291889\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+72}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.08333333333333323\\ \end{array} \]

Alternative 9: 60.8% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+233}:\\ \;\;\;\;\frac{y}{12.000000000000014}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-29}:\\ \;\;\;\;y \cdot 0.0692910599291889\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+72}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{12.000000000000014}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8e+233)
   (/ y 12.000000000000014)
   (if (<= y -1.05e-29)
     (* y 0.0692910599291889)
     (if (<= y 1.15e+72) x (/ y 12.000000000000014)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8e+233) {
		tmp = y / 12.000000000000014;
	} else if (y <= -1.05e-29) {
		tmp = y * 0.0692910599291889;
	} else if (y <= 1.15e+72) {
		tmp = x;
	} else {
		tmp = y / 12.000000000000014;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-8d+233)) then
        tmp = y / 12.000000000000014d0
    else if (y <= (-1.05d-29)) then
        tmp = y * 0.0692910599291889d0
    else if (y <= 1.15d+72) then
        tmp = x
    else
        tmp = y / 12.000000000000014d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -8e+233) {
		tmp = y / 12.000000000000014;
	} else if (y <= -1.05e-29) {
		tmp = y * 0.0692910599291889;
	} else if (y <= 1.15e+72) {
		tmp = x;
	} else {
		tmp = y / 12.000000000000014;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8e+233:
		tmp = y / 12.000000000000014
	elif y <= -1.05e-29:
		tmp = y * 0.0692910599291889
	elif y <= 1.15e+72:
		tmp = x
	else:
		tmp = y / 12.000000000000014
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8e+233)
		tmp = Float64(y / 12.000000000000014);
	elseif (y <= -1.05e-29)
		tmp = Float64(y * 0.0692910599291889);
	elseif (y <= 1.15e+72)
		tmp = x;
	else
		tmp = Float64(y / 12.000000000000014);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -8e+233)
		tmp = y / 12.000000000000014;
	elseif (y <= -1.05e-29)
		tmp = y * 0.0692910599291889;
	elseif (y <= 1.15e+72)
		tmp = x;
	else
		tmp = y / 12.000000000000014;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8e+233], N[(y / 12.000000000000014), $MachinePrecision], If[LessEqual[y, -1.05e-29], N[(y * 0.0692910599291889), $MachinePrecision], If[LessEqual[y, 1.15e+72], x, N[(y / 12.000000000000014), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.99999999999999979e233 or 1.15e72 < y

   1. Initial program 68.2%

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

      1. associate-/l* 73.4%

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

      2. fma-def 73.4%

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

      3. fma-def 73.4%

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

      4. fma-def 73.4%

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

   3. Simplified 73.4%

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

   4. Taylor expanded in z around 0 67.8%

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

   5. Taylor expanded in x around 0 57.1%

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

   6. Taylor expanded in z around 0 62.4%

      \[\leadsto \frac{y}{\color{blue}{12.000000000000014}} \]

   if -7.99999999999999979e233 < y < -1.04999999999999995e-29

   1. Initial program 54.2%

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

      1. +-commutative 54.2%

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

      2. associate-*r/ 68.1%

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

      3. fma-def 68.1%

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

      4. *-commutative 68.1%

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

      5. fma-def 68.1%

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

      6. fma-def 68.2%

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

      7. *-commutative 68.2%

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

      8. fma-def 68.2%

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

   3. Simplified 68.2%

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

   4. Taylor expanded in z around inf 76.9%

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

   5. Taylor expanded in y around inf 56.4%

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

   if -1.04999999999999995e-29 < y < 1.15e72

   1. Initial program 75.9%

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

      1. +-commutative 75.9%

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

      2. associate-*r/ 75.9%

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

      3. fma-def 75.9%

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

      4. *-commutative 75.9%

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

      5. fma-def 75.9%

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

      6. fma-def 75.9%

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

      7. *-commutative 75.9%

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

      8. fma-def 75.9%

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

   3. Simplified 75.9%

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

   4. Taylor expanded in y around 0 75.9%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+233}:\\ \;\;\;\;\frac{y}{12.000000000000014}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-29}:\\ \;\;\;\;y \cdot 0.0692910599291889\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+72}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{12.000000000000014}\\ \end{array} \]

Alternative 10: 78.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+234} \lor \neg \left(y \leq -3.1 \cdot 10^{+168}\right):\\ \;\;\;\;x + \frac{y}{12.000000000000014}\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.0692910599291889\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.3e+234) (not (<= y -3.1e+168)))
   (+ x (/ y 12.000000000000014))
   (* y 0.0692910599291889)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.3e+234) || !(y <= -3.1e+168)) {
		tmp = x + (y / 12.000000000000014);
	} else {
		tmp = 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 <= (-4.3d+234)) .or. (.not. (y <= (-3.1d+168)))) then
        tmp = x + (y / 12.000000000000014d0)
    else
        tmp = y * 0.0692910599291889d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.3e+234) || !(y <= -3.1e+168)) {
		tmp = x + (y / 12.000000000000014);
	} else {
		tmp = y * 0.0692910599291889;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.3e+234) or not (y <= -3.1e+168):
		tmp = x + (y / 12.000000000000014)
	else:
		tmp = y * 0.0692910599291889
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.3e+234) || !(y <= -3.1e+168))
		tmp = Float64(x + Float64(y / 12.000000000000014));
	else
		tmp = Float64(y * 0.0692910599291889);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.3e+234) || ~((y <= -3.1e+168)))
		tmp = x + (y / 12.000000000000014);
	else
		tmp = y * 0.0692910599291889;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.3e+234], N[Not[LessEqual[y, -3.1e+168]], $MachinePrecision]], N[(x + N[(y / 12.000000000000014), $MachinePrecision]), $MachinePrecision], N[(y * 0.0692910599291889), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.2999999999999998e234 or -3.09999999999999996e168 < y

   1. Initial program 71.7%

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

      1. associate-/l* 73.5%

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

      2. fma-def 73.5%

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

      3. fma-def 73.5%

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

      4. fma-def 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in z around 0 81.3%

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

   if -4.2999999999999998e234 < y < -3.09999999999999996e168

   1. Initial program 46.9%

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

      1. +-commutative 46.9%

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

      2. associate-*r/ 74.4%

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

      3. fma-def 74.4%

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

      4. *-commutative 74.4%

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

      5. fma-def 74.4%

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

      6. fma-def 74.4%

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

      7. *-commutative 74.4%

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

      8. fma-def 74.4%

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

   3. Simplified 74.4%

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

   4. Taylor expanded in z around inf 77.7%

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

   5. Taylor expanded in y around inf 72.7%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+234} \lor \neg \left(y \leq -3.1 \cdot 10^{+168}\right):\\ \;\;\;\;x + \frac{y}{12.000000000000014}\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.0692910599291889\\ \end{array} \]

Alternative 11: 99.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 5.6\right):\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{12.000000000000014}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.5) (not (<= z 5.6)))
   (+ x (/ y 14.431876219268936))
   (+ x (/ y 12.000000000000014))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.5) || !(z <= 5.6)) {
		tmp = x + (y / 14.431876219268936);
	} else {
		tmp = x + (y / 12.000000000000014);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-5.5d0)) .or. (.not. (z <= 5.6d0))) then
        tmp = x + (y / 14.431876219268936d0)
    else
        tmp = x + (y / 12.000000000000014d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.5) || !(z <= 5.6)) {
		tmp = x + (y / 14.431876219268936);
	} else {
		tmp = x + (y / 12.000000000000014);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.5) or not (z <= 5.6):
		tmp = x + (y / 14.431876219268936)
	else:
		tmp = x + (y / 12.000000000000014)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.5) || !(z <= 5.6))
		tmp = Float64(x + Float64(y / 14.431876219268936));
	else
		tmp = Float64(x + Float64(y / 12.000000000000014));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.5) || ~((z <= 5.6)))
		tmp = x + (y / 14.431876219268936);
	else
		tmp = x + (y / 12.000000000000014);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.5], N[Not[LessEqual[z, 5.6]], $MachinePrecision]], N[(x + N[(y / 14.431876219268936), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / 12.000000000000014), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5 or 5.5999999999999996 < z

   1. Initial program 38.1%

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

      1. associate-/l* 47.0%

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

      2. fma-def 47.0%

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

      3. fma-def 47.0%

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

      4. fma-def 47.0%

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

   3. Simplified 47.0%

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

   4. Taylor expanded in z around inf 99.1%

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

   if -5.5 < z < 5.5999999999999996

   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. associate-/l* 99.3%

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

      2. fma-def 99.3%

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

      3. fma-def 99.3%

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

      4. fma-def 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in z around 0 98.9%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \lor \neg \left(z \leq 5.6\right):\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{12.000000000000014}\\ \end{array} \]

Alternative 12: 60.2% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-29}:\\ \;\;\;\;y \cdot 0.0692910599291889\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+72}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.0692910599291889\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.05e-29)
   (* y 0.0692910599291889)
   (if (<= y 1.3e+72) x (* y 0.0692910599291889))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.05e-29) {
		tmp = y * 0.0692910599291889;
	} else if (y <= 1.3e+72) {
		tmp = x;
	} else {
		tmp = 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 <= (-1.05d-29)) then
        tmp = y * 0.0692910599291889d0
    else if (y <= 1.3d+72) then
        tmp = x
    else
        tmp = y * 0.0692910599291889d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.05e-29) {
		tmp = y * 0.0692910599291889;
	} else if (y <= 1.3e+72) {
		tmp = x;
	} else {
		tmp = y * 0.0692910599291889;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.05e-29:
		tmp = y * 0.0692910599291889
	elif y <= 1.3e+72:
		tmp = x
	else:
		tmp = y * 0.0692910599291889
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.05e-29)
		tmp = Float64(y * 0.0692910599291889);
	elseif (y <= 1.3e+72)
		tmp = x;
	else
		tmp = Float64(y * 0.0692910599291889);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.05e-29)
		tmp = y * 0.0692910599291889;
	elseif (y <= 1.3e+72)
		tmp = x;
	else
		tmp = y * 0.0692910599291889;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.05e-29], N[(y * 0.0692910599291889), $MachinePrecision], If[LessEqual[y, 1.3e+72], x, N[(y * 0.0692910599291889), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.04999999999999995e-29 or 1.29999999999999991e72 < y

   1. Initial program 61.9%

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

      1. +-commutative 61.9%

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

      2. associate-*r/ 71.3%

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

      3. fma-def 71.3%

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

      4. *-commutative 71.3%

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

      5. fma-def 71.3%

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

      6. fma-def 71.3%

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

      7. *-commutative 71.3%

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

      8. fma-def 71.3%

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

   3. Simplified 71.3%

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

   4. Taylor expanded in z around inf 65.0%

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

   5. Taylor expanded in y around inf 49.0%

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

   if -1.04999999999999995e-29 < y < 1.29999999999999991e72

   1. Initial program 75.9%

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

      1. +-commutative 75.9%

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

      2. associate-*r/ 75.9%

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

      3. fma-def 75.9%

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

      4. *-commutative 75.9%

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

      5. fma-def 75.9%

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

      6. fma-def 75.9%

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

      7. *-commutative 75.9%

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

      8. fma-def 75.9%

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

   3. Simplified 75.9%

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

   4. Taylor expanded in y around 0 75.9%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-29}:\\ \;\;\;\;y \cdot 0.0692910599291889\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+72}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.0692910599291889\\ \end{array} \]

Alternative 13: 50.6% 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 69.4%

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

   1. +-commutative 69.4%

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

   2. associate-*r/ 73.8%

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

   3. fma-def 73.8%

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

   4. *-commutative 73.8%

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

   5. fma-def 73.8%

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

   6. fma-def 73.8%

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

   7. *-commutative 73.8%

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

   8. fma-def 73.8%

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

3. Simplified 73.8%

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

4. Taylor expanded in y around 0 48.4%

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

5. Final simplification 48.4%

   \[\leadsto x \]

Developer target: 99.4% accurate, 0.8× 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 2023230 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (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))))