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

Percentage Accurate: 58.4% → 98.2%

Time: 18.2s

Alternatives: 23

Speedup: 2.8×

Specification

Math

\[\begin{array}{l} \\ \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (/
  (*
   (- x 2.0)
   (+
    (*
     (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y)
     x)
    z))
  (+
   (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)
   47.066876606)))

C

double code(double x, double y, double z) {
	return ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
}

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 - 2.0d0) * ((((((((x * 4.16438922228d0) + 78.6994924154d0) * x) + 137.519416416d0) * x) + y) * x) + z)) / (((((((x + 43.3400022514d0) * x) + 263.505074721d0) * x) + 313.399215894d0) * x) + 47.066876606d0)
end function

Java

public static double code(double x, double y, double z) {
	return ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
}

Python

def code(x, y, z):
	return ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision]

Initial Program: 58.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (/
  (*
   (- x 2.0)
   (+
    (*
     (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y)
     x)
    z))
  (+
   (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)
   47.066876606)))

C

double code(double x, double y, double z) {
	return ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
}

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 - 2.0d0) * ((((((((x * 4.16438922228d0) + 78.6994924154d0) * x) + 137.519416416d0) * x) + y) * x) + z)) / (((((((x + 43.3400022514d0) * x) + 263.505074721d0) * x) + 313.399215894d0) * x) + 47.066876606d0)
end function

Java

public static double code(double x, double y, double z) {
	return ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
}

Python

def code(x, y, z):
	return ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{x + -2}\\ t_1 := x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606\\ t_2 := z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)\\ \mathbf{if}\;\frac{\left(x - 2\right) \cdot t\_2}{t\_1} \leq 10^{+296}:\\ \;\;\;\;\frac{\frac{t\_2}{t\_1}}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}}{t\_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ 1.0 (+ x -2.0)))
        (t_1
         (+
          (*
           x
           (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
          47.066876606))
        (t_2
         (+
          z
          (*
           x
           (+
            y
            (*
             x
             (+
              137.519416416
              (* x (+ (* x 4.16438922228) 78.6994924154)))))))))
   (if (<= (/ (* (- x 2.0) t_2) t_1) 1e+296)
     (/ (/ t_2 t_1) t_0)
     (/
      (+
       4.16438922228
       (/
        (-
         (/ (+ 3451.550173699799 (/ (- y 124074.40615218398) x)) x)
         101.7851458539211)
        x))
      t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 / (x + -2.0);
	double t_1 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	double t_2 = z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))));
	double tmp;
	if ((((x - 2.0) * t_2) / t_1) <= 1e+296) {
		tmp = (t_2 / t_1) / t_0;
	} else {
		tmp = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = 1.0d0 / (x + (-2.0d0))
    t_1 = (x * ((x * ((x * (x + 43.3400022514d0)) + 263.505074721d0)) + 313.399215894d0)) + 47.066876606d0
    t_2 = z + (x * (y + (x * (137.519416416d0 + (x * ((x * 4.16438922228d0) + 78.6994924154d0))))))
    if ((((x - 2.0d0) * t_2) / t_1) <= 1d+296) then
        tmp = (t_2 / t_1) / t_0
    else
        tmp = (4.16438922228d0 + ((((3451.550173699799d0 + ((y - 124074.40615218398d0) / x)) / x) - 101.7851458539211d0) / x)) / t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 / (x + -2.0);
	double t_1 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	double t_2 = z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))));
	double tmp;
	if ((((x - 2.0) * t_2) / t_1) <= 1e+296) {
		tmp = (t_2 / t_1) / t_0;
	} else {
		tmp = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 / (x + -2.0)
	t_1 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606
	t_2 = z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))
	tmp = 0
	if (((x - 2.0) * t_2) / t_1) <= 1e+296:
		tmp = (t_2 / t_1) / t_0
	else:
		tmp = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 / Float64(x + -2.0))
	t_1 = Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)
	t_2 = Float64(z + Float64(x * Float64(y + Float64(x * Float64(137.519416416 + Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)))))))
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * t_2) / t_1) <= 1e+296)
		tmp = Float64(Float64(t_2 / t_1) / t_0);
	else
		tmp = Float64(Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(Float64(y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 / (x + -2.0);
	t_1 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	t_2 = z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))));
	tmp = 0.0;
	if ((((x - 2.0) * t_2) / t_1) <= 1e+296)
		tmp = (t_2 / t_1) / t_0;
	else
		tmp = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 / N[(x + -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]}, Block[{t$95$2 = N[(z + N[(x * N[(y + N[(x * N[(137.519416416 + N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision], 1e+296], N[(N[(t$95$2 / t$95$1), $MachinePrecision] / t$95$0), $MachinePrecision], N[(N[(4.16438922228 + N[(N[(N[(N[(3451.550173699799 + N[(N[(y - 124074.40615218398), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < 9.99999999999999981e295

   1. Initial program 97.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 98.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   6. Applied egg-rr 99.0%

      \[\leadsto \color{blue}{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{\frac{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}{x + -2}}} \]
   7. Step-by-step derivation

      1. div-inv N/A

         \[\leadsto \frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}\right) \cdot \color{blue}{\frac{1}{x + -2}}} \]

      2. associate-/r* N/A

         \[\leadsto \frac{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}}}{\color{blue}{\frac{1}{x + -2}}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}}\right), \color{blue}{\left(\frac{1}{x + -2}\right)}\right) \]

   8. Applied egg-rr 99.0%

      \[\leadsto \color{blue}{\frac{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}}{\frac{1}{x + -2}}} \]

   if 9.99999999999999981e295 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64)))

   1. Initial program 0.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 0.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   6. Applied egg-rr 0.1%

      \[\leadsto \color{blue}{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{\frac{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}{x + -2}}} \]
   7. Step-by-step derivation

      1. div-inv N/A

         \[\leadsto \frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}\right) \cdot \color{blue}{\frac{1}{x + -2}}} \]

      2. associate-/r* N/A

         \[\leadsto \frac{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}}}{\color{blue}{\frac{1}{x + -2}}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}}\right), \color{blue}{\left(\frac{1}{x + -2}\right)}\right) \]

   8. Applied egg-rr 0.1%

      \[\leadsto \color{blue}{\frac{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}}{\frac{1}{x + -2}}} \]

   9. Taylor expanded in x around -inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{104109730557}{25000000000} + -1 \cdot \frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)}, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{104109730557}{25000000000} + \left(\mathsf{neg}\left(\frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{104109730557}{25000000000} - \frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right), \mathsf{/.f64}\left(\color{blue}{1}, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)\right), \mathsf{/.f64}\left(\color{blue}{1}, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\left(\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

   11. Simplified 99.0%

       \[\leadsto \frac{\color{blue}{4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}}}{\frac{1}{x + -2}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 10^{+296}:\\ \;\;\;\;\frac{\frac{z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}}{\frac{1}{x + -2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}}{\frac{1}{x + -2}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606\\ t_1 := z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)\\ \mathbf{if}\;\frac{\left(x - 2\right) \cdot t\_1}{t\_0} \leq 10^{+296}:\\ \;\;\;\;\frac{t\_1}{\frac{t\_0}{x + -2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}}{\frac{1}{x + -2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          (*
           x
           (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
          47.066876606))
        (t_1
         (+
          z
          (*
           x
           (+
            y
            (*
             x
             (+
              137.519416416
              (* x (+ (* x 4.16438922228) 78.6994924154)))))))))
   (if (<= (/ (* (- x 2.0) t_1) t_0) 1e+296)
     (/ t_1 (/ t_0 (+ x -2.0)))
     (/
      (+
       4.16438922228
       (/
        (-
         (/ (+ 3451.550173699799 (/ (- y 124074.40615218398) x)) x)
         101.7851458539211)
        x))
      (/ 1.0 (+ x -2.0))))))

C

double code(double x, double y, double z) {
	double t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	double t_1 = z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))));
	double tmp;
	if ((((x - 2.0) * t_1) / t_0) <= 1e+296) {
		tmp = t_1 / (t_0 / (x + -2.0));
	} else {
		tmp = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / (1.0 / (x + -2.0));
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = (x * ((x * ((x * (x + 43.3400022514d0)) + 263.505074721d0)) + 313.399215894d0)) + 47.066876606d0
    t_1 = z + (x * (y + (x * (137.519416416d0 + (x * ((x * 4.16438922228d0) + 78.6994924154d0))))))
    if ((((x - 2.0d0) * t_1) / t_0) <= 1d+296) then
        tmp = t_1 / (t_0 / (x + (-2.0d0)))
    else
        tmp = (4.16438922228d0 + ((((3451.550173699799d0 + ((y - 124074.40615218398d0) / x)) / x) - 101.7851458539211d0) / x)) / (1.0d0 / (x + (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	double t_1 = z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))));
	double tmp;
	if ((((x - 2.0) * t_1) / t_0) <= 1e+296) {
		tmp = t_1 / (t_0 / (x + -2.0));
	} else {
		tmp = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / (1.0 / (x + -2.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606
	t_1 = z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))
	tmp = 0
	if (((x - 2.0) * t_1) / t_0) <= 1e+296:
		tmp = t_1 / (t_0 / (x + -2.0))
	else:
		tmp = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / (1.0 / (x + -2.0))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)
	t_1 = Float64(z + Float64(x * Float64(y + Float64(x * Float64(137.519416416 + Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)))))))
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * t_1) / t_0) <= 1e+296)
		tmp = Float64(t_1 / Float64(t_0 / Float64(x + -2.0)));
	else
		tmp = Float64(Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(Float64(y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / Float64(1.0 / Float64(x + -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	t_1 = z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))));
	tmp = 0.0;
	if ((((x - 2.0) * t_1) / t_0) <= 1e+296)
		tmp = t_1 / (t_0 / (x + -2.0));
	else
		tmp = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / (1.0 / (x + -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]}, Block[{t$95$1 = N[(z + N[(x * N[(y + N[(x * N[(137.519416416 + N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * t$95$1), $MachinePrecision] / t$95$0), $MachinePrecision], 1e+296], N[(t$95$1 / N[(t$95$0 / N[(x + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 + N[(N[(N[(N[(3451.550173699799 + N[(N[(y - 124074.40615218398), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / N[(1.0 / N[(x + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < 9.99999999999999981e295

   1. Initial program 97.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 98.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   6. Applied egg-rr 99.0%

      \[\leadsto \color{blue}{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{\frac{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}{x + -2}}} \]

   if 9.99999999999999981e295 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64)))

   1. Initial program 0.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 0.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   6. Applied egg-rr 0.1%

      \[\leadsto \color{blue}{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{\frac{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}{x + -2}}} \]
   7. Step-by-step derivation

      1. div-inv N/A

         \[\leadsto \frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}\right) \cdot \color{blue}{\frac{1}{x + -2}}} \]

      2. associate-/r* N/A

         \[\leadsto \frac{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}}}{\color{blue}{\frac{1}{x + -2}}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}}\right), \color{blue}{\left(\frac{1}{x + -2}\right)}\right) \]

   8. Applied egg-rr 0.1%

      \[\leadsto \color{blue}{\frac{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}}{\frac{1}{x + -2}}} \]

   9. Taylor expanded in x around -inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{104109730557}{25000000000} + -1 \cdot \frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)}, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{104109730557}{25000000000} + \left(\mathsf{neg}\left(\frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{104109730557}{25000000000} - \frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right), \mathsf{/.f64}\left(\color{blue}{1}, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)\right), \mathsf{/.f64}\left(\color{blue}{1}, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\left(\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

   11. Simplified 99.0%

       \[\leadsto \frac{\color{blue}{4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}}}{\frac{1}{x + -2}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 10^{+296}:\\ \;\;\;\;\frac{z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)}{\frac{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}{x + -2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}}{\frac{1}{x + -2}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606\\ t_1 := z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)\\ \mathbf{if}\;\frac{\left(x - 2\right) \cdot t\_1}{t\_0} \leq 10^{+296}:\\ \;\;\;\;t\_1 \cdot \frac{x + -2}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}}{\frac{1}{x + -2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          (*
           x
           (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
          47.066876606))
        (t_1
         (+
          z
          (*
           x
           (+
            y
            (*
             x
             (+
              137.519416416
              (* x (+ (* x 4.16438922228) 78.6994924154)))))))))
   (if (<= (/ (* (- x 2.0) t_1) t_0) 1e+296)
     (* t_1 (/ (+ x -2.0) t_0))
     (/
      (+
       4.16438922228
       (/
        (-
         (/ (+ 3451.550173699799 (/ (- y 124074.40615218398) x)) x)
         101.7851458539211)
        x))
      (/ 1.0 (+ x -2.0))))))

C

double code(double x, double y, double z) {
	double t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	double t_1 = z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))));
	double tmp;
	if ((((x - 2.0) * t_1) / t_0) <= 1e+296) {
		tmp = t_1 * ((x + -2.0) / t_0);
	} else {
		tmp = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / (1.0 / (x + -2.0));
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = (x * ((x * ((x * (x + 43.3400022514d0)) + 263.505074721d0)) + 313.399215894d0)) + 47.066876606d0
    t_1 = z + (x * (y + (x * (137.519416416d0 + (x * ((x * 4.16438922228d0) + 78.6994924154d0))))))
    if ((((x - 2.0d0) * t_1) / t_0) <= 1d+296) then
        tmp = t_1 * ((x + (-2.0d0)) / t_0)
    else
        tmp = (4.16438922228d0 + ((((3451.550173699799d0 + ((y - 124074.40615218398d0) / x)) / x) - 101.7851458539211d0) / x)) / (1.0d0 / (x + (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	double t_1 = z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))));
	double tmp;
	if ((((x - 2.0) * t_1) / t_0) <= 1e+296) {
		tmp = t_1 * ((x + -2.0) / t_0);
	} else {
		tmp = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / (1.0 / (x + -2.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606
	t_1 = z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))
	tmp = 0
	if (((x - 2.0) * t_1) / t_0) <= 1e+296:
		tmp = t_1 * ((x + -2.0) / t_0)
	else:
		tmp = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / (1.0 / (x + -2.0))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)
	t_1 = Float64(z + Float64(x * Float64(y + Float64(x * Float64(137.519416416 + Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)))))))
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * t_1) / t_0) <= 1e+296)
		tmp = Float64(t_1 * Float64(Float64(x + -2.0) / t_0));
	else
		tmp = Float64(Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(Float64(y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / Float64(1.0 / Float64(x + -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	t_1 = z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))));
	tmp = 0.0;
	if ((((x - 2.0) * t_1) / t_0) <= 1e+296)
		tmp = t_1 * ((x + -2.0) / t_0);
	else
		tmp = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / (1.0 / (x + -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]}, Block[{t$95$1 = N[(z + N[(x * N[(y + N[(x * N[(137.519416416 + N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * t$95$1), $MachinePrecision] / t$95$0), $MachinePrecision], 1e+296], N[(t$95$1 * N[(N[(x + -2.0), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 + N[(N[(N[(N[(3451.550173699799 + N[(N[(y - 124074.40615218398), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / N[(1.0 / N[(x + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < 9.99999999999999981e295

   1. Initial program 97.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 98.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   if 9.99999999999999981e295 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64)))

   1. Initial program 0.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 0.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   6. Applied egg-rr 0.1%

      \[\leadsto \color{blue}{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{\frac{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}{x + -2}}} \]
   7. Step-by-step derivation

      1. div-inv N/A

         \[\leadsto \frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}\right) \cdot \color{blue}{\frac{1}{x + -2}}} \]

      2. associate-/r* N/A

         \[\leadsto \frac{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}}}{\color{blue}{\frac{1}{x + -2}}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}}\right), \color{blue}{\left(\frac{1}{x + -2}\right)}\right) \]

   8. Applied egg-rr 0.1%

      \[\leadsto \color{blue}{\frac{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}}{\frac{1}{x + -2}}} \]

   9. Taylor expanded in x around -inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{104109730557}{25000000000} + -1 \cdot \frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)}, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{104109730557}{25000000000} + \left(\mathsf{neg}\left(\frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{104109730557}{25000000000} - \frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right), \mathsf{/.f64}\left(\color{blue}{1}, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)\right), \mathsf{/.f64}\left(\color{blue}{1}, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\left(\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

   11. Simplified 99.0%

       \[\leadsto \frac{\color{blue}{4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}}}{\frac{1}{x + -2}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 10^{+296}:\\ \;\;\;\;\left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\frac{4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}}{\frac{1}{x + -2}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}}{\frac{1}{x + -2}}\\ \mathbf{if}\;x \leq -4 \cdot 10^{+37}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+23}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (/
          (+
           4.16438922228
           (/
            (-
             (/ (+ 3451.550173699799 (/ (- y 124074.40615218398) x)) x)
             101.7851458539211)
            x))
          (/ 1.0 (+ x -2.0)))))
   (if (<= x -4e+37)
     t_0
     (if (<= x 6.2e+23)
       (/
        (* (- x 2.0) (+ z (* x (+ y (* x 137.519416416)))))
        (+
         (*
          x
          (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
         47.066876606))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / (1.0 / (x + -2.0));
	double tmp;
	if (x <= -4e+37) {
		tmp = t_0;
	} else if (x <= 6.2e+23) {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	} 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 = (4.16438922228d0 + ((((3451.550173699799d0 + ((y - 124074.40615218398d0) / x)) / x) - 101.7851458539211d0) / x)) / (1.0d0 / (x + (-2.0d0)))
    if (x <= (-4d+37)) then
        tmp = t_0
    else if (x <= 6.2d+23) then
        tmp = ((x - 2.0d0) * (z + (x * (y + (x * 137.519416416d0))))) / ((x * ((x * ((x * (x + 43.3400022514d0)) + 263.505074721d0)) + 313.399215894d0)) + 47.066876606d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / (1.0 / (x + -2.0));
	double tmp;
	if (x <= -4e+37) {
		tmp = t_0;
	} else if (x <= 6.2e+23) {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / (1.0 / (x + -2.0))
	tmp = 0
	if x <= -4e+37:
		tmp = t_0
	elif x <= 6.2e+23:
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(Float64(y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / Float64(1.0 / Float64(x + -2.0)))
	tmp = 0.0
	if (x <= -4e+37)
		tmp = t_0;
	elseif (x <= 6.2e+23)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(z + Float64(x * Float64(y + Float64(x * 137.519416416))))) / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / (1.0 / (x + -2.0));
	tmp = 0.0;
	if (x <= -4e+37)
		tmp = t_0;
	elseif (x <= 6.2e+23)
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.16438922228 + N[(N[(N[(N[(3451.550173699799 + N[(N[(y - 124074.40615218398), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / N[(1.0 / N[(x + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4e+37], t$95$0, If[LessEqual[x, 6.2e+23], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(z + N[(x * N[(y + N[(x * 137.519416416), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.99999999999999982e37 or 6.19999999999999941e23 < x

   1. Initial program 9.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 12.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   6. Applied egg-rr 12.5%

      \[\leadsto \color{blue}{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{\frac{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}{x + -2}}} \]
   7. Step-by-step derivation

      1. div-inv N/A

         \[\leadsto \frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}\right) \cdot \color{blue}{\frac{1}{x + -2}}} \]

      2. associate-/r* N/A

         \[\leadsto \frac{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}}}{\color{blue}{\frac{1}{x + -2}}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}}\right), \color{blue}{\left(\frac{1}{x + -2}\right)}\right) \]

   8. Applied egg-rr 12.5%

      \[\leadsto \color{blue}{\frac{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}}{\frac{1}{x + -2}}} \]

   9. Taylor expanded in x around -inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{104109730557}{25000000000} + -1 \cdot \frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)}, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{104109730557}{25000000000} + \left(\mathsf{neg}\left(\frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{104109730557}{25000000000} - \frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right), \mathsf{/.f64}\left(\color{blue}{1}, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)\right), \mathsf{/.f64}\left(\color{blue}{1}, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\left(\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

   11. Simplified 96.4%

       \[\leadsto \frac{\color{blue}{4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}}}{\frac{1}{x + -2}} \]

   if -3.99999999999999982e37 < x < 6.19999999999999941e23

   1. Initial program 99.6%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{4297481763}{31250000} \cdot x\right)}, y\right), x\right), z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right), x\right), \frac{263505074721}{1000000000}\right), x\right), \frac{156699607947}{500000000}\right), x\right), \frac{23533438303}{500000000}\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(x \cdot \frac{4297481763}{31250000}\right), y\right), x\right), z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right), x\right), \frac{263505074721}{1000000000}\right), x\right), \frac{156699607947}{500000000}\right), x\right), \frac{23533438303}{500000000}\right)\right) \]

      2. *-lowering-*.f64 98.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{4297481763}{31250000}\right), y\right), x\right), z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right), x\right), \frac{263505074721}{1000000000}\right), x\right), \frac{156699607947}{500000000}\right), x\right), \frac{23533438303}{500000000}\right)\right) \]

   5. Simplified 98.0%

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\color{blue}{x \cdot 137.519416416} + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+37}:\\ \;\;\;\;\frac{4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}}{\frac{1}{x + -2}}\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+23}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\frac{4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}}{\frac{1}{x + -2}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 96.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}}{\frac{1}{x + -2}}\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{+37}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+18}:\\ \;\;\;\;\frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (/
          (+
           4.16438922228
           (/
            (-
             (/ (+ 3451.550173699799 (/ (- y 124074.40615218398) x)) x)
             101.7851458539211)
            x))
          (/ 1.0 (+ x -2.0)))))
   (if (<= x -6.2e+37)
     t_0
     (if (<= x 3.8e+18)
       (*
        (/
         (+ x -2.0)
         (+
          (*
           x
           (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
          47.066876606))
        (+ z (* x (+ y (* x 137.519416416)))))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / (1.0 / (x + -2.0));
	double tmp;
	if (x <= -6.2e+37) {
		tmp = t_0;
	} else if (x <= 3.8e+18) {
		tmp = ((x + -2.0) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)) * (z + (x * (y + (x * 137.519416416))));
	} 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 = (4.16438922228d0 + ((((3451.550173699799d0 + ((y - 124074.40615218398d0) / x)) / x) - 101.7851458539211d0) / x)) / (1.0d0 / (x + (-2.0d0)))
    if (x <= (-6.2d+37)) then
        tmp = t_0
    else if (x <= 3.8d+18) then
        tmp = ((x + (-2.0d0)) / ((x * ((x * ((x * (x + 43.3400022514d0)) + 263.505074721d0)) + 313.399215894d0)) + 47.066876606d0)) * (z + (x * (y + (x * 137.519416416d0))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / (1.0 / (x + -2.0));
	double tmp;
	if (x <= -6.2e+37) {
		tmp = t_0;
	} else if (x <= 3.8e+18) {
		tmp = ((x + -2.0) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)) * (z + (x * (y + (x * 137.519416416))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / (1.0 / (x + -2.0))
	tmp = 0
	if x <= -6.2e+37:
		tmp = t_0
	elif x <= 3.8e+18:
		tmp = ((x + -2.0) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)) * (z + (x * (y + (x * 137.519416416))))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(Float64(y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / Float64(1.0 / Float64(x + -2.0)))
	tmp = 0.0
	if (x <= -6.2e+37)
		tmp = t_0;
	elseif (x <= 3.8e+18)
		tmp = Float64(Float64(Float64(x + -2.0) / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)) * Float64(z + Float64(x * Float64(y + Float64(x * 137.519416416)))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / (1.0 / (x + -2.0));
	tmp = 0.0;
	if (x <= -6.2e+37)
		tmp = t_0;
	elseif (x <= 3.8e+18)
		tmp = ((x + -2.0) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)) * (z + (x * (y + (x * 137.519416416))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.16438922228 + N[(N[(N[(N[(3451.550173699799 + N[(N[(y - 124074.40615218398), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / N[(1.0 / N[(x + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.2e+37], t$95$0, If[LessEqual[x, 3.8e+18], N[(N[(N[(x + -2.0), $MachinePrecision] / N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision] * N[(z + N[(x * N[(y + N[(x * 137.519416416), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.2000000000000004e37 or 3.8e18 < x

   1. Initial program 9.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 12.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   6. Applied egg-rr 12.5%

      \[\leadsto \color{blue}{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{\frac{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}{x + -2}}} \]
   7. Step-by-step derivation

      1. div-inv N/A

         \[\leadsto \frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}\right) \cdot \color{blue}{\frac{1}{x + -2}}} \]

      2. associate-/r* N/A

         \[\leadsto \frac{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}}}{\color{blue}{\frac{1}{x + -2}}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}}\right), \color{blue}{\left(\frac{1}{x + -2}\right)}\right) \]

   8. Applied egg-rr 12.5%

      \[\leadsto \color{blue}{\frac{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}}{\frac{1}{x + -2}}} \]

   9. Taylor expanded in x around -inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{104109730557}{25000000000} + -1 \cdot \frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)}, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{104109730557}{25000000000} + \left(\mathsf{neg}\left(\frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{104109730557}{25000000000} - \frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right), \mathsf{/.f64}\left(\color{blue}{1}, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)\right), \mathsf{/.f64}\left(\color{blue}{1}, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\left(\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

   11. Simplified 96.4%

       \[\leadsto \frac{\color{blue}{4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}}}{\frac{1}{x + -2}} \]

   if -6.2000000000000004e37 < x < 3.8e18

   1. Initial program 99.6%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(x \cdot \left(y + \frac{4297481763}{31250000} \cdot x\right)\right)}, z\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(y + \frac{4297481763}{31250000} \cdot x\right)\right), z\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{x}, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \left(\frac{4297481763}{31250000} \cdot x\right)\right)\right), z\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \left(x \cdot \frac{4297481763}{31250000}\right)\right)\right), z\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      4. *-lowering-*.f64 97.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \frac{4297481763}{31250000}\right)\right)\right), z\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

   7. Simplified 97.7%

      \[\leadsto \left(\color{blue}{x \cdot \left(y + x \cdot 137.519416416\right)} + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+37}:\\ \;\;\;\;\frac{4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}}{\frac{1}{x + -2}}\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+18}:\\ \;\;\;\;\frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}}{\frac{1}{x + -2}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -350:\\ \;\;\;\;x \cdot \left(\frac{-110.1139242984811 + \frac{\left(\frac{y}{x} - \frac{130977.50649958357}{x}\right) - -3655.1204654076414}{x}}{x} - -4.16438922228\right)\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\frac{z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)}{x \cdot \left(x \cdot -215.98570090975 + -168.4663270985\right) + -23.533438303}\\ \mathbf{else}:\\ \;\;\;\;\frac{4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}}{\frac{1}{x + -2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -350.0)
   (*
    x
    (-
     (/
      (+
       -110.1139242984811
       (/ (- (- (/ y x) (/ 130977.50649958357 x)) -3655.1204654076414) x))
      x)
     -4.16438922228))
   (if (<= x 2.0)
     (/
      (+
       z
       (*
        x
        (+
         y
         (* x (+ 137.519416416 (* x (+ (* x 4.16438922228) 78.6994924154)))))))
      (+ (* x (+ (* x -215.98570090975) -168.4663270985)) -23.533438303))
     (/
      (+
       4.16438922228
       (/
        (-
         (/ (+ 3451.550173699799 (/ (- y 124074.40615218398) x)) x)
         101.7851458539211)
        x))
      (/ 1.0 (+ x -2.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -350.0) {
		tmp = x * (((-110.1139242984811 + ((((y / x) - (130977.50649958357 / x)) - -3655.1204654076414) / x)) / x) - -4.16438922228);
	} else if (x <= 2.0) {
		tmp = (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))) / ((x * ((x * -215.98570090975) + -168.4663270985)) + -23.533438303);
	} else {
		tmp = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / (1.0 / (x + -2.0));
	}
	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) :: tmp
    if (x <= (-350.0d0)) then
        tmp = x * ((((-110.1139242984811d0) + ((((y / x) - (130977.50649958357d0 / x)) - (-3655.1204654076414d0)) / x)) / x) - (-4.16438922228d0))
    else if (x <= 2.0d0) then
        tmp = (z + (x * (y + (x * (137.519416416d0 + (x * ((x * 4.16438922228d0) + 78.6994924154d0))))))) / ((x * ((x * (-215.98570090975d0)) + (-168.4663270985d0))) + (-23.533438303d0))
    else
        tmp = (4.16438922228d0 + ((((3451.550173699799d0 + ((y - 124074.40615218398d0) / x)) / x) - 101.7851458539211d0) / x)) / (1.0d0 / (x + (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -350.0) {
		tmp = x * (((-110.1139242984811 + ((((y / x) - (130977.50649958357 / x)) - -3655.1204654076414) / x)) / x) - -4.16438922228);
	} else if (x <= 2.0) {
		tmp = (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))) / ((x * ((x * -215.98570090975) + -168.4663270985)) + -23.533438303);
	} else {
		tmp = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / (1.0 / (x + -2.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -350.0:
		tmp = x * (((-110.1139242984811 + ((((y / x) - (130977.50649958357 / x)) - -3655.1204654076414) / x)) / x) - -4.16438922228)
	elif x <= 2.0:
		tmp = (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))) / ((x * ((x * -215.98570090975) + -168.4663270985)) + -23.533438303)
	else:
		tmp = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / (1.0 / (x + -2.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -350.0)
		tmp = Float64(x * Float64(Float64(Float64(-110.1139242984811 + Float64(Float64(Float64(Float64(y / x) - Float64(130977.50649958357 / x)) - -3655.1204654076414) / x)) / x) - -4.16438922228));
	elseif (x <= 2.0)
		tmp = Float64(Float64(z + Float64(x * Float64(y + Float64(x * Float64(137.519416416 + Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154))))))) / Float64(Float64(x * Float64(Float64(x * -215.98570090975) + -168.4663270985)) + -23.533438303));
	else
		tmp = Float64(Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(Float64(y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / Float64(1.0 / Float64(x + -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -350.0)
		tmp = x * (((-110.1139242984811 + ((((y / x) - (130977.50649958357 / x)) - -3655.1204654076414) / x)) / x) - -4.16438922228);
	elseif (x <= 2.0)
		tmp = (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))) / ((x * ((x * -215.98570090975) + -168.4663270985)) + -23.533438303);
	else
		tmp = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / (1.0 / (x + -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -350.0], N[(x * N[(N[(N[(-110.1139242984811 + N[(N[(N[(N[(y / x), $MachinePrecision] - N[(130977.50649958357 / x), $MachinePrecision]), $MachinePrecision] - -3655.1204654076414), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - -4.16438922228), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.0], N[(N[(z + N[(x * N[(y + N[(x * N[(137.519416416 + N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(x * N[(N[(x * -215.98570090975), $MachinePrecision] + -168.4663270985), $MachinePrecision]), $MachinePrecision] + -23.533438303), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 + N[(N[(N[(N[(3451.550173699799 + N[(N[(y - 124074.40615218398), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / N[(1.0 / N[(x + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -350

   1. Initial program 14.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 17.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot x\right) \cdot \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right) \cdot \color{blue}{\left(-1 \cdot x\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right), \color{blue}{\left(-1 \cdot x\right)}\right) \]

   7. Simplified 95.1%

      \[\leadsto \color{blue}{\left(-4.16438922228 - \frac{-110.1139242984811 - \frac{\left(\frac{130977.50649958357}{x} - \frac{y}{x}\right) + -3655.1204654076414}{x}}{x}\right) \cdot \left(0 - x\right)} \]

   if -350 < x < 2

   1. Initial program 99.6%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   6. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{\frac{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}{x + -2}}} \]

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \color{blue}{\left(x \cdot \left(\frac{-863942803639}{4000000000} \cdot x - \frac{336932654197}{2000000000}\right) - \frac{23533438303}{1000000000}\right)}\right) \]
   8. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \left(x \cdot \left(\frac{-863942803639}{4000000000} \cdot x - \frac{336932654197}{2000000000}\right) + \color{blue}{\left(\mathsf{neg}\left(\frac{23533438303}{1000000000}\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \mathsf{+.f64}\left(\left(x \cdot \left(\frac{-863942803639}{4000000000} \cdot x - \frac{336932654197}{2000000000}\right)\right), \color{blue}{\left(\mathsf{neg}\left(\frac{23533438303}{1000000000}\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{-863942803639}{4000000000} \cdot x - \frac{336932654197}{2000000000}\right)\right), \left(\mathsf{neg}\left(\color{blue}{\frac{23533438303}{1000000000}}\right)\right)\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{-863942803639}{4000000000} \cdot x + \left(\mathsf{neg}\left(\frac{336932654197}{2000000000}\right)\right)\right)\right), \left(\mathsf{neg}\left(\frac{23533438303}{1000000000}\right)\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{-863942803639}{4000000000} \cdot x + \frac{-336932654197}{2000000000}\right)\right), \left(\mathsf{neg}\left(\frac{23533438303}{1000000000}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{-863942803639}{4000000000} \cdot x\right), \frac{-336932654197}{2000000000}\right)\right), \left(\mathsf{neg}\left(\frac{23533438303}{1000000000}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(x \cdot \frac{-863942803639}{4000000000}\right), \frac{-336932654197}{2000000000}\right)\right), \left(\mathsf{neg}\left(\frac{23533438303}{1000000000}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{-863942803639}{4000000000}\right), \frac{-336932654197}{2000000000}\right)\right), \left(\mathsf{neg}\left(\frac{23533438303}{1000000000}\right)\right)\right)\right) \]

      9. metadata-eval 98.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{-863942803639}{4000000000}\right), \frac{-336932654197}{2000000000}\right)\right), \frac{-23533438303}{1000000000}\right)\right) \]

   9. Simplified 98.2%

      \[\leadsto \frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{\color{blue}{x \cdot \left(x \cdot -215.98570090975 + -168.4663270985\right) + -23.533438303}} \]

   if 2 < x

   1. Initial program 24.0%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 25.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   6. Applied egg-rr 25.7%

      \[\leadsto \color{blue}{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{\frac{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}{x + -2}}} \]
   7. Step-by-step derivation

      1. div-inv N/A

         \[\leadsto \frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}\right) \cdot \color{blue}{\frac{1}{x + -2}}} \]

      2. associate-/r* N/A

         \[\leadsto \frac{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}}}{\color{blue}{\frac{1}{x + -2}}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}}\right), \color{blue}{\left(\frac{1}{x + -2}\right)}\right) \]

   8. Applied egg-rr 25.7%

      \[\leadsto \color{blue}{\frac{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}}{\frac{1}{x + -2}}} \]

   9. Taylor expanded in x around -inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{104109730557}{25000000000} + -1 \cdot \frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)}, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{104109730557}{25000000000} + \left(\mathsf{neg}\left(\frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{104109730557}{25000000000} - \frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right), \mathsf{/.f64}\left(\color{blue}{1}, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)\right), \mathsf{/.f64}\left(\color{blue}{1}, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\left(\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

   11. Simplified 89.5%

       \[\leadsto \frac{\color{blue}{4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}}}{\frac{1}{x + -2}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -350:\\ \;\;\;\;x \cdot \left(\frac{-110.1139242984811 + \frac{\left(\frac{y}{x} - \frac{130977.50649958357}{x}\right) - -3655.1204654076414}{x}}{x} - -4.16438922228\right)\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\frac{z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)}{x \cdot \left(x \cdot -215.98570090975 + -168.4663270985\right) + -23.533438303}\\ \mathbf{else}:\\ \;\;\;\;\frac{4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}}{\frac{1}{x + -2}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35:\\ \;\;\;\;x \cdot \left(\frac{-110.1139242984811 + \frac{\left(\frac{y}{x} - \frac{130977.50649958357}{x}\right) - -3655.1204654076414}{x}}{x} - -4.16438922228\right)\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\frac{z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)}{-23.533438303 + x \cdot -168.4663270985}\\ \mathbf{else}:\\ \;\;\;\;\frac{4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}}{\frac{1}{x + -2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.35)
   (*
    x
    (-
     (/
      (+
       -110.1139242984811
       (/ (- (- (/ y x) (/ 130977.50649958357 x)) -3655.1204654076414) x))
      x)
     -4.16438922228))
   (if (<= x 2.0)
     (/
      (+
       z
       (*
        x
        (+
         y
         (* x (+ 137.519416416 (* x (+ (* x 4.16438922228) 78.6994924154)))))))
      (+ -23.533438303 (* x -168.4663270985)))
     (/
      (+
       4.16438922228
       (/
        (-
         (/ (+ 3451.550173699799 (/ (- y 124074.40615218398) x)) x)
         101.7851458539211)
        x))
      (/ 1.0 (+ x -2.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.35) {
		tmp = x * (((-110.1139242984811 + ((((y / x) - (130977.50649958357 / x)) - -3655.1204654076414) / x)) / x) - -4.16438922228);
	} else if (x <= 2.0) {
		tmp = (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))) / (-23.533438303 + (x * -168.4663270985));
	} else {
		tmp = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / (1.0 / (x + -2.0));
	}
	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) :: tmp
    if (x <= (-1.35d0)) then
        tmp = x * ((((-110.1139242984811d0) + ((((y / x) - (130977.50649958357d0 / x)) - (-3655.1204654076414d0)) / x)) / x) - (-4.16438922228d0))
    else if (x <= 2.0d0) then
        tmp = (z + (x * (y + (x * (137.519416416d0 + (x * ((x * 4.16438922228d0) + 78.6994924154d0))))))) / ((-23.533438303d0) + (x * (-168.4663270985d0)))
    else
        tmp = (4.16438922228d0 + ((((3451.550173699799d0 + ((y - 124074.40615218398d0) / x)) / x) - 101.7851458539211d0) / x)) / (1.0d0 / (x + (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.35) {
		tmp = x * (((-110.1139242984811 + ((((y / x) - (130977.50649958357 / x)) - -3655.1204654076414) / x)) / x) - -4.16438922228);
	} else if (x <= 2.0) {
		tmp = (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))) / (-23.533438303 + (x * -168.4663270985));
	} else {
		tmp = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / (1.0 / (x + -2.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.35:
		tmp = x * (((-110.1139242984811 + ((((y / x) - (130977.50649958357 / x)) - -3655.1204654076414) / x)) / x) - -4.16438922228)
	elif x <= 2.0:
		tmp = (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))) / (-23.533438303 + (x * -168.4663270985))
	else:
		tmp = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / (1.0 / (x + -2.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.35)
		tmp = Float64(x * Float64(Float64(Float64(-110.1139242984811 + Float64(Float64(Float64(Float64(y / x) - Float64(130977.50649958357 / x)) - -3655.1204654076414) / x)) / x) - -4.16438922228));
	elseif (x <= 2.0)
		tmp = Float64(Float64(z + Float64(x * Float64(y + Float64(x * Float64(137.519416416 + Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154))))))) / Float64(-23.533438303 + Float64(x * -168.4663270985)));
	else
		tmp = Float64(Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(Float64(y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / Float64(1.0 / Float64(x + -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.35)
		tmp = x * (((-110.1139242984811 + ((((y / x) - (130977.50649958357 / x)) - -3655.1204654076414) / x)) / x) - -4.16438922228);
	elseif (x <= 2.0)
		tmp = (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))) / (-23.533438303 + (x * -168.4663270985));
	else
		tmp = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / (1.0 / (x + -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.35], N[(x * N[(N[(N[(-110.1139242984811 + N[(N[(N[(N[(y / x), $MachinePrecision] - N[(130977.50649958357 / x), $MachinePrecision]), $MachinePrecision] - -3655.1204654076414), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - -4.16438922228), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.0], N[(N[(z + N[(x * N[(y + N[(x * N[(137.519416416 + N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(-23.533438303 + N[(x * -168.4663270985), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 + N[(N[(N[(N[(3451.550173699799 + N[(N[(y - 124074.40615218398), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / N[(1.0 / N[(x + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3500000000000001

   1. Initial program 14.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 17.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot x\right) \cdot \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right) \cdot \color{blue}{\left(-1 \cdot x\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right), \color{blue}{\left(-1 \cdot x\right)}\right) \]

   7. Simplified 95.1%

      \[\leadsto \color{blue}{\left(-4.16438922228 - \frac{-110.1139242984811 - \frac{\left(\frac{130977.50649958357}{x} - \frac{y}{x}\right) + -3655.1204654076414}{x}}{x}\right) \cdot \left(0 - x\right)} \]

   if -1.3500000000000001 < x < 2

   1. Initial program 99.6%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   6. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{\frac{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}{x + -2}}} \]

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \color{blue}{\left(\frac{-336932654197}{2000000000} \cdot x - \frac{23533438303}{1000000000}\right)}\right) \]
   8. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \left(\frac{-336932654197}{2000000000} \cdot x + \color{blue}{\left(\mathsf{neg}\left(\frac{23533438303}{1000000000}\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \mathsf{+.f64}\left(\left(\frac{-336932654197}{2000000000} \cdot x\right), \color{blue}{\left(\mathsf{neg}\left(\frac{23533438303}{1000000000}\right)\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \mathsf{+.f64}\left(\left(x \cdot \frac{-336932654197}{2000000000}\right), \left(\mathsf{neg}\left(\color{blue}{\frac{23533438303}{1000000000}}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{-336932654197}{2000000000}\right), \left(\mathsf{neg}\left(\color{blue}{\frac{23533438303}{1000000000}}\right)\right)\right)\right) \]

      5. metadata-eval 97.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{-336932654197}{2000000000}\right), \frac{-23533438303}{1000000000}\right)\right) \]

   9. Simplified 97.9%

      \[\leadsto \frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{\color{blue}{x \cdot -168.4663270985 + -23.533438303}} \]

   if 2 < x

   1. Initial program 24.0%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 25.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   6. Applied egg-rr 25.7%

      \[\leadsto \color{blue}{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{\frac{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}{x + -2}}} \]
   7. Step-by-step derivation

      1. div-inv N/A

         \[\leadsto \frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}\right) \cdot \color{blue}{\frac{1}{x + -2}}} \]

      2. associate-/r* N/A

         \[\leadsto \frac{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}}}{\color{blue}{\frac{1}{x + -2}}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}}\right), \color{blue}{\left(\frac{1}{x + -2}\right)}\right) \]

   8. Applied egg-rr 25.7%

      \[\leadsto \color{blue}{\frac{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}}{\frac{1}{x + -2}}} \]

   9. Taylor expanded in x around -inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{104109730557}{25000000000} + -1 \cdot \frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)}, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{104109730557}{25000000000} + \left(\mathsf{neg}\left(\frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{104109730557}{25000000000} - \frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right), \mathsf{/.f64}\left(\color{blue}{1}, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)\right), \mathsf{/.f64}\left(\color{blue}{1}, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\left(\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

   11. Simplified 89.5%

       \[\leadsto \frac{\color{blue}{4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}}}{\frac{1}{x + -2}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35:\\ \;\;\;\;x \cdot \left(\frac{-110.1139242984811 + \frac{\left(\frac{y}{x} - \frac{130977.50649958357}{x}\right) - -3655.1204654076414}{x}}{x} - -4.16438922228\right)\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\frac{z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)}{-23.533438303 + x \cdot -168.4663270985}\\ \mathbf{else}:\\ \;\;\;\;\frac{4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}}{\frac{1}{x + -2}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 95.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.18:\\ \;\;\;\;x \cdot \left(\frac{-110.1139242984811 + \frac{\left(\frac{y}{x} - \frac{130977.50649958357}{x}\right) - -3655.1204654076414}{x}}{x} - -4.16438922228\right)\\ \mathbf{elif}\;x \leq 66000000:\\ \;\;\;\;\left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)\right) \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}}{\frac{1}{x + -2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.18)
   (*
    x
    (-
     (/
      (+
       -110.1139242984811
       (/ (- (- (/ y x) (/ 130977.50649958357 x)) -3655.1204654076414) x))
      x)
     -4.16438922228))
   (if (<= x 66000000.0)
     (*
      (+
       z
       (*
        x
        (+
         y
         (* x (+ 137.519416416 (* x (+ (* x 4.16438922228) 78.6994924154)))))))
      (+ -0.0424927283095952 (* x 0.3041881842569256)))
     (/
      (+
       4.16438922228
       (/
        (-
         (/ (+ 3451.550173699799 (/ (- y 124074.40615218398) x)) x)
         101.7851458539211)
        x))
      (/ 1.0 (+ x -2.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.18) {
		tmp = x * (((-110.1139242984811 + ((((y / x) - (130977.50649958357 / x)) - -3655.1204654076414) / x)) / x) - -4.16438922228);
	} else if (x <= 66000000.0) {
		tmp = (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))) * (-0.0424927283095952 + (x * 0.3041881842569256));
	} else {
		tmp = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / (1.0 / (x + -2.0));
	}
	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) :: tmp
    if (x <= (-0.18d0)) then
        tmp = x * ((((-110.1139242984811d0) + ((((y / x) - (130977.50649958357d0 / x)) - (-3655.1204654076414d0)) / x)) / x) - (-4.16438922228d0))
    else if (x <= 66000000.0d0) then
        tmp = (z + (x * (y + (x * (137.519416416d0 + (x * ((x * 4.16438922228d0) + 78.6994924154d0))))))) * ((-0.0424927283095952d0) + (x * 0.3041881842569256d0))
    else
        tmp = (4.16438922228d0 + ((((3451.550173699799d0 + ((y - 124074.40615218398d0) / x)) / x) - 101.7851458539211d0) / x)) / (1.0d0 / (x + (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.18) {
		tmp = x * (((-110.1139242984811 + ((((y / x) - (130977.50649958357 / x)) - -3655.1204654076414) / x)) / x) - -4.16438922228);
	} else if (x <= 66000000.0) {
		tmp = (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))) * (-0.0424927283095952 + (x * 0.3041881842569256));
	} else {
		tmp = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / (1.0 / (x + -2.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.18:
		tmp = x * (((-110.1139242984811 + ((((y / x) - (130977.50649958357 / x)) - -3655.1204654076414) / x)) / x) - -4.16438922228)
	elif x <= 66000000.0:
		tmp = (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))) * (-0.0424927283095952 + (x * 0.3041881842569256))
	else:
		tmp = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / (1.0 / (x + -2.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.18)
		tmp = Float64(x * Float64(Float64(Float64(-110.1139242984811 + Float64(Float64(Float64(Float64(y / x) - Float64(130977.50649958357 / x)) - -3655.1204654076414) / x)) / x) - -4.16438922228));
	elseif (x <= 66000000.0)
		tmp = Float64(Float64(z + Float64(x * Float64(y + Float64(x * Float64(137.519416416 + Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154))))))) * Float64(-0.0424927283095952 + Float64(x * 0.3041881842569256)));
	else
		tmp = Float64(Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(Float64(y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / Float64(1.0 / Float64(x + -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.18)
		tmp = x * (((-110.1139242984811 + ((((y / x) - (130977.50649958357 / x)) - -3655.1204654076414) / x)) / x) - -4.16438922228);
	elseif (x <= 66000000.0)
		tmp = (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))) * (-0.0424927283095952 + (x * 0.3041881842569256));
	else
		tmp = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / (1.0 / (x + -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.18], N[(x * N[(N[(N[(-110.1139242984811 + N[(N[(N[(N[(y / x), $MachinePrecision] - N[(130977.50649958357 / x), $MachinePrecision]), $MachinePrecision] - -3655.1204654076414), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - -4.16438922228), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 66000000.0], N[(N[(z + N[(x * N[(y + N[(x * N[(137.519416416 + N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-0.0424927283095952 + N[(x * 0.3041881842569256), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 + N[(N[(N[(N[(3451.550173699799 + N[(N[(y - 124074.40615218398), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / N[(1.0 / N[(x + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.17999999999999999

   1. Initial program 15.8%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 18.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot x\right) \cdot \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right) \cdot \color{blue}{\left(-1 \cdot x\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right), \color{blue}{\left(-1 \cdot x\right)}\right) \]

   7. Simplified 93.7%

      \[\leadsto \color{blue}{\left(-4.16438922228 - \frac{-110.1139242984811 - \frac{\left(\frac{130977.50649958357}{x} - \frac{y}{x}\right) + -3655.1204654076414}{x}}{x}\right) \cdot \left(0 - x\right)} \]

   if -0.17999999999999999 < x < 6.6e7

   1. Initial program 99.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} \cdot x - \frac{1000000000}{23533438303}\right)}\right) \]
   6. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \left(\frac{168466327098500000000}{553822718361107519809} \cdot x + \color{blue}{\left(\mathsf{neg}\left(\frac{1000000000}{23533438303}\right)\right)}\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \left(\frac{168466327098500000000}{553822718361107519809} \cdot x + \frac{-1000000000}{23533438303}\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \left(\frac{-1000000000}{23533438303} + \color{blue}{\frac{168466327098500000000}{553822718361107519809} \cdot x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\frac{-1000000000}{23533438303}, \color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} \cdot x\right)}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\frac{-1000000000}{23533438303}, \left(x \cdot \color{blue}{\frac{168466327098500000000}{553822718361107519809}}\right)\right)\right) \]

      6. *-lowering-*.f64 97.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\frac{-1000000000}{23533438303}, \mathsf{*.f64}\left(x, \color{blue}{\frac{168466327098500000000}{553822718361107519809}}\right)\right)\right) \]

   7. Simplified 97.4%

      \[\leadsto \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \color{blue}{\left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)} \]

   if 6.6e7 < x

   1. Initial program 22.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 24.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   6. Applied egg-rr 24.3%

      \[\leadsto \color{blue}{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{\frac{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}{x + -2}}} \]
   7. Step-by-step derivation

      1. div-inv N/A

         \[\leadsto \frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}\right) \cdot \color{blue}{\frac{1}{x + -2}}} \]

      2. associate-/r* N/A

         \[\leadsto \frac{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}}}{\color{blue}{\frac{1}{x + -2}}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}}\right), \color{blue}{\left(\frac{1}{x + -2}\right)}\right) \]

   8. Applied egg-rr 24.3%

      \[\leadsto \color{blue}{\frac{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}}{\frac{1}{x + -2}}} \]

   9. Taylor expanded in x around -inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{104109730557}{25000000000} + -1 \cdot \frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)}, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{104109730557}{25000000000} + \left(\mathsf{neg}\left(\frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{104109730557}{25000000000} - \frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right), \mathsf{/.f64}\left(\color{blue}{1}, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)\right), \mathsf{/.f64}\left(\color{blue}{1}, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\left(\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

   11. Simplified 91.0%

       \[\leadsto \frac{\color{blue}{4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}}}{\frac{1}{x + -2}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.18:\\ \;\;\;\;x \cdot \left(\frac{-110.1139242984811 + \frac{\left(\frac{y}{x} - \frac{130977.50649958357}{x}\right) - -3655.1204654076414}{x}}{x} - -4.16438922228\right)\\ \mathbf{elif}\;x \leq 66000000:\\ \;\;\;\;\left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)\right) \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}}{\frac{1}{x + -2}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 95.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.18:\\ \;\;\;\;x \cdot \left(\frac{-110.1139242984811 + \frac{\left(\frac{y}{x} - \frac{130977.50649958357}{x}\right) - -3655.1204654076414}{x}}{x} - -4.16438922228\right)\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\frac{z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)}{-23.533438303}\\ \mathbf{else}:\\ \;\;\;\;\frac{4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}}{\frac{1}{x + -2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.18)
   (*
    x
    (-
     (/
      (+
       -110.1139242984811
       (/ (- (- (/ y x) (/ 130977.50649958357 x)) -3655.1204654076414) x))
      x)
     -4.16438922228))
   (if (<= x 2.0)
     (/
      (+
       z
       (*
        x
        (+
         y
         (* x (+ 137.519416416 (* x (+ (* x 4.16438922228) 78.6994924154)))))))
      -23.533438303)
     (/
      (+
       4.16438922228
       (/
        (-
         (/ (+ 3451.550173699799 (/ (- y 124074.40615218398) x)) x)
         101.7851458539211)
        x))
      (/ 1.0 (+ x -2.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.18) {
		tmp = x * (((-110.1139242984811 + ((((y / x) - (130977.50649958357 / x)) - -3655.1204654076414) / x)) / x) - -4.16438922228);
	} else if (x <= 2.0) {
		tmp = (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))) / -23.533438303;
	} else {
		tmp = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / (1.0 / (x + -2.0));
	}
	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) :: tmp
    if (x <= (-0.18d0)) then
        tmp = x * ((((-110.1139242984811d0) + ((((y / x) - (130977.50649958357d0 / x)) - (-3655.1204654076414d0)) / x)) / x) - (-4.16438922228d0))
    else if (x <= 2.0d0) then
        tmp = (z + (x * (y + (x * (137.519416416d0 + (x * ((x * 4.16438922228d0) + 78.6994924154d0))))))) / (-23.533438303d0)
    else
        tmp = (4.16438922228d0 + ((((3451.550173699799d0 + ((y - 124074.40615218398d0) / x)) / x) - 101.7851458539211d0) / x)) / (1.0d0 / (x + (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.18) {
		tmp = x * (((-110.1139242984811 + ((((y / x) - (130977.50649958357 / x)) - -3655.1204654076414) / x)) / x) - -4.16438922228);
	} else if (x <= 2.0) {
		tmp = (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))) / -23.533438303;
	} else {
		tmp = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / (1.0 / (x + -2.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.18:
		tmp = x * (((-110.1139242984811 + ((((y / x) - (130977.50649958357 / x)) - -3655.1204654076414) / x)) / x) - -4.16438922228)
	elif x <= 2.0:
		tmp = (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))) / -23.533438303
	else:
		tmp = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / (1.0 / (x + -2.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.18)
		tmp = Float64(x * Float64(Float64(Float64(-110.1139242984811 + Float64(Float64(Float64(Float64(y / x) - Float64(130977.50649958357 / x)) - -3655.1204654076414) / x)) / x) - -4.16438922228));
	elseif (x <= 2.0)
		tmp = Float64(Float64(z + Float64(x * Float64(y + Float64(x * Float64(137.519416416 + Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154))))))) / -23.533438303);
	else
		tmp = Float64(Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(Float64(y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / Float64(1.0 / Float64(x + -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.18)
		tmp = x * (((-110.1139242984811 + ((((y / x) - (130977.50649958357 / x)) - -3655.1204654076414) / x)) / x) - -4.16438922228);
	elseif (x <= 2.0)
		tmp = (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))) / -23.533438303;
	else
		tmp = (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)) / (1.0 / (x + -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.18], N[(x * N[(N[(N[(-110.1139242984811 + N[(N[(N[(N[(y / x), $MachinePrecision] - N[(130977.50649958357 / x), $MachinePrecision]), $MachinePrecision] - -3655.1204654076414), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - -4.16438922228), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.0], N[(N[(z + N[(x * N[(y + N[(x * N[(137.519416416 + N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / -23.533438303), $MachinePrecision], N[(N[(4.16438922228 + N[(N[(N[(N[(3451.550173699799 + N[(N[(y - 124074.40615218398), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / N[(1.0 / N[(x + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.17999999999999999

   1. Initial program 15.8%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 18.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot x\right) \cdot \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right) \cdot \color{blue}{\left(-1 \cdot x\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right), \color{blue}{\left(-1 \cdot x\right)}\right) \]

   7. Simplified 93.7%

      \[\leadsto \color{blue}{\left(-4.16438922228 - \frac{-110.1139242984811 - \frac{\left(\frac{130977.50649958357}{x} - \frac{y}{x}\right) + -3655.1204654076414}{x}}{x}\right) \cdot \left(0 - x\right)} \]

   if -0.17999999999999999 < x < 2

   1. Initial program 99.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   6. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{\frac{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}{x + -2}}} \]

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \color{blue}{\frac{-23533438303}{1000000000}}\right) \]
   8. Step-by-step derivation

   9. Simplified 97.7%

      \[\leadsto \frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{\color{blue}{-23.533438303}} \]

   if 2 < x

   1. Initial program 24.0%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 25.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   6. Applied egg-rr 25.7%

      \[\leadsto \color{blue}{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{\frac{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}{x + -2}}} \]
   7. Step-by-step derivation

      1. div-inv N/A

         \[\leadsto \frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}\right) \cdot \color{blue}{\frac{1}{x + -2}}} \]

      2. associate-/r* N/A

         \[\leadsto \frac{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}}}{\color{blue}{\frac{1}{x + -2}}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}}\right), \color{blue}{\left(\frac{1}{x + -2}\right)}\right) \]

   8. Applied egg-rr 25.7%

      \[\leadsto \color{blue}{\frac{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}}{\frac{1}{x + -2}}} \]

   9. Taylor expanded in x around -inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{104109730557}{25000000000} + -1 \cdot \frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)}, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{104109730557}{25000000000} + \left(\mathsf{neg}\left(\frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{104109730557}{25000000000} - \frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right), \mathsf{/.f64}\left(\color{blue}{1}, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)\right), \mathsf{/.f64}\left(\color{blue}{1}, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\left(\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

   11. Simplified 89.5%

       \[\leadsto \frac{\color{blue}{4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}}}{\frac{1}{x + -2}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.18:\\ \;\;\;\;x \cdot \left(\frac{-110.1139242984811 + \frac{\left(\frac{y}{x} - \frac{130977.50649958357}{x}\right) - -3655.1204654076414}{x}}{x} - -4.16438922228\right)\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\frac{z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)}{-23.533438303}\\ \mathbf{else}:\\ \;\;\;\;\frac{4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}}{\frac{1}{x + -2}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 95.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(\frac{-110.1139242984811 + \frac{\left(\frac{y}{x} - \frac{130977.50649958357}{x}\right) - -3655.1204654076414}{x}}{x} - -4.16438922228\right)\\ \mathbf{if}\;x \leq -0.18:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\frac{z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)}{-23.533438303}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          x
          (-
           (/
            (+
             -110.1139242984811
             (/
              (- (- (/ y x) (/ 130977.50649958357 x)) -3655.1204654076414)
              x))
            x)
           -4.16438922228))))
   (if (<= x -0.18)
     t_0
     (if (<= x 2.0)
       (/
        (+
         z
         (*
          x
          (+
           y
           (*
            x
            (+ 137.519416416 (* x (+ (* x 4.16438922228) 78.6994924154)))))))
        -23.533438303)
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (((-110.1139242984811 + ((((y / x) - (130977.50649958357 / x)) - -3655.1204654076414) / x)) / x) - -4.16438922228);
	double tmp;
	if (x <= -0.18) {
		tmp = t_0;
	} else if (x <= 2.0) {
		tmp = (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))) / -23.533438303;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * ((((-110.1139242984811d0) + ((((y / x) - (130977.50649958357d0 / x)) - (-3655.1204654076414d0)) / x)) / x) - (-4.16438922228d0))
    if (x <= (-0.18d0)) then
        tmp = t_0
    else if (x <= 2.0d0) then
        tmp = (z + (x * (y + (x * (137.519416416d0 + (x * ((x * 4.16438922228d0) + 78.6994924154d0))))))) / (-23.533438303d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (((-110.1139242984811 + ((((y / x) - (130977.50649958357 / x)) - -3655.1204654076414) / x)) / x) - -4.16438922228);
	double tmp;
	if (x <= -0.18) {
		tmp = t_0;
	} else if (x <= 2.0) {
		tmp = (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))) / -23.533438303;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (((-110.1139242984811 + ((((y / x) - (130977.50649958357 / x)) - -3655.1204654076414) / x)) / x) - -4.16438922228)
	tmp = 0
	if x <= -0.18:
		tmp = t_0
	elif x <= 2.0:
		tmp = (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))) / -23.533438303
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(Float64(Float64(-110.1139242984811 + Float64(Float64(Float64(Float64(y / x) - Float64(130977.50649958357 / x)) - -3655.1204654076414) / x)) / x) - -4.16438922228))
	tmp = 0.0
	if (x <= -0.18)
		tmp = t_0;
	elseif (x <= 2.0)
		tmp = Float64(Float64(z + Float64(x * Float64(y + Float64(x * Float64(137.519416416 + Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154))))))) / -23.533438303);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (((-110.1139242984811 + ((((y / x) - (130977.50649958357 / x)) - -3655.1204654076414) / x)) / x) - -4.16438922228);
	tmp = 0.0;
	if (x <= -0.18)
		tmp = t_0;
	elseif (x <= 2.0)
		tmp = (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))) / -23.533438303;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(N[(N[(-110.1139242984811 + N[(N[(N[(N[(y / x), $MachinePrecision] - N[(130977.50649958357 / x), $MachinePrecision]), $MachinePrecision] - -3655.1204654076414), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - -4.16438922228), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.18], t$95$0, If[LessEqual[x, 2.0], N[(N[(z + N[(x * N[(y + N[(x * N[(137.519416416 + N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / -23.533438303), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.17999999999999999 or 2 < x

   1. Initial program 19.6%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 22.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot x\right) \cdot \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right) \cdot \color{blue}{\left(-1 \cdot x\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right), \color{blue}{\left(-1 \cdot x\right)}\right) \]

   7. Simplified 91.7%

      \[\leadsto \color{blue}{\left(-4.16438922228 - \frac{-110.1139242984811 - \frac{\left(\frac{130977.50649958357}{x} - \frac{y}{x}\right) + -3655.1204654076414}{x}}{x}\right) \cdot \left(0 - x\right)} \]

   if -0.17999999999999999 < x < 2

   1. Initial program 99.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   6. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{\frac{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}{x + -2}}} \]

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \color{blue}{\frac{-23533438303}{1000000000}}\right) \]
   8. Step-by-step derivation

   9. Simplified 97.7%

      \[\leadsto \frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{\color{blue}{-23.533438303}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.18:\\ \;\;\;\;x \cdot \left(\frac{-110.1139242984811 + \frac{\left(\frac{y}{x} - \frac{130977.50649958357}{x}\right) - -3655.1204654076414}{x}}{x} - -4.16438922228\right)\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\frac{z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)}{-23.533438303}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{-110.1139242984811 + \frac{\left(\frac{y}{x} - \frac{130977.50649958357}{x}\right) - -3655.1204654076414}{x}}{x} - -4.16438922228\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 92.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+16}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\frac{z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)}{-23.533438303}\\ \mathbf{else}:\\ \;\;\;\;\frac{4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}}{\frac{1}{x + -2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.8e+16)
   (* x 4.16438922228)
   (if (<= x 2.0)
     (/
      (+
       z
       (*
        x
        (+
         y
         (* x (+ 137.519416416 (* x (+ (* x 4.16438922228) 78.6994924154)))))))
      -23.533438303)
     (/
      (- 4.16438922228 (/ (+ 101.7851458539211 (/ -3451.550173699799 x)) x))
      (/ 1.0 (+ x -2.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.8e+16) {
		tmp = x * 4.16438922228;
	} else if (x <= 2.0) {
		tmp = (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))) / -23.533438303;
	} else {
		tmp = (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x)) / (1.0 / (x + -2.0));
	}
	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) :: tmp
    if (x <= (-3.8d+16)) then
        tmp = x * 4.16438922228d0
    else if (x <= 2.0d0) then
        tmp = (z + (x * (y + (x * (137.519416416d0 + (x * ((x * 4.16438922228d0) + 78.6994924154d0))))))) / (-23.533438303d0)
    else
        tmp = (4.16438922228d0 - ((101.7851458539211d0 + ((-3451.550173699799d0) / x)) / x)) / (1.0d0 / (x + (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.8e+16) {
		tmp = x * 4.16438922228;
	} else if (x <= 2.0) {
		tmp = (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))) / -23.533438303;
	} else {
		tmp = (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x)) / (1.0 / (x + -2.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.8e+16:
		tmp = x * 4.16438922228
	elif x <= 2.0:
		tmp = (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))) / -23.533438303
	else:
		tmp = (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x)) / (1.0 / (x + -2.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.8e+16)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 2.0)
		tmp = Float64(Float64(z + Float64(x * Float64(y + Float64(x * Float64(137.519416416 + Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154))))))) / -23.533438303);
	else
		tmp = Float64(Float64(4.16438922228 - Float64(Float64(101.7851458539211 + Float64(-3451.550173699799 / x)) / x)) / Float64(1.0 / Float64(x + -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.8e+16)
		tmp = x * 4.16438922228;
	elseif (x <= 2.0)
		tmp = (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))) / -23.533438303;
	else
		tmp = (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x)) / (1.0 / (x + -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.8e+16], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 2.0], N[(N[(z + N[(x * N[(y + N[(x * N[(137.519416416 + N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / -23.533438303), $MachinePrecision], N[(N[(4.16438922228 - N[(N[(101.7851458539211 + N[(-3451.550173699799 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / N[(1.0 / N[(x + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.8e16

   1. Initial program 11.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 14.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x \cdot \color{blue}{\frac{104109730557}{25000000000}} \]

      2. *-lowering-*.f64 91.0%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\frac{104109730557}{25000000000}}\right) \]

   7. Simplified 91.0%

      \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

   if -3.8e16 < x < 2

   1. Initial program 99.6%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   6. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{\frac{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}{x + -2}}} \]

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \color{blue}{\frac{-23533438303}{1000000000}}\right) \]
   8. Step-by-step derivation

   9. Simplified 95.8%

      \[\leadsto \frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{\color{blue}{-23.533438303}} \]

   if 2 < x

   1. Initial program 24.0%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 25.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   6. Applied egg-rr 25.7%

      \[\leadsto \color{blue}{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{\frac{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}{x + -2}}} \]
   7. Step-by-step derivation

      1. div-inv N/A

         \[\leadsto \frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}\right) \cdot \color{blue}{\frac{1}{x + -2}}} \]

      2. associate-/r* N/A

         \[\leadsto \frac{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}}}{\color{blue}{\frac{1}{x + -2}}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}}\right), \color{blue}{\left(\frac{1}{x + -2}\right)}\right) \]

   8. Applied egg-rr 25.7%

      \[\leadsto \color{blue}{\frac{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}}{\frac{1}{x + -2}}} \]

   9. Taylor expanded in x around -inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{104109730557}{25000000000} + -1 \cdot \frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x}\right)}, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{104109730557}{25000000000} + \left(\mathsf{neg}\left(\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x}\right)\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{104109730557}{25000000000} - \frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x}\right), \mathsf{/.f64}\left(\color{blue}{1}, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x}\right)\right), \mathsf{/.f64}\left(\color{blue}{1}, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\left(\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       5. sub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\left(\frac{12723143231740136880149}{125000000000000000000} + \left(\mathsf{neg}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}\right)\right)\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \left(\mathsf{neg}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}\right)\right)\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       7. associate-*r/ N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \left(\mathsf{neg}\left(\frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot 1}{x}\right)\right)\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       8. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \left(\mathsf{neg}\left(\frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}\right)\right)\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       9. distribute-neg-frac N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \left(\frac{\mathsf{neg}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}\right)}{x}\right)\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

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

           \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}\right)\right), x\right)\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       11. metadata-eval 77.9%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\frac{-2157218858562374472887084159837293}{625000000000000000000000000000}, x\right)\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

   11. Simplified 77.9%

       \[\leadsto \frac{\color{blue}{4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}}}{\frac{1}{x + -2}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+16}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\frac{z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)}{-23.533438303}\\ \mathbf{else}:\\ \;\;\;\;\frac{4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}}{\frac{1}{x + -2}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 92.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+16}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)\right) \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;\frac{4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}}{\frac{1}{x + -2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.8e+16)
   (* x 4.16438922228)
   (if (<= x 2.0)
     (*
      (+
       z
       (*
        x
        (+
         y
         (* x (+ 137.519416416 (* x (+ (* x 4.16438922228) 78.6994924154)))))))
      -0.0424927283095952)
     (/
      (- 4.16438922228 (/ (+ 101.7851458539211 (/ -3451.550173699799 x)) x))
      (/ 1.0 (+ x -2.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.8e+16) {
		tmp = x * 4.16438922228;
	} else if (x <= 2.0) {
		tmp = (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))) * -0.0424927283095952;
	} else {
		tmp = (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x)) / (1.0 / (x + -2.0));
	}
	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) :: tmp
    if (x <= (-3.8d+16)) then
        tmp = x * 4.16438922228d0
    else if (x <= 2.0d0) then
        tmp = (z + (x * (y + (x * (137.519416416d0 + (x * ((x * 4.16438922228d0) + 78.6994924154d0))))))) * (-0.0424927283095952d0)
    else
        tmp = (4.16438922228d0 - ((101.7851458539211d0 + ((-3451.550173699799d0) / x)) / x)) / (1.0d0 / (x + (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.8e+16) {
		tmp = x * 4.16438922228;
	} else if (x <= 2.0) {
		tmp = (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))) * -0.0424927283095952;
	} else {
		tmp = (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x)) / (1.0 / (x + -2.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.8e+16:
		tmp = x * 4.16438922228
	elif x <= 2.0:
		tmp = (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))) * -0.0424927283095952
	else:
		tmp = (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x)) / (1.0 / (x + -2.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.8e+16)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 2.0)
		tmp = Float64(Float64(z + Float64(x * Float64(y + Float64(x * Float64(137.519416416 + Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154))))))) * -0.0424927283095952);
	else
		tmp = Float64(Float64(4.16438922228 - Float64(Float64(101.7851458539211 + Float64(-3451.550173699799 / x)) / x)) / Float64(1.0 / Float64(x + -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.8e+16)
		tmp = x * 4.16438922228;
	elseif (x <= 2.0)
		tmp = (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))) * -0.0424927283095952;
	else
		tmp = (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x)) / (1.0 / (x + -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.8e+16], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 2.0], N[(N[(z + N[(x * N[(y + N[(x * N[(137.519416416 + N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -0.0424927283095952), $MachinePrecision], N[(N[(4.16438922228 - N[(N[(101.7851458539211 + N[(-3451.550173699799 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / N[(1.0 / N[(x + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.8e16

   1. Initial program 11.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 14.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x \cdot \color{blue}{\frac{104109730557}{25000000000}} \]

      2. *-lowering-*.f64 91.0%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\frac{104109730557}{25000000000}}\right) \]

   7. Simplified 91.0%

      \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

   if -3.8e16 < x < 2

   1. Initial program 99.6%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \color{blue}{\frac{-1000000000}{23533438303}}\right) \]
   6. Step-by-step derivation

   7. Simplified 95.4%

      \[\leadsto \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \color{blue}{-0.0424927283095952} \]

   if 2 < x

   1. Initial program 24.0%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 25.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   6. Applied egg-rr 25.7%

      \[\leadsto \color{blue}{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{\frac{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}{x + -2}}} \]
   7. Step-by-step derivation

      1. div-inv N/A

         \[\leadsto \frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}\right) \cdot \color{blue}{\frac{1}{x + -2}}} \]

      2. associate-/r* N/A

         \[\leadsto \frac{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}}}{\color{blue}{\frac{1}{x + -2}}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}}\right), \color{blue}{\left(\frac{1}{x + -2}\right)}\right) \]

   8. Applied egg-rr 25.7%

      \[\leadsto \color{blue}{\frac{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}}{\frac{1}{x + -2}}} \]

   9. Taylor expanded in x around -inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{104109730557}{25000000000} + -1 \cdot \frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x}\right)}, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{104109730557}{25000000000} + \left(\mathsf{neg}\left(\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x}\right)\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{104109730557}{25000000000} - \frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x}\right), \mathsf{/.f64}\left(\color{blue}{1}, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x}\right)\right), \mathsf{/.f64}\left(\color{blue}{1}, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\left(\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       5. sub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\left(\frac{12723143231740136880149}{125000000000000000000} + \left(\mathsf{neg}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}\right)\right)\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \left(\mathsf{neg}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}\right)\right)\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       7. associate-*r/ N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \left(\mathsf{neg}\left(\frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot 1}{x}\right)\right)\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       8. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \left(\mathsf{neg}\left(\frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}\right)\right)\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       9. distribute-neg-frac N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \left(\frac{\mathsf{neg}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}\right)}{x}\right)\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

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

           \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}\right)\right), x\right)\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       11. metadata-eval 77.9%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\frac{-2157218858562374472887084159837293}{625000000000000000000000000000}, x\right)\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

   11. Simplified 77.9%

       \[\leadsto \frac{\color{blue}{4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}}}{\frac{1}{x + -2}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+16}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)\right) \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;\frac{4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}}{\frac{1}{x + -2}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 89.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+16}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 66000000:\\ \;\;\;\;z \cdot -0.0424927283095952 + x \cdot \left(0.0212463641547976 \cdot \left(z + y \cdot -2\right) + z \cdot 0.28294182010212804\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}}{\frac{1}{x + -2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.8e+16)
   (* x 4.16438922228)
   (if (<= x 66000000.0)
     (+
      (* z -0.0424927283095952)
      (*
       x
       (+ (* 0.0212463641547976 (+ z (* y -2.0))) (* z 0.28294182010212804))))
     (/
      (- 4.16438922228 (/ (+ 101.7851458539211 (/ -3451.550173699799 x)) x))
      (/ 1.0 (+ x -2.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.8e+16) {
		tmp = x * 4.16438922228;
	} else if (x <= 66000000.0) {
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) + (z * 0.28294182010212804)));
	} else {
		tmp = (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x)) / (1.0 / (x + -2.0));
	}
	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) :: tmp
    if (x <= (-3.8d+16)) then
        tmp = x * 4.16438922228d0
    else if (x <= 66000000.0d0) then
        tmp = (z * (-0.0424927283095952d0)) + (x * ((0.0212463641547976d0 * (z + (y * (-2.0d0)))) + (z * 0.28294182010212804d0)))
    else
        tmp = (4.16438922228d0 - ((101.7851458539211d0 + ((-3451.550173699799d0) / x)) / x)) / (1.0d0 / (x + (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.8e+16) {
		tmp = x * 4.16438922228;
	} else if (x <= 66000000.0) {
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) + (z * 0.28294182010212804)));
	} else {
		tmp = (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x)) / (1.0 / (x + -2.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.8e+16:
		tmp = x * 4.16438922228
	elif x <= 66000000.0:
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) + (z * 0.28294182010212804)))
	else:
		tmp = (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x)) / (1.0 / (x + -2.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.8e+16)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 66000000.0)
		tmp = Float64(Float64(z * -0.0424927283095952) + Float64(x * Float64(Float64(0.0212463641547976 * Float64(z + Float64(y * -2.0))) + Float64(z * 0.28294182010212804))));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(Float64(101.7851458539211 + Float64(-3451.550173699799 / x)) / x)) / Float64(1.0 / Float64(x + -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.8e+16)
		tmp = x * 4.16438922228;
	elseif (x <= 66000000.0)
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) + (z * 0.28294182010212804)));
	else
		tmp = (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x)) / (1.0 / (x + -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.8e+16], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 66000000.0], N[(N[(z * -0.0424927283095952), $MachinePrecision] + N[(x * N[(N[(0.0212463641547976 * N[(z + N[(y * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * 0.28294182010212804), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(N[(101.7851458539211 + N[(-3451.550173699799 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / N[(1.0 / N[(x + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.8e16

   1. Initial program 11.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 14.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x \cdot \color{blue}{\frac{104109730557}{25000000000}} \]

      2. *-lowering-*.f64 91.0%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\frac{104109730557}{25000000000}}\right) \]

   7. Simplified 91.0%

      \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

   if -3.8e16 < x < 6.6e7

   1. Initial program 99.6%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{-1000000000}{23533438303} \cdot z\right), \color{blue}{\left(x \cdot \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, z\right), \left(\color{blue}{x} \cdot \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, z\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)}\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, z\right), \mathsf{*.f64}\left(x, \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) + \color{blue}{\left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809} \cdot z\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, z\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right)\right), \color{blue}{\left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809} \cdot z\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, z\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, \left(z + -2 \cdot y\right)\right), \left(\mathsf{neg}\left(\color{blue}{\frac{-156699607947000000000}{553822718361107519809} \cdot z}\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, z\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, \mathsf{+.f64}\left(z, \left(-2 \cdot y\right)\right)\right), \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809} \cdot \color{blue}{z}\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, z\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(-2, y\right)\right)\right), \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809} \cdot z\right)\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, z\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(-2, y\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \frac{-156699607947000000000}{553822718361107519809}\right)\right)\right)\right)\right) \]

      10. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, z\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(-2, y\right)\right)\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right)}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, z\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(-2, y\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right)}\right)\right)\right)\right) \]

      12. metadata-eval 88.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, z\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(-2, y\right)\right)\right), \mathsf{*.f64}\left(z, \frac{156699607947000000000}{553822718361107519809}\right)\right)\right)\right) \]

   7. Simplified 88.8%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z + x \cdot \left(0.0212463641547976 \cdot \left(z + -2 \cdot y\right) + z \cdot 0.28294182010212804\right)} \]

   if 6.6e7 < x

   1. Initial program 22.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 24.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   6. Applied egg-rr 24.3%

      \[\leadsto \color{blue}{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{\frac{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}{x + -2}}} \]
   7. Step-by-step derivation

      1. div-inv N/A

         \[\leadsto \frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}\right) \cdot \color{blue}{\frac{1}{x + -2}}} \]

      2. associate-/r* N/A

         \[\leadsto \frac{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}}}{\color{blue}{\frac{1}{x + -2}}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}}\right), \color{blue}{\left(\frac{1}{x + -2}\right)}\right) \]

   8. Applied egg-rr 24.3%

      \[\leadsto \color{blue}{\frac{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}}{\frac{1}{x + -2}}} \]

   9. Taylor expanded in x around -inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{104109730557}{25000000000} + -1 \cdot \frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x}\right)}, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{104109730557}{25000000000} + \left(\mathsf{neg}\left(\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x}\right)\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{104109730557}{25000000000} - \frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x}\right), \mathsf{/.f64}\left(\color{blue}{1}, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x}\right)\right), \mathsf{/.f64}\left(\color{blue}{1}, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\left(\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       5. sub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\left(\frac{12723143231740136880149}{125000000000000000000} + \left(\mathsf{neg}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}\right)\right)\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \left(\mathsf{neg}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}\right)\right)\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       7. associate-*r/ N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \left(\mathsf{neg}\left(\frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot 1}{x}\right)\right)\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       8. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \left(\mathsf{neg}\left(\frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}\right)\right)\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       9. distribute-neg-frac N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \left(\frac{\mathsf{neg}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}\right)}{x}\right)\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

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

           \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}\right)\right), x\right)\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       11. metadata-eval 79.4%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\frac{-2157218858562374472887084159837293}{625000000000000000000000000000}, x\right)\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

   11. Simplified 79.4%

       \[\leadsto \frac{\color{blue}{4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}}}{\frac{1}{x + -2}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+16}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 66000000:\\ \;\;\;\;z \cdot -0.0424927283095952 + x \cdot \left(0.0212463641547976 \cdot \left(z + y \cdot -2\right) + z \cdot 0.28294182010212804\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}}{\frac{1}{x + -2}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 76.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1000:\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{188.81341671388108}{x}\right)\\ \mathbf{elif}\;x \leq 66000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot z}{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}}{\frac{1}{x + -2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1000.0)
   (* x (- 4.16438922228 (/ 188.81341671388108 x)))
   (if (<= x 66000000.0)
     (/
      (* (- x 2.0) z)
      (+ 47.066876606 (* x (+ 313.399215894 (* x 263.505074721)))))
     (/
      (- 4.16438922228 (/ (+ 101.7851458539211 (/ -3451.550173699799 x)) x))
      (/ 1.0 (+ x -2.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1000.0) {
		tmp = x * (4.16438922228 - (188.81341671388108 / x));
	} else if (x <= 66000000.0) {
		tmp = ((x - 2.0) * z) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	} else {
		tmp = (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x)) / (1.0 / (x + -2.0));
	}
	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) :: tmp
    if (x <= (-1000.0d0)) then
        tmp = x * (4.16438922228d0 - (188.81341671388108d0 / x))
    else if (x <= 66000000.0d0) then
        tmp = ((x - 2.0d0) * z) / (47.066876606d0 + (x * (313.399215894d0 + (x * 263.505074721d0))))
    else
        tmp = (4.16438922228d0 - ((101.7851458539211d0 + ((-3451.550173699799d0) / x)) / x)) / (1.0d0 / (x + (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1000.0) {
		tmp = x * (4.16438922228 - (188.81341671388108 / x));
	} else if (x <= 66000000.0) {
		tmp = ((x - 2.0) * z) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	} else {
		tmp = (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x)) / (1.0 / (x + -2.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1000.0:
		tmp = x * (4.16438922228 - (188.81341671388108 / x))
	elif x <= 66000000.0:
		tmp = ((x - 2.0) * z) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))))
	else:
		tmp = (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x)) / (1.0 / (x + -2.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1000.0)
		tmp = Float64(x * Float64(4.16438922228 - Float64(188.81341671388108 / x)));
	elseif (x <= 66000000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * z) / Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(x * 263.505074721)))));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(Float64(101.7851458539211 + Float64(-3451.550173699799 / x)) / x)) / Float64(1.0 / Float64(x + -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1000.0)
		tmp = x * (4.16438922228 - (188.81341671388108 / x));
	elseif (x <= 66000000.0)
		tmp = ((x - 2.0) * z) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	else
		tmp = (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x)) / (1.0 / (x + -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1000.0], N[(x * N[(4.16438922228 - N[(188.81341671388108 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 66000000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * z), $MachinePrecision] / N[(47.066876606 + N[(x * N[(313.399215894 + N[(x * 263.505074721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(N[(101.7851458539211 + N[(-3451.550173699799 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / N[(1.0 / N[(x + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1e3

   1. Initial program 14.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 17.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{104109730557}{25000000000} \cdot {x}^{4}\right)}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \left({x}^{4}\right)\right), \mathsf{/.f64}\left(\color{blue}{\mathsf{+.f64}\left(x, -2\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \left({x}^{\left(3 + 1\right)}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      3. pow-plus N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \left({x}^{3} \cdot x\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \color{blue}{-2}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \mathsf{*.f64}\left(\left({x}^{3}\right), x\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \color{blue}{-2}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      5. cube-mult N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \mathsf{*.f64}\left(\left(x \cdot \left(x \cdot x\right)\right), x\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \mathsf{*.f64}\left(\left(x \cdot {x}^{2}\right), x\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left({x}^{2}\right)\right), x\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      8. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left(x \cdot x\right)\right), x\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      9. *-lowering-*.f64 8.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right), x\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

   7. Simplified 8.3%

      \[\leadsto \color{blue}{\left(4.16438922228 \cdot \left(\left(x \cdot \left(x \cdot x\right)\right) \cdot x\right)\right)} \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \]

   8. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{23601677089235136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{23601677089235136880149}{125000000000000000000} \cdot \frac{1}{x}\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \color{blue}{\left(\frac{23601677089235136880149}{125000000000000000000} \cdot \frac{1}{x}\right)}\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\frac{23601677089235136880149}{125000000000000000000} \cdot 1}{\color{blue}{x}}\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\frac{23601677089235136880149}{125000000000000000000}}{x}\right)\right)\right) \]

      5. /-lowering-/.f64 88.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\frac{23601677089235136880149}{125000000000000000000}, \color{blue}{x}\right)\right)\right) \]

   10. Simplified 88.2%

       \[\leadsto \color{blue}{x \cdot \left(4.16438922228 - \frac{188.81341671388108}{x}\right)} \]

   if -1e3 < x < 6.6e7

   1. Initial program 99.6%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 2\right), \color{blue}{z}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right), x\right), \frac{263505074721}{1000000000}\right), x\right), \frac{156699607947}{500000000}\right), x\right), \frac{23533438303}{500000000}\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 71.3%

      \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{z}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 2\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{263505074721}{1000000000} \cdot x\right)}, \frac{156699607947}{500000000}\right), x\right), \frac{23533438303}{500000000}\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 2\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(x \cdot \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), x\right), \frac{23533438303}{500000000}\right)\right) \]

      2. *-lowering-*.f64 69.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 2\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), x\right), \frac{23533438303}{500000000}\right)\right) \]

   8. Simplified 69.4%

      \[\leadsto \frac{\left(x - 2\right) \cdot z}{\left(\color{blue}{x \cdot 263.505074721} + 313.399215894\right) \cdot x + 47.066876606} \]

   if 6.6e7 < x

   1. Initial program 22.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 24.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   6. Applied egg-rr 24.3%

      \[\leadsto \color{blue}{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{\frac{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}{x + -2}}} \]
   7. Step-by-step derivation

      1. div-inv N/A

         \[\leadsto \frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}\right) \cdot \color{blue}{\frac{1}{x + -2}}} \]

      2. associate-/r* N/A

         \[\leadsto \frac{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}}}{\color{blue}{\frac{1}{x + -2}}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}}\right), \color{blue}{\left(\frac{1}{x + -2}\right)}\right) \]

   8. Applied egg-rr 24.3%

      \[\leadsto \color{blue}{\frac{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}}{\frac{1}{x + -2}}} \]

   9. Taylor expanded in x around -inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{104109730557}{25000000000} + -1 \cdot \frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x}\right)}, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{104109730557}{25000000000} + \left(\mathsf{neg}\left(\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x}\right)\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{104109730557}{25000000000} - \frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x}\right), \mathsf{/.f64}\left(\color{blue}{1}, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x}\right)\right), \mathsf{/.f64}\left(\color{blue}{1}, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\left(\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       5. sub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\left(\frac{12723143231740136880149}{125000000000000000000} + \left(\mathsf{neg}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}\right)\right)\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \left(\mathsf{neg}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}\right)\right)\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       7. associate-*r/ N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \left(\mathsf{neg}\left(\frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot 1}{x}\right)\right)\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       8. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \left(\mathsf{neg}\left(\frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}\right)\right)\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       9. distribute-neg-frac N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \left(\frac{\mathsf{neg}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}\right)}{x}\right)\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

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

           \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}\right)\right), x\right)\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

       11. metadata-eval 79.4%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\frac{-2157218858562374472887084159837293}{625000000000000000000000000000}, x\right)\right), x\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, -2\right)\right)\right) \]

   11. Simplified 79.4%

       \[\leadsto \frac{\color{blue}{4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}}}{\frac{1}{x + -2}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1000:\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{188.81341671388108}{x}\right)\\ \mathbf{elif}\;x \leq 66000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot z}{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}}{\frac{1}{x + -2}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 76.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{188.81341671388108}{x}\right)\\ \mathbf{elif}\;x \leq 66000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot z}{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5)
   (* x (- 4.16438922228 (/ 188.81341671388108 x)))
   (if (<= x 66000000.0)
     (/
      (* (- x 2.0) z)
      (+ 47.066876606 (* x (+ 313.399215894 (* x 263.505074721)))))
     (* x (- 4.16438922228 (/ 110.1139242984811 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = x * (4.16438922228 - (188.81341671388108 / x));
	} else if (x <= 66000000.0) {
		tmp = ((x - 2.0) * z) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	} else {
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-5.5d0)) then
        tmp = x * (4.16438922228d0 - (188.81341671388108d0 / x))
    else if (x <= 66000000.0d0) then
        tmp = ((x - 2.0d0) * z) / (47.066876606d0 + (x * (313.399215894d0 + (x * 263.505074721d0))))
    else
        tmp = x * (4.16438922228d0 - (110.1139242984811d0 / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = x * (4.16438922228 - (188.81341671388108 / x));
	} else if (x <= 66000000.0) {
		tmp = ((x - 2.0) * z) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	} else {
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.5:
		tmp = x * (4.16438922228 - (188.81341671388108 / x))
	elif x <= 66000000.0:
		tmp = ((x - 2.0) * z) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))))
	else:
		tmp = x * (4.16438922228 - (110.1139242984811 / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5)
		tmp = Float64(x * Float64(4.16438922228 - Float64(188.81341671388108 / x)));
	elseif (x <= 66000000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * z) / Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(x * 263.505074721)))));
	else
		tmp = Float64(x * Float64(4.16438922228 - Float64(110.1139242984811 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.5)
		tmp = x * (4.16438922228 - (188.81341671388108 / x));
	elseif (x <= 66000000.0)
		tmp = ((x - 2.0) * z) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	else
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5], N[(x * N[(4.16438922228 - N[(188.81341671388108 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 66000000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * z), $MachinePrecision] / N[(47.066876606 + N[(x * N[(313.399215894 + N[(x * 263.505074721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5

   1. Initial program 14.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 17.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{104109730557}{25000000000} \cdot {x}^{4}\right)}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \left({x}^{4}\right)\right), \mathsf{/.f64}\left(\color{blue}{\mathsf{+.f64}\left(x, -2\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \left({x}^{\left(3 + 1\right)}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      3. pow-plus N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \left({x}^{3} \cdot x\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \color{blue}{-2}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \mathsf{*.f64}\left(\left({x}^{3}\right), x\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \color{blue}{-2}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      5. cube-mult N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \mathsf{*.f64}\left(\left(x \cdot \left(x \cdot x\right)\right), x\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \mathsf{*.f64}\left(\left(x \cdot {x}^{2}\right), x\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left({x}^{2}\right)\right), x\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      8. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left(x \cdot x\right)\right), x\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      9. *-lowering-*.f64 8.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right), x\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

   7. Simplified 8.3%

      \[\leadsto \color{blue}{\left(4.16438922228 \cdot \left(\left(x \cdot \left(x \cdot x\right)\right) \cdot x\right)\right)} \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \]

   8. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{23601677089235136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{23601677089235136880149}{125000000000000000000} \cdot \frac{1}{x}\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \color{blue}{\left(\frac{23601677089235136880149}{125000000000000000000} \cdot \frac{1}{x}\right)}\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\frac{23601677089235136880149}{125000000000000000000} \cdot 1}{\color{blue}{x}}\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\frac{23601677089235136880149}{125000000000000000000}}{x}\right)\right)\right) \]

      5. /-lowering-/.f64 88.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\frac{23601677089235136880149}{125000000000000000000}, \color{blue}{x}\right)\right)\right) \]

   10. Simplified 88.2%

       \[\leadsto \color{blue}{x \cdot \left(4.16438922228 - \frac{188.81341671388108}{x}\right)} \]

   if -5.5 < x < 6.6e7

   1. Initial program 99.6%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 2\right), \color{blue}{z}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right), x\right), \frac{263505074721}{1000000000}\right), x\right), \frac{156699607947}{500000000}\right), x\right), \frac{23533438303}{500000000}\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 71.3%

      \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{z}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 2\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{263505074721}{1000000000} \cdot x\right)}, \frac{156699607947}{500000000}\right), x\right), \frac{23533438303}{500000000}\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 2\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(x \cdot \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), x\right), \frac{23533438303}{500000000}\right)\right) \]

      2. *-lowering-*.f64 69.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 2\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), x\right), \frac{23533438303}{500000000}\right)\right) \]

   8. Simplified 69.4%

      \[\leadsto \frac{\left(x - 2\right) \cdot z}{\left(\color{blue}{x \cdot 263.505074721} + 313.399215894\right) \cdot x + 47.066876606} \]

   if 6.6e7 < x

   1. Initial program 22.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 24.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \color{blue}{\left(\frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)}\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\frac{13764240537310136880149}{125000000000000000000} \cdot 1}{\color{blue}{x}}\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\frac{13764240537310136880149}{125000000000000000000}}{x}\right)\right)\right) \]

      5. /-lowering-/.f64 79.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\frac{13764240537310136880149}{125000000000000000000}, \color{blue}{x}\right)\right)\right) \]

   7. Simplified 79.2%

      \[\leadsto \color{blue}{x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{188.81341671388108}{x}\right)\\ \mathbf{elif}\;x \leq 66000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot z}{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 76.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35:\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{188.81341671388108}{x}\right)\\ \mathbf{elif}\;x \leq 66000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot z}{47.066876606 + x \cdot 313.399215894}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.35)
   (* x (- 4.16438922228 (/ 188.81341671388108 x)))
   (if (<= x 66000000.0)
     (/ (* (- x 2.0) z) (+ 47.066876606 (* x 313.399215894)))
     (* x (- 4.16438922228 (/ 110.1139242984811 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.35) {
		tmp = x * (4.16438922228 - (188.81341671388108 / x));
	} else if (x <= 66000000.0) {
		tmp = ((x - 2.0) * z) / (47.066876606 + (x * 313.399215894));
	} else {
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.35d0)) then
        tmp = x * (4.16438922228d0 - (188.81341671388108d0 / x))
    else if (x <= 66000000.0d0) then
        tmp = ((x - 2.0d0) * z) / (47.066876606d0 + (x * 313.399215894d0))
    else
        tmp = x * (4.16438922228d0 - (110.1139242984811d0 / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.35) {
		tmp = x * (4.16438922228 - (188.81341671388108 / x));
	} else if (x <= 66000000.0) {
		tmp = ((x - 2.0) * z) / (47.066876606 + (x * 313.399215894));
	} else {
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.35:
		tmp = x * (4.16438922228 - (188.81341671388108 / x))
	elif x <= 66000000.0:
		tmp = ((x - 2.0) * z) / (47.066876606 + (x * 313.399215894))
	else:
		tmp = x * (4.16438922228 - (110.1139242984811 / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.35)
		tmp = Float64(x * Float64(4.16438922228 - Float64(188.81341671388108 / x)));
	elseif (x <= 66000000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * z) / Float64(47.066876606 + Float64(x * 313.399215894)));
	else
		tmp = Float64(x * Float64(4.16438922228 - Float64(110.1139242984811 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.35)
		tmp = x * (4.16438922228 - (188.81341671388108 / x));
	elseif (x <= 66000000.0)
		tmp = ((x - 2.0) * z) / (47.066876606 + (x * 313.399215894));
	else
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.35], N[(x * N[(4.16438922228 - N[(188.81341671388108 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 66000000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * z), $MachinePrecision] / N[(47.066876606 + N[(x * 313.399215894), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3500000000000001

   1. Initial program 14.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 17.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{104109730557}{25000000000} \cdot {x}^{4}\right)}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \left({x}^{4}\right)\right), \mathsf{/.f64}\left(\color{blue}{\mathsf{+.f64}\left(x, -2\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \left({x}^{\left(3 + 1\right)}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      3. pow-plus N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \left({x}^{3} \cdot x\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \color{blue}{-2}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \mathsf{*.f64}\left(\left({x}^{3}\right), x\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \color{blue}{-2}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      5. cube-mult N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \mathsf{*.f64}\left(\left(x \cdot \left(x \cdot x\right)\right), x\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \mathsf{*.f64}\left(\left(x \cdot {x}^{2}\right), x\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left({x}^{2}\right)\right), x\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      8. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left(x \cdot x\right)\right), x\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      9. *-lowering-*.f64 8.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right), x\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

   7. Simplified 8.3%

      \[\leadsto \color{blue}{\left(4.16438922228 \cdot \left(\left(x \cdot \left(x \cdot x\right)\right) \cdot x\right)\right)} \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \]

   8. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{23601677089235136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{23601677089235136880149}{125000000000000000000} \cdot \frac{1}{x}\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \color{blue}{\left(\frac{23601677089235136880149}{125000000000000000000} \cdot \frac{1}{x}\right)}\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\frac{23601677089235136880149}{125000000000000000000} \cdot 1}{\color{blue}{x}}\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\frac{23601677089235136880149}{125000000000000000000}}{x}\right)\right)\right) \]

      5. /-lowering-/.f64 88.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\frac{23601677089235136880149}{125000000000000000000}, \color{blue}{x}\right)\right)\right) \]

   10. Simplified 88.2%

       \[\leadsto \color{blue}{x \cdot \left(4.16438922228 - \frac{188.81341671388108}{x}\right)} \]

   if -1.3500000000000001 < x < 6.6e7

   1. Initial program 99.6%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 2\right), \color{blue}{z}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right), x\right), \frac{263505074721}{1000000000}\right), x\right), \frac{156699607947}{500000000}\right), x\right), \frac{23533438303}{500000000}\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 71.3%

      \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{z}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 2\right), z\right), \mathsf{+.f64}\left(\color{blue}{\left(\frac{156699607947}{500000000} \cdot x\right)}, \frac{23533438303}{500000000}\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 2\right), z\right), \mathsf{+.f64}\left(\left(x \cdot \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)\right) \]

      2. *-lowering-*.f64 69.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 2\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)\right) \]

   8. Simplified 69.2%

      \[\leadsto \frac{\left(x - 2\right) \cdot z}{\color{blue}{x \cdot 313.399215894} + 47.066876606} \]

   if 6.6e7 < x

   1. Initial program 22.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 24.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \color{blue}{\left(\frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)}\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\frac{13764240537310136880149}{125000000000000000000} \cdot 1}{\color{blue}{x}}\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\frac{13764240537310136880149}{125000000000000000000}}{x}\right)\right)\right) \]

      5. /-lowering-/.f64 79.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\frac{13764240537310136880149}{125000000000000000000}, \color{blue}{x}\right)\right)\right) \]

   7. Simplified 79.2%

      \[\leadsto \color{blue}{x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35:\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{188.81341671388108}{x}\right)\\ \mathbf{elif}\;x \leq 66000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot z}{47.066876606 + x \cdot 313.399215894}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 75.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.75 \cdot 10^{-39}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 66000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot z}{47.066876606}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.75e-39)
   (* x 4.16438922228)
   (if (<= x 66000000.0)
     (/ (* (- x 2.0) z) 47.066876606)
     (* x (- 4.16438922228 (/ 110.1139242984811 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.75e-39) {
		tmp = x * 4.16438922228;
	} else if (x <= 66000000.0) {
		tmp = ((x - 2.0) * z) / 47.066876606;
	} else {
		tmp = x * (4.16438922228 - (110.1139242984811 / 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 <= (-2.75d-39)) then
        tmp = x * 4.16438922228d0
    else if (x <= 66000000.0d0) then
        tmp = ((x - 2.0d0) * z) / 47.066876606d0
    else
        tmp = x * (4.16438922228d0 - (110.1139242984811d0 / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.75e-39) {
		tmp = x * 4.16438922228;
	} else if (x <= 66000000.0) {
		tmp = ((x - 2.0) * z) / 47.066876606;
	} else {
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.75e-39:
		tmp = x * 4.16438922228
	elif x <= 66000000.0:
		tmp = ((x - 2.0) * z) / 47.066876606
	else:
		tmp = x * (4.16438922228 - (110.1139242984811 / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.75e-39)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 66000000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * z) / 47.066876606);
	else
		tmp = Float64(x * Float64(4.16438922228 - Float64(110.1139242984811 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.75e-39)
		tmp = x * 4.16438922228;
	elseif (x <= 66000000.0)
		tmp = ((x - 2.0) * z) / 47.066876606;
	else
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.75e-39], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 66000000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * z), $MachinePrecision] / 47.066876606), $MachinePrecision], N[(x * N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.75000000000000009e-39

   1. Initial program 23.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 25.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x \cdot \color{blue}{\frac{104109730557}{25000000000}} \]

      2. *-lowering-*.f64 79.9%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\frac{104109730557}{25000000000}}\right) \]

   7. Simplified 79.9%

      \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

   if -2.75000000000000009e-39 < x < 6.6e7

   1. Initial program 99.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 2\right), \color{blue}{z}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right), x\right), \frac{263505074721}{1000000000}\right), x\right), \frac{156699607947}{500000000}\right), x\right), \frac{23533438303}{500000000}\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 73.5%

      \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{z}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 2\right), z\right), \color{blue}{\frac{23533438303}{500000000}}\right) \]
   7. Step-by-step derivation

   8. Simplified 72.2%

      \[\leadsto \frac{\left(x - 2\right) \cdot z}{\color{blue}{47.066876606}} \]

   if 6.6e7 < x

   1. Initial program 22.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 24.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \color{blue}{\left(\frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)}\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\frac{13764240537310136880149}{125000000000000000000} \cdot 1}{\color{blue}{x}}\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\frac{13764240537310136880149}{125000000000000000000}}{x}\right)\right)\right) \]

      5. /-lowering-/.f64 79.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\frac{13764240537310136880149}{125000000000000000000}, \color{blue}{x}\right)\right)\right) \]

   7. Simplified 79.2%

      \[\leadsto \color{blue}{x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 18: 76.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.17:\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{188.81341671388108}{x}\right)\\ \mathbf{elif}\;x \leq 66000000:\\ \;\;\;\;z \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.17)
   (* x (- 4.16438922228 (/ 188.81341671388108 x)))
   (if (<= x 66000000.0)
     (* z (+ -0.0424927283095952 (* x 0.3041881842569256)))
     (* x (- 4.16438922228 (/ 110.1139242984811 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.17) {
		tmp = x * (4.16438922228 - (188.81341671388108 / x));
	} else if (x <= 66000000.0) {
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256));
	} else {
		tmp = x * (4.16438922228 - (110.1139242984811 / 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 <= (-0.17d0)) then
        tmp = x * (4.16438922228d0 - (188.81341671388108d0 / x))
    else if (x <= 66000000.0d0) then
        tmp = z * ((-0.0424927283095952d0) + (x * 0.3041881842569256d0))
    else
        tmp = x * (4.16438922228d0 - (110.1139242984811d0 / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.17) {
		tmp = x * (4.16438922228 - (188.81341671388108 / x));
	} else if (x <= 66000000.0) {
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256));
	} else {
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.17:
		tmp = x * (4.16438922228 - (188.81341671388108 / x))
	elif x <= 66000000.0:
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256))
	else:
		tmp = x * (4.16438922228 - (110.1139242984811 / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.17)
		tmp = Float64(x * Float64(4.16438922228 - Float64(188.81341671388108 / x)));
	elseif (x <= 66000000.0)
		tmp = Float64(z * Float64(-0.0424927283095952 + Float64(x * 0.3041881842569256)));
	else
		tmp = Float64(x * Float64(4.16438922228 - Float64(110.1139242984811 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.17)
		tmp = x * (4.16438922228 - (188.81341671388108 / x));
	elseif (x <= 66000000.0)
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256));
	else
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.17], N[(x * N[(4.16438922228 - N[(188.81341671388108 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 66000000.0], N[(z * N[(-0.0424927283095952 + N[(x * 0.3041881842569256), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.170000000000000012

   1. Initial program 15.8%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 18.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{104109730557}{25000000000} \cdot {x}^{4}\right)}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \left({x}^{4}\right)\right), \mathsf{/.f64}\left(\color{blue}{\mathsf{+.f64}\left(x, -2\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \left({x}^{\left(3 + 1\right)}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      3. pow-plus N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \left({x}^{3} \cdot x\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \color{blue}{-2}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \mathsf{*.f64}\left(\left({x}^{3}\right), x\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \color{blue}{-2}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      5. cube-mult N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \mathsf{*.f64}\left(\left(x \cdot \left(x \cdot x\right)\right), x\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \mathsf{*.f64}\left(\left(x \cdot {x}^{2}\right), x\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left({x}^{2}\right)\right), x\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      8. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left(x \cdot x\right)\right), x\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      9. *-lowering-*.f64 8.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{104109730557}{25000000000}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right), x\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

   7. Simplified 8.2%

      \[\leadsto \color{blue}{\left(4.16438922228 \cdot \left(\left(x \cdot \left(x \cdot x\right)\right) \cdot x\right)\right)} \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \]

   8. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{23601677089235136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{23601677089235136880149}{125000000000000000000} \cdot \frac{1}{x}\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \color{blue}{\left(\frac{23601677089235136880149}{125000000000000000000} \cdot \frac{1}{x}\right)}\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\frac{23601677089235136880149}{125000000000000000000} \cdot 1}{\color{blue}{x}}\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\frac{23601677089235136880149}{125000000000000000000}}{x}\right)\right)\right) \]

      5. /-lowering-/.f64 86.9%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\frac{23601677089235136880149}{125000000000000000000}, \color{blue}{x}\right)\right)\right) \]

   10. Simplified 86.9%

       \[\leadsto \color{blue}{x \cdot \left(4.16438922228 - \frac{188.81341671388108}{x}\right)} \]

   if -0.170000000000000012 < x < 6.6e7

   1. Initial program 99.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{z}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 70.9%

      \[\leadsto \color{blue}{z} \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \]

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} \cdot x - \frac{1000000000}{23533438303}\right)}\right) \]
   9. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\frac{168466327098500000000}{553822718361107519809} \cdot x + \color{blue}{\left(\mathsf{neg}\left(\frac{1000000000}{23533438303}\right)\right)}\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\frac{168466327098500000000}{553822718361107519809} \cdot x + \frac{-1000000000}{23533438303}\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\frac{-1000000000}{23533438303} + \color{blue}{\frac{168466327098500000000}{553822718361107519809} \cdot x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{-1000000000}{23533438303}, \color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} \cdot x\right)}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{-1000000000}{23533438303}, \left(x \cdot \color{blue}{\frac{168466327098500000000}{553822718361107519809}}\right)\right)\right) \]

      6. *-lowering-*.f64 69.2%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{-1000000000}{23533438303}, \mathsf{*.f64}\left(x, \color{blue}{\frac{168466327098500000000}{553822718361107519809}}\right)\right)\right) \]

   10. Simplified 69.2%

       \[\leadsto z \cdot \color{blue}{\left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)} \]

   if 6.6e7 < x

   1. Initial program 22.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 24.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \color{blue}{\left(\frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)}\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\frac{13764240537310136880149}{125000000000000000000} \cdot 1}{\color{blue}{x}}\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\frac{13764240537310136880149}{125000000000000000000}}{x}\right)\right)\right) \]

      5. /-lowering-/.f64 79.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\frac{13764240537310136880149}{125000000000000000000}, \color{blue}{x}\right)\right)\right) \]

   7. Simplified 79.2%

      \[\leadsto \color{blue}{x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 19: 74.7% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.75 \cdot 10^{-39}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-33}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.75e-39)
   (* x 4.16438922228)
   (if (<= x 3e-33)
     (* z -0.0424927283095952)
     (* x (- 4.16438922228 (/ 110.1139242984811 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.75e-39) {
		tmp = x * 4.16438922228;
	} else if (x <= 3e-33) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = x * (4.16438922228 - (110.1139242984811 / 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 <= (-2.75d-39)) then
        tmp = x * 4.16438922228d0
    else if (x <= 3d-33) then
        tmp = z * (-0.0424927283095952d0)
    else
        tmp = x * (4.16438922228d0 - (110.1139242984811d0 / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.75e-39) {
		tmp = x * 4.16438922228;
	} else if (x <= 3e-33) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.75e-39:
		tmp = x * 4.16438922228
	elif x <= 3e-33:
		tmp = z * -0.0424927283095952
	else:
		tmp = x * (4.16438922228 - (110.1139242984811 / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.75e-39)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 3e-33)
		tmp = Float64(z * -0.0424927283095952);
	else
		tmp = Float64(x * Float64(4.16438922228 - Float64(110.1139242984811 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.75e-39)
		tmp = x * 4.16438922228;
	elseif (x <= 3e-33)
		tmp = z * -0.0424927283095952;
	else
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.75e-39], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 3e-33], N[(z * -0.0424927283095952), $MachinePrecision], N[(x * N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.75000000000000009e-39

   1. Initial program 23.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 25.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x \cdot \color{blue}{\frac{104109730557}{25000000000}} \]

      2. *-lowering-*.f64 79.9%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\frac{104109730557}{25000000000}}\right) \]

   7. Simplified 79.9%

      \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

   if -2.75000000000000009e-39 < x < 3.0000000000000002e-33

   1. Initial program 99.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 75.0%

         \[\leadsto \mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, \color{blue}{z}\right) \]

   7. Simplified 75.0%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]

   if 3.0000000000000002e-33 < x

   1. Initial program 30.3%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 32.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \color{blue}{\left(\frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)}\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\frac{13764240537310136880149}{125000000000000000000} \cdot 1}{\color{blue}{x}}\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\frac{13764240537310136880149}{125000000000000000000}}{x}\right)\right)\right) \]

      5. /-lowering-/.f64 71.8%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\frac{13764240537310136880149}{125000000000000000000}, \color{blue}{x}\right)\right)\right) \]

   7. Simplified 71.8%

      \[\leadsto \color{blue}{x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.75 \cdot 10^{-39}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-33}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 74.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.75 \cdot 10^{-39}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-33}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228 + -110.1139242984811\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.75e-39)
   (* x 4.16438922228)
   (if (<= x 3e-33)
     (* z -0.0424927283095952)
     (+ (* x 4.16438922228) -110.1139242984811))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.75e-39) {
		tmp = x * 4.16438922228;
	} else if (x <= 3e-33) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = (x * 4.16438922228) + -110.1139242984811;
	}
	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 <= (-2.75d-39)) then
        tmp = x * 4.16438922228d0
    else if (x <= 3d-33) then
        tmp = z * (-0.0424927283095952d0)
    else
        tmp = (x * 4.16438922228d0) + (-110.1139242984811d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.75e-39) {
		tmp = x * 4.16438922228;
	} else if (x <= 3e-33) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = (x * 4.16438922228) + -110.1139242984811;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.75e-39:
		tmp = x * 4.16438922228
	elif x <= 3e-33:
		tmp = z * -0.0424927283095952
	else:
		tmp = (x * 4.16438922228) + -110.1139242984811
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.75e-39)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 3e-33)
		tmp = Float64(z * -0.0424927283095952);
	else
		tmp = Float64(Float64(x * 4.16438922228) + -110.1139242984811);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.75e-39)
		tmp = x * 4.16438922228;
	elseif (x <= 3e-33)
		tmp = z * -0.0424927283095952;
	else
		tmp = (x * 4.16438922228) + -110.1139242984811;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.75e-39], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 3e-33], N[(z * -0.0424927283095952), $MachinePrecision], N[(N[(x * 4.16438922228), $MachinePrecision] + -110.1139242984811), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.75000000000000009e-39

   1. Initial program 23.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 25.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x \cdot \color{blue}{\frac{104109730557}{25000000000}} \]

      2. *-lowering-*.f64 79.9%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\frac{104109730557}{25000000000}}\right) \]

   7. Simplified 79.9%

      \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

   if -2.75000000000000009e-39 < x < 3.0000000000000002e-33

   1. Initial program 99.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 75.0%

         \[\leadsto \mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, \color{blue}{z}\right) \]

   7. Simplified 75.0%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]

   if 3.0000000000000002e-33 < x

   1. Initial program 30.3%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 32.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{x \cdot \left(x - 2\right)}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} + \frac{\left(z + {x}^{2} \cdot \left(\frac{4297481763}{31250000} + x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right)\right)\right) \cdot \left(x - 2\right)}{y \cdot \left(\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)\right)}\right)} \]

   7. Simplified 30.4%

      \[\leadsto \color{blue}{y \cdot \left(\frac{x + -2}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)} \cdot \left(x + \frac{z + x \cdot \left(x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)}{y}\right)\right)} \]

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot \left(\frac{104109730557}{25000000000} \cdot \frac{1}{y} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x \cdot y}\right)\right)}\right) \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{104109730557}{25000000000} \cdot \frac{1}{y} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x \cdot y}\right)}\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \left(\frac{104109730557}{25000000000} \cdot \frac{1}{y} + \color{blue}{\left(\mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x \cdot y}\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{104109730557}{25000000000} \cdot \frac{1}{y}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x \cdot y}\right)\right)}\right)\right)\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{\frac{104109730557}{25000000000} \cdot 1}{y}\right), \left(\mathsf{neg}\left(\color{blue}{\frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x \cdot y}}\right)\right)\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{\frac{104109730557}{25000000000}}{y}\right), \left(\mathsf{neg}\left(\color{blue}{\frac{13764240537310136880149}{125000000000000000000}} \cdot \frac{1}{x \cdot y}\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\frac{104109730557}{25000000000}, y\right), \left(\mathsf{neg}\left(\color{blue}{\frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x \cdot y}}\right)\right)\right)\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\frac{104109730557}{25000000000}, y\right), \left(\mathsf{neg}\left(\frac{\frac{13764240537310136880149}{125000000000000000000} \cdot 1}{x \cdot y}\right)\right)\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\frac{104109730557}{25000000000}, y\right), \left(\mathsf{neg}\left(\frac{\frac{13764240537310136880149}{125000000000000000000}}{x \cdot y}\right)\right)\right)\right)\right) \]

      9. distribute-neg-frac N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\frac{104109730557}{25000000000}, y\right), \left(\frac{\mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000}\right)}{\color{blue}{x \cdot y}}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\frac{104109730557}{25000000000}, y\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000}\right)\right), \color{blue}{\left(x \cdot y\right)}\right)\right)\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\frac{104109730557}{25000000000}, y\right), \mathsf{/.f64}\left(\frac{-13764240537310136880149}{125000000000000000000}, \left(\color{blue}{x} \cdot y\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 45.2%

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\frac{104109730557}{25000000000}, y\right), \mathsf{/.f64}\left(\frac{-13764240537310136880149}{125000000000000000000}, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right)\right)\right) \]

   10. Simplified 45.2%

       \[\leadsto y \cdot \color{blue}{\left(x \cdot \left(\frac{4.16438922228}{y} + \frac{-110.1139242984811}{x \cdot y}\right)\right)} \]

   11. Taylor expanded in x around 0

       \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x - \frac{13764240537310136880149}{125000000000000000000}} \]
   12. Step-by-step derivation

       1. sub-neg N/A

          \[\leadsto \frac{104109730557}{25000000000} \cdot x + \color{blue}{\left(\mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000}\right)\right)} \]

       2. metadata-eval N/A

          \[\leadsto \frac{104109730557}{25000000000} \cdot x + \frac{-13764240537310136880149}{125000000000000000000} \]

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

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{104109730557}{25000000000} \cdot x\right), \color{blue}{\frac{-13764240537310136880149}{125000000000000000000}}\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \frac{104109730557}{25000000000}\right), \frac{-13764240537310136880149}{125000000000000000000}\right) \]

       5. *-lowering-*.f64 71.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{-13764240537310136880149}{125000000000000000000}\right) \]

   13. Simplified 71.7%

       \[\leadsto \color{blue}{x \cdot 4.16438922228 + -110.1139242984811} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.75 \cdot 10^{-39}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-33}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228 + -110.1139242984811\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 75.5% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.75 \cdot 10^{-39}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.75e-39)
   (* x 4.16438922228)
   (if (<= x 2.0) (* z -0.0424927283095952) (* x 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.75e-39) {
		tmp = x * 4.16438922228;
	} else if (x <= 2.0) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = x * 4.16438922228;
	}
	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 <= (-2.75d-39)) then
        tmp = x * 4.16438922228d0
    else if (x <= 2.0d0) then
        tmp = z * (-0.0424927283095952d0)
    else
        tmp = x * 4.16438922228d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.75e-39) {
		tmp = x * 4.16438922228;
	} else if (x <= 2.0) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.75e-39:
		tmp = x * 4.16438922228
	elif x <= 2.0:
		tmp = z * -0.0424927283095952
	else:
		tmp = x * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.75e-39)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 2.0)
		tmp = Float64(z * -0.0424927283095952);
	else
		tmp = Float64(x * 4.16438922228);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.75e-39)
		tmp = x * 4.16438922228;
	elseif (x <= 2.0)
		tmp = z * -0.0424927283095952;
	else
		tmp = x * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.75e-39], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 2.0], N[(z * -0.0424927283095952), $MachinePrecision], N[(x * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.75000000000000009e-39 or 2 < x

   1. Initial program 23.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 25.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x \cdot \color{blue}{\frac{104109730557}{25000000000}} \]

      2. *-lowering-*.f64 78.7%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\frac{104109730557}{25000000000}}\right) \]

   7. Simplified 78.7%

      \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

   if -2.75000000000000009e-39 < x < 2

   1. Initial program 99.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      2. associate-/l* N/A

         \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 72.4%

         \[\leadsto \mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, \color{blue}{z}\right) \]

   7. Simplified 72.4%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.75 \cdot 10^{-39}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 35.2% accurate, 12.3× speedup

Math

\[\begin{array}{l} \\ z \cdot -0.0424927283095952 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* z -0.0424927283095952))

C

double code(double x, double y, double z) {
	return z * -0.0424927283095952;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = z * (-0.0424927283095952d0)
end function

Java

public static double code(double x, double y, double z) {
	return z * -0.0424927283095952;
}

Python

def code(x, y, z):
	return z * -0.0424927283095952

Julia

function code(x, y, z)
	return Float64(z * -0.0424927283095952)
end

MATLAB

function tmp = code(x, y, z)
	tmp = z * -0.0424927283095952;
end

Wolfram

code[x_, y_, z_] := N[(z * -0.0424927283095952), $MachinePrecision]

Derivation

1. Initial program 63.1%

   \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
2. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

   2. associate-/l* N/A

      \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

      \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

3. Simplified 64.0%

   \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
4. Add Preprocessing

5. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z} \]
6. Step-by-step derivation

   1. *-lowering-*.f64 39.3%

      \[\leadsto \mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, \color{blue}{z}\right) \]

7. Simplified 39.3%

   \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]

8. Final simplification 39.3%

   \[\leadsto z \cdot -0.0424927283095952 \]
9. Add Preprocessing

Alternative 23: 3.3% accurate, 37.0× speedup

Math

\[\begin{array}{l} \\ -110.1139242984811 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 -110.1139242984811)

C

double code(double x, double y, double z) {
	return -110.1139242984811;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = -110.1139242984811d0
end function

Java

public static double code(double x, double y, double z) {
	return -110.1139242984811;
}

Python

def code(x, y, z):
	return -110.1139242984811

Julia

function code(x, y, z)
	return -110.1139242984811
end

MATLAB

function tmp = code(x, y, z)
	tmp = -110.1139242984811;
end

Wolfram

code[x_, y_, z_] := -110.1139242984811

Derivation

1. Initial program 63.1%

   \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
2. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \frac{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

   2. associate-/l* N/A

      \[\leadsto \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \color{blue}{\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

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

      \[\leadsto \mathsf{*.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

3. Simplified 64.0%

   \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
4. Add Preprocessing

5. Taylor expanded in y around inf

   \[\leadsto \color{blue}{y \cdot \left(\frac{x \cdot \left(x - 2\right)}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} + \frac{\left(z + {x}^{2} \cdot \left(\frac{4297481763}{31250000} + x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right)\right)\right) \cdot \left(x - 2\right)}{y \cdot \left(\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)\right)}\right)} \]

7. Simplified 55.6%

   \[\leadsto \color{blue}{y \cdot \left(\frac{x + -2}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)} \cdot \left(x + \frac{z + x \cdot \left(x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)}{y}\right)\right)} \]

8. Taylor expanded in x around inf

   \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot \left(\frac{104109730557}{25000000000} \cdot \frac{1}{y} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x \cdot y}\right)\right)}\right) \]
9. Step-by-step derivation

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

      \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{104109730557}{25000000000} \cdot \frac{1}{y} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x \cdot y}\right)}\right)\right) \]

   2. sub-neg N/A

      \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \left(\frac{104109730557}{25000000000} \cdot \frac{1}{y} + \color{blue}{\left(\mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x \cdot y}\right)\right)}\right)\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{104109730557}{25000000000} \cdot \frac{1}{y}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x \cdot y}\right)\right)}\right)\right)\right) \]

   4. associate-*r/ N/A

      \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{\frac{104109730557}{25000000000} \cdot 1}{y}\right), \left(\mathsf{neg}\left(\color{blue}{\frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x \cdot y}}\right)\right)\right)\right)\right) \]

   5. metadata-eval N/A

      \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{\frac{104109730557}{25000000000}}{y}\right), \left(\mathsf{neg}\left(\color{blue}{\frac{13764240537310136880149}{125000000000000000000}} \cdot \frac{1}{x \cdot y}\right)\right)\right)\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\frac{104109730557}{25000000000}, y\right), \left(\mathsf{neg}\left(\color{blue}{\frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x \cdot y}}\right)\right)\right)\right)\right) \]

   7. associate-*r/ N/A

      \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\frac{104109730557}{25000000000}, y\right), \left(\mathsf{neg}\left(\frac{\frac{13764240537310136880149}{125000000000000000000} \cdot 1}{x \cdot y}\right)\right)\right)\right)\right) \]

   8. metadata-eval N/A

      \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\frac{104109730557}{25000000000}, y\right), \left(\mathsf{neg}\left(\frac{\frac{13764240537310136880149}{125000000000000000000}}{x \cdot y}\right)\right)\right)\right)\right) \]

   9. distribute-neg-frac N/A

      \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\frac{104109730557}{25000000000}, y\right), \left(\frac{\mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000}\right)}{\color{blue}{x \cdot y}}\right)\right)\right)\right) \]

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

       \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\frac{104109730557}{25000000000}, y\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000}\right)\right), \color{blue}{\left(x \cdot y\right)}\right)\right)\right)\right) \]

   11. metadata-eval N/A

       \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\frac{104109730557}{25000000000}, y\right), \mathsf{/.f64}\left(\frac{-13764240537310136880149}{125000000000000000000}, \left(\color{blue}{x} \cdot y\right)\right)\right)\right)\right) \]

   12. *-lowering-*.f64 27.4%

       \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\frac{104109730557}{25000000000}, y\right), \mathsf{/.f64}\left(\frac{-13764240537310136880149}{125000000000000000000}, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right)\right)\right) \]

10. Simplified 27.4%

    \[\leadsto y \cdot \color{blue}{\left(x \cdot \left(\frac{4.16438922228}{y} + \frac{-110.1139242984811}{x \cdot y}\right)\right)} \]

11. Taylor expanded in x around 0

    \[\leadsto \color{blue}{\frac{-13764240537310136880149}{125000000000000000000}} \]
12. Step-by-step derivation

13. Simplified 3.5%

    \[\leadsto \color{blue}{-110.1139242984811} \]
14. Add Preprocessing

Developer Target 1: 98.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\frac{y}{x \cdot x} + 4.16438922228 \cdot x\right) - 110.1139242984811\\ \mathbf{if}\;x < -3.326128725870005 \cdot 10^{+62}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x < 9.429991714554673 \cdot 10^{+55}:\\ \;\;\;\;\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(263.505074721 \cdot x + \left(43.3400022514 \cdot \left(x \cdot x\right) + x \cdot \left(x \cdot x\right)\right)\right) + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811)))
   (if (< x -3.326128725870005e+62)
     t_0
     (if (< x 9.429991714554673e+55)
       (*
        (/ (- x 2.0) 1.0)
        (/
         (+
          (*
           (+
            (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
            y)
           x)
          z)
         (+
          (*
           (+
            (+ (* 263.505074721 x) (+ (* 43.3400022514 (* x x)) (* x (* x x))))
            313.399215894)
           x)
          47.066876606)))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811;
	double tmp;
	if (x < -3.326128725870005e+62) {
		tmp = t_0;
	} else if (x < 9.429991714554673e+55) {
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * x)))) + 313.399215894) * x) + 47.066876606));
	} 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 = ((y / (x * x)) + (4.16438922228d0 * x)) - 110.1139242984811d0
    if (x < (-3.326128725870005d+62)) then
        tmp = t_0
    else if (x < 9.429991714554673d+55) then
        tmp = ((x - 2.0d0) / 1.0d0) * (((((((((x * 4.16438922228d0) + 78.6994924154d0) * x) + 137.519416416d0) * x) + y) * x) + z) / (((((263.505074721d0 * x) + ((43.3400022514d0 * (x * x)) + (x * (x * x)))) + 313.399215894d0) * x) + 47.066876606d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811;
	double tmp;
	if (x < -3.326128725870005e+62) {
		tmp = t_0;
	} else if (x < 9.429991714554673e+55) {
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * x)))) + 313.399215894) * x) + 47.066876606));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811
	tmp = 0
	if x < -3.326128725870005e+62:
		tmp = t_0
	elif x < 9.429991714554673e+55:
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * x)))) + 313.399215894) * x) + 47.066876606))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y / Float64(x * x)) + Float64(4.16438922228 * x)) - 110.1139242984811)
	tmp = 0.0
	if (x < -3.326128725870005e+62)
		tmp = t_0;
	elseif (x < 9.429991714554673e+55)
		tmp = Float64(Float64(Float64(x - 2.0) / 1.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / Float64(Float64(Float64(Float64(Float64(263.505074721 * x) + Float64(Float64(43.3400022514 * Float64(x * x)) + Float64(x * Float64(x * x)))) + 313.399215894) * x) + 47.066876606)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811;
	tmp = 0.0;
	if (x < -3.326128725870005e+62)
		tmp = t_0;
	elseif (x < 9.429991714554673e+55)
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * x)))) + 313.399215894) * x) + 47.066876606));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y / N[(x * x), $MachinePrecision]), $MachinePrecision] + N[(4.16438922228 * x), $MachinePrecision]), $MachinePrecision] - 110.1139242984811), $MachinePrecision]}, If[Less[x, -3.326128725870005e+62], t$95$0, If[Less[x, 9.429991714554673e+55], N[(N[(N[(x - 2.0), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision] / N[(N[(N[(N[(N[(263.505074721 * x), $MachinePrecision] + N[(N[(43.3400022514 * N[(x * x), $MachinePrecision]), $MachinePrecision] + N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024138 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -332612872587000500000000000000000000000000000000000000000000000) (- (+ (/ y (* x x)) (* 104109730557/25000000000 x)) 1101139242984811/10000000000000) (if (< x 94299917145546730000000000000000000000000000000000000000) (* (/ (- x 2) 1) (/ (+ (* (+ (* (+ (* (+ (* x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z) (+ (* (+ (+ (* 263505074721/1000000000 x) (+ (* 216700011257/5000000000 (* x x)) (* x (* x x)))) 156699607947/500000000) x) 23533438303/500000000))) (- (+ (/ y (* x x)) (* 104109730557/25000000000 x)) 1101139242984811/10000000000000))))

  (/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))