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

Percentage Accurate: 69.4% → 98.8%

Time: 13.3s

Alternatives: 14

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: 69.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot 0.14677053705526136 - y \cdot 0.14954831483277858\\ t_1 := y \cdot 0.024873069133884835 + t\_0 \cdot 1.794579777993345\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+19}:\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \mathbf{elif}\;z \leq 0.235:\\ \;\;\;\;x + \left(\left(y \cdot 0.08333333333333323 + \left(z \cdot t\_0 - {z}^{2} \cdot \left(t\_1 - y \cdot 0.020681775887746497\right)\right)\right) - {z}^{3} \cdot \left(0.29847682960661837 \cdot t\_0 + 1.794579777993345 \cdot \left(y \cdot 0.020681775887746497 - t\_1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\left(14.431876219268936 + \frac{101.23733352003822}{{z}^{2}}\right) - \frac{15.646356830292042}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* y 0.14677053705526136) (* y 0.14954831483277858)))
        (t_1 (+ (* y 0.024873069133884835) (* t_0 1.794579777993345))))
   (if (<= z -5.8e+19)
     (+ x (/ y 14.431876219268936))
     (if (<= z 0.235)
       (+
        x
        (-
         (+
          (* y 0.08333333333333323)
          (- (* z t_0) (* (pow z 2.0) (- t_1 (* y 0.020681775887746497)))))
         (*
          (pow z 3.0)
          (+
           (* 0.29847682960661837 t_0)
           (* 1.794579777993345 (- (* y 0.020681775887746497) t_1))))))
       (+
        x
        (/
         y
         (-
          (+ 14.431876219268936 (/ 101.23733352003822 (pow z 2.0)))
          (/ 15.646356830292042 z))))))))

C

double code(double x, double y, double z) {
	double t_0 = (y * 0.14677053705526136) - (y * 0.14954831483277858);
	double t_1 = (y * 0.024873069133884835) + (t_0 * 1.794579777993345);
	double tmp;
	if (z <= -5.8e+19) {
		tmp = x + (y / 14.431876219268936);
	} else if (z <= 0.235) {
		tmp = x + (((y * 0.08333333333333323) + ((z * t_0) - (pow(z, 2.0) * (t_1 - (y * 0.020681775887746497))))) - (pow(z, 3.0) * ((0.29847682960661837 * t_0) + (1.794579777993345 * ((y * 0.020681775887746497) - t_1)))));
	} else {
		tmp = x + (y / ((14.431876219268936 + (101.23733352003822 / pow(z, 2.0))) - (15.646356830292042 / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (y * 0.14677053705526136d0) - (y * 0.14954831483277858d0)
    t_1 = (y * 0.024873069133884835d0) + (t_0 * 1.794579777993345d0)
    if (z <= (-5.8d+19)) then
        tmp = x + (y / 14.431876219268936d0)
    else if (z <= 0.235d0) then
        tmp = x + (((y * 0.08333333333333323d0) + ((z * t_0) - ((z ** 2.0d0) * (t_1 - (y * 0.020681775887746497d0))))) - ((z ** 3.0d0) * ((0.29847682960661837d0 * t_0) + (1.794579777993345d0 * ((y * 0.020681775887746497d0) - t_1)))))
    else
        tmp = x + (y / ((14.431876219268936d0 + (101.23733352003822d0 / (z ** 2.0d0))) - (15.646356830292042d0 / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y * 0.14677053705526136) - (y * 0.14954831483277858);
	double t_1 = (y * 0.024873069133884835) + (t_0 * 1.794579777993345);
	double tmp;
	if (z <= -5.8e+19) {
		tmp = x + (y / 14.431876219268936);
	} else if (z <= 0.235) {
		tmp = x + (((y * 0.08333333333333323) + ((z * t_0) - (Math.pow(z, 2.0) * (t_1 - (y * 0.020681775887746497))))) - (Math.pow(z, 3.0) * ((0.29847682960661837 * t_0) + (1.794579777993345 * ((y * 0.020681775887746497) - t_1)))));
	} else {
		tmp = x + (y / ((14.431876219268936 + (101.23733352003822 / Math.pow(z, 2.0))) - (15.646356830292042 / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y * 0.14677053705526136) - (y * 0.14954831483277858)
	t_1 = (y * 0.024873069133884835) + (t_0 * 1.794579777993345)
	tmp = 0
	if z <= -5.8e+19:
		tmp = x + (y / 14.431876219268936)
	elif z <= 0.235:
		tmp = x + (((y * 0.08333333333333323) + ((z * t_0) - (math.pow(z, 2.0) * (t_1 - (y * 0.020681775887746497))))) - (math.pow(z, 3.0) * ((0.29847682960661837 * t_0) + (1.794579777993345 * ((y * 0.020681775887746497) - t_1)))))
	else:
		tmp = x + (y / ((14.431876219268936 + (101.23733352003822 / math.pow(z, 2.0))) - (15.646356830292042 / z)))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * 0.14677053705526136) - Float64(y * 0.14954831483277858))
	t_1 = Float64(Float64(y * 0.024873069133884835) + Float64(t_0 * 1.794579777993345))
	tmp = 0.0
	if (z <= -5.8e+19)
		tmp = Float64(x + Float64(y / 14.431876219268936));
	elseif (z <= 0.235)
		tmp = Float64(x + Float64(Float64(Float64(y * 0.08333333333333323) + Float64(Float64(z * t_0) - Float64((z ^ 2.0) * Float64(t_1 - Float64(y * 0.020681775887746497))))) - Float64((z ^ 3.0) * Float64(Float64(0.29847682960661837 * t_0) + Float64(1.794579777993345 * Float64(Float64(y * 0.020681775887746497) - t_1))))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(14.431876219268936 + Float64(101.23733352003822 / (z ^ 2.0))) - Float64(15.646356830292042 / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y * 0.14677053705526136) - (y * 0.14954831483277858);
	t_1 = (y * 0.024873069133884835) + (t_0 * 1.794579777993345);
	tmp = 0.0;
	if (z <= -5.8e+19)
		tmp = x + (y / 14.431876219268936);
	elseif (z <= 0.235)
		tmp = x + (((y * 0.08333333333333323) + ((z * t_0) - ((z ^ 2.0) * (t_1 - (y * 0.020681775887746497))))) - ((z ^ 3.0) * ((0.29847682960661837 * t_0) + (1.794579777993345 * ((y * 0.020681775887746497) - t_1)))));
	else
		tmp = x + (y / ((14.431876219268936 + (101.23733352003822 / (z ^ 2.0))) - (15.646356830292042 / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * 0.14677053705526136), $MachinePrecision] - N[(y * 0.14954831483277858), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(y * 0.024873069133884835), $MachinePrecision] + N[(t$95$0 * 1.794579777993345), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e+19], N[(x + N[(y / 14.431876219268936), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.235], N[(x + N[(N[(N[(y * 0.08333333333333323), $MachinePrecision] + N[(N[(z * t$95$0), $MachinePrecision] - N[(N[Power[z, 2.0], $MachinePrecision] * N[(t$95$1 - N[(y * 0.020681775887746497), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[Power[z, 3.0], $MachinePrecision] * N[(N[(0.29847682960661837 * t$95$0), $MachinePrecision] + N[(1.794579777993345 * N[(N[(y * 0.020681775887746497), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(14.431876219268936 + N[(101.23733352003822 / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(15.646356830292042 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.8e19

   1. Initial program 34.9%

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

      1. +-commutative 34.9%

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

      2. *-commutative 34.9%

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

      3. associate-/l* 50.6%

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

      4. fma-define 50.6%

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

      5. *-commutative 50.6%

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

      6. fma-define 50.6%

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

      7. fma-define 50.6%

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

      8. *-commutative 50.6%

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

      9. fma-define 50.6%

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

   3. Simplified 50.6%

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

      1. fma-undefine 50.6%

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

      2. fma-undefine 50.6%

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

      3. *-commutative 50.6%

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

      4. fma-define 50.6%

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

      5. fma-undefine 50.6%

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

      6. *-commutative 50.6%

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

      7. associate-*r/ 34.9%

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

      8. associate-*l/ 50.6%

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

      9. clear-num 50.6%

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

      10. associate-*l/ 50.8%

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

      11. *-un-lft-identity 50.8%

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

      12. *-commutative 50.8%

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

      13. fma-undefine 50.8%

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

      14. fma-define 50.8%

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

      15. *-commutative 50.8%

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

      16. fma-undefine 50.8%

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

   6. Applied egg-rr 50.8%

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

   7. Taylor expanded in z around inf 100.0%

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

   if -5.8e19 < z < 0.23499999999999999

   1. Initial program 99.6%

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

      1. remove-double-neg 99.6%

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

      2. distribute-lft-neg-out 99.6%

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

      3. distribute-neg-frac 99.6%

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

      4. associate-/l* 99.8%

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

      5. distribute-lft-neg-in 99.8%

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

      6. remove-double-neg 99.8%

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

      7. fma-define 99.8%

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

      8. fma-define 99.8%

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

      9. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.7%

      \[\leadsto x + \color{blue}{\left(-1 \cdot \left({z}^{3} \cdot \left(0.29847682960661837 \cdot \left(0.14677053705526136 \cdot y - 0.14954831483277858 \cdot y\right) + 1.794579777993345 \cdot \left(0.020681775887746497 \cdot y - \left(0.024873069133884835 \cdot y + 1.794579777993345 \cdot \left(0.14677053705526136 \cdot y - 0.14954831483277858 \cdot y\right)\right)\right)\right)\right) + \left(0.08333333333333323 \cdot y + \left(z \cdot \left(0.14677053705526136 \cdot y - 0.14954831483277858 \cdot y\right) + {z}^{2} \cdot \left(0.020681775887746497 \cdot y - \left(0.024873069133884835 \cdot y + 1.794579777993345 \cdot \left(0.14677053705526136 \cdot y - 0.14954831483277858 \cdot y\right)\right)\right)\right)\right)\right)} \]

   if 0.23499999999999999 < z

   1. Initial program 47.4%

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

      1. +-commutative 47.4%

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

      2. *-commutative 47.4%

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

      3. associate-/l* 61.8%

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

      4. fma-define 61.8%

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

      5. *-commutative 61.8%

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

      6. fma-define 61.8%

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

      7. fma-define 61.8%

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

      8. *-commutative 61.8%

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

      9. fma-define 61.8%

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

   3. Simplified 61.8%

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

      1. fma-undefine 61.8%

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

      2. fma-undefine 61.8%

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

      3. *-commutative 61.8%

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

      4. fma-define 61.8%

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

      5. fma-undefine 61.8%

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

      6. *-commutative 61.8%

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

      7. associate-*r/ 47.4%

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

      8. associate-*l/ 64.0%

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

      9. clear-num 64.0%

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

      10. associate-*l/ 64.0%

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

      11. *-un-lft-identity 64.0%

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

      12. *-commutative 64.0%

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

      13. fma-undefine 64.0%

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

      14. fma-define 64.0%

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

      15. *-commutative 64.0%

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

      16. fma-undefine 64.0%

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

   6. Applied egg-rr 64.0%

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

   7. Taylor expanded in z around inf 99.9%

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

      1. associate-*r/ 99.9%

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

      2. metadata-eval 99.9%

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

      3. associate-*r/ 99.9%

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

      4. metadata-eval 99.9%

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

   9. Simplified 99.9%

      \[\leadsto \frac{y}{\color{blue}{\left(14.431876219268936 + \frac{101.23733352003822}{{z}^{2}}\right) - \frac{15.646356830292042}{z}}} + x \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+19}:\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \mathbf{elif}\;z \leq 0.235:\\ \;\;\;\;x + \left(\left(y \cdot 0.08333333333333323 + \left(z \cdot \left(y \cdot 0.14677053705526136 - y \cdot 0.14954831483277858\right) - {z}^{2} \cdot \left(\left(y \cdot 0.024873069133884835 + \left(y \cdot 0.14677053705526136 - y \cdot 0.14954831483277858\right) \cdot 1.794579777993345\right) - y \cdot 0.020681775887746497\right)\right)\right) - {z}^{3} \cdot \left(0.29847682960661837 \cdot \left(y \cdot 0.14677053705526136 - y \cdot 0.14954831483277858\right) + 1.794579777993345 \cdot \left(y \cdot 0.020681775887746497 - \left(y \cdot 0.024873069133884835 + \left(y \cdot 0.14677053705526136 - y \cdot 0.14954831483277858\right) \cdot 1.794579777993345\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\left(14.431876219268936 + \frac{101.23733352003822}{{z}^{2}}\right) - \frac{15.646356830292042}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} \leq 10^{+299}:\\ \;\;\;\;x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (/
       (*
        y
        (+
         (* z (+ (* z 0.0692910599291889) 0.4917317610505968))
         0.279195317918525))
       (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
      1e+299)
   (+
    x
    (*
     y
     (/
      (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
      (fma (+ z 6.012459259764103) z 3.350343815022304))))
   (+ x (/ y 14.431876219268936))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((y * ((z * ((z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / ((z * (z + 6.012459259764103)) + 3.350343815022304)) <= 1e+299) {
		tmp = x + (y * (fma(fma(z, 0.0692910599291889, 0.4917317610505968), z, 0.279195317918525) / fma((z + 6.012459259764103), z, 3.350343815022304)));
	} else {
		tmp = x + (y / 14.431876219268936);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / Float64(Float64(z * Float64(z + 6.012459259764103)) + 3.350343815022304)) <= 1e+299)
		tmp = Float64(x + Float64(y * Float64(fma(fma(z, 0.0692910599291889, 0.4917317610505968), z, 0.279195317918525) / fma(Float64(z + 6.012459259764103), z, 3.350343815022304))));
	else
		tmp = Float64(x + Float64(y / 14.431876219268936));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(y * N[(N[(z * N[(N[(z * 0.0692910599291889), $MachinePrecision] + 0.4917317610505968), $MachinePrecision]), $MachinePrecision] + 0.279195317918525), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(z + 6.012459259764103), $MachinePrecision]), $MachinePrecision] + 3.350343815022304), $MachinePrecision]), $MachinePrecision], 1e+299], N[(x + N[(y * N[(N[(N[(z * 0.0692910599291889 + 0.4917317610505968), $MachinePrecision] * z + 0.279195317918525), $MachinePrecision] / N[(N[(z + 6.012459259764103), $MachinePrecision] * z + 3.350343815022304), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / 14.431876219268936), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 692910599291889/10000000000000000) 307332350656623/625000000000000) z) 11167812716741/40000000000000)) (+.f64 (*.f64 (+.f64 z 6012459259764103/1000000000000000) z) 104698244219447/31250000000000)) < 1.0000000000000001e299

   1. Initial program 95.3%

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

      1. remove-double-neg 95.3%

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

      2. distribute-lft-neg-out 95.3%

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

      3. distribute-neg-frac 95.3%

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

      4. associate-/l* 99.8%

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

      5. distribute-lft-neg-in 99.8%

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

      6. remove-double-neg 99.8%

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

      7. fma-define 99.8%

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

      8. fma-define 99.8%

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

      9. fma-define 99.8%

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

   3. Simplified 99.8%

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

   if 1.0000000000000001e299 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 692910599291889/10000000000000000) 307332350656623/625000000000000) z) 11167812716741/40000000000000)) (+.f64 (*.f64 (+.f64 z 6012459259764103/1000000000000000) z) 104698244219447/31250000000000))

   1. Initial program 1.3%

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

      1. +-commutative 1.3%

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

      2. *-commutative 1.3%

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

      3. associate-/l* 18.3%

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

      4. fma-define 18.3%

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

      5. *-commutative 18.3%

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

      6. fma-define 18.3%

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

      7. fma-define 18.3%

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

      8. *-commutative 18.3%

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

      9. fma-define 18.3%

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

   3. Simplified 18.3%

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

      1. fma-undefine 18.3%

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

      2. fma-undefine 18.3%

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

      3. *-commutative 18.3%

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

      4. fma-define 18.3%

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

      5. fma-undefine 18.3%

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

      6. *-commutative 18.3%

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

      7. associate-*r/ 1.3%

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

      8. associate-*l/ 18.3%

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

      9. clear-num 18.3%

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

      10. associate-*l/ 18.3%

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

      11. *-un-lft-identity 18.3%

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

      12. *-commutative 18.3%

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

      13. fma-undefine 18.3%

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

      14. fma-define 18.3%

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

      15. *-commutative 18.3%

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

      16. fma-undefine 18.3%

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

   6. Applied egg-rr 18.3%

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

   7. Taylor expanded in z around inf 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} \leq 10^{+299}:\\ \;\;\;\;x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right), z, 0.279195317918525\right)}{\mathsf{fma}\left(z + 6.012459259764103, z, 3.350343815022304\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+34} \lor \neg \left(z \leq 1.62 \cdot 10^{+22}\right):\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(0.279195317918525 + \left(0.0692910599291889 \cdot {z}^{2} + z \cdot 0.4917317610505968\right)\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.65e+34) (not (<= z 1.62e+22)))
   (+ x (/ y 14.431876219268936))
   (+
    x
    (/
     (*
      y
      (+
       0.279195317918525
       (+ (* 0.0692910599291889 (pow z 2.0)) (* z 0.4917317610505968))))
     (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.65e+34) || !(z <= 1.62e+22)) {
		tmp = x + (y / 14.431876219268936);
	} else {
		tmp = x + ((y * (0.279195317918525 + ((0.0692910599291889 * pow(z, 2.0)) + (z * 0.4917317610505968)))) / ((z * (z + 6.012459259764103)) + 3.350343815022304));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.65d+34)) .or. (.not. (z <= 1.62d+22))) then
        tmp = x + (y / 14.431876219268936d0)
    else
        tmp = x + ((y * (0.279195317918525d0 + ((0.0692910599291889d0 * (z ** 2.0d0)) + (z * 0.4917317610505968d0)))) / ((z * (z + 6.012459259764103d0)) + 3.350343815022304d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.65e+34) || !(z <= 1.62e+22)) {
		tmp = x + (y / 14.431876219268936);
	} else {
		tmp = x + ((y * (0.279195317918525 + ((0.0692910599291889 * Math.pow(z, 2.0)) + (z * 0.4917317610505968)))) / ((z * (z + 6.012459259764103)) + 3.350343815022304));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.65e+34) or not (z <= 1.62e+22):
		tmp = x + (y / 14.431876219268936)
	else:
		tmp = x + ((y * (0.279195317918525 + ((0.0692910599291889 * math.pow(z, 2.0)) + (z * 0.4917317610505968)))) / ((z * (z + 6.012459259764103)) + 3.350343815022304))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.65e+34) || !(z <= 1.62e+22))
		tmp = Float64(x + Float64(y / 14.431876219268936));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(0.279195317918525 + Float64(Float64(0.0692910599291889 * (z ^ 2.0)) + Float64(z * 0.4917317610505968)))) / Float64(Float64(z * Float64(z + 6.012459259764103)) + 3.350343815022304)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.65e+34) || ~((z <= 1.62e+22)))
		tmp = x + (y / 14.431876219268936);
	else
		tmp = x + ((y * (0.279195317918525 + ((0.0692910599291889 * (z ^ 2.0)) + (z * 0.4917317610505968)))) / ((z * (z + 6.012459259764103)) + 3.350343815022304));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.65e+34], N[Not[LessEqual[z, 1.62e+22]], $MachinePrecision]], N[(x + N[(y / 14.431876219268936), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(0.279195317918525 + N[(N[(0.0692910599291889 * N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision] + N[(z * 0.4917317610505968), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(z + 6.012459259764103), $MachinePrecision]), $MachinePrecision] + 3.350343815022304), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.64999999999999994e34 or 1.62e22 < z

   1. Initial program 33.5%

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

      1. +-commutative 33.5%

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

      2. *-commutative 33.5%

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

      3. associate-/l* 50.5%

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

      4. fma-define 50.5%

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

      5. *-commutative 50.5%

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

      6. fma-define 50.5%

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

      7. fma-define 50.5%

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

      8. *-commutative 50.5%

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

      9. fma-define 50.5%

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

   3. Simplified 50.5%

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

      1. fma-undefine 50.5%

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

      2. fma-undefine 50.5%

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

      3. *-commutative 50.5%

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

      4. fma-define 50.5%

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

      5. fma-undefine 50.5%

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

      6. *-commutative 50.5%

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

      7. associate-*r/ 33.5%

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

      8. associate-*l/ 51.7%

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

      9. clear-num 51.7%

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

      10. associate-*l/ 51.8%

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

      11. *-un-lft-identity 51.8%

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

      12. *-commutative 51.8%

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

      13. fma-undefine 51.8%

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

      14. fma-define 51.8%

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

      15. *-commutative 51.8%

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

      16. fma-undefine 51.8%

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

   6. Applied egg-rr 51.8%

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

   7. Taylor expanded in z around inf 100.0%

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

   if -1.64999999999999994e34 < z < 1.62e22

   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 99.7%

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

   4. Taylor expanded in y around 0 99.7%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+34} \lor \neg \left(z \leq 1.62 \cdot 10^{+22}\right):\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(0.279195317918525 + \left(0.0692910599291889 \cdot {z}^{2} + z \cdot 0.4917317610505968\right)\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+66}:\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \mathbf{elif}\;z \leq 0.235:\\ \;\;\;\;\frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\left(14.431876219268936 + \frac{101.23733352003822}{{z}^{2}}\right) - \frac{15.646356830292042}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7e+66)
   (+ x (/ y 14.431876219268936))
   (if (<= z 0.235)
     (+
      (/
       (*
        y
        (+
         (* z (+ (* z 0.0692910599291889) 0.4917317610505968))
         0.279195317918525))
       (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
      x)
     (+
      x
      (/
       y
       (-
        (+ 14.431876219268936 (/ 101.23733352003822 (pow z 2.0)))
        (/ 15.646356830292042 z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7e+66) {
		tmp = x + (y / 14.431876219268936);
	} else if (z <= 0.235) {
		tmp = ((y * ((z * ((z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / ((z * (z + 6.012459259764103)) + 3.350343815022304)) + x;
	} else {
		tmp = x + (y / ((14.431876219268936 + (101.23733352003822 / pow(z, 2.0))) - (15.646356830292042 / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-7d+66)) then
        tmp = x + (y / 14.431876219268936d0)
    else if (z <= 0.235d0) then
        tmp = ((y * ((z * ((z * 0.0692910599291889d0) + 0.4917317610505968d0)) + 0.279195317918525d0)) / ((z * (z + 6.012459259764103d0)) + 3.350343815022304d0)) + x
    else
        tmp = x + (y / ((14.431876219268936d0 + (101.23733352003822d0 / (z ** 2.0d0))) - (15.646356830292042d0 / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -7e+66) {
		tmp = x + (y / 14.431876219268936);
	} else if (z <= 0.235) {
		tmp = ((y * ((z * ((z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / ((z * (z + 6.012459259764103)) + 3.350343815022304)) + x;
	} else {
		tmp = x + (y / ((14.431876219268936 + (101.23733352003822 / Math.pow(z, 2.0))) - (15.646356830292042 / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7e+66:
		tmp = x + (y / 14.431876219268936)
	elif z <= 0.235:
		tmp = ((y * ((z * ((z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / ((z * (z + 6.012459259764103)) + 3.350343815022304)) + x
	else:
		tmp = x + (y / ((14.431876219268936 + (101.23733352003822 / math.pow(z, 2.0))) - (15.646356830292042 / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7e+66)
		tmp = Float64(x + Float64(y / 14.431876219268936));
	elseif (z <= 0.235)
		tmp = Float64(Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / Float64(Float64(z * Float64(z + 6.012459259764103)) + 3.350343815022304)) + x);
	else
		tmp = Float64(x + Float64(y / Float64(Float64(14.431876219268936 + Float64(101.23733352003822 / (z ^ 2.0))) - Float64(15.646356830292042 / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -7e+66)
		tmp = x + (y / 14.431876219268936);
	elseif (z <= 0.235)
		tmp = ((y * ((z * ((z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / ((z * (z + 6.012459259764103)) + 3.350343815022304)) + x;
	else
		tmp = x + (y / ((14.431876219268936 + (101.23733352003822 / (z ^ 2.0))) - (15.646356830292042 / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7e+66], N[(x + N[(y / 14.431876219268936), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.235], N[(N[(N[(y * N[(N[(z * N[(N[(z * 0.0692910599291889), $MachinePrecision] + 0.4917317610505968), $MachinePrecision]), $MachinePrecision] + 0.279195317918525), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(z + 6.012459259764103), $MachinePrecision]), $MachinePrecision] + 3.350343815022304), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(y / N[(N[(14.431876219268936 + N[(101.23733352003822 / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(15.646356830292042 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.9999999999999994e66

   1. Initial program 23.1%

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

      1. +-commutative 23.1%

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

      2. *-commutative 23.1%

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

      3. associate-/l* 41.8%

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

      4. fma-define 41.8%

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

      5. *-commutative 41.8%

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

      6. fma-define 41.8%

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

      7. fma-define 41.8%

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

      8. *-commutative 41.8%

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

      9. fma-define 41.8%

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

   3. Simplified 41.8%

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

      1. fma-undefine 41.8%

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

      2. fma-undefine 41.8%

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

      3. *-commutative 41.8%

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

      4. fma-define 41.8%

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

      5. fma-undefine 41.8%

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

      6. *-commutative 41.8%

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

      7. associate-*r/ 23.1%

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

      8. associate-*l/ 41.8%

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

      9. clear-num 41.8%

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

      10. associate-*l/ 41.9%

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

      11. *-un-lft-identity 41.9%

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

      12. *-commutative 41.9%

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

      13. fma-undefine 41.9%

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

      14. fma-define 41.9%

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

      15. *-commutative 41.9%

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

      16. fma-undefine 41.9%

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

   6. Applied egg-rr 41.9%

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

   7. Taylor expanded in z around inf 100.0%

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

   if -6.9999999999999994e66 < z < 0.23499999999999999

   1. Initial program 99.7%

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

   if 0.23499999999999999 < z

   1. Initial program 47.4%

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

      1. +-commutative 47.4%

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

      2. *-commutative 47.4%

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

      3. associate-/l* 61.8%

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

      4. fma-define 61.8%

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

      5. *-commutative 61.8%

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

      6. fma-define 61.8%

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

      7. fma-define 61.8%

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

      8. *-commutative 61.8%

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

      9. fma-define 61.8%

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

   3. Simplified 61.8%

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

      1. fma-undefine 61.8%

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

      2. fma-undefine 61.8%

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

      3. *-commutative 61.8%

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

      4. fma-define 61.8%

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

      5. fma-undefine 61.8%

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

      6. *-commutative 61.8%

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

      7. associate-*r/ 47.4%

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

      8. associate-*l/ 64.0%

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

      9. clear-num 64.0%

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

      10. associate-*l/ 64.0%

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

      11. *-un-lft-identity 64.0%

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

      12. *-commutative 64.0%

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

      13. fma-undefine 64.0%

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

      14. fma-define 64.0%

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

      15. *-commutative 64.0%

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

      16. fma-undefine 64.0%

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

   6. Applied egg-rr 64.0%

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

   7. Taylor expanded in z around inf 99.9%

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

      1. associate-*r/ 99.9%

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

      2. metadata-eval 99.9%

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

      3. associate-*r/ 99.9%

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

      4. metadata-eval 99.9%

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

   9. Simplified 99.9%

      \[\leadsto \frac{y}{\color{blue}{\left(14.431876219268936 + \frac{101.23733352003822}{{z}^{2}}\right) - \frac{15.646356830292042}{z}}} + x \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+66}:\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \mathbf{elif}\;z \leq 0.235:\\ \;\;\;\;\frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\left(14.431876219268936 + \frac{101.23733352003822}{{z}^{2}}\right) - \frac{15.646356830292042}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+66} \lor \neg \left(z \leq 3700000000000\right):\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -7e+66) (not (<= z 3700000000000.0)))
   (+ x (/ y 14.431876219268936))
   (+
    (/
     (*
      y
      (+
       (* z (+ (* z 0.0692910599291889) 0.4917317610505968))
       0.279195317918525))
     (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
    x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7e+66) || !(z <= 3700000000000.0)) {
		tmp = x + (y / 14.431876219268936);
	} else {
		tmp = ((y * ((z * ((z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / ((z * (z + 6.012459259764103)) + 3.350343815022304)) + 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 ((z <= (-7d+66)) .or. (.not. (z <= 3700000000000.0d0))) then
        tmp = x + (y / 14.431876219268936d0)
    else
        tmp = ((y * ((z * ((z * 0.0692910599291889d0) + 0.4917317610505968d0)) + 0.279195317918525d0)) / ((z * (z + 6.012459259764103d0)) + 3.350343815022304d0)) + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7e+66) || !(z <= 3700000000000.0)) {
		tmp = x + (y / 14.431876219268936);
	} else {
		tmp = ((y * ((z * ((z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / ((z * (z + 6.012459259764103)) + 3.350343815022304)) + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -7e+66) or not (z <= 3700000000000.0):
		tmp = x + (y / 14.431876219268936)
	else:
		tmp = ((y * ((z * ((z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / ((z * (z + 6.012459259764103)) + 3.350343815022304)) + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -7e+66) || !(z <= 3700000000000.0))
		tmp = Float64(x + Float64(y / 14.431876219268936));
	else
		tmp = Float64(Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / Float64(Float64(z * Float64(z + 6.012459259764103)) + 3.350343815022304)) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -7e+66) || ~((z <= 3700000000000.0)))
		tmp = x + (y / 14.431876219268936);
	else
		tmp = ((y * ((z * ((z * 0.0692910599291889) + 0.4917317610505968)) + 0.279195317918525)) / ((z * (z + 6.012459259764103)) + 3.350343815022304)) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -7e+66], N[Not[LessEqual[z, 3700000000000.0]], $MachinePrecision]], N[(x + N[(y / 14.431876219268936), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * N[(N[(z * N[(N[(z * 0.0692910599291889), $MachinePrecision] + 0.4917317610505968), $MachinePrecision]), $MachinePrecision] + 0.279195317918525), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(z + 6.012459259764103), $MachinePrecision]), $MachinePrecision] + 3.350343815022304), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.9999999999999994e66 or 3.7e12 < z

   1. Initial program 32.1%

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

      1. +-commutative 32.1%

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

      2. *-commutative 32.1%

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

      3. associate-/l* 49.5%

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

      4. fma-define 49.5%

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

      5. *-commutative 49.5%

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

      6. fma-define 49.5%

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

      7. fma-define 49.5%

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

      8. *-commutative 49.5%

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

      9. fma-define 49.5%

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

   3. Simplified 49.5%

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

      1. fma-undefine 49.5%

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

      2. fma-undefine 49.5%

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

      3. *-commutative 49.5%

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

      4. fma-define 49.5%

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

      5. fma-undefine 49.5%

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

      6. *-commutative 49.5%

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

      7. associate-*r/ 32.1%

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

      8. associate-*l/ 50.8%

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

      9. clear-num 50.8%

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

      10. associate-*l/ 50.8%

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

      11. *-un-lft-identity 50.8%

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

      12. *-commutative 50.8%

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

      13. fma-undefine 50.8%

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

      14. fma-define 50.8%

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

      15. *-commutative 50.8%

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

      16. fma-undefine 50.8%

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

   6. Applied egg-rr 50.8%

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

   7. Taylor expanded in z around inf 99.9%

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

   if -6.9999999999999994e66 < z < 3.7e12

   1. Initial program 99.7%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+66} \lor \neg \left(z \leq 3700000000000\right):\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525\right)}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304} + x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+124} \lor \neg \left(y \leq 2.2 \cdot 10^{+149}\right) \land y \leq 3.2 \cdot 10^{+235}:\\ \;\;\;\;y \cdot 0.08333333333333323\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.2e+124) (and (not (<= y 2.2e+149)) (<= y 3.2e+235)))
   (* y 0.08333333333333323)
   (+ x (* y 0.0692910599291889))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.2e+124) || (!(y <= 2.2e+149) && (y <= 3.2e+235))) {
		tmp = y * 0.08333333333333323;
	} else {
		tmp = x + (y * 0.0692910599291889);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-3.2d+124)) .or. (.not. (y <= 2.2d+149)) .and. (y <= 3.2d+235)) then
        tmp = y * 0.08333333333333323d0
    else
        tmp = x + (y * 0.0692910599291889d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.2e+124) || (!(y <= 2.2e+149) && (y <= 3.2e+235))) {
		tmp = y * 0.08333333333333323;
	} else {
		tmp = x + (y * 0.0692910599291889);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.2e+124) or (not (y <= 2.2e+149) and (y <= 3.2e+235)):
		tmp = y * 0.08333333333333323
	else:
		tmp = x + (y * 0.0692910599291889)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.2e+124) || (!(y <= 2.2e+149) && (y <= 3.2e+235)))
		tmp = Float64(y * 0.08333333333333323);
	else
		tmp = Float64(x + Float64(y * 0.0692910599291889));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.2e+124) || (~((y <= 2.2e+149)) && (y <= 3.2e+235)))
		tmp = y * 0.08333333333333323;
	else
		tmp = x + (y * 0.0692910599291889);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.2e+124], And[N[Not[LessEqual[y, 2.2e+149]], $MachinePrecision], LessEqual[y, 3.2e+235]]], N[(y * 0.08333333333333323), $MachinePrecision], N[(x + N[(y * 0.0692910599291889), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.19999999999999993e124 or 2.2e149 < y < 3.20000000000000006e235

   1. Initial program 69.2%

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

      1. +-commutative 69.2%

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

      2. *-commutative 69.2%

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

      3. associate-/l* 86.4%

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

      4. fma-define 86.4%

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

      5. *-commutative 86.4%

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

      6. fma-define 86.4%

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

      7. fma-define 86.4%

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

      8. *-commutative 86.4%

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

      9. fma-define 86.4%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in z around 0 78.1%

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

      1. +-commutative 78.1%

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

      2. fma-define 78.1%

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

   7. Simplified 78.1%

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

   8. Taylor expanded in y around inf 69.4%

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

   if -3.19999999999999993e124 < y < 2.2e149 or 3.20000000000000006e235 < y

   1. Initial program 74.4%

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

      1. +-commutative 74.4%

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

      2. *-commutative 74.4%

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

      3. associate-/l* 78.4%

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

      4. fma-define 78.4%

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

      5. *-commutative 78.4%

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

      6. fma-define 78.4%

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

      7. fma-define 78.4%

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

      8. *-commutative 78.4%

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

      9. fma-define 78.4%

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

   3. Simplified 78.4%

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

   5. Taylor expanded in z around inf 86.0%

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

      1. +-commutative 86.0%

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

   7. Simplified 86.0%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+124} \lor \neg \left(y \leq 2.2 \cdot 10^{+149}\right) \land y \leq 3.2 \cdot 10^{+235}:\\ \;\;\;\;y \cdot 0.08333333333333323\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+19}:\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \mathbf{elif}\;z \leq 0.235:\\ \;\;\;\;x + \frac{y}{12.000000000000014}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.8e+19)
   (+ x (/ y 14.431876219268936))
   (if (<= z 0.235)
     (+ x (/ y 12.000000000000014))
     (+ x (* y (+ 0.0692910599291889 (/ 0.07512208616047561 z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.8e+19) {
		tmp = x + (y / 14.431876219268936);
	} else if (z <= 0.235) {
		tmp = x + (y / 12.000000000000014);
	} 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 <= (-5.8d+19)) then
        tmp = x + (y / 14.431876219268936d0)
    else if (z <= 0.235d0) then
        tmp = x + (y / 12.000000000000014d0)
    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 <= -5.8e+19) {
		tmp = x + (y / 14.431876219268936);
	} else if (z <= 0.235) {
		tmp = x + (y / 12.000000000000014);
	} else {
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.8e+19:
		tmp = x + (y / 14.431876219268936)
	elif z <= 0.235:
		tmp = x + (y / 12.000000000000014)
	else:
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.8e+19)
		tmp = Float64(x + Float64(y / 14.431876219268936));
	elseif (z <= 0.235)
		tmp = Float64(x + Float64(y / 12.000000000000014));
	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 <= -5.8e+19)
		tmp = x + (y / 14.431876219268936);
	elseif (z <= 0.235)
		tmp = x + (y / 12.000000000000014);
	else
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.8e+19], N[(x + N[(y / 14.431876219268936), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.235], N[(x + N[(y / 12.000000000000014), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(0.0692910599291889 + N[(0.07512208616047561 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.8e19

   1. Initial program 34.9%

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

      1. +-commutative 34.9%

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

      2. *-commutative 34.9%

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

      3. associate-/l* 50.6%

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

      4. fma-define 50.6%

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

      5. *-commutative 50.6%

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

      6. fma-define 50.6%

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

      7. fma-define 50.6%

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

      8. *-commutative 50.6%

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

      9. fma-define 50.6%

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

   3. Simplified 50.6%

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

      1. fma-undefine 50.6%

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

      2. fma-undefine 50.6%

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

      3. *-commutative 50.6%

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

      4. fma-define 50.6%

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

      5. fma-undefine 50.6%

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

      6. *-commutative 50.6%

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

      7. associate-*r/ 34.9%

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

      8. associate-*l/ 50.6%

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

      9. clear-num 50.6%

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

      10. associate-*l/ 50.8%

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

      11. *-un-lft-identity 50.8%

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

      12. *-commutative 50.8%

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

      13. fma-undefine 50.8%

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

      14. fma-define 50.8%

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

      15. *-commutative 50.8%

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

      16. fma-undefine 50.8%

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

   6. Applied egg-rr 50.8%

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

   7. Taylor expanded in z around inf 100.0%

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

   if -5.8e19 < z < 0.23499999999999999

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-/l* 99.6%

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

      4. fma-define 99.6%

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

      5. *-commutative 99.6%

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

      6. fma-define 99.6%

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

      7. fma-define 99.6%

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

      8. *-commutative 99.6%

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

      9. fma-define 99.6%

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

   3. Simplified 99.6%

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

      1. fma-undefine 99.6%

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

      2. fma-undefine 99.6%

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

      3. *-commutative 99.6%

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

      4. fma-define 99.6%

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

      5. fma-undefine 99.6%

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

      6. *-commutative 99.6%

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

      7. associate-*r/ 99.6%

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

      8. associate-*l/ 99.8%

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

      9. clear-num 99.1%

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

      10. associate-*l/ 99.4%

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

      11. *-un-lft-identity 99.4%

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

      12. *-commutative 99.4%

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

      13. fma-undefine 99.4%

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

      14. fma-define 99.4%

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

      15. *-commutative 99.4%

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

      16. fma-undefine 99.4%

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

   6. Applied egg-rr 99.4%

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

   7. Taylor expanded in z around 0 98.6%

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

   if 0.23499999999999999 < z

   1. Initial program 47.4%

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

      1. remove-double-neg 47.4%

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

      2. distribute-lft-neg-out 47.4%

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

      3. distribute-neg-frac 47.4%

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

      4. associate-/l* 64.0%

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

      5. distribute-lft-neg-in 64.0%

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

      6. remove-double-neg 64.0%

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

      7. fma-define 64.0%

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

      8. fma-define 64.0%

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

      9. fma-define 64.0%

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

   3. Simplified 64.0%

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

   5. Taylor expanded in z around inf 99.3%

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

      1. associate-*r/ 99.3%

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

      2. metadata-eval 99.3%

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

   7. Simplified 99.3%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+19}:\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \mathbf{elif}\;z \leq 0.235:\\ \;\;\;\;x + \frac{y}{12.000000000000014}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+19}:\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \mathbf{elif}\;z \leq 0.235:\\ \;\;\;\;x + y \cdot \left(0.08333333333333323 + z \cdot -0.00277777777751721\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.8e+19)
   (+ x (/ y 14.431876219268936))
   (if (<= z 0.235)
     (+ x (* y (+ 0.08333333333333323 (* z -0.00277777777751721))))
     (+ x (* y (+ 0.0692910599291889 (/ 0.07512208616047561 z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.8e+19) {
		tmp = x + (y / 14.431876219268936);
	} else if (z <= 0.235) {
		tmp = x + (y * (0.08333333333333323 + (z * -0.00277777777751721)));
	} else {
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-5.8d+19)) then
        tmp = x + (y / 14.431876219268936d0)
    else if (z <= 0.235d0) then
        tmp = x + (y * (0.08333333333333323d0 + (z * (-0.00277777777751721d0))))
    else
        tmp = x + (y * (0.0692910599291889d0 + (0.07512208616047561d0 / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.8e+19) {
		tmp = x + (y / 14.431876219268936);
	} else if (z <= 0.235) {
		tmp = x + (y * (0.08333333333333323 + (z * -0.00277777777751721)));
	} else {
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.8e+19:
		tmp = x + (y / 14.431876219268936)
	elif z <= 0.235:
		tmp = x + (y * (0.08333333333333323 + (z * -0.00277777777751721)))
	else:
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.8e+19)
		tmp = Float64(x + Float64(y / 14.431876219268936));
	elseif (z <= 0.235)
		tmp = Float64(x + Float64(y * Float64(0.08333333333333323 + Float64(z * -0.00277777777751721))));
	else
		tmp = Float64(x + Float64(y * Float64(0.0692910599291889 + Float64(0.07512208616047561 / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.8e+19)
		tmp = x + (y / 14.431876219268936);
	elseif (z <= 0.235)
		tmp = x + (y * (0.08333333333333323 + (z * -0.00277777777751721)));
	else
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.8e+19], N[(x + N[(y / 14.431876219268936), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.235], N[(x + N[(y * N[(0.08333333333333323 + N[(z * -0.00277777777751721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(0.0692910599291889 + N[(0.07512208616047561 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.8e19

   1. Initial program 34.9%

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

      1. +-commutative 34.9%

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

      2. *-commutative 34.9%

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

      3. associate-/l* 50.6%

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

      4. fma-define 50.6%

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

      5. *-commutative 50.6%

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

      6. fma-define 50.6%

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

      7. fma-define 50.6%

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

      8. *-commutative 50.6%

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

      9. fma-define 50.6%

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

   3. Simplified 50.6%

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

      1. fma-undefine 50.6%

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

      2. fma-undefine 50.6%

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

      3. *-commutative 50.6%

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

      4. fma-define 50.6%

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

      5. fma-undefine 50.6%

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

      6. *-commutative 50.6%

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

      7. associate-*r/ 34.9%

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

      8. associate-*l/ 50.6%

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

      9. clear-num 50.6%

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

      10. associate-*l/ 50.8%

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

      11. *-un-lft-identity 50.8%

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

      12. *-commutative 50.8%

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

      13. fma-undefine 50.8%

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

      14. fma-define 50.8%

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

      15. *-commutative 50.8%

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

      16. fma-undefine 50.8%

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

   6. Applied egg-rr 50.8%

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

   7. Taylor expanded in z around inf 100.0%

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

   if -5.8e19 < z < 0.23499999999999999

   1. Initial program 99.6%

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

      1. remove-double-neg 99.6%

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

      2. distribute-lft-neg-out 99.6%

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

      3. distribute-neg-frac 99.6%

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

      4. associate-/l* 99.8%

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

      5. distribute-lft-neg-in 99.8%

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

      6. remove-double-neg 99.8%

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

      7. fma-define 99.8%

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

      8. fma-define 99.8%

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

      9. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.1%

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

   if 0.23499999999999999 < z

   1. Initial program 47.4%

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

      1. remove-double-neg 47.4%

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

      2. distribute-lft-neg-out 47.4%

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

      3. distribute-neg-frac 47.4%

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

      4. associate-/l* 64.0%

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

      5. distribute-lft-neg-in 64.0%

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

      6. remove-double-neg 64.0%

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

      7. fma-define 64.0%

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

      8. fma-define 64.0%

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

      9. fma-define 64.0%

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

   3. Simplified 64.0%

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

   5. Taylor expanded in z around inf 99.3%

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

      1. associate-*r/ 99.3%

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

      2. metadata-eval 99.3%

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

   7. Simplified 99.3%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+19}:\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \mathbf{elif}\;z \leq 0.235:\\ \;\;\;\;x + y \cdot \left(0.08333333333333323 + z \cdot -0.00277777777751721\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+19}:\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \mathbf{elif}\;z \leq 0.235:\\ \;\;\;\;x + \frac{y}{12.000000000000014 + z \cdot 0.39999999996247915}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.8e+19)
   (+ x (/ y 14.431876219268936))
   (if (<= z 0.235)
     (+ x (/ y (+ 12.000000000000014 (* z 0.39999999996247915))))
     (+ x (* y (+ 0.0692910599291889 (/ 0.07512208616047561 z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.8e+19) {
		tmp = x + (y / 14.431876219268936);
	} else if (z <= 0.235) {
		tmp = x + (y / (12.000000000000014 + (z * 0.39999999996247915)));
	} 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 <= (-5.8d+19)) then
        tmp = x + (y / 14.431876219268936d0)
    else if (z <= 0.235d0) then
        tmp = x + (y / (12.000000000000014d0 + (z * 0.39999999996247915d0)))
    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 <= -5.8e+19) {
		tmp = x + (y / 14.431876219268936);
	} else if (z <= 0.235) {
		tmp = x + (y / (12.000000000000014 + (z * 0.39999999996247915)));
	} else {
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.8e+19:
		tmp = x + (y / 14.431876219268936)
	elif z <= 0.235:
		tmp = x + (y / (12.000000000000014 + (z * 0.39999999996247915)))
	else:
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.8e+19)
		tmp = Float64(x + Float64(y / 14.431876219268936));
	elseif (z <= 0.235)
		tmp = Float64(x + Float64(y / Float64(12.000000000000014 + Float64(z * 0.39999999996247915))));
	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 <= -5.8e+19)
		tmp = x + (y / 14.431876219268936);
	elseif (z <= 0.235)
		tmp = x + (y / (12.000000000000014 + (z * 0.39999999996247915)));
	else
		tmp = x + (y * (0.0692910599291889 + (0.07512208616047561 / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.8e+19], N[(x + N[(y / 14.431876219268936), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.235], N[(x + N[(y / N[(12.000000000000014 + N[(z * 0.39999999996247915), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(0.0692910599291889 + N[(0.07512208616047561 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.8e19

   1. Initial program 34.9%

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

      1. +-commutative 34.9%

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

      2. *-commutative 34.9%

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

      3. associate-/l* 50.6%

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

      4. fma-define 50.6%

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

      5. *-commutative 50.6%

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

      6. fma-define 50.6%

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

      7. fma-define 50.6%

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

      8. *-commutative 50.6%

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

      9. fma-define 50.6%

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

   3. Simplified 50.6%

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

      1. fma-undefine 50.6%

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

      2. fma-undefine 50.6%

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

      3. *-commutative 50.6%

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

      4. fma-define 50.6%

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

      5. fma-undefine 50.6%

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

      6. *-commutative 50.6%

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

      7. associate-*r/ 34.9%

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

      8. associate-*l/ 50.6%

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

      9. clear-num 50.6%

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

      10. associate-*l/ 50.8%

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

      11. *-un-lft-identity 50.8%

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

      12. *-commutative 50.8%

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

      13. fma-undefine 50.8%

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

      14. fma-define 50.8%

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

      15. *-commutative 50.8%

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

      16. fma-undefine 50.8%

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

   6. Applied egg-rr 50.8%

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

   7. Taylor expanded in z around inf 100.0%

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

   if -5.8e19 < z < 0.23499999999999999

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-/l* 99.6%

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

      4. fma-define 99.6%

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

      5. *-commutative 99.6%

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

      6. fma-define 99.6%

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

      7. fma-define 99.6%

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

      8. *-commutative 99.6%

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

      9. fma-define 99.6%

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

   3. Simplified 99.6%

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

      1. fma-undefine 99.6%

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

      2. fma-undefine 99.6%

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

      3. *-commutative 99.6%

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

      4. fma-define 99.6%

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

      5. fma-undefine 99.6%

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

      6. *-commutative 99.6%

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

      7. associate-*r/ 99.6%

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

      8. associate-*l/ 99.8%

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

      9. clear-num 99.1%

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

      10. associate-*l/ 99.4%

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

      11. *-un-lft-identity 99.4%

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

      12. *-commutative 99.4%

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

      13. fma-undefine 99.4%

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

      14. fma-define 99.4%

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

      15. *-commutative 99.4%

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

      16. fma-undefine 99.4%

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

   6. Applied egg-rr 99.4%

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

   7. Taylor expanded in z around 0 99.2%

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

      1. *-commutative 99.2%

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

   9. Simplified 99.2%

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

   if 0.23499999999999999 < z

   1. Initial program 47.4%

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

      1. remove-double-neg 47.4%

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

      2. distribute-lft-neg-out 47.4%

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

      3. distribute-neg-frac 47.4%

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

      4. associate-/l* 64.0%

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

      5. distribute-lft-neg-in 64.0%

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

      6. remove-double-neg 64.0%

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

      7. fma-define 64.0%

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

      8. fma-define 64.0%

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

      9. fma-define 64.0%

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

   3. Simplified 64.0%

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

   5. Taylor expanded in z around inf 99.3%

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

      1. associate-*r/ 99.3%

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

      2. metadata-eval 99.3%

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

   7. Simplified 99.3%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+19}:\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \mathbf{elif}\;z \leq 0.235:\\ \;\;\;\;x + \frac{y}{12.000000000000014 + z \cdot 0.39999999996247915}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 98.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+19} \lor \neg \left(z \leq 0.235\right):\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.08333333333333323\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.8e+19) (not (<= z 0.235)))
   (+ x (* y 0.0692910599291889))
   (+ x (* y 0.08333333333333323))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.8e+19) || !(z <= 0.235)) {
		tmp = x + (y * 0.0692910599291889);
	} else {
		tmp = x + (y * 0.08333333333333323);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-5.8d+19)) .or. (.not. (z <= 0.235d0))) then
        tmp = x + (y * 0.0692910599291889d0)
    else
        tmp = x + (y * 0.08333333333333323d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.8e+19) || !(z <= 0.235)) {
		tmp = x + (y * 0.0692910599291889);
	} else {
		tmp = x + (y * 0.08333333333333323);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.8e+19) or not (z <= 0.235):
		tmp = x + (y * 0.0692910599291889)
	else:
		tmp = x + (y * 0.08333333333333323)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.8e+19) || !(z <= 0.235))
		tmp = Float64(x + Float64(y * 0.0692910599291889));
	else
		tmp = Float64(x + Float64(y * 0.08333333333333323));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.8e+19) || ~((z <= 0.235)))
		tmp = x + (y * 0.0692910599291889);
	else
		tmp = x + (y * 0.08333333333333323);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.8e+19], N[Not[LessEqual[z, 0.235]], $MachinePrecision]], N[(x + N[(y * 0.0692910599291889), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 0.08333333333333323), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.8e19 or 0.23499999999999999 < z

   1. Initial program 41.0%

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

      1. +-commutative 41.0%

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

      2. *-commutative 41.0%

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

      3. associate-/l* 56.1%

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

      4. fma-define 56.1%

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

      5. *-commutative 56.1%

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

      6. fma-define 56.1%

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

      7. fma-define 56.1%

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

      8. *-commutative 56.1%

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

      9. fma-define 56.1%

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

   3. Simplified 56.1%

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

   5. Taylor expanded in z around inf 99.0%

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

      1. +-commutative 99.0%

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

   7. Simplified 99.0%

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

   if -5.8e19 < z < 0.23499999999999999

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-/l* 99.6%

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

      4. fma-define 99.6%

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

      5. *-commutative 99.6%

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

      6. fma-define 99.6%

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

      7. fma-define 99.6%

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

      8. *-commutative 99.6%

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

      9. fma-define 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around 0 98.5%

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

      1. +-commutative 98.5%

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

   7. Simplified 98.5%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+19} \lor \neg \left(z \leq 0.235\right):\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 0.08333333333333323\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 98.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+19} \lor \neg \left(z \leq 0.235\right):\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{12.000000000000014}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.8e+19) (not (<= z 0.235)))
   (+ x (* y 0.0692910599291889))
   (+ x (/ y 12.000000000000014))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.8e+19) || !(z <= 0.235)) {
		tmp = x + (y * 0.0692910599291889);
	} else {
		tmp = x + (y / 12.000000000000014);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-5.8d+19)) .or. (.not. (z <= 0.235d0))) then
        tmp = x + (y * 0.0692910599291889d0)
    else
        tmp = x + (y / 12.000000000000014d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.8e+19) || !(z <= 0.235)) {
		tmp = x + (y * 0.0692910599291889);
	} else {
		tmp = x + (y / 12.000000000000014);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.8e+19) or not (z <= 0.235):
		tmp = x + (y * 0.0692910599291889)
	else:
		tmp = x + (y / 12.000000000000014)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.8e+19) || !(z <= 0.235))
		tmp = Float64(x + Float64(y * 0.0692910599291889));
	else
		tmp = Float64(x + Float64(y / 12.000000000000014));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.8e+19) || ~((z <= 0.235)))
		tmp = x + (y * 0.0692910599291889);
	else
		tmp = x + (y / 12.000000000000014);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.8e+19], N[Not[LessEqual[z, 0.235]], $MachinePrecision]], N[(x + N[(y * 0.0692910599291889), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / 12.000000000000014), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.8e19 or 0.23499999999999999 < z

   1. Initial program 41.0%

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

      1. +-commutative 41.0%

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

      2. *-commutative 41.0%

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

      3. associate-/l* 56.1%

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

      4. fma-define 56.1%

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

      5. *-commutative 56.1%

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

      6. fma-define 56.1%

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

      7. fma-define 56.1%

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

      8. *-commutative 56.1%

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

      9. fma-define 56.1%

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

   3. Simplified 56.1%

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

   5. Taylor expanded in z around inf 99.0%

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

      1. +-commutative 99.0%

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

   7. Simplified 99.0%

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

   if -5.8e19 < z < 0.23499999999999999

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-/l* 99.6%

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

      4. fma-define 99.6%

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

      5. *-commutative 99.6%

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

      6. fma-define 99.6%

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

      7. fma-define 99.6%

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

      8. *-commutative 99.6%

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

      9. fma-define 99.6%

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

   3. Simplified 99.6%

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

      1. fma-undefine 99.6%

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

      2. fma-undefine 99.6%

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

      3. *-commutative 99.6%

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

      4. fma-define 99.6%

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

      5. fma-undefine 99.6%

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

      6. *-commutative 99.6%

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

      7. associate-*r/ 99.6%

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

      8. associate-*l/ 99.8%

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

      9. clear-num 99.1%

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

      10. associate-*l/ 99.4%

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

      11. *-un-lft-identity 99.4%

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

      12. *-commutative 99.4%

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

      13. fma-undefine 99.4%

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

      14. fma-define 99.4%

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

      15. *-commutative 99.4%

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

      16. fma-undefine 99.4%

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

   6. Applied egg-rr 99.4%

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

   7. Taylor expanded in z around 0 98.6%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+19} \lor \neg \left(z \leq 0.235\right):\\ \;\;\;\;x + y \cdot 0.0692910599291889\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{12.000000000000014}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 98.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+19} \lor \neg \left(z \leq 0.235\right):\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{12.000000000000014}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.8e+19) (not (<= z 0.235)))
   (+ x (/ y 14.431876219268936))
   (+ x (/ y 12.000000000000014))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.8e+19) || !(z <= 0.235)) {
		tmp = x + (y / 14.431876219268936);
	} else {
		tmp = x + (y / 12.000000000000014);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-5.8d+19)) .or. (.not. (z <= 0.235d0))) then
        tmp = x + (y / 14.431876219268936d0)
    else
        tmp = x + (y / 12.000000000000014d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.8e+19) || !(z <= 0.235)) {
		tmp = x + (y / 14.431876219268936);
	} else {
		tmp = x + (y / 12.000000000000014);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.8e+19) or not (z <= 0.235):
		tmp = x + (y / 14.431876219268936)
	else:
		tmp = x + (y / 12.000000000000014)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.8e+19) || !(z <= 0.235))
		tmp = Float64(x + Float64(y / 14.431876219268936));
	else
		tmp = Float64(x + Float64(y / 12.000000000000014));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.8e+19) || ~((z <= 0.235)))
		tmp = x + (y / 14.431876219268936);
	else
		tmp = x + (y / 12.000000000000014);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.8e+19], N[Not[LessEqual[z, 0.235]], $MachinePrecision]], N[(x + N[(y / 14.431876219268936), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / 12.000000000000014), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.8e19 or 0.23499999999999999 < z

   1. Initial program 41.0%

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

      1. +-commutative 41.0%

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

      2. *-commutative 41.0%

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

      3. associate-/l* 56.1%

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

      4. fma-define 56.1%

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

      5. *-commutative 56.1%

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

      6. fma-define 56.1%

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

      7. fma-define 56.1%

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

      8. *-commutative 56.1%

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

      9. fma-define 56.1%

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

   3. Simplified 56.1%

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

      1. fma-undefine 56.1%

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

      2. fma-undefine 56.1%

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

      3. *-commutative 56.1%

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

      4. fma-define 56.1%

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

      5. fma-undefine 56.1%

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

      6. *-commutative 56.1%

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

      7. associate-*r/ 41.0%

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

      8. associate-*l/ 57.1%

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

      9. clear-num 57.1%

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

      10. associate-*l/ 57.2%

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

      11. *-un-lft-identity 57.2%

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

      12. *-commutative 57.2%

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

      13. fma-undefine 57.2%

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

      14. fma-define 57.2%

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

      15. *-commutative 57.2%

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

      16. fma-undefine 57.2%

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

   6. Applied egg-rr 57.2%

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

   7. Taylor expanded in z around inf 99.4%

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

   if -5.8e19 < z < 0.23499999999999999

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-/l* 99.6%

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

      4. fma-define 99.6%

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

      5. *-commutative 99.6%

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

      6. fma-define 99.6%

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

      7. fma-define 99.6%

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

      8. *-commutative 99.6%

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

      9. fma-define 99.6%

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

   3. Simplified 99.6%

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

      1. fma-undefine 99.6%

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

      2. fma-undefine 99.6%

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

      3. *-commutative 99.6%

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

      4. fma-define 99.6%

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

      5. fma-undefine 99.6%

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

      6. *-commutative 99.6%

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

      7. associate-*r/ 99.6%

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

      8. associate-*l/ 99.8%

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

      9. clear-num 99.1%

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

      10. associate-*l/ 99.4%

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

      11. *-un-lft-identity 99.4%

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

      12. *-commutative 99.4%

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

      13. fma-undefine 99.4%

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

      14. fma-define 99.4%

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

      15. *-commutative 99.4%

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

      16. fma-undefine 99.4%

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

   6. Applied egg-rr 99.4%

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

   7. Taylor expanded in z around 0 98.6%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+19} \lor \neg \left(z \leq 0.235\right):\\ \;\;\;\;x + \frac{y}{14.431876219268936}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{12.000000000000014}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 60.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-143}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-77}:\\ \;\;\;\;y \cdot 0.08333333333333323\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.1e-143) x (if (<= x 2.3e-77) (* y 0.08333333333333323) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.1e-143) {
		tmp = x;
	} else if (x <= 2.3e-77) {
		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 <= (-2.1d-143)) then
        tmp = x
    else if (x <= 2.3d-77) 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 <= -2.1e-143) {
		tmp = x;
	} else if (x <= 2.3e-77) {
		tmp = y * 0.08333333333333323;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.1e-143:
		tmp = x
	elif x <= 2.3e-77:
		tmp = y * 0.08333333333333323
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.1e-143)
		tmp = x;
	elseif (x <= 2.3e-77)
		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 <= -2.1e-143)
		tmp = x;
	elseif (x <= 2.3e-77)
		tmp = y * 0.08333333333333323;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.1e-143], x, If[LessEqual[x, 2.3e-77], N[(y * 0.08333333333333323), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1000000000000001e-143 or 2.29999999999999999e-77 < x

   1. Initial program 72.5%

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

      1. +-commutative 72.5%

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

      2. *-commutative 72.5%

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

      3. associate-/l* 79.8%

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

      4. fma-define 79.8%

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

      5. *-commutative 79.8%

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

      6. fma-define 79.8%

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

      7. fma-define 79.8%

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

      8. *-commutative 79.8%

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

      9. fma-define 79.8%

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

   3. Simplified 79.8%

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

   5. Taylor expanded in y around 0 75.4%

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

   if -2.1000000000000001e-143 < x < 2.29999999999999999e-77

   1. Initial program 74.7%

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

      1. +-commutative 74.7%

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

      2. *-commutative 74.7%

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

      3. associate-/l* 80.5%

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

      4. fma-define 80.6%

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

      5. *-commutative 80.6%

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

      6. fma-define 80.6%

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

      7. fma-define 80.6%

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

      8. *-commutative 80.6%

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

      9. fma-define 80.6%

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

   3. Simplified 80.6%

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

   5. Taylor expanded in z around 0 67.3%

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

      1. +-commutative 67.3%

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

      2. fma-define 67.3%

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

   7. Simplified 67.3%

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

   8. Taylor expanded in y around inf 60.9%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-143}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-77}:\\ \;\;\;\;y \cdot 0.08333333333333323\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 49.9% 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 73.3%

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

   1. +-commutative 73.3%

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

   2. *-commutative 73.3%

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

   3. associate-/l* 80.1%

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

   4. fma-define 80.1%

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

   5. *-commutative 80.1%

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

   6. fma-define 80.1%

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

   7. fma-define 80.1%

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

   8. *-commutative 80.1%

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

   9. fma-define 80.1%

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

3. Simplified 80.1%

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

5. Taylor expanded in y around 0 50.9%

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

6. Final simplification 50.9%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.4% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024053 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, B"
  :precision binary64

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

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