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

Percentage Accurate: 69.8% → 99.3%

Time: 15.6s

Alternatives: 13

Speedup: 1.4×

Specification

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (+
  x
  (/
   (*
    y
    (+
     (* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
     0.279195317918525))
   (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))

C

double code(double x, double y, double z) {
	return x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((y * ((((z * 0.0692910599291889d0) + 0.4917317610505968d0) * z) + 0.279195317918525d0)) / (((z + 6.012459259764103d0) * z) + 3.350343815022304d0))
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304));
}

Python

def code(x, y, z):
	return x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / Float64(Float64(Float64(z + 6.012459259764103) * z) + 3.350343815022304)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304));
end

Wolfram

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

Initial Program: 69.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (+
  x
  (/
   (*
    y
    (+
     (* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
     0.279195317918525))
   (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))

C

double code(double x, double y, double z) {
	return x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((y * ((((z * 0.0692910599291889d0) + 0.4917317610505968d0) * z) + 0.279195317918525d0)) / (((z + 6.012459259764103d0) * z) + 3.350343815022304d0))
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304));
}

Python

def code(x, y, z):
	return x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / Float64(Float64(Float64(z + 6.012459259764103) * z) + 3.350343815022304)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304));
end

Wolfram

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

Alternative 1: 99.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+49}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \mathbf{elif}\;z \leq 350000000:\\ \;\;\;\;\frac{y \cdot \left(0.279195317918525 + z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right)\right)}{3.350343815022304 + z \cdot \left(z + 6.012459259764103\right)} + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 - \frac{-0.07512208616047561}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.1e+49)
   (+ x (* y 0.0692910599291889))
   (if (<= z 350000000.0)
     (+
      (/
       (*
        y
        (+
         0.279195317918525
         (* z (+ (* z 0.0692910599291889) 0.4917317610505968))))
       (+ 3.350343815022304 (* z (+ z 6.012459259764103))))
      x)
     (+ x (* y (- 0.0692910599291889 (/ -0.07512208616047561 z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.1e+49) {
		tmp = x + (y * 0.0692910599291889);
	} else if (z <= 350000000.0) {
		tmp = ((y * (0.279195317918525 + (z * ((z * 0.0692910599291889) + 0.4917317610505968)))) / (3.350343815022304 + (z * (z + 6.012459259764103)))) + x;
	} else {
		tmp = x + (y * (0.0692910599291889 - (-0.07512208616047561 / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-4.1d+49)) then
        tmp = x + (y * 0.0692910599291889d0)
    else if (z <= 350000000.0d0) then
        tmp = ((y * (0.279195317918525d0 + (z * ((z * 0.0692910599291889d0) + 0.4917317610505968d0)))) / (3.350343815022304d0 + (z * (z + 6.012459259764103d0)))) + x
    else
        tmp = x + (y * (0.0692910599291889d0 - ((-0.07512208616047561d0) / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.1e+49) {
		tmp = x + (y * 0.0692910599291889);
	} else if (z <= 350000000.0) {
		tmp = ((y * (0.279195317918525 + (z * ((z * 0.0692910599291889) + 0.4917317610505968)))) / (3.350343815022304 + (z * (z + 6.012459259764103)))) + x;
	} else {
		tmp = x + (y * (0.0692910599291889 - (-0.07512208616047561 / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.1e+49:
		tmp = x + (y * 0.0692910599291889)
	elif z <= 350000000.0:
		tmp = ((y * (0.279195317918525 + (z * ((z * 0.0692910599291889) + 0.4917317610505968)))) / (3.350343815022304 + (z * (z + 6.012459259764103)))) + x
	else:
		tmp = x + (y * (0.0692910599291889 - (-0.07512208616047561 / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.1e+49)
		tmp = Float64(x + Float64(y * 0.0692910599291889));
	elseif (z <= 350000000.0)
		tmp = Float64(Float64(Float64(y * Float64(0.279195317918525 + Float64(z * Float64(Float64(z * 0.0692910599291889) + 0.4917317610505968)))) / Float64(3.350343815022304 + Float64(z * Float64(z + 6.012459259764103)))) + x);
	else
		tmp = Float64(x + Float64(y * Float64(0.0692910599291889 - Float64(-0.07512208616047561 / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.1e+49)
		tmp = x + (y * 0.0692910599291889);
	elseif (z <= 350000000.0)
		tmp = ((y * (0.279195317918525 + (z * ((z * 0.0692910599291889) + 0.4917317610505968)))) / (3.350343815022304 + (z * (z + 6.012459259764103)))) + x;
	else
		tmp = x + (y * (0.0692910599291889 - (-0.07512208616047561 / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.1e+49], N[(x + N[(y * 0.0692910599291889), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 350000000.0], N[(N[(N[(y * N[(0.279195317918525 + N[(z * N[(N[(z * 0.0692910599291889), $MachinePrecision] + 0.4917317610505968), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.350343815022304 + N[(z * N[(z + 6.012459259764103), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(y * N[(0.0692910599291889 - N[(-0.07512208616047561 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.1e49

   1. Initial program 22.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{692910599291889}{10000000000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{692910599291889}{10000000000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{692910599291889}{10000000000000000}}\right)\right) \]

      3. *-lowering-*.f64 99.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{692910599291889}{10000000000000000}}\right)\right) \]

   5. Simplified 99.5%

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

   if -4.1e49 < z < 3.5e8

   1. Initial program 99.6%

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

   if 3.5e8 < z

   1. Initial program 36.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\left(x + \left(\frac{692910599291889}{10000000000000000} \cdot y + \frac{307332350656623}{625000000000000} \cdot \frac{y}{z}\right)\right) - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(\left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{307332350656623}{625000000000000} \cdot \frac{y}{z}\right) - \color{blue}{\frac{4166096748901211929300981260567}{10000000000000000000000000000000}} \cdot \frac{y}{z} \]

      2. associate--l+ N/A

         \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \color{blue}{\left(\frac{307332350656623}{625000000000000} \cdot \frac{y}{z} - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}\right)} \]

      3. distribute-rgt-out-- N/A

         \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{y}{z} \cdot \color{blue}{\left(\frac{307332350656623}{625000000000000} - \frac{4166096748901211929300981260567}{10000000000000000000000000000000}\right)} \]

      4. metadata-eval N/A

         \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{y}{z} \cdot \frac{751220861604756070699018739433}{10000000000000000000000000000000} \]

      5. metadata-eval N/A

         \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{y}{z} \cdot \frac{\frac{-751220861604756070699018739433}{10000000000000000000000000000000}}{\color{blue}{-1}} \]

      6. metadata-eval N/A

         \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{y}{z} \cdot \frac{\frac{-307332350656623}{625000000000000} - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000}}{-1} \]

      7. times-frac N/A

         \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{y \cdot \left(\frac{-307332350656623}{625000000000000} - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000}\right)}{\color{blue}{z \cdot -1}} \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{\color{blue}{z} \cdot -1} \]

      9. *-commutative N/A

         \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{-1 \cdot \color{blue}{z}} \]

      10. mul-1-neg N/A

          \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{\mathsf{neg}\left(z\right)} \]

      11. distribute-neg-frac2 N/A

          \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \left(\mathsf{neg}\left(\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right)\right) \]

      12. mul-1-neg N/A

          \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + -1 \cdot \color{blue}{\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}} \]

      13. associate-+r+ N/A

          \[\leadsto x + \color{blue}{\left(\frac{692910599291889}{10000000000000000} \cdot y + -1 \cdot \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right)} \]

      14. +-commutative N/A

          \[\leadsto x + \left(-1 \cdot \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z} + \color{blue}{\frac{692910599291889}{10000000000000000} \cdot y}\right) \]

      15. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z} + \frac{692910599291889}{10000000000000000} \cdot y\right)}\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{692910599291889}{10000000000000000} \cdot y + \color{blue}{-1 \cdot \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}}\right)\right) \]

      17. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{692910599291889}{10000000000000000} \cdot y + \left(\mathsf{neg}\left(\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right)\right)\right)\right) \]

      18. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{692910599291889}{10000000000000000} \cdot y - \color{blue}{\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}}\right)\right) \]

   5. Simplified 99.6%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+49}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \mathbf{elif}\;z \leq 350000000:\\ \;\;\;\;\frac{y \cdot \left(0.279195317918525 + z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right)\right)}{3.350343815022304 + z \cdot \left(z + 6.012459259764103\right)} + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 - \frac{-0.07512208616047561}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3.350343815022304 + z \cdot \left(z + 6.012459259764103\right)\\ \mathbf{if}\;\frac{y \cdot \left(0.279195317918525 + z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right)\right)}{t\_0} \leq 5 \cdot 10^{+298}:\\ \;\;\;\;\left(0.279195317918525 + \left(z \cdot 0.4917317610505968 + 0.0692910599291889 \cdot \left(z \cdot z\right)\right)\right) \cdot \frac{y}{t\_0} + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 3.350343815022304 (* z (+ z 6.012459259764103)))))
   (if (<=
        (/
         (*
          y
          (+
           0.279195317918525
           (* z (+ (* z 0.0692910599291889) 0.4917317610505968))))
         t_0)
        5e+298)
     (+
      (*
       (+
        0.279195317918525
        (+ (* z 0.4917317610505968) (* 0.0692910599291889 (* z z))))
       (/ y t_0))
      x)
     (+ x (* y 0.0692910599291889)))))

C

double code(double x, double y, double z) {
	double t_0 = 3.350343815022304 + (z * (z + 6.012459259764103));
	double tmp;
	if (((y * (0.279195317918525 + (z * ((z * 0.0692910599291889) + 0.4917317610505968)))) / t_0) <= 5e+298) {
		tmp = ((0.279195317918525 + ((z * 0.4917317610505968) + (0.0692910599291889 * (z * z)))) * (y / t_0)) + x;
	} else {
		tmp = x + (y * 0.0692910599291889);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 3.350343815022304d0 + (z * (z + 6.012459259764103d0))
    if (((y * (0.279195317918525d0 + (z * ((z * 0.0692910599291889d0) + 0.4917317610505968d0)))) / t_0) <= 5d+298) then
        tmp = ((0.279195317918525d0 + ((z * 0.4917317610505968d0) + (0.0692910599291889d0 * (z * z)))) * (y / t_0)) + x
    else
        tmp = x + (y * 0.0692910599291889d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 3.350343815022304 + (z * (z + 6.012459259764103));
	double tmp;
	if (((y * (0.279195317918525 + (z * ((z * 0.0692910599291889) + 0.4917317610505968)))) / t_0) <= 5e+298) {
		tmp = ((0.279195317918525 + ((z * 0.4917317610505968) + (0.0692910599291889 * (z * z)))) * (y / t_0)) + x;
	} else {
		tmp = x + (y * 0.0692910599291889);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 3.350343815022304 + (z * (z + 6.012459259764103))
	tmp = 0
	if ((y * (0.279195317918525 + (z * ((z * 0.0692910599291889) + 0.4917317610505968)))) / t_0) <= 5e+298:
		tmp = ((0.279195317918525 + ((z * 0.4917317610505968) + (0.0692910599291889 * (z * z)))) * (y / t_0)) + x
	else:
		tmp = x + (y * 0.0692910599291889)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(3.350343815022304 + Float64(z * Float64(z + 6.012459259764103)))
	tmp = 0.0
	if (Float64(Float64(y * Float64(0.279195317918525 + Float64(z * Float64(Float64(z * 0.0692910599291889) + 0.4917317610505968)))) / t_0) <= 5e+298)
		tmp = Float64(Float64(Float64(0.279195317918525 + Float64(Float64(z * 0.4917317610505968) + Float64(0.0692910599291889 * Float64(z * z)))) * Float64(y / t_0)) + x);
	else
		tmp = Float64(x + Float64(y * 0.0692910599291889));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 3.350343815022304 + (z * (z + 6.012459259764103));
	tmp = 0.0;
	if (((y * (0.279195317918525 + (z * ((z * 0.0692910599291889) + 0.4917317610505968)))) / t_0) <= 5e+298)
		tmp = ((0.279195317918525 + ((z * 0.4917317610505968) + (0.0692910599291889 * (z * z)))) * (y / t_0)) + x;
	else
		tmp = x + (y * 0.0692910599291889);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(3.350343815022304 + N[(z * N[(z + 6.012459259764103), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(y * N[(0.279195317918525 + N[(z * N[(N[(z * 0.0692910599291889), $MachinePrecision] + 0.4917317610505968), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision], 5e+298], N[(N[(N[(0.279195317918525 + N[(N[(z * 0.4917317610505968), $MachinePrecision] + N[(0.0692910599291889 * N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(y / t$95$0), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(y * 0.0692910599291889), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 692910599291889/10000000000000000 binary64)) #s(literal 307332350656623/625000000000000 binary64)) z) #s(literal 11167812716741/40000000000000 binary64))) (+.f64 (*.f64 (+.f64 z #s(literal 6012459259764103/1000000000000000 binary64)) z) #s(literal 104698244219447/31250000000000 binary64))) < 5.0000000000000003e298

   1. Initial program 97.1%

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

      1. +-commutative N/A

         \[\leadsto \frac{y \cdot \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} + \color{blue}{x} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y \cdot \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right), \color{blue}{x}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right) \cdot y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right), x\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right) \cdot \frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right), x\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(z \cdot \left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(z \cdot \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \left(\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\left(\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\left(z \cdot \left(z + \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(z + \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      15. +-lowering-+.f64 98.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

   4. Applied egg-rr 98.3%

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

      1. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(z \cdot \left(\frac{307332350656623}{625000000000000} + z \cdot \frac{692910599291889}{10000000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      2. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(z \cdot \frac{307332350656623}{625000000000000} + z \cdot \left(z \cdot \frac{692910599291889}{10000000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(\frac{307332350656623}{625000000000000} \cdot z + z \cdot \left(z \cdot \frac{692910599291889}{10000000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(\frac{307332350656623}{625000000000000} \cdot z\right), \left(z \cdot \left(z \cdot \frac{692910599291889}{10000000000000000}\right)\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(z \cdot \frac{307332350656623}{625000000000000}\right), \left(z \cdot \left(z \cdot \frac{692910599291889}{10000000000000000}\right)\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{307332350656623}{625000000000000}\right), \left(z \cdot \left(z \cdot \frac{692910599291889}{10000000000000000}\right)\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{307332350656623}{625000000000000}\right), \left(\left(z \cdot \frac{692910599291889}{10000000000000000}\right) \cdot z\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{307332350656623}{625000000000000}\right), \left(\left(\frac{692910599291889}{10000000000000000} \cdot z\right) \cdot z\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      9. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{307332350656623}{625000000000000}\right), \left(\frac{692910599291889}{10000000000000000} \cdot \left(z \cdot z\right)\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{307332350656623}{625000000000000}\right), \mathsf{*.f64}\left(\frac{692910599291889}{10000000000000000}, \left(z \cdot z\right)\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      11. *-lowering-*.f64 98.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{307332350656623}{625000000000000}\right), \mathsf{*.f64}\left(\frac{692910599291889}{10000000000000000}, \mathsf{*.f64}\left(z, z\right)\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

   6. Applied egg-rr 98.3%

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

   if 5.0000000000000003e298 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 692910599291889/10000000000000000 binary64)) #s(literal 307332350656623/625000000000000 binary64)) z) #s(literal 11167812716741/40000000000000 binary64))) (+.f64 (*.f64 (+.f64 z #s(literal 6012459259764103/1000000000000000 binary64)) z) #s(literal 104698244219447/31250000000000 binary64)))

   1. Initial program 0.6%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{692910599291889}{10000000000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{692910599291889}{10000000000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{692910599291889}{10000000000000000}}\right)\right) \]

      3. *-lowering-*.f64 99.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{692910599291889}{10000000000000000}}\right)\right) \]

   5. Simplified 99.5%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(0.279195317918525 + z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right)\right)}{3.350343815022304 + z \cdot \left(z + 6.012459259764103\right)} \leq 5 \cdot 10^{+298}:\\ \;\;\;\;\left(0.279195317918525 + \left(z \cdot 0.4917317610505968 + 0.0692910599291889 \cdot \left(z \cdot z\right)\right)\right) \cdot \frac{y}{3.350343815022304 + z \cdot \left(z + 6.012459259764103\right)} + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3.350343815022304 + z \cdot \left(z + 6.012459259764103\right)\\ t_1 := 0.279195317918525 + z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right)\\ \mathbf{if}\;\frac{y \cdot t\_1}{t\_0} \leq 5 \cdot 10^{+298}:\\ \;\;\;\;x + \frac{y}{t\_0} \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 3.350343815022304 (* z (+ z 6.012459259764103))))
        (t_1
         (+
          0.279195317918525
          (* z (+ (* z 0.0692910599291889) 0.4917317610505968)))))
   (if (<= (/ (* y t_1) t_0) 5e+298)
     (+ x (* (/ y t_0) t_1))
     (+ x (* y 0.0692910599291889)))))

C

double code(double x, double y, double z) {
	double t_0 = 3.350343815022304 + (z * (z + 6.012459259764103));
	double t_1 = 0.279195317918525 + (z * ((z * 0.0692910599291889) + 0.4917317610505968));
	double tmp;
	if (((y * t_1) / t_0) <= 5e+298) {
		tmp = x + ((y / t_0) * t_1);
	} else {
		tmp = x + (y * 0.0692910599291889);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 3.350343815022304d0 + (z * (z + 6.012459259764103d0))
    t_1 = 0.279195317918525d0 + (z * ((z * 0.0692910599291889d0) + 0.4917317610505968d0))
    if (((y * t_1) / t_0) <= 5d+298) then
        tmp = x + ((y / t_0) * t_1)
    else
        tmp = x + (y * 0.0692910599291889d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 3.350343815022304 + (z * (z + 6.012459259764103));
	double t_1 = 0.279195317918525 + (z * ((z * 0.0692910599291889) + 0.4917317610505968));
	double tmp;
	if (((y * t_1) / t_0) <= 5e+298) {
		tmp = x + ((y / t_0) * t_1);
	} else {
		tmp = x + (y * 0.0692910599291889);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 3.350343815022304 + (z * (z + 6.012459259764103))
	t_1 = 0.279195317918525 + (z * ((z * 0.0692910599291889) + 0.4917317610505968))
	tmp = 0
	if ((y * t_1) / t_0) <= 5e+298:
		tmp = x + ((y / t_0) * t_1)
	else:
		tmp = x + (y * 0.0692910599291889)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(3.350343815022304 + Float64(z * Float64(z + 6.012459259764103)))
	t_1 = Float64(0.279195317918525 + Float64(z * Float64(Float64(z * 0.0692910599291889) + 0.4917317610505968)))
	tmp = 0.0
	if (Float64(Float64(y * t_1) / t_0) <= 5e+298)
		tmp = Float64(x + Float64(Float64(y / t_0) * t_1));
	else
		tmp = Float64(x + Float64(y * 0.0692910599291889));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 3.350343815022304 + (z * (z + 6.012459259764103));
	t_1 = 0.279195317918525 + (z * ((z * 0.0692910599291889) + 0.4917317610505968));
	tmp = 0.0;
	if (((y * t_1) / t_0) <= 5e+298)
		tmp = x + ((y / t_0) * t_1);
	else
		tmp = x + (y * 0.0692910599291889);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(3.350343815022304 + N[(z * N[(z + 6.012459259764103), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(0.279195317918525 + N[(z * N[(N[(z * 0.0692910599291889), $MachinePrecision] + 0.4917317610505968), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(y * t$95$1), $MachinePrecision] / t$95$0), $MachinePrecision], 5e+298], N[(x + N[(N[(y / t$95$0), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 0.0692910599291889), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 692910599291889/10000000000000000 binary64)) #s(literal 307332350656623/625000000000000 binary64)) z) #s(literal 11167812716741/40000000000000 binary64))) (+.f64 (*.f64 (+.f64 z #s(literal 6012459259764103/1000000000000000 binary64)) z) #s(literal 104698244219447/31250000000000 binary64))) < 5.0000000000000003e298

   1. Initial program 97.1%

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

      1. +-commutative N/A

         \[\leadsto \frac{y \cdot \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} + \color{blue}{x} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y \cdot \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right), \color{blue}{x}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right) \cdot y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right), x\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right) \cdot \frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right), x\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(z \cdot \left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(z \cdot \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \left(\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\left(\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\left(z \cdot \left(z + \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(z + \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      15. +-lowering-+.f64 98.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

   4. Applied egg-rr 98.3%

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

   if 5.0000000000000003e298 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 692910599291889/10000000000000000 binary64)) #s(literal 307332350656623/625000000000000 binary64)) z) #s(literal 11167812716741/40000000000000 binary64))) (+.f64 (*.f64 (+.f64 z #s(literal 6012459259764103/1000000000000000 binary64)) z) #s(literal 104698244219447/31250000000000 binary64)))

   1. Initial program 0.6%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{692910599291889}{10000000000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{692910599291889}{10000000000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{692910599291889}{10000000000000000}}\right)\right) \]

      3. *-lowering-*.f64 99.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{692910599291889}{10000000000000000}}\right)\right) \]

   5. Simplified 99.5%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(0.279195317918525 + z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right)\right)}{3.350343815022304 + z \cdot \left(z + 6.012459259764103\right)} \leq 5 \cdot 10^{+298}:\\ \;\;\;\;x + \frac{y}{3.350343815022304 + z \cdot \left(z + 6.012459259764103\right)} \cdot \left(0.279195317918525 + z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;x + \left(y \cdot 0.0692910599291889 + \frac{\frac{y \cdot -0.4046220386999212}{z} - y \cdot -0.07512208616047561}{z}\right)\\ \mathbf{elif}\;z \leq 4.4:\\ \;\;\;\;y \cdot 0.08333333333333323 + \left(x + z \cdot \left(y \cdot -0.00277777777751721 + z \cdot \left(y \cdot 0.0007936505811533442\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 0.0692910599291889 + \frac{y \cdot 0.07512208616047561}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.4)
   (+
    x
    (+
     (* y 0.0692910599291889)
     (/ (- (/ (* y -0.4046220386999212) z) (* y -0.07512208616047561)) z)))
   (if (<= z 4.4)
     (+
      (* y 0.08333333333333323)
      (+
       x
       (* z (+ (* y -0.00277777777751721) (* z (* y 0.0007936505811533442))))))
     (+ x (+ (* y 0.0692910599291889) (/ (* y 0.07512208616047561) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.4) {
		tmp = x + ((y * 0.0692910599291889) + ((((y * -0.4046220386999212) / z) - (y * -0.07512208616047561)) / z));
	} else if (z <= 4.4) {
		tmp = (y * 0.08333333333333323) + (x + (z * ((y * -0.00277777777751721) + (z * (y * 0.0007936505811533442)))));
	} else {
		tmp = x + ((y * 0.0692910599291889) + ((y * 0.07512208616047561) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-5.4d0)) then
        tmp = x + ((y * 0.0692910599291889d0) + ((((y * (-0.4046220386999212d0)) / z) - (y * (-0.07512208616047561d0))) / z))
    else if (z <= 4.4d0) then
        tmp = (y * 0.08333333333333323d0) + (x + (z * ((y * (-0.00277777777751721d0)) + (z * (y * 0.0007936505811533442d0)))))
    else
        tmp = x + ((y * 0.0692910599291889d0) + ((y * 0.07512208616047561d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.4) {
		tmp = x + ((y * 0.0692910599291889) + ((((y * -0.4046220386999212) / z) - (y * -0.07512208616047561)) / z));
	} else if (z <= 4.4) {
		tmp = (y * 0.08333333333333323) + (x + (z * ((y * -0.00277777777751721) + (z * (y * 0.0007936505811533442)))));
	} else {
		tmp = x + ((y * 0.0692910599291889) + ((y * 0.07512208616047561) / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.4:
		tmp = x + ((y * 0.0692910599291889) + ((((y * -0.4046220386999212) / z) - (y * -0.07512208616047561)) / z))
	elif z <= 4.4:
		tmp = (y * 0.08333333333333323) + (x + (z * ((y * -0.00277777777751721) + (z * (y * 0.0007936505811533442)))))
	else:
		tmp = x + ((y * 0.0692910599291889) + ((y * 0.07512208616047561) / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.4)
		tmp = Float64(x + Float64(Float64(y * 0.0692910599291889) + Float64(Float64(Float64(Float64(y * -0.4046220386999212) / z) - Float64(y * -0.07512208616047561)) / z)));
	elseif (z <= 4.4)
		tmp = Float64(Float64(y * 0.08333333333333323) + Float64(x + Float64(z * Float64(Float64(y * -0.00277777777751721) + Float64(z * Float64(y * 0.0007936505811533442))))));
	else
		tmp = Float64(x + Float64(Float64(y * 0.0692910599291889) + Float64(Float64(y * 0.07512208616047561) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.4)
		tmp = x + ((y * 0.0692910599291889) + ((((y * -0.4046220386999212) / z) - (y * -0.07512208616047561)) / z));
	elseif (z <= 4.4)
		tmp = (y * 0.08333333333333323) + (x + (z * ((y * -0.00277777777751721) + (z * (y * 0.0007936505811533442)))));
	else
		tmp = x + ((y * 0.0692910599291889) + ((y * 0.07512208616047561) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.4], N[(x + N[(N[(y * 0.0692910599291889), $MachinePrecision] + N[(N[(N[(N[(y * -0.4046220386999212), $MachinePrecision] / z), $MachinePrecision] - N[(y * -0.07512208616047561), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4], N[(N[(y * 0.08333333333333323), $MachinePrecision] + N[(x + N[(z * N[(N[(y * -0.00277777777751721), $MachinePrecision] + N[(z * N[(y * 0.0007936505811533442), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * 0.0692910599291889), $MachinePrecision] + N[(N[(y * 0.07512208616047561), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4000000000000004

   1. Initial program 31.1%

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

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(-1 \cdot \frac{\frac{11167812716741}{40000000000000} \cdot y - \left(\frac{-6012459259764103}{1000000000000000} \cdot \left(\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y\right) + \frac{72546523146905574025723165383}{312500000000000000000000000000} \cdot y\right)}{z} + \frac{-307332350656623}{625000000000000} \cdot y\right) - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z} + \frac{692910599291889}{10000000000000000} \cdot y\right)} \]

   5. Simplified 98.3%

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

   if -5.4000000000000004 < z < 4.4000000000000004

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(\frac{279195317918525}{3350343815022304} \cdot y + z \cdot \left(\left(\frac{307332350656623}{2093964884388940} \cdot y + z \cdot \left(\frac{692910599291889}{33503438150223040} \cdot y - \left(\frac{272651677654809570312500000}{10961722342634967150292985809} \cdot y + \frac{6012459259764103}{3350343815022304} \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)\right)\right) - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)} \]

   5. Simplified 99.2%

      \[\leadsto \color{blue}{y \cdot 0.08333333333333323 + \left(x + z \cdot \left(y \cdot -0.00277777777751721 + z \cdot \left(y \cdot 0.0007936505811533442\right)\right)\right)} \]

   if 4.4000000000000004 < z

   1. Initial program 39.9%

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

      1. +-commutative N/A

         \[\leadsto \frac{y \cdot \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} + \color{blue}{x} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y \cdot \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right), \color{blue}{x}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right) \cdot y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right), x\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right) \cdot \frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right), x\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(z \cdot \left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(z \cdot \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \left(\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\left(\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\left(z \cdot \left(z + \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(z + \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      15. +-lowering-+.f64 43.5%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

   4. Applied egg-rr 43.5%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(\left(\frac{692910599291889}{10000000000000000} \cdot y + \frac{307332350656623}{625000000000000} \cdot \frac{y}{z}\right) - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}\right)}, x\right) \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{692910599291889}{10000000000000000} \cdot y + \left(\frac{307332350656623}{625000000000000} \cdot \frac{y}{z} - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}\right)\right), x\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{692910599291889}{10000000000000000} \cdot y + \left(\frac{\frac{307332350656623}{625000000000000} \cdot y}{z} - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}\right)\right), x\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{692910599291889}{10000000000000000} \cdot y + \left(\frac{\frac{307332350656623}{625000000000000} \cdot y}{z} - \frac{\frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right)\right), x\right) \]

      4. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{692910599291889}{10000000000000000} \cdot y + \frac{\frac{307332350656623}{625000000000000} \cdot y - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right), x\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(\frac{692910599291889}{10000000000000000} \cdot y\right), \left(\frac{\frac{307332350656623}{625000000000000} \cdot y - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right)\right), x\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \frac{692910599291889}{10000000000000000}\right), \left(\frac{\frac{307332350656623}{625000000000000} \cdot y - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right)\right), x\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{692910599291889}{10000000000000000}\right), \left(\frac{\frac{307332350656623}{625000000000000} \cdot y - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right)\right), x\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{692910599291889}{10000000000000000}\right), \mathsf{/.f64}\left(\left(\frac{307332350656623}{625000000000000} \cdot y - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y\right), z\right)\right), x\right) \]

      9. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{692910599291889}{10000000000000000}\right), \mathsf{/.f64}\left(\left(y \cdot \left(\frac{307332350656623}{625000000000000} - \frac{4166096748901211929300981260567}{10000000000000000000000000000000}\right)\right), z\right)\right), x\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{692910599291889}{10000000000000000}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{307332350656623}{625000000000000} - \frac{4166096748901211929300981260567}{10000000000000000000000000000000}\right)\right), z\right)\right), x\right) \]

      11. metadata-eval 99.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{692910599291889}{10000000000000000}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \frac{751220861604756070699018739433}{10000000000000000000000000000000}\right), z\right)\right), x\right) \]

   7. Simplified 99.6%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;x + \left(y \cdot 0.0692910599291889 + \frac{\frac{y \cdot -0.4046220386999212}{z} - y \cdot -0.07512208616047561}{z}\right)\\ \mathbf{elif}\;z \leq 4.4:\\ \;\;\;\;y \cdot 0.08333333333333323 + \left(x + z \cdot \left(y \cdot -0.00277777777751721 + z \cdot \left(y \cdot 0.0007936505811533442\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 0.0692910599291889 + \frac{y \cdot 0.07512208616047561}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 - \frac{-0.07512208616047561}{z}\right)\\ \mathbf{elif}\;z \leq 4.4:\\ \;\;\;\;y \cdot 0.08333333333333323 + \left(x + z \cdot \left(y \cdot -0.00277777777751721 + z \cdot \left(y \cdot 0.0007936505811533442\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 0.0692910599291889 + \frac{y \cdot 0.07512208616047561}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.4)
   (+ x (* y (- 0.0692910599291889 (/ -0.07512208616047561 z))))
   (if (<= z 4.4)
     (+
      (* y 0.08333333333333323)
      (+
       x
       (* z (+ (* y -0.00277777777751721) (* z (* y 0.0007936505811533442))))))
     (+ x (+ (* y 0.0692910599291889) (/ (* y 0.07512208616047561) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.4) {
		tmp = x + (y * (0.0692910599291889 - (-0.07512208616047561 / z)));
	} else if (z <= 4.4) {
		tmp = (y * 0.08333333333333323) + (x + (z * ((y * -0.00277777777751721) + (z * (y * 0.0007936505811533442)))));
	} else {
		tmp = x + ((y * 0.0692910599291889) + ((y * 0.07512208616047561) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-5.4d0)) then
        tmp = x + (y * (0.0692910599291889d0 - ((-0.07512208616047561d0) / z)))
    else if (z <= 4.4d0) then
        tmp = (y * 0.08333333333333323d0) + (x + (z * ((y * (-0.00277777777751721d0)) + (z * (y * 0.0007936505811533442d0)))))
    else
        tmp = x + ((y * 0.0692910599291889d0) + ((y * 0.07512208616047561d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.4) {
		tmp = x + (y * (0.0692910599291889 - (-0.07512208616047561 / z)));
	} else if (z <= 4.4) {
		tmp = (y * 0.08333333333333323) + (x + (z * ((y * -0.00277777777751721) + (z * (y * 0.0007936505811533442)))));
	} else {
		tmp = x + ((y * 0.0692910599291889) + ((y * 0.07512208616047561) / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.4:
		tmp = x + (y * (0.0692910599291889 - (-0.07512208616047561 / z)))
	elif z <= 4.4:
		tmp = (y * 0.08333333333333323) + (x + (z * ((y * -0.00277777777751721) + (z * (y * 0.0007936505811533442)))))
	else:
		tmp = x + ((y * 0.0692910599291889) + ((y * 0.07512208616047561) / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.4)
		tmp = Float64(x + Float64(y * Float64(0.0692910599291889 - Float64(-0.07512208616047561 / z))));
	elseif (z <= 4.4)
		tmp = Float64(Float64(y * 0.08333333333333323) + Float64(x + Float64(z * Float64(Float64(y * -0.00277777777751721) + Float64(z * Float64(y * 0.0007936505811533442))))));
	else
		tmp = Float64(x + Float64(Float64(y * 0.0692910599291889) + Float64(Float64(y * 0.07512208616047561) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.4)
		tmp = x + (y * (0.0692910599291889 - (-0.07512208616047561 / z)));
	elseif (z <= 4.4)
		tmp = (y * 0.08333333333333323) + (x + (z * ((y * -0.00277777777751721) + (z * (y * 0.0007936505811533442)))));
	else
		tmp = x + ((y * 0.0692910599291889) + ((y * 0.07512208616047561) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.4], N[(x + N[(y * N[(0.0692910599291889 - N[(-0.07512208616047561 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4], N[(N[(y * 0.08333333333333323), $MachinePrecision] + N[(x + N[(z * N[(N[(y * -0.00277777777751721), $MachinePrecision] + N[(z * N[(y * 0.0007936505811533442), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * 0.0692910599291889), $MachinePrecision] + N[(N[(y * 0.07512208616047561), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4000000000000004

   1. Initial program 31.1%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\left(x + \left(\frac{692910599291889}{10000000000000000} \cdot y + \frac{307332350656623}{625000000000000} \cdot \frac{y}{z}\right)\right) - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(\left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{307332350656623}{625000000000000} \cdot \frac{y}{z}\right) - \color{blue}{\frac{4166096748901211929300981260567}{10000000000000000000000000000000}} \cdot \frac{y}{z} \]

      2. associate--l+ N/A

         \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \color{blue}{\left(\frac{307332350656623}{625000000000000} \cdot \frac{y}{z} - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}\right)} \]

      3. distribute-rgt-out-- N/A

         \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{y}{z} \cdot \color{blue}{\left(\frac{307332350656623}{625000000000000} - \frac{4166096748901211929300981260567}{10000000000000000000000000000000}\right)} \]

      4. metadata-eval N/A

         \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{y}{z} \cdot \frac{751220861604756070699018739433}{10000000000000000000000000000000} \]

      5. metadata-eval N/A

         \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{y}{z} \cdot \frac{\frac{-751220861604756070699018739433}{10000000000000000000000000000000}}{\color{blue}{-1}} \]

      6. metadata-eval N/A

         \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{y}{z} \cdot \frac{\frac{-307332350656623}{625000000000000} - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000}}{-1} \]

      7. times-frac N/A

         \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{y \cdot \left(\frac{-307332350656623}{625000000000000} - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000}\right)}{\color{blue}{z \cdot -1}} \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{\color{blue}{z} \cdot -1} \]

      9. *-commutative N/A

         \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{-1 \cdot \color{blue}{z}} \]

      10. mul-1-neg N/A

          \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{\mathsf{neg}\left(z\right)} \]

      11. distribute-neg-frac2 N/A

          \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \left(\mathsf{neg}\left(\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right)\right) \]

      12. mul-1-neg N/A

          \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + -1 \cdot \color{blue}{\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}} \]

      13. associate-+r+ N/A

          \[\leadsto x + \color{blue}{\left(\frac{692910599291889}{10000000000000000} \cdot y + -1 \cdot \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right)} \]

      14. +-commutative N/A

          \[\leadsto x + \left(-1 \cdot \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z} + \color{blue}{\frac{692910599291889}{10000000000000000} \cdot y}\right) \]

      15. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z} + \frac{692910599291889}{10000000000000000} \cdot y\right)}\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{692910599291889}{10000000000000000} \cdot y + \color{blue}{-1 \cdot \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}}\right)\right) \]

      17. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{692910599291889}{10000000000000000} \cdot y + \left(\mathsf{neg}\left(\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right)\right)\right)\right) \]

      18. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{692910599291889}{10000000000000000} \cdot y - \color{blue}{\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}}\right)\right) \]

   5. Simplified 98.2%

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

   if -5.4000000000000004 < z < 4.4000000000000004

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(\frac{279195317918525}{3350343815022304} \cdot y + z \cdot \left(\left(\frac{307332350656623}{2093964884388940} \cdot y + z \cdot \left(\frac{692910599291889}{33503438150223040} \cdot y - \left(\frac{272651677654809570312500000}{10961722342634967150292985809} \cdot y + \frac{6012459259764103}{3350343815022304} \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)\right)\right) - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)} \]

   5. Simplified 99.2%

      \[\leadsto \color{blue}{y \cdot 0.08333333333333323 + \left(x + z \cdot \left(y \cdot -0.00277777777751721 + z \cdot \left(y \cdot 0.0007936505811533442\right)\right)\right)} \]

   if 4.4000000000000004 < z

   1. Initial program 39.9%

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

      1. +-commutative N/A

         \[\leadsto \frac{y \cdot \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} + \color{blue}{x} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y \cdot \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right), \color{blue}{x}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right) \cdot y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right), x\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right) \cdot \frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right), x\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(z \cdot \left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(z \cdot \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \left(\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\left(\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\left(z \cdot \left(z + \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(z + \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      15. +-lowering-+.f64 43.5%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

   4. Applied egg-rr 43.5%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(\left(\frac{692910599291889}{10000000000000000} \cdot y + \frac{307332350656623}{625000000000000} \cdot \frac{y}{z}\right) - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}\right)}, x\right) \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{692910599291889}{10000000000000000} \cdot y + \left(\frac{307332350656623}{625000000000000} \cdot \frac{y}{z} - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}\right)\right), x\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{692910599291889}{10000000000000000} \cdot y + \left(\frac{\frac{307332350656623}{625000000000000} \cdot y}{z} - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}\right)\right), x\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{692910599291889}{10000000000000000} \cdot y + \left(\frac{\frac{307332350656623}{625000000000000} \cdot y}{z} - \frac{\frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right)\right), x\right) \]

      4. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{692910599291889}{10000000000000000} \cdot y + \frac{\frac{307332350656623}{625000000000000} \cdot y - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right), x\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(\frac{692910599291889}{10000000000000000} \cdot y\right), \left(\frac{\frac{307332350656623}{625000000000000} \cdot y - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right)\right), x\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \frac{692910599291889}{10000000000000000}\right), \left(\frac{\frac{307332350656623}{625000000000000} \cdot y - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right)\right), x\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{692910599291889}{10000000000000000}\right), \left(\frac{\frac{307332350656623}{625000000000000} \cdot y - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right)\right), x\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{692910599291889}{10000000000000000}\right), \mathsf{/.f64}\left(\left(\frac{307332350656623}{625000000000000} \cdot y - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y\right), z\right)\right), x\right) \]

      9. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{692910599291889}{10000000000000000}\right), \mathsf{/.f64}\left(\left(y \cdot \left(\frac{307332350656623}{625000000000000} - \frac{4166096748901211929300981260567}{10000000000000000000000000000000}\right)\right), z\right)\right), x\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{692910599291889}{10000000000000000}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{307332350656623}{625000000000000} - \frac{4166096748901211929300981260567}{10000000000000000000000000000000}\right)\right), z\right)\right), x\right) \]

      11. metadata-eval 99.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{692910599291889}{10000000000000000}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \frac{751220861604756070699018739433}{10000000000000000000000000000000}\right), z\right)\right), x\right) \]

   7. Simplified 99.6%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 - \frac{-0.07512208616047561}{z}\right)\\ \mathbf{elif}\;z \leq 4.4:\\ \;\;\;\;y \cdot 0.08333333333333323 + \left(x + z \cdot \left(y \cdot -0.00277777777751721 + z \cdot \left(y \cdot 0.0007936505811533442\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 0.0692910599291889 + \frac{y \cdot 0.07512208616047561}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 - \frac{-0.07512208616047561}{z}\right)\\ \mathbf{elif}\;z \leq 6:\\ \;\;\;\;x + y \cdot \left(0.08333333333333323 + z \cdot -0.00277777777751721\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 0.0692910599291889 + \frac{y \cdot 0.07512208616047561}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.4)
   (+ x (* y (- 0.0692910599291889 (/ -0.07512208616047561 z))))
   (if (<= z 6.0)
     (+ x (* y (+ 0.08333333333333323 (* z -0.00277777777751721))))
     (+ x (+ (* y 0.0692910599291889) (/ (* y 0.07512208616047561) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.4) {
		tmp = x + (y * (0.0692910599291889 - (-0.07512208616047561 / z)));
	} else if (z <= 6.0) {
		tmp = x + (y * (0.08333333333333323 + (z * -0.00277777777751721)));
	} else {
		tmp = x + ((y * 0.0692910599291889) + ((y * 0.07512208616047561) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-5.4d0)) then
        tmp = x + (y * (0.0692910599291889d0 - ((-0.07512208616047561d0) / z)))
    else if (z <= 6.0d0) then
        tmp = x + (y * (0.08333333333333323d0 + (z * (-0.00277777777751721d0))))
    else
        tmp = x + ((y * 0.0692910599291889d0) + ((y * 0.07512208616047561d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.4) {
		tmp = x + (y * (0.0692910599291889 - (-0.07512208616047561 / z)));
	} else if (z <= 6.0) {
		tmp = x + (y * (0.08333333333333323 + (z * -0.00277777777751721)));
	} else {
		tmp = x + ((y * 0.0692910599291889) + ((y * 0.07512208616047561) / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.4:
		tmp = x + (y * (0.0692910599291889 - (-0.07512208616047561 / z)))
	elif z <= 6.0:
		tmp = x + (y * (0.08333333333333323 + (z * -0.00277777777751721)))
	else:
		tmp = x + ((y * 0.0692910599291889) + ((y * 0.07512208616047561) / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.4)
		tmp = Float64(x + Float64(y * Float64(0.0692910599291889 - Float64(-0.07512208616047561 / z))));
	elseif (z <= 6.0)
		tmp = Float64(x + Float64(y * Float64(0.08333333333333323 + Float64(z * -0.00277777777751721))));
	else
		tmp = Float64(x + Float64(Float64(y * 0.0692910599291889) + Float64(Float64(y * 0.07512208616047561) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.4)
		tmp = x + (y * (0.0692910599291889 - (-0.07512208616047561 / z)));
	elseif (z <= 6.0)
		tmp = x + (y * (0.08333333333333323 + (z * -0.00277777777751721)));
	else
		tmp = x + ((y * 0.0692910599291889) + ((y * 0.07512208616047561) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.4], N[(x + N[(y * N[(0.0692910599291889 - N[(-0.07512208616047561 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.0], N[(x + N[(y * N[(0.08333333333333323 + N[(z * -0.00277777777751721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * 0.0692910599291889), $MachinePrecision] + N[(N[(y * 0.07512208616047561), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4000000000000004

   1. Initial program 31.1%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\left(x + \left(\frac{692910599291889}{10000000000000000} \cdot y + \frac{307332350656623}{625000000000000} \cdot \frac{y}{z}\right)\right) - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(\left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{307332350656623}{625000000000000} \cdot \frac{y}{z}\right) - \color{blue}{\frac{4166096748901211929300981260567}{10000000000000000000000000000000}} \cdot \frac{y}{z} \]

      2. associate--l+ N/A

         \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \color{blue}{\left(\frac{307332350656623}{625000000000000} \cdot \frac{y}{z} - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}\right)} \]

      3. distribute-rgt-out-- N/A

         \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{y}{z} \cdot \color{blue}{\left(\frac{307332350656623}{625000000000000} - \frac{4166096748901211929300981260567}{10000000000000000000000000000000}\right)} \]

      4. metadata-eval N/A

         \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{y}{z} \cdot \frac{751220861604756070699018739433}{10000000000000000000000000000000} \]

      5. metadata-eval N/A

         \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{y}{z} \cdot \frac{\frac{-751220861604756070699018739433}{10000000000000000000000000000000}}{\color{blue}{-1}} \]

      6. metadata-eval N/A

         \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{y}{z} \cdot \frac{\frac{-307332350656623}{625000000000000} - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000}}{-1} \]

      7. times-frac N/A

         \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{y \cdot \left(\frac{-307332350656623}{625000000000000} - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000}\right)}{\color{blue}{z \cdot -1}} \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{\color{blue}{z} \cdot -1} \]

      9. *-commutative N/A

         \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{-1 \cdot \color{blue}{z}} \]

      10. mul-1-neg N/A

          \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{\mathsf{neg}\left(z\right)} \]

      11. distribute-neg-frac2 N/A

          \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \left(\mathsf{neg}\left(\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right)\right) \]

      12. mul-1-neg N/A

          \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + -1 \cdot \color{blue}{\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}} \]

      13. associate-+r+ N/A

          \[\leadsto x + \color{blue}{\left(\frac{692910599291889}{10000000000000000} \cdot y + -1 \cdot \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right)} \]

      14. +-commutative N/A

          \[\leadsto x + \left(-1 \cdot \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z} + \color{blue}{\frac{692910599291889}{10000000000000000} \cdot y}\right) \]

      15. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z} + \frac{692910599291889}{10000000000000000} \cdot y\right)}\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{692910599291889}{10000000000000000} \cdot y + \color{blue}{-1 \cdot \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}}\right)\right) \]

      17. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{692910599291889}{10000000000000000} \cdot y + \left(\mathsf{neg}\left(\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right)\right)\right)\right) \]

      18. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{692910599291889}{10000000000000000} \cdot y - \color{blue}{\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}}\right)\right) \]

   5. Simplified 98.2%

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

   if -5.4000000000000004 < z < 6

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(\frac{279195317918525}{3350343815022304} \cdot y + z \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{279195317918525}{3350343815022304} \cdot y + z \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{279195317918525}{3350343815022304} + \color{blue}{z} \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{279195317918525}{3350343815022304} + \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right) \cdot \color{blue}{z}\right)\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{279195317918525}{3350343815022304} + \left(y \cdot \left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right)\right) \cdot z\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{279195317918525}{3350343815022304} + y \cdot \color{blue}{\left(\left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right) \cdot z\right)}\right)\right) \]

      6. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\frac{279195317918525}{3350343815022304} + \left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right) \cdot z\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{279195317918525}{3350343815022304} + \left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right) \cdot z\right)}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{279195317918525}{3350343815022304}, \color{blue}{\left(\left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right) \cdot z\right)}\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{279195317918525}{3350343815022304}, \left(z \cdot \color{blue}{\left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right)}\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{279195317918525}{3350343815022304}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right)}\right)\right)\right)\right) \]

      11. metadata-eval 98.9%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{279195317918525}{3350343815022304}, \mathsf{*.f64}\left(z, \frac{-155900051080628738716045985239}{56124018394291031809500087342080}\right)\right)\right)\right) \]

   5. Simplified 98.9%

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

   if 6 < z

   1. Initial program 39.9%

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

      1. +-commutative N/A

         \[\leadsto \frac{y \cdot \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} + \color{blue}{x} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y \cdot \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right), \color{blue}{x}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right) \cdot y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right), x\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right) \cdot \frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right), x\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(z \cdot \left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(z \cdot \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \left(\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\left(\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\left(z \cdot \left(z + \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(z + \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      15. +-lowering-+.f64 43.5%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

   4. Applied egg-rr 43.5%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(\left(\frac{692910599291889}{10000000000000000} \cdot y + \frac{307332350656623}{625000000000000} \cdot \frac{y}{z}\right) - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}\right)}, x\right) \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{692910599291889}{10000000000000000} \cdot y + \left(\frac{307332350656623}{625000000000000} \cdot \frac{y}{z} - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}\right)\right), x\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{692910599291889}{10000000000000000} \cdot y + \left(\frac{\frac{307332350656623}{625000000000000} \cdot y}{z} - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}\right)\right), x\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{692910599291889}{10000000000000000} \cdot y + \left(\frac{\frac{307332350656623}{625000000000000} \cdot y}{z} - \frac{\frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right)\right), x\right) \]

      4. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{692910599291889}{10000000000000000} \cdot y + \frac{\frac{307332350656623}{625000000000000} \cdot y - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right), x\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(\frac{692910599291889}{10000000000000000} \cdot y\right), \left(\frac{\frac{307332350656623}{625000000000000} \cdot y - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right)\right), x\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \frac{692910599291889}{10000000000000000}\right), \left(\frac{\frac{307332350656623}{625000000000000} \cdot y - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right)\right), x\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{692910599291889}{10000000000000000}\right), \left(\frac{\frac{307332350656623}{625000000000000} \cdot y - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right)\right), x\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{692910599291889}{10000000000000000}\right), \mathsf{/.f64}\left(\left(\frac{307332350656623}{625000000000000} \cdot y - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y\right), z\right)\right), x\right) \]

      9. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{692910599291889}{10000000000000000}\right), \mathsf{/.f64}\left(\left(y \cdot \left(\frac{307332350656623}{625000000000000} - \frac{4166096748901211929300981260567}{10000000000000000000000000000000}\right)\right), z\right)\right), x\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{692910599291889}{10000000000000000}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{307332350656623}{625000000000000} - \frac{4166096748901211929300981260567}{10000000000000000000000000000000}\right)\right), z\right)\right), x\right) \]

      11. metadata-eval 99.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{692910599291889}{10000000000000000}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \frac{751220861604756070699018739433}{10000000000000000000000000000000}\right), z\right)\right), x\right) \]

   7. Simplified 99.6%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 - \frac{-0.07512208616047561}{z}\right)\\ \mathbf{elif}\;z \leq 6:\\ \;\;\;\;x + y \cdot \left(0.08333333333333323 + z \cdot -0.00277777777751721\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 0.0692910599291889 + \frac{y \cdot 0.07512208616047561}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + y \cdot \left(0.0692910599291889 - \frac{-0.07512208616047561}{z}\right)\\ \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 4.9:\\ \;\;\;\;x + y \cdot \left(0.08333333333333323 + z \cdot -0.00277777777751721\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* y (- 0.0692910599291889 (/ -0.07512208616047561 z))))))
   (if (<= z -5.4)
     t_0
     (if (<= z 4.9)
       (+ x (* y (+ 0.08333333333333323 (* z -0.00277777777751721))))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y * (0.0692910599291889 - (-0.07512208616047561 / z)));
	double tmp;
	if (z <= -5.4) {
		tmp = t_0;
	} else if (z <= 4.9) {
		tmp = x + (y * (0.08333333333333323 + (z * -0.00277777777751721)));
	} 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 = x + (y * (0.0692910599291889d0 - ((-0.07512208616047561d0) / z)))
    if (z <= (-5.4d0)) then
        tmp = t_0
    else if (z <= 4.9d0) then
        tmp = x + (y * (0.08333333333333323d0 + (z * (-0.00277777777751721d0))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (y * (0.0692910599291889 - (-0.07512208616047561 / z)));
	double tmp;
	if (z <= -5.4) {
		tmp = t_0;
	} else if (z <= 4.9) {
		tmp = x + (y * (0.08333333333333323 + (z * -0.00277777777751721)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y * (0.0692910599291889 - (-0.07512208616047561 / z)))
	tmp = 0
	if z <= -5.4:
		tmp = t_0
	elif z <= 4.9:
		tmp = x + (y * (0.08333333333333323 + (z * -0.00277777777751721)))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y * Float64(0.0692910599291889 - Float64(-0.07512208616047561 / z))))
	tmp = 0.0
	if (z <= -5.4)
		tmp = t_0;
	elseif (z <= 4.9)
		tmp = Float64(x + Float64(y * Float64(0.08333333333333323 + Float64(z * -0.00277777777751721))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (y * (0.0692910599291889 - (-0.07512208616047561 / z)));
	tmp = 0.0;
	if (z <= -5.4)
		tmp = t_0;
	elseif (z <= 4.9)
		tmp = x + (y * (0.08333333333333323 + (z * -0.00277777777751721)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(y * N[(0.0692910599291889 - N[(-0.07512208616047561 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.4], t$95$0, If[LessEqual[z, 4.9], N[(x + N[(y * N[(0.08333333333333323 + N[(z * -0.00277777777751721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4000000000000004 or 4.9000000000000004 < z

   1. Initial program 35.8%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\left(x + \left(\frac{692910599291889}{10000000000000000} \cdot y + \frac{307332350656623}{625000000000000} \cdot \frac{y}{z}\right)\right) - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(\left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{307332350656623}{625000000000000} \cdot \frac{y}{z}\right) - \color{blue}{\frac{4166096748901211929300981260567}{10000000000000000000000000000000}} \cdot \frac{y}{z} \]

      2. associate--l+ N/A

         \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \color{blue}{\left(\frac{307332350656623}{625000000000000} \cdot \frac{y}{z} - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}\right)} \]

      3. distribute-rgt-out-- N/A

         \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{y}{z} \cdot \color{blue}{\left(\frac{307332350656623}{625000000000000} - \frac{4166096748901211929300981260567}{10000000000000000000000000000000}\right)} \]

      4. metadata-eval N/A

         \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{y}{z} \cdot \frac{751220861604756070699018739433}{10000000000000000000000000000000} \]

      5. metadata-eval N/A

         \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{y}{z} \cdot \frac{\frac{-751220861604756070699018739433}{10000000000000000000000000000000}}{\color{blue}{-1}} \]

      6. metadata-eval N/A

         \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{y}{z} \cdot \frac{\frac{-307332350656623}{625000000000000} - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000}}{-1} \]

      7. times-frac N/A

         \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{y \cdot \left(\frac{-307332350656623}{625000000000000} - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000}\right)}{\color{blue}{z \cdot -1}} \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{\color{blue}{z} \cdot -1} \]

      9. *-commutative N/A

         \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{-1 \cdot \color{blue}{z}} \]

      10. mul-1-neg N/A

          \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{\mathsf{neg}\left(z\right)} \]

      11. distribute-neg-frac2 N/A

          \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + \left(\mathsf{neg}\left(\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right)\right) \]

      12. mul-1-neg N/A

          \[\leadsto \left(x + \frac{692910599291889}{10000000000000000} \cdot y\right) + -1 \cdot \color{blue}{\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}} \]

      13. associate-+r+ N/A

          \[\leadsto x + \color{blue}{\left(\frac{692910599291889}{10000000000000000} \cdot y + -1 \cdot \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right)} \]

      14. +-commutative N/A

          \[\leadsto x + \left(-1 \cdot \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z} + \color{blue}{\frac{692910599291889}{10000000000000000} \cdot y}\right) \]

      15. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z} + \frac{692910599291889}{10000000000000000} \cdot y\right)}\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{692910599291889}{10000000000000000} \cdot y + \color{blue}{-1 \cdot \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}}\right)\right) \]

      17. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{692910599291889}{10000000000000000} \cdot y + \left(\mathsf{neg}\left(\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}\right)\right)\right)\right) \]

      18. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{692910599291889}{10000000000000000} \cdot y - \color{blue}{\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}}\right)\right) \]

   5. Simplified 98.9%

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

   if -5.4000000000000004 < z < 4.9000000000000004

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(\frac{279195317918525}{3350343815022304} \cdot y + z \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{279195317918525}{3350343815022304} \cdot y + z \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{279195317918525}{3350343815022304} + \color{blue}{z} \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{279195317918525}{3350343815022304} + \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right) \cdot \color{blue}{z}\right)\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{279195317918525}{3350343815022304} + \left(y \cdot \left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right)\right) \cdot z\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{279195317918525}{3350343815022304} + y \cdot \color{blue}{\left(\left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right) \cdot z\right)}\right)\right) \]

      6. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\frac{279195317918525}{3350343815022304} + \left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right) \cdot z\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{279195317918525}{3350343815022304} + \left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right) \cdot z\right)}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{279195317918525}{3350343815022304}, \color{blue}{\left(\left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right) \cdot z\right)}\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{279195317918525}{3350343815022304}, \left(z \cdot \color{blue}{\left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right)}\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{279195317918525}{3350343815022304}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right)}\right)\right)\right)\right) \]

      11. metadata-eval 98.9%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{279195317918525}{3350343815022304}, \mathsf{*.f64}\left(z, \frac{-155900051080628738716045985239}{56124018394291031809500087342080}\right)\right)\right)\right) \]

   5. Simplified 98.9%

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

Alternative 8: 99.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + y \cdot 0.0692910599291889\\ \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 5:\\ \;\;\;\;x + y \cdot \left(0.08333333333333323 + z \cdot -0.00277777777751721\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* y 0.0692910599291889))))
   (if (<= z -5.4)
     t_0
     (if (<= z 5.0)
       (+ x (* y (+ 0.08333333333333323 (* z -0.00277777777751721))))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y * 0.0692910599291889);
	double tmp;
	if (z <= -5.4) {
		tmp = t_0;
	} else if (z <= 5.0) {
		tmp = x + (y * (0.08333333333333323 + (z * -0.00277777777751721)));
	} 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 = x + (y * 0.0692910599291889d0)
    if (z <= (-5.4d0)) then
        tmp = t_0
    else if (z <= 5.0d0) then
        tmp = x + (y * (0.08333333333333323d0 + (z * (-0.00277777777751721d0))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (y * 0.0692910599291889);
	double tmp;
	if (z <= -5.4) {
		tmp = t_0;
	} else if (z <= 5.0) {
		tmp = x + (y * (0.08333333333333323 + (z * -0.00277777777751721)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y * 0.0692910599291889)
	tmp = 0
	if z <= -5.4:
		tmp = t_0
	elif z <= 5.0:
		tmp = x + (y * (0.08333333333333323 + (z * -0.00277777777751721)))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y * 0.0692910599291889))
	tmp = 0.0
	if (z <= -5.4)
		tmp = t_0;
	elseif (z <= 5.0)
		tmp = Float64(x + Float64(y * Float64(0.08333333333333323 + Float64(z * -0.00277777777751721))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (y * 0.0692910599291889);
	tmp = 0.0;
	if (z <= -5.4)
		tmp = t_0;
	elseif (z <= 5.0)
		tmp = x + (y * (0.08333333333333323 + (z * -0.00277777777751721)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(y * 0.0692910599291889), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.4], t$95$0, If[LessEqual[z, 5.0], N[(x + N[(y * N[(0.08333333333333323 + N[(z * -0.00277777777751721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4000000000000004 or 5 < z

   1. Initial program 35.8%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{692910599291889}{10000000000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{692910599291889}{10000000000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{692910599291889}{10000000000000000}}\right)\right) \]

      3. *-lowering-*.f64 98.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{692910599291889}{10000000000000000}}\right)\right) \]

   5. Simplified 98.4%

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

   if -5.4000000000000004 < z < 5

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(\frac{279195317918525}{3350343815022304} \cdot y + z \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{279195317918525}{3350343815022304} \cdot y + z \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{279195317918525}{3350343815022304} + \color{blue}{z} \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{279195317918525}{3350343815022304} + \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right) \cdot \color{blue}{z}\right)\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{279195317918525}{3350343815022304} + \left(y \cdot \left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right)\right) \cdot z\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{279195317918525}{3350343815022304} + y \cdot \color{blue}{\left(\left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right) \cdot z\right)}\right)\right) \]

      6. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\frac{279195317918525}{3350343815022304} + \left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right) \cdot z\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{279195317918525}{3350343815022304} + \left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right) \cdot z\right)}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{279195317918525}{3350343815022304}, \color{blue}{\left(\left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right) \cdot z\right)}\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{279195317918525}{3350343815022304}, \left(z \cdot \color{blue}{\left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right)}\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{279195317918525}{3350343815022304}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right)}\right)\right)\right)\right) \]

      11. metadata-eval 98.9%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{279195317918525}{3350343815022304}, \mathsf{*.f64}\left(z, \frac{-155900051080628738716045985239}{56124018394291031809500087342080}\right)\right)\right)\right) \]

   5. Simplified 98.9%

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

Alternative 9: 98.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + y \cdot 0.0692910599291889\\ \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 6.4:\\ \;\;\;\;x + y \cdot 0.08333333333333323\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* y 0.0692910599291889))))
   (if (<= z -5.4) t_0 (if (<= z 6.4) (+ x (* y 0.08333333333333323)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y * 0.0692910599291889);
	double tmp;
	if (z <= -5.4) {
		tmp = t_0;
	} else if (z <= 6.4) {
		tmp = x + (y * 0.08333333333333323);
	} 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 = x + (y * 0.0692910599291889d0)
    if (z <= (-5.4d0)) then
        tmp = t_0
    else if (z <= 6.4d0) then
        tmp = x + (y * 0.08333333333333323d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (y * 0.0692910599291889);
	double tmp;
	if (z <= -5.4) {
		tmp = t_0;
	} else if (z <= 6.4) {
		tmp = x + (y * 0.08333333333333323);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y * 0.0692910599291889)
	tmp = 0
	if z <= -5.4:
		tmp = t_0
	elif z <= 6.4:
		tmp = x + (y * 0.08333333333333323)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y * 0.0692910599291889))
	tmp = 0.0
	if (z <= -5.4)
		tmp = t_0;
	elseif (z <= 6.4)
		tmp = Float64(x + Float64(y * 0.08333333333333323));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (y * 0.0692910599291889);
	tmp = 0.0;
	if (z <= -5.4)
		tmp = t_0;
	elseif (z <= 6.4)
		tmp = x + (y * 0.08333333333333323);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(y * 0.0692910599291889), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.4], t$95$0, If[LessEqual[z, 6.4], N[(x + N[(y * 0.08333333333333323), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4000000000000004 or 6.4000000000000004 < z

   1. Initial program 35.8%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{692910599291889}{10000000000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{692910599291889}{10000000000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{692910599291889}{10000000000000000}}\right)\right) \]

      3. *-lowering-*.f64 98.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{692910599291889}{10000000000000000}}\right)\right) \]

   5. Simplified 98.4%

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

   if -5.4000000000000004 < z < 6.4000000000000004

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \frac{279195317918525}{3350343815022304} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{279195317918525}{3350343815022304} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{279195317918525}{3350343815022304}}\right)\right) \]

      3. *-lowering-*.f64 98.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{279195317918525}{3350343815022304}}\right)\right) \]

   5. Simplified 98.5%

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

Alternative 10: 77.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + y \cdot 0.0692910599291889\\ \mathbf{if}\;x \leq -9 \cdot 10^{-195}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{-207}:\\ \;\;\;\;y \cdot 0.08333333333333323\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* y 0.0692910599291889))))
   (if (<= x -9e-195) t_0 (if (<= x 4.9e-207) (* y 0.08333333333333323) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y * 0.0692910599291889);
	double tmp;
	if (x <= -9e-195) {
		tmp = t_0;
	} else if (x <= 4.9e-207) {
		tmp = y * 0.08333333333333323;
	} 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 = x + (y * 0.0692910599291889d0)
    if (x <= (-9d-195)) then
        tmp = t_0
    else if (x <= 4.9d-207) then
        tmp = y * 0.08333333333333323d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (y * 0.0692910599291889);
	double tmp;
	if (x <= -9e-195) {
		tmp = t_0;
	} else if (x <= 4.9e-207) {
		tmp = y * 0.08333333333333323;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y * 0.0692910599291889)
	tmp = 0
	if x <= -9e-195:
		tmp = t_0
	elif x <= 4.9e-207:
		tmp = y * 0.08333333333333323
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y * 0.0692910599291889))
	tmp = 0.0
	if (x <= -9e-195)
		tmp = t_0;
	elseif (x <= 4.9e-207)
		tmp = Float64(y * 0.08333333333333323);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (y * 0.0692910599291889);
	tmp = 0.0;
	if (x <= -9e-195)
		tmp = t_0;
	elseif (x <= 4.9e-207)
		tmp = y * 0.08333333333333323;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(y * 0.0692910599291889), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9e-195], t$95$0, If[LessEqual[x, 4.9e-207], N[(y * 0.08333333333333323), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -9e-195 or 4.9e-207 < x

   1. Initial program 66.8%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{692910599291889}{10000000000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{692910599291889}{10000000000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{692910599291889}{10000000000000000}}\right)\right) \]

      3. *-lowering-*.f64 83.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{692910599291889}{10000000000000000}}\right)\right) \]

   5. Simplified 83.4%

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

   if -9e-195 < x < 4.9e-207

   1. Initial program 87.0%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \frac{279195317918525}{3350343815022304} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{279195317918525}{3350343815022304} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{279195317918525}{3350343815022304}}\right)\right) \]

      3. *-lowering-*.f64 76.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{279195317918525}{3350343815022304}}\right)\right) \]

   5. Simplified 76.8%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{279195317918525}{3350343815022304} \cdot y} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 69.8%

         \[\leadsto \mathsf{*.f64}\left(\frac{279195317918525}{3350343815022304}, \color{blue}{y}\right) \]

   8. Simplified 69.8%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-195}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{-207}:\\ \;\;\;\;y \cdot 0.08333333333333323\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-146}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-171}:\\ \;\;\;\;y \cdot 0.08333333333333323\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5e-146) x (if (<= x 3.9e-171) (* y 0.08333333333333323) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5e-146) {
		tmp = x;
	} else if (x <= 3.9e-171) {
		tmp = y * 0.08333333333333323;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-5.5d-146)) then
        tmp = x
    else if (x <= 3.9d-171) then
        tmp = y * 0.08333333333333323d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5e-146) {
		tmp = x;
	} else if (x <= 3.9e-171) {
		tmp = y * 0.08333333333333323;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.5e-146:
		tmp = x
	elif x <= 3.9e-171:
		tmp = y * 0.08333333333333323
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5e-146)
		tmp = x;
	elseif (x <= 3.9e-171)
		tmp = Float64(y * 0.08333333333333323);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.5e-146)
		tmp = x;
	elseif (x <= 3.9e-171)
		tmp = y * 0.08333333333333323;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5e-146], x, If[LessEqual[x, 3.9e-171], N[(y * 0.08333333333333323), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.49999999999999998e-146 or 3.8999999999999998e-171 < x

   1. Initial program 68.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 64.9%

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

   if -5.49999999999999998e-146 < x < 3.8999999999999998e-171

   1. Initial program 73.4%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \frac{279195317918525}{3350343815022304} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{279195317918525}{3350343815022304} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{279195317918525}{3350343815022304}}\right)\right) \]

      3. *-lowering-*.f64 68.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{279195317918525}{3350343815022304}}\right)\right) \]

   5. Simplified 68.1%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{279195317918525}{3350343815022304} \cdot y} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 58.9%

         \[\leadsto \mathsf{*.f64}\left(\frac{279195317918525}{3350343815022304}, \color{blue}{y}\right) \]

   8. Simplified 58.9%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-146}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-171}:\\ \;\;\;\;y \cdot 0.08333333333333323\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-145}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-166}:\\ \;\;\;\;y \cdot 0.0692910599291889\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -9e-145) x (if (<= x 2.15e-166) (* y 0.0692910599291889) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -9e-145) {
		tmp = x;
	} else if (x <= 2.15e-166) {
		tmp = y * 0.0692910599291889;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-9d-145)) then
        tmp = x
    else if (x <= 2.15d-166) then
        tmp = y * 0.0692910599291889d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -9e-145) {
		tmp = x;
	} else if (x <= 2.15e-166) {
		tmp = y * 0.0692910599291889;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -9e-145:
		tmp = x
	elif x <= 2.15e-166:
		tmp = y * 0.0692910599291889
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -9e-145)
		tmp = x;
	elseif (x <= 2.15e-166)
		tmp = Float64(y * 0.0692910599291889);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -9e-145)
		tmp = x;
	elseif (x <= 2.15e-166)
		tmp = y * 0.0692910599291889;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -9e-145], x, If[LessEqual[x, 2.15e-166], N[(y * 0.0692910599291889), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -9.0000000000000001e-145 or 2.15e-166 < x

   1. Initial program 68.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 65.3%

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

   if -9.0000000000000001e-145 < x < 2.15e-166

   1. Initial program 73.0%

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

      1. +-commutative N/A

         \[\leadsto \frac{y \cdot \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} + \color{blue}{x} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y \cdot \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right), \color{blue}{x}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right) \cdot y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right), x\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right) \cdot \frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right), x\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(z \cdot \left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(z \cdot \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \left(\frac{y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}\right)\right), x\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \left(\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\left(\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\left(z \cdot \left(z + \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(z + \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

      15. +-lowering-+.f64 70.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{692910599291889}{10000000000000000}\right), \frac{307332350656623}{625000000000000}\right)\right), \frac{11167812716741}{40000000000000}\right), \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, \frac{6012459259764103}{1000000000000000}\right)\right), \frac{104698244219447}{31250000000000}\right)\right)\right), x\right) \]

   4. Applied egg-rr 70.7%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(\frac{692910599291889}{10000000000000000} \cdot y\right)}, x\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot \frac{692910599291889}{10000000000000000}\right), x\right) \]

      2. *-lowering-*.f64 60.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{692910599291889}{10000000000000000}\right), x\right) \]

   7. Simplified 60.2%

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

   8. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{692910599291889}{10000000000000000} \cdot y} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 50.0%

         \[\leadsto \mathsf{*.f64}\left(\frac{692910599291889}{10000000000000000}, \color{blue}{y}\right) \]

   10. Simplified 50.0%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-145}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-166}:\\ \;\;\;\;y \cdot 0.0692910599291889\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

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 69.9%

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

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 52.5%

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

Developer Target 1: 99.4% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024192 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, B"
  :precision binary64

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

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