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

Percentage Accurate: 58.4% → 98.4%

Time: 19.3s

Alternatives: 22

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: 98.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606\\ t_1 := x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right) + z\\ \mathbf{if}\;\frac{\left(x - 2\right) \cdot t\_1}{t\_0} \leq 10^{+300}:\\ \;\;\;\;\frac{\frac{t\_1}{t\_0} \cdot \left(x \cdot \left(x \cdot x\right) + -8\right)}{\left(x \cdot x + 4\right) - x \cdot -2}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          (*
           x
           (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
          47.066876606))
        (t_1
         (+
          (*
           x
           (+
            y
            (*
             x
             (+ 137.519416416 (* x (+ (* x 4.16438922228) 78.6994924154))))))
          z)))
   (if (<= (/ (* (- x 2.0) t_1) t_0) 1e+300)
     (/ (* (/ t_1 t_0) (+ (* x (* x x)) -8.0)) (- (+ (* x x) 4.0) (* x -2.0)))
     (*
      (+ x -2.0)
      (+
       4.16438922228
       (/
        (-
         (/ (+ 3451.550173699799 (/ (- y 124074.40615218398) x)) x)
         101.7851458539211)
        x))))))

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 = (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))))) + z;
	double tmp;
	if ((((x - 2.0) * t_1) / t_0) <= 1e+300) {
		tmp = ((t_1 / t_0) * ((x * (x * x)) + -8.0)) / (((x * x) + 4.0) - (x * -2.0));
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / 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) :: 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 = (x * (y + (x * (137.519416416d0 + (x * ((x * 4.16438922228d0) + 78.6994924154d0)))))) + z
    if ((((x - 2.0d0) * t_1) / t_0) <= 1d+300) then
        tmp = ((t_1 / t_0) * ((x * (x * x)) + (-8.0d0))) / (((x * x) + 4.0d0) - (x * (-2.0d0)))
    else
        tmp = (x + (-2.0d0)) * (4.16438922228d0 + ((((3451.550173699799d0 + ((y - 124074.40615218398d0) / x)) / x) - 101.7851458539211d0) / x))
    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 = (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))))) + z;
	double tmp;
	if ((((x - 2.0) * t_1) / t_0) <= 1e+300) {
		tmp = ((t_1 / t_0) * ((x * (x * x)) + -8.0)) / (((x * x) + 4.0) - (x * -2.0));
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606
	t_1 = (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))))) + z
	tmp = 0
	if (((x - 2.0) * t_1) / t_0) <= 1e+300:
		tmp = ((t_1 / t_0) * ((x * (x * x)) + -8.0)) / (((x * x) + 4.0) - (x * -2.0))
	else:
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x))
	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(Float64(x * Float64(y + Float64(x * Float64(137.519416416 + Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)))))) + z)
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * t_1) / t_0) <= 1e+300)
		tmp = Float64(Float64(Float64(t_1 / t_0) * Float64(Float64(x * Float64(x * x)) + -8.0)) / Float64(Float64(Float64(x * x) + 4.0) - Float64(x * -2.0)));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(Float64(y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)));
	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 = (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))))) + z;
	tmp = 0.0;
	if ((((x - 2.0) * t_1) / t_0) <= 1e+300)
		tmp = ((t_1 / t_0) * ((x * (x * x)) + -8.0)) / (((x * x) + 4.0) - (x * -2.0));
	else
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	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[(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] + z), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * t$95$1), $MachinePrecision] / t$95$0), $MachinePrecision], 1e+300], N[(N[(N[(t$95$1 / t$95$0), $MachinePrecision] * N[(N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision] + -8.0), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(x * x), $MachinePrecision] + 4.0), $MachinePrecision] - N[(x * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * 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]), $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))) < 1.0000000000000001e300

   1. Initial program 97.1%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 97.7%

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

   6. Applied egg-rr 97.7%

      \[\leadsto \color{blue}{\frac{\frac{z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \cdot \left(x \cdot \left(x \cdot x\right) + -8\right)}{\left(x \cdot x + 4\right) - x \cdot -2}} \]

   if 1.0000000000000001e300 < (/.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 0.2%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 5.0%

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

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

   7. Simplified 99.1%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 10^{+300}:\\ \;\;\;\;\frac{\frac{x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \cdot \left(x \cdot \left(x \cdot x\right) + -8\right)}{\left(x \cdot x + 4\right) - x \cdot -2}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606\\ t_1 := x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right) + z\\ \mathbf{if}\;\frac{\left(x - 2\right) \cdot t\_1}{t\_0} \leq 10^{+300}:\\ \;\;\;\;\frac{t\_1}{t\_0} \cdot \left(x + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          (*
           x
           (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
          47.066876606))
        (t_1
         (+
          (*
           x
           (+
            y
            (*
             x
             (+ 137.519416416 (* x (+ (* x 4.16438922228) 78.6994924154))))))
          z)))
   (if (<= (/ (* (- x 2.0) t_1) t_0) 1e+300)
     (* (/ t_1 t_0) (+ x -2.0))
     (*
      (+ x -2.0)
      (+
       4.16438922228
       (/
        (-
         (/ (+ 3451.550173699799 (/ (- y 124074.40615218398) x)) x)
         101.7851458539211)
        x))))))

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 = (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))))) + z;
	double tmp;
	if ((((x - 2.0) * t_1) / t_0) <= 1e+300) {
		tmp = (t_1 / t_0) * (x + -2.0);
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / 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) :: 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 = (x * (y + (x * (137.519416416d0 + (x * ((x * 4.16438922228d0) + 78.6994924154d0)))))) + z
    if ((((x - 2.0d0) * t_1) / t_0) <= 1d+300) then
        tmp = (t_1 / t_0) * (x + (-2.0d0))
    else
        tmp = (x + (-2.0d0)) * (4.16438922228d0 + ((((3451.550173699799d0 + ((y - 124074.40615218398d0) / x)) / x) - 101.7851458539211d0) / x))
    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 = (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))))) + z;
	double tmp;
	if ((((x - 2.0) * t_1) / t_0) <= 1e+300) {
		tmp = (t_1 / t_0) * (x + -2.0);
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606
	t_1 = (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))))) + z
	tmp = 0
	if (((x - 2.0) * t_1) / t_0) <= 1e+300:
		tmp = (t_1 / t_0) * (x + -2.0)
	else:
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x))
	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(Float64(x * Float64(y + Float64(x * Float64(137.519416416 + Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)))))) + z)
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * t_1) / t_0) <= 1e+300)
		tmp = Float64(Float64(t_1 / t_0) * Float64(x + -2.0));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(Float64(y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)));
	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 = (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))))) + z;
	tmp = 0.0;
	if ((((x - 2.0) * t_1) / t_0) <= 1e+300)
		tmp = (t_1 / t_0) * (x + -2.0);
	else
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	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[(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] + z), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * t$95$1), $MachinePrecision] / t$95$0), $MachinePrecision], 1e+300], N[(N[(t$95$1 / t$95$0), $MachinePrecision] * N[(x + -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * 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]), $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))) < 1.0000000000000001e300

   1. Initial program 97.1%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 97.7%

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

   if 1.0000000000000001e300 < (/.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 0.2%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 5.0%

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

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

   7. Simplified 99.1%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 10^{+300}:\\ \;\;\;\;\frac{x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \cdot \left(x + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{if}\;x \leq -8 \cdot 10^{+22}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+23}:\\ \;\;\;\;\frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (+ x -2.0)
          (+
           4.16438922228
           (/
            (-
             (/ (+ 3451.550173699799 (/ (- y 124074.40615218398) x)) x)
             101.7851458539211)
            x)))))
   (if (<= x -8e+22)
     t_0
     (if (<= x 9.5e+23)
       (*
        (/
         (+ 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 = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	double tmp;
	if (x <= -8e+22) {
		tmp = t_0;
	} else if (x <= 9.5e+23) {
		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 = (x + (-2.0d0)) * (4.16438922228d0 + ((((3451.550173699799d0 + ((y - 124074.40615218398d0) / x)) / x) - 101.7851458539211d0) / x))
    if (x <= (-8d+22)) then
        tmp = t_0
    else if (x <= 9.5d+23) 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 = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	double tmp;
	if (x <= -8e+22) {
		tmp = t_0;
	} else if (x <= 9.5e+23) {
		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 = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x))
	tmp = 0
	if x <= -8e+22:
		tmp = t_0
	elif x <= 9.5e+23:
		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(x + -2.0) * Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(Float64(y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)))
	tmp = 0.0
	if (x <= -8e+22)
		tmp = t_0;
	elseif (x <= 9.5e+23)
		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 = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	tmp = 0.0;
	if (x <= -8e+22)
		tmp = t_0;
	elseif (x <= 9.5e+23)
		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[(x + -2.0), $MachinePrecision] * 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]), $MachinePrecision]}, If[LessEqual[x, -8e+22], t$95$0, If[LessEqual[x, 9.5e+23], 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 < -8e22 or 9.50000000000000038e23 < x

   1. Initial program 8.3%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 12.6%

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

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

   7. Simplified 98.3%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right)} \]

   if -8e22 < x < 9.50000000000000038e23

   1. Initial program 98.3%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 98.9%

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

   6. Applied egg-rr 98.7%

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

   7. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 96.8%

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

   9. Simplified 96.8%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+22}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+23}:\\ \;\;\;\;\frac{x + -2}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)}{x \cdot x}\\ \mathbf{if}\;x \leq -1.04 \cdot 10^{+77}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq -37:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\frac{z \cdot -2 + x \cdot \left(z + y \cdot -2\right)}{47.066876606 + x \cdot 313.399215894}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+99}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (/
          (+
           y
           (* x (+ 137.519416416 (* x (+ (* x 4.16438922228) 78.6994924154)))))
          (* x x))))
   (if (<= x -1.04e+77)
     (* x 4.16438922228)
     (if (<= x -37.0)
       t_0
       (if (<= x 2.0)
         (/
          (+ (* z -2.0) (* x (+ z (* y -2.0))))
          (+ 47.066876606 (* x 313.399215894)))
         (if (<= x 2e+99) t_0 (* x 4.16438922228)))))))

C

double code(double x, double y, double z) {
	double t_0 = (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))) / (x * x);
	double tmp;
	if (x <= -1.04e+77) {
		tmp = x * 4.16438922228;
	} else if (x <= -37.0) {
		tmp = t_0;
	} else if (x <= 2.0) {
		tmp = ((z * -2.0) + (x * (z + (y * -2.0)))) / (47.066876606 + (x * 313.399215894));
	} else if (x <= 2e+99) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = (y + (x * (137.519416416d0 + (x * ((x * 4.16438922228d0) + 78.6994924154d0))))) / (x * x)
    if (x <= (-1.04d+77)) then
        tmp = x * 4.16438922228d0
    else if (x <= (-37.0d0)) then
        tmp = t_0
    else if (x <= 2.0d0) then
        tmp = ((z * (-2.0d0)) + (x * (z + (y * (-2.0d0))))) / (47.066876606d0 + (x * 313.399215894d0))
    else if (x <= 2d+99) then
        tmp = t_0
    else
        tmp = x * 4.16438922228d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))) / (x * x);
	double tmp;
	if (x <= -1.04e+77) {
		tmp = x * 4.16438922228;
	} else if (x <= -37.0) {
		tmp = t_0;
	} else if (x <= 2.0) {
		tmp = ((z * -2.0) + (x * (z + (y * -2.0)))) / (47.066876606 + (x * 313.399215894));
	} else if (x <= 2e+99) {
		tmp = t_0;
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))) / (x * x)
	tmp = 0
	if x <= -1.04e+77:
		tmp = x * 4.16438922228
	elif x <= -37.0:
		tmp = t_0
	elif x <= 2.0:
		tmp = ((z * -2.0) + (x * (z + (y * -2.0)))) / (47.066876606 + (x * 313.399215894))
	elif x <= 2e+99:
		tmp = t_0
	else:
		tmp = x * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y + Float64(x * Float64(137.519416416 + Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154))))) / Float64(x * x))
	tmp = 0.0
	if (x <= -1.04e+77)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= -37.0)
		tmp = t_0;
	elseif (x <= 2.0)
		tmp = Float64(Float64(Float64(z * -2.0) + Float64(x * Float64(z + Float64(y * -2.0)))) / Float64(47.066876606 + Float64(x * 313.399215894)));
	elseif (x <= 2e+99)
		tmp = t_0;
	else
		tmp = Float64(x * 4.16438922228);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))) / (x * x);
	tmp = 0.0;
	if (x <= -1.04e+77)
		tmp = x * 4.16438922228;
	elseif (x <= -37.0)
		tmp = t_0;
	elseif (x <= 2.0)
		tmp = ((z * -2.0) + (x * (z + (y * -2.0)))) / (47.066876606 + (x * 313.399215894));
	elseif (x <= 2e+99)
		tmp = t_0;
	else
		tmp = x * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y + N[(x * N[(137.519416416 + N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.04e+77], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, -37.0], t$95$0, If[LessEqual[x, 2.0], N[(N[(N[(z * -2.0), $MachinePrecision] + N[(x * N[(z + N[(y * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(47.066876606 + N[(x * 313.399215894), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2e+99], t$95$0, N[(x * 4.16438922228), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.04e77 or 1.9999999999999999e99 < x

   1. Initial program 0.0%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 99.1%

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

   7. Simplified 99.1%

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

   if -1.04e77 < x < -37 or 2 < x < 1.9999999999999999e99

   1. Initial program 58.2%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 75.2%

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

   6. Applied egg-rr 75.2%

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

   7. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \color{blue}{\left(\frac{1}{{x}^{3}}\right)}\right) \]
   8. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \mathsf{/.f64}\left(1, \color{blue}{\left({x}^{3}\right)}\right)\right) \]

      2. cube-mult N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \mathsf{/.f64}\left(1, \left(x \cdot \color{blue}{\left(x \cdot x\right)}\right)\right)\right) \]

      3. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \mathsf{/.f64}\left(1, \left(x \cdot {x}^{\color{blue}{2}}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \mathsf{/.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left({x}^{2}\right)}\right)\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \mathsf{/.f64}\left(1, \mathsf{*.f64}\left(x, \left(x \cdot \color{blue}{x}\right)\right)\right)\right) \]

      6. *-lowering-*.f64 66.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \mathsf{/.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \color{blue}{x}\right)\right)\right)\right) \]

   9. Simplified 66.3%

      \[\leadsto \left(z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)\right) \cdot \color{blue}{\frac{1}{x \cdot \left(x \cdot x\right)}} \]

   10. Taylor expanded in z around 0

       \[\leadsto \color{blue}{\frac{y + x \cdot \left(\frac{4297481763}{31250000} + x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right)\right)}{{x}^{2}}} \]
   11. Step-by-step derivation

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

          \[\leadsto \mathsf{/.f64}\left(\left(y + x \cdot \left(\frac{4297481763}{31250000} + x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right)\right)\right), \color{blue}{\left({x}^{2}\right)}\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(y, \left(x \cdot \left(\frac{4297481763}{31250000} + x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right)\right)\right)\right), \left({\color{blue}{x}}^{2}\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \left(\frac{4297481763}{31250000} + x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right)\right)\right)\right), \left({x}^{2}\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{4297481763}{31250000}, \left(x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right)\right)\right)\right)\right), \left({x}^{2}\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{4297481763}{31250000}, \mathsf{*.f64}\left(x, \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right)\right)\right)\right)\right), \left({x}^{2}\right)\right) \]

       6. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{4297481763}{31250000}, \mathsf{*.f64}\left(x, \left(\frac{104109730557}{25000000000} \cdot x + \frac{393497462077}{5000000000}\right)\right)\right)\right)\right), \left({x}^{2}\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{4297481763}{31250000}, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{104109730557}{25000000000} \cdot x\right), \frac{393497462077}{5000000000}\right)\right)\right)\right)\right), \left({x}^{2}\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{4297481763}{31250000}, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(x \cdot \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right)\right)\right)\right), \left({x}^{2}\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{4297481763}{31250000}, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right)\right)\right)\right), \left({x}^{2}\right)\right) \]

       10. unpow2 N/A

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

       11. *-lowering-*.f64 73.2%

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

   12. Simplified 73.2%

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

   if -37 < 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. Add Preprocessing

   3. Taylor expanded in x around 0

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

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

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. *-lowering-*.f64 92.1%

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

   5. Simplified 92.1%

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

   6. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 91.5%

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

   8. Simplified 91.5%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.04 \cdot 10^{+77}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq -37:\\ \;\;\;\;\frac{y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)}{x \cdot x}\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\frac{z \cdot -2 + x \cdot \left(z + y \cdot -2\right)}{47.066876606 + x \cdot 313.399215894}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+99}:\\ \;\;\;\;\frac{y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)}{x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 92.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)}{x \cdot x}\\ \mathbf{if}\;x \leq -1.04 \cdot 10^{+77}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq -0.68:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.155:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + x \cdot \left(y \cdot 0.0212463641547976 + z \cdot -0.14147091005106402\right)\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+98}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (/
          (+
           y
           (* x (+ 137.519416416 (* x (+ (* x 4.16438922228) 78.6994924154)))))
          (* x x))))
   (if (<= x -1.04e+77)
     (* x 4.16438922228)
     (if (<= x -0.68)
       t_0
       (if (<= x 0.155)
         (*
          (+ x -2.0)
          (+
           (* z 0.0212463641547976)
           (* x (+ (* y 0.0212463641547976) (* z -0.14147091005106402)))))
         (if (<= x 3e+98) t_0 (* x 4.16438922228)))))))

C

double code(double x, double y, double z) {
	double t_0 = (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))) / (x * x);
	double tmp;
	if (x <= -1.04e+77) {
		tmp = x * 4.16438922228;
	} else if (x <= -0.68) {
		tmp = t_0;
	} else if (x <= 0.155) {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) + (z * -0.14147091005106402))));
	} else if (x <= 3e+98) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = (y + (x * (137.519416416d0 + (x * ((x * 4.16438922228d0) + 78.6994924154d0))))) / (x * x)
    if (x <= (-1.04d+77)) then
        tmp = x * 4.16438922228d0
    else if (x <= (-0.68d0)) then
        tmp = t_0
    else if (x <= 0.155d0) then
        tmp = (x + (-2.0d0)) * ((z * 0.0212463641547976d0) + (x * ((y * 0.0212463641547976d0) + (z * (-0.14147091005106402d0)))))
    else if (x <= 3d+98) then
        tmp = t_0
    else
        tmp = x * 4.16438922228d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))) / (x * x);
	double tmp;
	if (x <= -1.04e+77) {
		tmp = x * 4.16438922228;
	} else if (x <= -0.68) {
		tmp = t_0;
	} else if (x <= 0.155) {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) + (z * -0.14147091005106402))));
	} else if (x <= 3e+98) {
		tmp = t_0;
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))) / (x * x)
	tmp = 0
	if x <= -1.04e+77:
		tmp = x * 4.16438922228
	elif x <= -0.68:
		tmp = t_0
	elif x <= 0.155:
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) + (z * -0.14147091005106402))))
	elif x <= 3e+98:
		tmp = t_0
	else:
		tmp = x * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y + Float64(x * Float64(137.519416416 + Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154))))) / Float64(x * x))
	tmp = 0.0
	if (x <= -1.04e+77)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= -0.68)
		tmp = t_0;
	elseif (x <= 0.155)
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(z * 0.0212463641547976) + Float64(x * Float64(Float64(y * 0.0212463641547976) + Float64(z * -0.14147091005106402)))));
	elseif (x <= 3e+98)
		tmp = t_0;
	else
		tmp = Float64(x * 4.16438922228);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))) / (x * x);
	tmp = 0.0;
	if (x <= -1.04e+77)
		tmp = x * 4.16438922228;
	elseif (x <= -0.68)
		tmp = t_0;
	elseif (x <= 0.155)
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) + (z * -0.14147091005106402))));
	elseif (x <= 3e+98)
		tmp = t_0;
	else
		tmp = x * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y + N[(x * N[(137.519416416 + N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.04e+77], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, -0.68], t$95$0, If[LessEqual[x, 0.155], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(z * 0.0212463641547976), $MachinePrecision] + N[(x * N[(N[(y * 0.0212463641547976), $MachinePrecision] + N[(z * -0.14147091005106402), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3e+98], t$95$0, N[(x * 4.16438922228), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.04e77 or 3.0000000000000001e98 < x

   1. Initial program 0.0%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 99.1%

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

   7. Simplified 99.1%

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

   if -1.04e77 < x < -0.680000000000000049 or 0.154999999999999999 < x < 3.0000000000000001e98

   1. Initial program 60.5%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 76.6%

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

   6. Applied egg-rr 76.6%

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

   7. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \color{blue}{\left(\frac{1}{{x}^{3}}\right)}\right) \]
   8. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \mathsf{/.f64}\left(1, \color{blue}{\left({x}^{3}\right)}\right)\right) \]

      2. cube-mult N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \mathsf{/.f64}\left(1, \left(x \cdot \color{blue}{\left(x \cdot x\right)}\right)\right)\right) \]

      3. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \mathsf{/.f64}\left(1, \left(x \cdot {x}^{\color{blue}{2}}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \mathsf{/.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left({x}^{2}\right)}\right)\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \mathsf{/.f64}\left(1, \mathsf{*.f64}\left(x, \left(x \cdot \color{blue}{x}\right)\right)\right)\right) \]

      6. *-lowering-*.f64 62.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right)\right), \mathsf{/.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \color{blue}{x}\right)\right)\right)\right) \]

   9. Simplified 62.6%

      \[\leadsto \left(z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)\right) \cdot \color{blue}{\frac{1}{x \cdot \left(x \cdot x\right)}} \]

   10. Taylor expanded in z around 0

       \[\leadsto \color{blue}{\frac{y + x \cdot \left(\frac{4297481763}{31250000} + x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right)\right)}{{x}^{2}}} \]
   11. Step-by-step derivation

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

          \[\leadsto \mathsf{/.f64}\left(\left(y + x \cdot \left(\frac{4297481763}{31250000} + x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right)\right)\right), \color{blue}{\left({x}^{2}\right)}\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(y, \left(x \cdot \left(\frac{4297481763}{31250000} + x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right)\right)\right)\right), \left({\color{blue}{x}}^{2}\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \left(\frac{4297481763}{31250000} + x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right)\right)\right)\right), \left({x}^{2}\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{4297481763}{31250000}, \left(x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right)\right)\right)\right)\right), \left({x}^{2}\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{4297481763}{31250000}, \mathsf{*.f64}\left(x, \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right)\right)\right)\right)\right), \left({x}^{2}\right)\right) \]

       6. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{4297481763}{31250000}, \mathsf{*.f64}\left(x, \left(\frac{104109730557}{25000000000} \cdot x + \frac{393497462077}{5000000000}\right)\right)\right)\right)\right), \left({x}^{2}\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{4297481763}{31250000}, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{104109730557}{25000000000} \cdot x\right), \frac{393497462077}{5000000000}\right)\right)\right)\right)\right), \left({x}^{2}\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{4297481763}{31250000}, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(x \cdot \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right)\right)\right)\right), \left({x}^{2}\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{4297481763}{31250000}, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right)\right)\right)\right), \left({x}^{2}\right)\right) \]

       10. unpow2 N/A

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

       11. *-lowering-*.f64 69.1%

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

   12. Simplified 69.1%

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

   if -0.680000000000000049 < x < 0.154999999999999999

   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. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \color{blue}{\left(\frac{500000000}{23533438303} \cdot z + x \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right) \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\left(\frac{500000000}{23533438303} \cdot z\right), \color{blue}{\left(x \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\left(z \cdot \frac{500000000}{23533438303}\right), \left(\color{blue}{x} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \left(\color{blue}{x} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)}\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \left(\frac{500000000}{23533438303} \cdot y + \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{500000000}{23533438303} \cdot y\right), \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \left(\mathsf{neg}\left(\color{blue}{\frac{78349803973500000000}{553822718361107519809} \cdot z}\right)\right)\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \left(\mathsf{neg}\left(z \cdot \frac{78349803973500000000}{553822718361107519809}\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809}\right)\right)}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809}\right)\right)}\right)\right)\right)\right)\right) \]

      11. metadata-eval 92.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(z, \frac{-78349803973500000000}{553822718361107519809}\right)\right)\right)\right)\right) \]

   7. Simplified 92.0%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(z \cdot 0.0212463641547976 + x \cdot \left(0.0212463641547976 \cdot y + z \cdot -0.14147091005106402\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.04 \cdot 10^{+77}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq -0.68:\\ \;\;\;\;\frac{y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)}{x \cdot x}\\ \mathbf{elif}\;x \leq 0.155:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + x \cdot \left(y \cdot 0.0212463641547976 + z \cdot -0.14147091005106402\right)\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+98}:\\ \;\;\;\;\frac{y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)}{x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 95.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{if}\;x \leq -37:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 76:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right) + z\right)}{47.066876606 + x \cdot 313.399215894}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (+ x -2.0)
          (+
           4.16438922228
           (/
            (-
             (/ (+ 3451.550173699799 (/ (- y 124074.40615218398) x)) x)
             101.7851458539211)
            x)))))
   (if (<= x -37.0)
     t_0
     (if (<= x 76.0)
       (/
        (*
         (- x 2.0)
         (+
          (*
           x
           (+
            y
            (*
             x
             (+ 137.519416416 (* x (+ (* x 4.16438922228) 78.6994924154))))))
          z))
        (+ 47.066876606 (* x 313.399215894)))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	double tmp;
	if (x <= -37.0) {
		tmp = t_0;
	} else if (x <= 76.0) {
		tmp = ((x - 2.0) * ((x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))))) + z)) / (47.066876606 + (x * 313.399215894));
	} 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 + (-2.0d0)) * (4.16438922228d0 + ((((3451.550173699799d0 + ((y - 124074.40615218398d0) / x)) / x) - 101.7851458539211d0) / x))
    if (x <= (-37.0d0)) then
        tmp = t_0
    else if (x <= 76.0d0) then
        tmp = ((x - 2.0d0) * ((x * (y + (x * (137.519416416d0 + (x * ((x * 4.16438922228d0) + 78.6994924154d0)))))) + z)) / (47.066876606d0 + (x * 313.399215894d0))
    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 + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	double tmp;
	if (x <= -37.0) {
		tmp = t_0;
	} else if (x <= 76.0) {
		tmp = ((x - 2.0) * ((x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))))) + z)) / (47.066876606 + (x * 313.399215894));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x))
	tmp = 0
	if x <= -37.0:
		tmp = t_0
	elif x <= 76.0:
		tmp = ((x - 2.0) * ((x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))))) + z)) / (47.066876606 + (x * 313.399215894))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(Float64(y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)))
	tmp = 0.0
	if (x <= -37.0)
		tmp = t_0;
	elseif (x <= 76.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(x * Float64(y + Float64(x * Float64(137.519416416 + Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)))))) + z)) / Float64(47.066876606 + Float64(x * 313.399215894)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	tmp = 0.0;
	if (x <= -37.0)
		tmp = t_0;
	elseif (x <= 76.0)
		tmp = ((x - 2.0) * ((x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))))) + z)) / (47.066876606 + (x * 313.399215894));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + -2.0), $MachinePrecision] * 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]), $MachinePrecision]}, If[LessEqual[x, -37.0], t$95$0, If[LessEqual[x, 76.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(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] + z), $MachinePrecision]), $MachinePrecision] / N[(47.066876606 + N[(x * 313.399215894), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -37 or 76 < x

   1. Initial program 15.6%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 20.2%

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

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

   7. Simplified 92.8%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right)} \]

   if -37 < x < 76

   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. Step-by-step derivation

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-in N/A

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

      4. flip-+ N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. *-commutative N/A

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

      9. div-sub N/A

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

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

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right), x\right), \frac{4297481763}{31250000}\right), x\right), y\right), x\right), z\right)\right), \mathsf{+.f64}\left(\color{blue}{\left(\frac{156699607947}{500000000} \cdot x\right)}, \frac{23533438303}{500000000}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right), x\right), \frac{4297481763}{31250000}\right), x\right), y\right), x\right), z\right)\right), \mathsf{+.f64}\left(\left(x \cdot \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)\right) \]

      2. *-lowering-*.f64 97.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right), x\right), \frac{4297481763}{31250000}\right), x\right), y\right), x\right), z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)\right) \]

   7. Simplified 97.5%

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\color{blue}{x \cdot 313.399215894} + 47.066876606} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -37:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{elif}\;x \leq 76:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right) + z\right)}{47.066876606 + x \cdot 313.399215894}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{if}\;x \leq -37:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 48:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{47.066876606 + x \cdot 313.399215894}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (+ x -2.0)
          (+
           4.16438922228
           (/
            (-
             (/ (+ 3451.550173699799 (/ (- y 124074.40615218398) x)) x)
             101.7851458539211)
            x)))))
   (if (<= x -37.0)
     t_0
     (if (<= x 48.0)
       (/
        (* (- x 2.0) (+ z (* x (+ y (* x 137.519416416)))))
        (+ 47.066876606 (* x 313.399215894)))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	double tmp;
	if (x <= -37.0) {
		tmp = t_0;
	} else if (x <= 48.0) {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * 313.399215894));
	} 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 + (-2.0d0)) * (4.16438922228d0 + ((((3451.550173699799d0 + ((y - 124074.40615218398d0) / x)) / x) - 101.7851458539211d0) / x))
    if (x <= (-37.0d0)) then
        tmp = t_0
    else if (x <= 48.0d0) then
        tmp = ((x - 2.0d0) * (z + (x * (y + (x * 137.519416416d0))))) / (47.066876606d0 + (x * 313.399215894d0))
    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 + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	double tmp;
	if (x <= -37.0) {
		tmp = t_0;
	} else if (x <= 48.0) {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * 313.399215894));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x))
	tmp = 0
	if x <= -37.0:
		tmp = t_0
	elif x <= 48.0:
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * 313.399215894))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(Float64(y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)))
	tmp = 0.0
	if (x <= -37.0)
		tmp = t_0;
	elseif (x <= 48.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(z + Float64(x * Float64(y + Float64(x * 137.519416416))))) / Float64(47.066876606 + Float64(x * 313.399215894)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	tmp = 0.0;
	if (x <= -37.0)
		tmp = t_0;
	elseif (x <= 48.0)
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * 313.399215894));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + -2.0), $MachinePrecision] * 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]), $MachinePrecision]}, If[LessEqual[x, -37.0], t$95$0, If[LessEqual[x, 48.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(z + N[(x * N[(y + N[(x * 137.519416416), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(47.066876606 + N[(x * 313.399215894), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -37 or 48 < x

   1. Initial program 15.6%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 20.2%

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

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

   7. Simplified 92.8%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right)} \]

   if -37 < x < 48

   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 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 97.4%

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

   8. Simplified 97.4%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -37:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{elif}\;x \leq 48:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{47.066876606 + x \cdot 313.399215894}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 95.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{if}\;x \leq -0.175:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\left(x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right) + z\right) \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (+ x -2.0)
          (+
           4.16438922228
           (/
            (-
             (/ (+ 3451.550173699799 (/ (- y 124074.40615218398) x)) x)
             101.7851458539211)
            x)))))
   (if (<= x -0.175)
     t_0
     (if (<= x 2.0)
       (*
        (+
         (*
          x
          (+
           y
           (*
            x
            (+ 137.519416416 (* x (+ (* x 4.16438922228) 78.6994924154))))))
         z)
        -0.0424927283095952)
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	double tmp;
	if (x <= -0.175) {
		tmp = t_0;
	} else if (x <= 2.0) {
		tmp = ((x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))))) + z) * -0.0424927283095952;
	} 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 + (-2.0d0)) * (4.16438922228d0 + ((((3451.550173699799d0 + ((y - 124074.40615218398d0) / x)) / x) - 101.7851458539211d0) / x))
    if (x <= (-0.175d0)) then
        tmp = t_0
    else if (x <= 2.0d0) then
        tmp = ((x * (y + (x * (137.519416416d0 + (x * ((x * 4.16438922228d0) + 78.6994924154d0)))))) + z) * (-0.0424927283095952d0)
    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 + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	double tmp;
	if (x <= -0.175) {
		tmp = t_0;
	} else if (x <= 2.0) {
		tmp = ((x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))))) + z) * -0.0424927283095952;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x))
	tmp = 0
	if x <= -0.175:
		tmp = t_0
	elif x <= 2.0:
		tmp = ((x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))))) + z) * -0.0424927283095952
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(Float64(y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)))
	tmp = 0.0
	if (x <= -0.175)
		tmp = t_0;
	elseif (x <= 2.0)
		tmp = Float64(Float64(Float64(x * Float64(y + Float64(x * Float64(137.519416416 + Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)))))) + z) * -0.0424927283095952);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	tmp = 0.0;
	if (x <= -0.175)
		tmp = t_0;
	elseif (x <= 2.0)
		tmp = ((x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))))) + z) * -0.0424927283095952;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + -2.0), $MachinePrecision] * 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]), $MachinePrecision]}, If[LessEqual[x, -0.175], t$95$0, If[LessEqual[x, 2.0], N[(N[(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] + z), $MachinePrecision] * -0.0424927283095952), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.17499999999999999 or 2 < x

   1. Initial program 16.3%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 20.8%

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

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

   7. Simplified 92.0%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right)} \]

   if -0.17499999999999999 < 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. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.7%

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

   6. Applied egg-rr 99.4%

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

   7. Taylor expanded in x around 0

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

   9. Simplified 96.4%

      \[\leadsto \left(z + x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)\right) \cdot \color{blue}{-0.0424927283095952} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.175:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\left(x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right) + z\right) \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 93.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{if}\;x \leq -37:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 7:\\ \;\;\;\;\frac{z \cdot -2 + x \cdot \left(z + y \cdot -2\right)}{47.066876606 + x \cdot 313.399215894}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (+ x -2.0)
          (+
           4.16438922228
           (/
            (-
             (/ (+ 3451.550173699799 (/ (- y 124074.40615218398) x)) x)
             101.7851458539211)
            x)))))
   (if (<= x -37.0)
     t_0
     (if (<= x 7.0)
       (/
        (+ (* z -2.0) (* x (+ z (* y -2.0))))
        (+ 47.066876606 (* x 313.399215894)))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	double tmp;
	if (x <= -37.0) {
		tmp = t_0;
	} else if (x <= 7.0) {
		tmp = ((z * -2.0) + (x * (z + (y * -2.0)))) / (47.066876606 + (x * 313.399215894));
	} 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 + (-2.0d0)) * (4.16438922228d0 + ((((3451.550173699799d0 + ((y - 124074.40615218398d0) / x)) / x) - 101.7851458539211d0) / x))
    if (x <= (-37.0d0)) then
        tmp = t_0
    else if (x <= 7.0d0) then
        tmp = ((z * (-2.0d0)) + (x * (z + (y * (-2.0d0))))) / (47.066876606d0 + (x * 313.399215894d0))
    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 + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	double tmp;
	if (x <= -37.0) {
		tmp = t_0;
	} else if (x <= 7.0) {
		tmp = ((z * -2.0) + (x * (z + (y * -2.0)))) / (47.066876606 + (x * 313.399215894));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x))
	tmp = 0
	if x <= -37.0:
		tmp = t_0
	elif x <= 7.0:
		tmp = ((z * -2.0) + (x * (z + (y * -2.0)))) / (47.066876606 + (x * 313.399215894))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(Float64(y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)))
	tmp = 0.0
	if (x <= -37.0)
		tmp = t_0;
	elseif (x <= 7.0)
		tmp = Float64(Float64(Float64(z * -2.0) + Float64(x * Float64(z + Float64(y * -2.0)))) / Float64(47.066876606 + Float64(x * 313.399215894)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	tmp = 0.0;
	if (x <= -37.0)
		tmp = t_0;
	elseif (x <= 7.0)
		tmp = ((z * -2.0) + (x * (z + (y * -2.0)))) / (47.066876606 + (x * 313.399215894));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + -2.0), $MachinePrecision] * 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]), $MachinePrecision]}, If[LessEqual[x, -37.0], t$95$0, If[LessEqual[x, 7.0], N[(N[(N[(z * -2.0), $MachinePrecision] + N[(x * N[(z + N[(y * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(47.066876606 + N[(x * 313.399215894), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -37 or 7 < x

   1. Initial program 15.6%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 20.2%

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

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

   7. Simplified 92.8%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right)} \]

   if -37 < x < 7

   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

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

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

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. *-lowering-*.f64 92.1%

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

   5. Simplified 92.1%

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

   6. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 91.5%

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

   8. Simplified 91.5%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -37:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{elif}\;x \leq 7:\\ \;\;\;\;\frac{z \cdot -2 + x \cdot \left(z + y \cdot -2\right)}{47.066876606 + x \cdot 313.399215894}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.225:\\ \;\;\;\;\left(x \cdot \left(1 - \frac{2}{x}\right)\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)\\ \mathbf{elif}\;x \leq 90000000000:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + x \cdot \left(y \cdot 0.0212463641547976 + z \cdot -0.14147091005106402\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.225)
   (*
    (* x (- 1.0 (/ 2.0 x)))
    (- 4.16438922228 (/ (+ 101.7851458539211 (/ -3451.550173699799 x)) x)))
   (if (<= x 90000000000.0)
     (*
      (+ x -2.0)
      (+
       (* z 0.0212463641547976)
       (* x (+ (* y 0.0212463641547976) (* z -0.14147091005106402)))))
     (* x 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.225) {
		tmp = (x * (1.0 - (2.0 / x))) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x));
	} else if (x <= 90000000000.0) {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) + (z * -0.14147091005106402))));
	} 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 <= (-0.225d0)) then
        tmp = (x * (1.0d0 - (2.0d0 / x))) * (4.16438922228d0 - ((101.7851458539211d0 + ((-3451.550173699799d0) / x)) / x))
    else if (x <= 90000000000.0d0) then
        tmp = (x + (-2.0d0)) * ((z * 0.0212463641547976d0) + (x * ((y * 0.0212463641547976d0) + (z * (-0.14147091005106402d0)))))
    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 <= -0.225) {
		tmp = (x * (1.0 - (2.0 / x))) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x));
	} else if (x <= 90000000000.0) {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) + (z * -0.14147091005106402))));
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.225:
		tmp = (x * (1.0 - (2.0 / x))) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x))
	elif x <= 90000000000.0:
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) + (z * -0.14147091005106402))))
	else:
		tmp = x * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.225)
		tmp = Float64(Float64(x * Float64(1.0 - Float64(2.0 / x))) * Float64(4.16438922228 - Float64(Float64(101.7851458539211 + Float64(-3451.550173699799 / x)) / x)));
	elseif (x <= 90000000000.0)
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(z * 0.0212463641547976) + Float64(x * Float64(Float64(y * 0.0212463641547976) + Float64(z * -0.14147091005106402)))));
	else
		tmp = Float64(x * 4.16438922228);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.225)
		tmp = (x * (1.0 - (2.0 / x))) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x));
	elseif (x <= 90000000000.0)
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) + (z * -0.14147091005106402))));
	else
		tmp = x * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.225], N[(N[(x * N[(1.0 - N[(2.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(4.16438922228 - N[(N[(101.7851458539211 + N[(-3451.550173699799 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 90000000000.0], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(z * 0.0212463641547976), $MachinePrecision] + N[(x * N[(N[(y * 0.0212463641547976), $MachinePrecision] + N[(z * -0.14147091005106402), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.225000000000000006

   1. Initial program 21.2%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 21.2%

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

   5. Taylor expanded in x around inf

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. distribute-neg-in N/A

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

      4. +-commutative N/A

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

      5. metadata-eval N/A

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

      6. sub-neg N/A

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. distribute-neg-in N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. sub-neg N/A

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

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

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

      15. associate-*r/ N/A

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

      16. metadata-eval N/A

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

      17. /-lowering-/.f64 21.2%

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

   7. Simplified 21.2%

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

   8. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

      5. sub-neg N/A

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

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

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

      7. associate-*r/ N/A

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

      8. metadata-eval N/A

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

      9. distribute-neg-frac N/A

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

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

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

      11. metadata-eval 83.8%

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

   10. Simplified 83.8%

       \[\leadsto \left(x \cdot \left(1 - \frac{2}{x}\right)\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)} \]

   if -0.225000000000000006 < x < 9e10

   1. Initial program 99.0%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.0%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \color{blue}{\left(\frac{500000000}{23533438303} \cdot z + x \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right) \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\left(\frac{500000000}{23533438303} \cdot z\right), \color{blue}{\left(x \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\left(z \cdot \frac{500000000}{23533438303}\right), \left(\color{blue}{x} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \left(\color{blue}{x} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)}\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \left(\frac{500000000}{23533438303} \cdot y + \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{500000000}{23533438303} \cdot y\right), \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \left(\mathsf{neg}\left(\color{blue}{\frac{78349803973500000000}{553822718361107519809} \cdot z}\right)\right)\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \left(\mathsf{neg}\left(z \cdot \frac{78349803973500000000}{553822718361107519809}\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809}\right)\right)}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809}\right)\right)}\right)\right)\right)\right)\right) \]

      11. metadata-eval 88.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(z, \frac{-78349803973500000000}{553822718361107519809}\right)\right)\right)\right)\right) \]

   7. Simplified 88.9%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(z \cdot 0.0212463641547976 + x \cdot \left(0.0212463641547976 \cdot y + z \cdot -0.14147091005106402\right)\right)} \]

   if 9e10 < x

   1. Initial program 7.2%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 16.7%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 87.9%

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

   7. Simplified 87.9%

      \[\leadsto \color{blue}{x \cdot 4.16438922228} \]
3. Recombined 3 regimes into one program.

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.225:\\ \;\;\;\;\left(x \cdot \left(1 - \frac{2}{x}\right)\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)\\ \mathbf{elif}\;x \leq 90000000000:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + x \cdot \left(y \cdot 0.0212463641547976 + z \cdot -0.14147091005106402\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 88.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.18:\\ \;\;\;\;\left(x \cdot \left(1 - \frac{2}{x}\right)\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+23}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + 0.0212463641547976 \cdot \left(x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot \left(x + -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.18)
   (*
    (* x (- 1.0 (/ 2.0 x)))
    (- 4.16438922228 (/ (+ 101.7851458539211 (/ -3451.550173699799 x)) x)))
   (if (<= x 7.5e+23)
     (* (+ x -2.0) (+ (* z 0.0212463641547976) (* 0.0212463641547976 (* x y))))
     (* 4.16438922228 (+ x -2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.18) {
		tmp = (x * (1.0 - (2.0 / x))) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x));
	} else if (x <= 7.5e+23) {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (0.0212463641547976 * (x * y)));
	} else {
		tmp = 4.16438922228 * (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 * (1.0d0 - (2.0d0 / x))) * (4.16438922228d0 - ((101.7851458539211d0 + ((-3451.550173699799d0) / x)) / x))
    else if (x <= 7.5d+23) then
        tmp = (x + (-2.0d0)) * ((z * 0.0212463641547976d0) + (0.0212463641547976d0 * (x * y)))
    else
        tmp = 4.16438922228d0 * (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 * (1.0 - (2.0 / x))) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x));
	} else if (x <= 7.5e+23) {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (0.0212463641547976 * (x * y)));
	} else {
		tmp = 4.16438922228 * (x + -2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.18:
		tmp = (x * (1.0 - (2.0 / x))) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x))
	elif x <= 7.5e+23:
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (0.0212463641547976 * (x * y)))
	else:
		tmp = 4.16438922228 * (x + -2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.18)
		tmp = Float64(Float64(x * Float64(1.0 - Float64(2.0 / x))) * Float64(4.16438922228 - Float64(Float64(101.7851458539211 + Float64(-3451.550173699799 / x)) / x)));
	elseif (x <= 7.5e+23)
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(z * 0.0212463641547976) + Float64(0.0212463641547976 * Float64(x * y))));
	else
		tmp = Float64(4.16438922228 * 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 * (1.0 - (2.0 / x))) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x));
	elseif (x <= 7.5e+23)
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (0.0212463641547976 * (x * y)));
	else
		tmp = 4.16438922228 * (x + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.18], N[(N[(x * N[(1.0 - N[(2.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(4.16438922228 - N[(N[(101.7851458539211 + N[(-3451.550173699799 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e+23], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(z * 0.0212463641547976), $MachinePrecision] + N[(0.0212463641547976 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.16438922228 * N[(x + -2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.17999999999999999

   1. Initial program 21.2%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 21.2%

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

   5. Taylor expanded in x around inf

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. distribute-neg-in N/A

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

      4. +-commutative N/A

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

      5. metadata-eval N/A

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

      6. sub-neg N/A

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. distribute-neg-in N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. sub-neg N/A

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

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

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

      15. associate-*r/ N/A

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

      16. metadata-eval N/A

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

      17. /-lowering-/.f64 21.2%

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

   7. Simplified 21.2%

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

   8. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

      5. sub-neg N/A

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

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

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

      7. associate-*r/ N/A

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

      8. metadata-eval N/A

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

      9. distribute-neg-frac N/A

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

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

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

      11. metadata-eval 83.8%

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

   10. Simplified 83.8%

       \[\leadsto \left(x \cdot \left(1 - \frac{2}{x}\right)\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)} \]

   if -0.17999999999999999 < x < 7.49999999999999987e23

   1. Initial program 98.3%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.0%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \color{blue}{\left(\frac{500000000}{23533438303} \cdot z + x \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right) \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\left(\frac{500000000}{23533438303} \cdot z\right), \color{blue}{\left(x \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\left(z \cdot \frac{500000000}{23533438303}\right), \left(\color{blue}{x} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \left(\color{blue}{x} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)}\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \left(\frac{500000000}{23533438303} \cdot y + \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{500000000}{23533438303} \cdot y\right), \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \left(\mathsf{neg}\left(\color{blue}{\frac{78349803973500000000}{553822718361107519809} \cdot z}\right)\right)\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \left(\mathsf{neg}\left(z \cdot \frac{78349803973500000000}{553822718361107519809}\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809}\right)\right)}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809}\right)\right)}\right)\right)\right)\right)\right) \]

      11. metadata-eval 87.7%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(z, \frac{-78349803973500000000}{553822718361107519809}\right)\right)\right)\right)\right) \]

   7. Simplified 87.7%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(z \cdot 0.0212463641547976 + x \cdot \left(0.0212463641547976 \cdot y + z \cdot -0.14147091005106402\right)\right)} \]

   8. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \color{blue}{\left(\frac{500000000}{23533438303} \cdot \left(x \cdot y\right)\right)}\right)\right) \]
   9. Step-by-step derivation

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

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

      2. *-lowering-*.f64 87.6%

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

   10. Simplified 87.6%

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

   if 7.49999999999999987e23 < x

   1. Initial program 5.6%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 13.9%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \color{blue}{\frac{104109730557}{25000000000}}\right) \]
   6. Step-by-step derivation

   7. Simplified 90.9%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.18:\\ \;\;\;\;\left(x \cdot \left(1 - \frac{2}{x}\right)\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+23}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + 0.0212463641547976 \cdot \left(x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot \left(x + -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 88.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.175:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{\frac{3655.1204654076414}{x} + -110.1139242984811}{x}\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+23}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + 0.0212463641547976 \cdot \left(x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot \left(x + -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.175)
   (*
    x
    (+ 4.16438922228 (/ (+ (/ 3655.1204654076414 x) -110.1139242984811) x)))
   (if (<= x 7.5e+23)
     (* (+ x -2.0) (+ (* z 0.0212463641547976) (* 0.0212463641547976 (* x y))))
     (* 4.16438922228 (+ x -2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.175) {
		tmp = x * (4.16438922228 + (((3655.1204654076414 / x) + -110.1139242984811) / x));
	} else if (x <= 7.5e+23) {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (0.0212463641547976 * (x * y)));
	} else {
		tmp = 4.16438922228 * (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 <= (-0.175d0)) then
        tmp = x * (4.16438922228d0 + (((3655.1204654076414d0 / x) + (-110.1139242984811d0)) / x))
    else if (x <= 7.5d+23) then
        tmp = (x + (-2.0d0)) * ((z * 0.0212463641547976d0) + (0.0212463641547976d0 * (x * y)))
    else
        tmp = 4.16438922228d0 * (x + (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.175) {
		tmp = x * (4.16438922228 + (((3655.1204654076414 / x) + -110.1139242984811) / x));
	} else if (x <= 7.5e+23) {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (0.0212463641547976 * (x * y)));
	} else {
		tmp = 4.16438922228 * (x + -2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.175:
		tmp = x * (4.16438922228 + (((3655.1204654076414 / x) + -110.1139242984811) / x))
	elif x <= 7.5e+23:
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (0.0212463641547976 * (x * y)))
	else:
		tmp = 4.16438922228 * (x + -2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.175)
		tmp = Float64(x * Float64(4.16438922228 + Float64(Float64(Float64(3655.1204654076414 / x) + -110.1139242984811) / x)));
	elseif (x <= 7.5e+23)
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(z * 0.0212463641547976) + Float64(0.0212463641547976 * Float64(x * y))));
	else
		tmp = Float64(4.16438922228 * Float64(x + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.175)
		tmp = x * (4.16438922228 + (((3655.1204654076414 / x) + -110.1139242984811) / x));
	elseif (x <= 7.5e+23)
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (0.0212463641547976 * (x * y)));
	else
		tmp = 4.16438922228 * (x + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.175], N[(x * N[(4.16438922228 + N[(N[(N[(3655.1204654076414 / x), $MachinePrecision] + -110.1139242984811), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e+23], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(z * 0.0212463641547976), $MachinePrecision] + N[(0.0212463641547976 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.16438922228 * N[(x + -2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.17499999999999999

   1. Initial program 21.2%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 21.2%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(\frac{104109730557}{25000000000} + \frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{{x}^{2}}\right) - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\left(\frac{104109730557}{25000000000} + \frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{{x}^{2}}\right) - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{104109730557}{25000000000} + \color{blue}{\left(\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{{x}^{2}} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)}\right)\right) \]

      3. unpow2 N/A

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

      4. associate-/r* N/A

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

      5. metadata-eval N/A

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

      6. associate-*r/ N/A

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

      7. associate-*r/ N/A

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

      8. metadata-eval N/A

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

      9. div-sub N/A

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

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

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

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

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

      12. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\left(\frac{2284450290879775841688574159837293}{625000000000000000000000000000} \cdot \frac{1}{x} + \left(\mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000}\right)\right)\right), x\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{2284450290879775841688574159837293}{625000000000000000000000000000} \cdot \frac{1}{x}\right), \left(\mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000}\right)\right)\right), x\right)\right)\right) \]

      14. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000} \cdot 1}{x}\right), \left(\mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000}\right)\right)\right), x\right)\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x}\right), \left(\mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000}\right)\right)\right), x\right)\right)\right) \]

      16. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\frac{2284450290879775841688574159837293}{625000000000000000000000000000}, x\right), \left(\mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000}\right)\right)\right), x\right)\right)\right) \]

      17. metadata-eval 83.8%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\frac{2284450290879775841688574159837293}{625000000000000000000000000000}, x\right), \frac{-13764240537310136880149}{125000000000000000000}\right), x\right)\right)\right) \]

   7. Simplified 83.8%

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

   if -0.17499999999999999 < x < 7.49999999999999987e23

   1. Initial program 98.3%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.0%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \color{blue}{\left(\frac{500000000}{23533438303} \cdot z + x \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right) \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\left(\frac{500000000}{23533438303} \cdot z\right), \color{blue}{\left(x \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\left(z \cdot \frac{500000000}{23533438303}\right), \left(\color{blue}{x} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \left(\color{blue}{x} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)}\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \left(\frac{500000000}{23533438303} \cdot y + \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{500000000}{23533438303} \cdot y\right), \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \left(\mathsf{neg}\left(\color{blue}{\frac{78349803973500000000}{553822718361107519809} \cdot z}\right)\right)\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \left(\mathsf{neg}\left(z \cdot \frac{78349803973500000000}{553822718361107519809}\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809}\right)\right)}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809}\right)\right)}\right)\right)\right)\right)\right) \]

      11. metadata-eval 87.7%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(z, \frac{-78349803973500000000}{553822718361107519809}\right)\right)\right)\right)\right) \]

   7. Simplified 87.7%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(z \cdot 0.0212463641547976 + x \cdot \left(0.0212463641547976 \cdot y + z \cdot -0.14147091005106402\right)\right)} \]

   8. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \color{blue}{\left(\frac{500000000}{23533438303} \cdot \left(x \cdot y\right)\right)}\right)\right) \]
   9. Step-by-step derivation

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

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

      2. *-lowering-*.f64 87.6%

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

   10. Simplified 87.6%

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

   if 7.49999999999999987e23 < x

   1. Initial program 5.6%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 13.9%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \color{blue}{\frac{104109730557}{25000000000}}\right) \]
   6. Step-by-step derivation

   7. Simplified 90.9%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.175:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{\frac{3655.1204654076414}{x} + -110.1139242984811}{x}\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+23}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + 0.0212463641547976 \cdot \left(x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot \left(x + -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 74.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-101}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(0.0212463641547976 \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+23}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot \left(x + -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5)
   (* x (+ 4.16438922228 (/ -110.1139242984811 x)))
   (if (<= x -7.2e-101)
     (* (+ x -2.0) (* 0.0212463641547976 (* x y)))
     (if (<= x 7.5e+23)
       (* (+ x -2.0) (* z 0.0212463641547976))
       (* 4.16438922228 (+ x -2.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	} else if (x <= -7.2e-101) {
		tmp = (x + -2.0) * (0.0212463641547976 * (x * y));
	} else if (x <= 7.5e+23) {
		tmp = (x + -2.0) * (z * 0.0212463641547976);
	} else {
		tmp = 4.16438922228 * (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 <= (-5.5d0)) then
        tmp = x * (4.16438922228d0 + ((-110.1139242984811d0) / x))
    else if (x <= (-7.2d-101)) then
        tmp = (x + (-2.0d0)) * (0.0212463641547976d0 * (x * y))
    else if (x <= 7.5d+23) then
        tmp = (x + (-2.0d0)) * (z * 0.0212463641547976d0)
    else
        tmp = 4.16438922228d0 * (x + (-2.0d0))
    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 + (-110.1139242984811 / x));
	} else if (x <= -7.2e-101) {
		tmp = (x + -2.0) * (0.0212463641547976 * (x * y));
	} else if (x <= 7.5e+23) {
		tmp = (x + -2.0) * (z * 0.0212463641547976);
	} else {
		tmp = 4.16438922228 * (x + -2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.5:
		tmp = x * (4.16438922228 + (-110.1139242984811 / x))
	elif x <= -7.2e-101:
		tmp = (x + -2.0) * (0.0212463641547976 * (x * y))
	elif x <= 7.5e+23:
		tmp = (x + -2.0) * (z * 0.0212463641547976)
	else:
		tmp = 4.16438922228 * (x + -2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5)
		tmp = Float64(x * Float64(4.16438922228 + Float64(-110.1139242984811 / x)));
	elseif (x <= -7.2e-101)
		tmp = Float64(Float64(x + -2.0) * Float64(0.0212463641547976 * Float64(x * y)));
	elseif (x <= 7.5e+23)
		tmp = Float64(Float64(x + -2.0) * Float64(z * 0.0212463641547976));
	else
		tmp = Float64(4.16438922228 * Float64(x + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.5)
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	elseif (x <= -7.2e-101)
		tmp = (x + -2.0) * (0.0212463641547976 * (x * y));
	elseif (x <= 7.5e+23)
		tmp = (x + -2.0) * (z * 0.0212463641547976);
	else
		tmp = 4.16438922228 * (x + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5], N[(x * N[(4.16438922228 + N[(-110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.2e-101], N[(N[(x + -2.0), $MachinePrecision] * N[(0.0212463641547976 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e+23], N[(N[(x + -2.0), $MachinePrecision] * N[(z * 0.0212463641547976), $MachinePrecision]), $MachinePrecision], N[(4.16438922228 * N[(x + -2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.5

   1. Initial program 21.2%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 21.2%

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

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

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

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. distribute-neg-frac N/A

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

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

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

      8. metadata-eval 83.7%

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

   7. Simplified 83.7%

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

   if -5.5 < x < -7.19999999999999999e-101

   1. Initial program 99.5%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \color{blue}{\left(\frac{500000000}{23533438303} \cdot z + x \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right) \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\left(\frac{500000000}{23533438303} \cdot z\right), \color{blue}{\left(x \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\left(z \cdot \frac{500000000}{23533438303}\right), \left(\color{blue}{x} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \left(\color{blue}{x} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)}\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \left(\frac{500000000}{23533438303} \cdot y + \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{500000000}{23533438303} \cdot y\right), \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \left(\mathsf{neg}\left(\color{blue}{\frac{78349803973500000000}{553822718361107519809} \cdot z}\right)\right)\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \left(\mathsf{neg}\left(z \cdot \frac{78349803973500000000}{553822718361107519809}\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809}\right)\right)}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809}\right)\right)}\right)\right)\right)\right)\right) \]

      11. metadata-eval 77.5%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(z, \frac{-78349803973500000000}{553822718361107519809}\right)\right)\right)\right)\right) \]

   7. Simplified 77.5%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(z \cdot 0.0212463641547976 + x \cdot \left(0.0212463641547976 \cdot y + z \cdot -0.14147091005106402\right)\right)} \]

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \color{blue}{\left(\frac{500000000}{23533438303} \cdot \left(x \cdot y\right)\right)}\right) \]
   9. Step-by-step derivation

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

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

      2. *-lowering-*.f64 57.4%

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

   10. Simplified 57.4%

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

   if -7.19999999999999999e-101 < x < 7.49999999999999987e23

   1. Initial program 98.1%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 98.9%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 73.7%

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

   7. Simplified 73.7%

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

   if 7.49999999999999987e23 < x

   1. Initial program 5.6%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 13.9%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \color{blue}{\frac{104109730557}{25000000000}}\right) \]
   6. Step-by-step derivation

   7. Simplified 90.9%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{4.16438922228} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-101}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(0.0212463641547976 \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+23}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot \left(x + -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 74.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.12:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-100}:\\ \;\;\;\;0.0212463641547976 \cdot \left(x \cdot \left(y \cdot \left(x + -2\right)\right)\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+23}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot \left(x + -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.12)
   (* x (+ 4.16438922228 (/ -110.1139242984811 x)))
   (if (<= x -2e-100)
     (* 0.0212463641547976 (* x (* y (+ x -2.0))))
     (if (<= x 7.5e+23)
       (* (+ x -2.0) (* z 0.0212463641547976))
       (* 4.16438922228 (+ x -2.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.12) {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	} else if (x <= -2e-100) {
		tmp = 0.0212463641547976 * (x * (y * (x + -2.0)));
	} else if (x <= 7.5e+23) {
		tmp = (x + -2.0) * (z * 0.0212463641547976);
	} else {
		tmp = 4.16438922228 * (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 <= (-0.12d0)) then
        tmp = x * (4.16438922228d0 + ((-110.1139242984811d0) / x))
    else if (x <= (-2d-100)) then
        tmp = 0.0212463641547976d0 * (x * (y * (x + (-2.0d0))))
    else if (x <= 7.5d+23) then
        tmp = (x + (-2.0d0)) * (z * 0.0212463641547976d0)
    else
        tmp = 4.16438922228d0 * (x + (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.12) {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	} else if (x <= -2e-100) {
		tmp = 0.0212463641547976 * (x * (y * (x + -2.0)));
	} else if (x <= 7.5e+23) {
		tmp = (x + -2.0) * (z * 0.0212463641547976);
	} else {
		tmp = 4.16438922228 * (x + -2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.12:
		tmp = x * (4.16438922228 + (-110.1139242984811 / x))
	elif x <= -2e-100:
		tmp = 0.0212463641547976 * (x * (y * (x + -2.0)))
	elif x <= 7.5e+23:
		tmp = (x + -2.0) * (z * 0.0212463641547976)
	else:
		tmp = 4.16438922228 * (x + -2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.12)
		tmp = Float64(x * Float64(4.16438922228 + Float64(-110.1139242984811 / x)));
	elseif (x <= -2e-100)
		tmp = Float64(0.0212463641547976 * Float64(x * Float64(y * Float64(x + -2.0))));
	elseif (x <= 7.5e+23)
		tmp = Float64(Float64(x + -2.0) * Float64(z * 0.0212463641547976));
	else
		tmp = Float64(4.16438922228 * Float64(x + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.12)
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	elseif (x <= -2e-100)
		tmp = 0.0212463641547976 * (x * (y * (x + -2.0)));
	elseif (x <= 7.5e+23)
		tmp = (x + -2.0) * (z * 0.0212463641547976);
	else
		tmp = 4.16438922228 * (x + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.12], N[(x * N[(4.16438922228 + N[(-110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2e-100], N[(0.0212463641547976 * N[(x * N[(y * N[(x + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e+23], N[(N[(x + -2.0), $MachinePrecision] * N[(z * 0.0212463641547976), $MachinePrecision]), $MachinePrecision], N[(4.16438922228 * N[(x + -2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -0.12

   1. Initial program 21.2%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 21.2%

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

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

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

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. distribute-neg-frac N/A

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

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

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

      8. metadata-eval 83.7%

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

   7. Simplified 83.7%

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

   if -0.12 < x < -2e-100

   1. Initial program 99.5%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \color{blue}{\left(\frac{500000000}{23533438303} \cdot z + x \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right) \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\left(\frac{500000000}{23533438303} \cdot z\right), \color{blue}{\left(x \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\left(z \cdot \frac{500000000}{23533438303}\right), \left(\color{blue}{x} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \left(\color{blue}{x} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)}\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \left(\frac{500000000}{23533438303} \cdot y + \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{500000000}{23533438303} \cdot y\right), \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \left(\mathsf{neg}\left(\color{blue}{\frac{78349803973500000000}{553822718361107519809} \cdot z}\right)\right)\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \left(\mathsf{neg}\left(z \cdot \frac{78349803973500000000}{553822718361107519809}\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809}\right)\right)}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809}\right)\right)}\right)\right)\right)\right)\right) \]

      11. metadata-eval 77.5%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(z, \frac{-78349803973500000000}{553822718361107519809}\right)\right)\right)\right)\right) \]

   7. Simplified 77.5%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(z \cdot 0.0212463641547976 + x \cdot \left(0.0212463641547976 \cdot y + z \cdot -0.14147091005106402\right)\right)} \]

   8. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{500000000}{23533438303} \cdot \left(x \cdot \left(y \cdot \left(x - 2\right)\right)\right)} \]
   9. Step-by-step derivation

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

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

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

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 57.4%

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

   10. Simplified 57.4%

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

   if -2e-100 < x < 7.49999999999999987e23

   1. Initial program 98.1%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 98.9%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 73.7%

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

   7. Simplified 73.7%

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

   if 7.49999999999999987e23 < x

   1. Initial program 5.6%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 13.9%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \color{blue}{\frac{104109730557}{25000000000}}\right) \]
   6. Step-by-step derivation

   7. Simplified 90.9%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{4.16438922228} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.12:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-100}:\\ \;\;\;\;0.0212463641547976 \cdot \left(x \cdot \left(y \cdot \left(x + -2\right)\right)\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+23}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot \left(x + -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 74.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.172:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-101}:\\ \;\;\;\;-0.0424927283095952 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+23}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot \left(x + -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.172)
   (* x (+ 4.16438922228 (/ -110.1139242984811 x)))
   (if (<= x -6.8e-101)
     (* -0.0424927283095952 (* x y))
     (if (<= x 7.5e+23)
       (* (+ x -2.0) (* z 0.0212463641547976))
       (* 4.16438922228 (+ x -2.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.172) {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	} else if (x <= -6.8e-101) {
		tmp = -0.0424927283095952 * (x * y);
	} else if (x <= 7.5e+23) {
		tmp = (x + -2.0) * (z * 0.0212463641547976);
	} else {
		tmp = 4.16438922228 * (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 <= (-0.172d0)) then
        tmp = x * (4.16438922228d0 + ((-110.1139242984811d0) / x))
    else if (x <= (-6.8d-101)) then
        tmp = (-0.0424927283095952d0) * (x * y)
    else if (x <= 7.5d+23) then
        tmp = (x + (-2.0d0)) * (z * 0.0212463641547976d0)
    else
        tmp = 4.16438922228d0 * (x + (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.172) {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	} else if (x <= -6.8e-101) {
		tmp = -0.0424927283095952 * (x * y);
	} else if (x <= 7.5e+23) {
		tmp = (x + -2.0) * (z * 0.0212463641547976);
	} else {
		tmp = 4.16438922228 * (x + -2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.172:
		tmp = x * (4.16438922228 + (-110.1139242984811 / x))
	elif x <= -6.8e-101:
		tmp = -0.0424927283095952 * (x * y)
	elif x <= 7.5e+23:
		tmp = (x + -2.0) * (z * 0.0212463641547976)
	else:
		tmp = 4.16438922228 * (x + -2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.172)
		tmp = Float64(x * Float64(4.16438922228 + Float64(-110.1139242984811 / x)));
	elseif (x <= -6.8e-101)
		tmp = Float64(-0.0424927283095952 * Float64(x * y));
	elseif (x <= 7.5e+23)
		tmp = Float64(Float64(x + -2.0) * Float64(z * 0.0212463641547976));
	else
		tmp = Float64(4.16438922228 * Float64(x + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.172)
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	elseif (x <= -6.8e-101)
		tmp = -0.0424927283095952 * (x * y);
	elseif (x <= 7.5e+23)
		tmp = (x + -2.0) * (z * 0.0212463641547976);
	else
		tmp = 4.16438922228 * (x + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.172], N[(x * N[(4.16438922228 + N[(-110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.8e-101], N[(-0.0424927283095952 * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e+23], N[(N[(x + -2.0), $MachinePrecision] * N[(z * 0.0212463641547976), $MachinePrecision]), $MachinePrecision], N[(4.16438922228 * N[(x + -2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -0.17199999999999999

   1. Initial program 21.2%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 21.2%

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

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

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

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. distribute-neg-frac N/A

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

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

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

      8. metadata-eval 83.7%

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

   7. Simplified 83.7%

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

   if -0.17199999999999999 < x < -6.79999999999999978e-101

   1. Initial program 99.5%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 63.0%

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

   7. Simplified 63.0%

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

   8. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot \left(x \cdot y\right)} \]
   9. Step-by-step derivation

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

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

      2. *-lowering-*.f64 57.3%

         \[\leadsto \mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   10. Simplified 57.3%

       \[\leadsto \color{blue}{-0.0424927283095952 \cdot \left(x \cdot y\right)} \]

   if -6.79999999999999978e-101 < x < 7.49999999999999987e23

   1. Initial program 98.1%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 98.9%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 73.7%

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

   7. Simplified 73.7%

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

   if 7.49999999999999987e23 < x

   1. Initial program 5.6%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 13.9%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \color{blue}{\frac{104109730557}{25000000000}}\right) \]
   6. Step-by-step derivation

   7. Simplified 90.9%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{4.16438922228} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.172:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-101}:\\ \;\;\;\;-0.0424927283095952 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+23}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot \left(x + -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 75.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \mathbf{if}\;x \leq -0.036:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-100}:\\ \;\;\;\;-0.0424927283095952 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 18000:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ 4.16438922228 (/ -110.1139242984811 x)))))
   (if (<= x -0.036)
     t_0
     (if (<= x -2.9e-100)
       (* -0.0424927283095952 (* x y))
       (if (<= x 18000.0) (* z -0.0424927283095952) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = x * (4.16438922228 + (-110.1139242984811 / x));
	double tmp;
	if (x <= -0.036) {
		tmp = t_0;
	} else if (x <= -2.9e-100) {
		tmp = -0.0424927283095952 * (x * y);
	} else if (x <= 18000.0) {
		tmp = z * -0.0424927283095952;
	} 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 * (4.16438922228d0 + ((-110.1139242984811d0) / x))
    if (x <= (-0.036d0)) then
        tmp = t_0
    else if (x <= (-2.9d-100)) then
        tmp = (-0.0424927283095952d0) * (x * y)
    else if (x <= 18000.0d0) then
        tmp = z * (-0.0424927283095952d0)
    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 * (4.16438922228 + (-110.1139242984811 / x));
	double tmp;
	if (x <= -0.036) {
		tmp = t_0;
	} else if (x <= -2.9e-100) {
		tmp = -0.0424927283095952 * (x * y);
	} else if (x <= 18000.0) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (4.16438922228 + (-110.1139242984811 / x))
	tmp = 0
	if x <= -0.036:
		tmp = t_0
	elif x <= -2.9e-100:
		tmp = -0.0424927283095952 * (x * y)
	elif x <= 18000.0:
		tmp = z * -0.0424927283095952
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(4.16438922228 + Float64(-110.1139242984811 / x)))
	tmp = 0.0
	if (x <= -0.036)
		tmp = t_0;
	elseif (x <= -2.9e-100)
		tmp = Float64(-0.0424927283095952 * Float64(x * y));
	elseif (x <= 18000.0)
		tmp = Float64(z * -0.0424927283095952);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (4.16438922228 + (-110.1139242984811 / x));
	tmp = 0.0;
	if (x <= -0.036)
		tmp = t_0;
	elseif (x <= -2.9e-100)
		tmp = -0.0424927283095952 * (x * y);
	elseif (x <= 18000.0)
		tmp = z * -0.0424927283095952;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(4.16438922228 + N[(-110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.036], t$95$0, If[LessEqual[x, -2.9e-100], N[(-0.0424927283095952 * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 18000.0], N[(z * -0.0424927283095952), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.0359999999999999973 or 18000 < x

   1. Initial program 15.0%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 19.6%

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

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

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

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. distribute-neg-frac N/A

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

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

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

      8. metadata-eval 84.4%

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

   7. Simplified 84.4%

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

   if -0.0359999999999999973 < x < -2.89999999999999975e-100

   1. Initial program 99.5%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 63.0%

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

   7. Simplified 63.0%

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

   8. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot \left(x \cdot y\right)} \]
   9. Step-by-step derivation

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

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

      2. *-lowering-*.f64 57.3%

         \[\leadsto \mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   10. Simplified 57.3%

       \[\leadsto \color{blue}{-0.0424927283095952 \cdot \left(x \cdot y\right)} \]

   if -2.89999999999999975e-100 < x < 18000

   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. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 76.2%

         \[\leadsto \mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, \color{blue}{z}\right) \]

   7. Simplified 76.2%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.036:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-100}:\\ \;\;\;\;-0.0424927283095952 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 18000:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 89.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{\frac{3655.1204654076414}{x} + -110.1139242984811}{x}\right)\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;-2 \cdot \left(z \cdot 0.0212463641547976 + 0.0212463641547976 \cdot \left(x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5)
   (*
    x
    (+ 4.16438922228 (/ (+ (/ 3655.1204654076414 x) -110.1139242984811) x)))
   (if (<= x 2.0)
     (* -2.0 (+ (* z 0.0212463641547976) (* 0.0212463641547976 (* x y))))
     (* x 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = x * (4.16438922228 + (((3655.1204654076414 / x) + -110.1139242984811) / x));
	} else if (x <= 2.0) {
		tmp = -2.0 * ((z * 0.0212463641547976) + (0.0212463641547976 * (x * y)));
	} 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 <= (-5.5d0)) then
        tmp = x * (4.16438922228d0 + (((3655.1204654076414d0 / x) + (-110.1139242984811d0)) / x))
    else if (x <= 2.0d0) then
        tmp = (-2.0d0) * ((z * 0.0212463641547976d0) + (0.0212463641547976d0 * (x * y)))
    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 <= -5.5) {
		tmp = x * (4.16438922228 + (((3655.1204654076414 / x) + -110.1139242984811) / x));
	} else if (x <= 2.0) {
		tmp = -2.0 * ((z * 0.0212463641547976) + (0.0212463641547976 * (x * y)));
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.5:
		tmp = x * (4.16438922228 + (((3655.1204654076414 / x) + -110.1139242984811) / x))
	elif x <= 2.0:
		tmp = -2.0 * ((z * 0.0212463641547976) + (0.0212463641547976 * (x * y)))
	else:
		tmp = x * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5)
		tmp = Float64(x * Float64(4.16438922228 + Float64(Float64(Float64(3655.1204654076414 / x) + -110.1139242984811) / x)));
	elseif (x <= 2.0)
		tmp = Float64(-2.0 * Float64(Float64(z * 0.0212463641547976) + Float64(0.0212463641547976 * Float64(x * y))));
	else
		tmp = Float64(x * 4.16438922228);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.5)
		tmp = x * (4.16438922228 + (((3655.1204654076414 / x) + -110.1139242984811) / x));
	elseif (x <= 2.0)
		tmp = -2.0 * ((z * 0.0212463641547976) + (0.0212463641547976 * (x * y)));
	else
		tmp = x * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5], N[(x * N[(4.16438922228 + N[(N[(N[(3655.1204654076414 / x), $MachinePrecision] + -110.1139242984811), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.0], N[(-2.0 * N[(N[(z * 0.0212463641547976), $MachinePrecision] + N[(0.0212463641547976 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5

   1. Initial program 21.2%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + \color{blue}{z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{/.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}\right)}\right)\right) \]

   3. Simplified 21.2%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(\frac{104109730557}{25000000000} + \frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{{x}^{2}}\right) - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\left(\frac{104109730557}{25000000000} + \frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{{x}^{2}}\right) - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{104109730557}{25000000000} + \color{blue}{\left(\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{{x}^{2}} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)}\right)\right) \]

      3. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{104109730557}{25000000000} + \left(\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x \cdot x} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)\right)\right) \]

      4. associate-/r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{104109730557}{25000000000} + \left(\frac{\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x}}{x} - \color{blue}{\frac{13764240537310136880149}{125000000000000000000}} \cdot \frac{1}{x}\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{104109730557}{25000000000} + \left(\frac{\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000} \cdot 1}{x}}{x} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)\right)\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{104109730557}{25000000000} + \left(\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{104109730557}{25000000000} + \left(\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x} - \frac{\frac{13764240537310136880149}{125000000000000000000} \cdot 1}{\color{blue}{x}}\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{104109730557}{25000000000} + \left(\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x} - \frac{\frac{13764240537310136880149}{125000000000000000000}}{x}\right)\right)\right) \]

      9. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{104109730557}{25000000000} + \frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000} \cdot \frac{1}{x} - \frac{13764240537310136880149}{125000000000000000000}}{\color{blue}{x}}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{104109730557}{25000000000}, \color{blue}{\left(\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000} \cdot \frac{1}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x}\right)}\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\left(\frac{2284450290879775841688574159837293}{625000000000000000000000000000} \cdot \frac{1}{x} - \frac{13764240537310136880149}{125000000000000000000}\right), \color{blue}{x}\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\left(\frac{2284450290879775841688574159837293}{625000000000000000000000000000} \cdot \frac{1}{x} + \left(\mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000}\right)\right)\right), x\right)\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{2284450290879775841688574159837293}{625000000000000000000000000000} \cdot \frac{1}{x}\right), \left(\mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000}\right)\right)\right), x\right)\right)\right) \]

      14. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000} \cdot 1}{x}\right), \left(\mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000}\right)\right)\right), x\right)\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x}\right), \left(\mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000}\right)\right)\right), x\right)\right)\right) \]

      16. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\frac{2284450290879775841688574159837293}{625000000000000000000000000000}, x\right), \left(\mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000}\right)\right)\right), x\right)\right)\right) \]

      17. metadata-eval 83.8%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\frac{2284450290879775841688574159837293}{625000000000000000000000000000}, x\right), \frac{-13764240537310136880149}{125000000000000000000}\right), x\right)\right)\right) \]

   7. Simplified 83.8%

      \[\leadsto \color{blue}{x \cdot \left(4.16438922228 + \frac{\frac{3655.1204654076414}{x} + -110.1139242984811}{x}\right)} \]

   if -5.5 < 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. associate-/l* N/A

         \[\leadsto \left(x - 2\right) \cdot \color{blue}{\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x - 2\right), \color{blue}{\left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x + \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + \color{blue}{z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{/.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}\right)}\right)\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \color{blue}{\left(\frac{500000000}{23533438303} \cdot z + x \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right) \]
   6. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\left(\frac{500000000}{23533438303} \cdot z\right), \color{blue}{\left(x \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\left(z \cdot \frac{500000000}{23533438303}\right), \left(\color{blue}{x} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \left(\color{blue}{x} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)}\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \left(\frac{500000000}{23533438303} \cdot y + \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right)\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{500000000}{23533438303} \cdot y\right), \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \left(\mathsf{neg}\left(\color{blue}{\frac{78349803973500000000}{553822718361107519809} \cdot z}\right)\right)\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \left(\mathsf{neg}\left(z \cdot \frac{78349803973500000000}{553822718361107519809}\right)\right)\right)\right)\right)\right) \]

      9. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809}\right)\right)}\right)\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809}\right)\right)}\right)\right)\right)\right)\right) \]

      11. metadata-eval 91.4%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(z, \frac{-78349803973500000000}{553822718361107519809}\right)\right)\right)\right)\right) \]

   7. Simplified 91.4%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(z \cdot 0.0212463641547976 + x \cdot \left(0.0212463641547976 \cdot y + z \cdot -0.14147091005106402\right)\right)} \]

   8. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \color{blue}{\left(\frac{500000000}{23533438303} \cdot \left(x \cdot y\right)\right)}\right)\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(\frac{500000000}{23533438303}, \color{blue}{\left(x \cdot y\right)}\right)\right)\right) \]

      2. *-lowering-*.f64 91.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(\frac{500000000}{23533438303}, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right)\right) \]

   10. Simplified 91.2%

       \[\leadsto \left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + \color{blue}{0.0212463641547976 \cdot \left(x \cdot y\right)}\right) \]

   11. Taylor expanded in x around 0

       \[\leadsto \mathsf{*.f64}\left(\color{blue}{-2}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(\frac{500000000}{23533438303}, \mathsf{*.f64}\left(x, y\right)\right)\right)\right) \]
   12. Step-by-step derivation

   13. Simplified 91.2%

       \[\leadsto \color{blue}{-2} \cdot \left(z \cdot 0.0212463641547976 + 0.0212463641547976 \cdot \left(x \cdot y\right)\right) \]

   if 2 < x

   1. Initial program 11.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \left(x - 2\right) \cdot \color{blue}{\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x - 2\right), \color{blue}{\left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x + \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + \color{blue}{z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{/.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}\right)}\right)\right) \]

   3. Simplified 20.5%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 82.4%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\frac{104109730557}{25000000000}}\right) \]

   7. Simplified 82.4%

      \[\leadsto \color{blue}{x \cdot 4.16438922228} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 18: 89.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.175:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;-2 \cdot \left(z \cdot 0.0212463641547976 + 0.0212463641547976 \cdot \left(x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.175)
   (* x (+ 4.16438922228 (/ -110.1139242984811 x)))
   (if (<= x 2.0)
     (* -2.0 (+ (* z 0.0212463641547976) (* 0.0212463641547976 (* x y))))
     (* x 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.175) {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	} else if (x <= 2.0) {
		tmp = -2.0 * ((z * 0.0212463641547976) + (0.0212463641547976 * (x * y)));
	} 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 <= (-0.175d0)) then
        tmp = x * (4.16438922228d0 + ((-110.1139242984811d0) / x))
    else if (x <= 2.0d0) then
        tmp = (-2.0d0) * ((z * 0.0212463641547976d0) + (0.0212463641547976d0 * (x * y)))
    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 <= -0.175) {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	} else if (x <= 2.0) {
		tmp = -2.0 * ((z * 0.0212463641547976) + (0.0212463641547976 * (x * y)));
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.175:
		tmp = x * (4.16438922228 + (-110.1139242984811 / x))
	elif x <= 2.0:
		tmp = -2.0 * ((z * 0.0212463641547976) + (0.0212463641547976 * (x * y)))
	else:
		tmp = x * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.175)
		tmp = Float64(x * Float64(4.16438922228 + Float64(-110.1139242984811 / x)));
	elseif (x <= 2.0)
		tmp = Float64(-2.0 * Float64(Float64(z * 0.0212463641547976) + Float64(0.0212463641547976 * Float64(x * y))));
	else
		tmp = Float64(x * 4.16438922228);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.175)
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	elseif (x <= 2.0)
		tmp = -2.0 * ((z * 0.0212463641547976) + (0.0212463641547976 * (x * y)));
	else
		tmp = x * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.175], N[(x * N[(4.16438922228 + N[(-110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.0], N[(-2.0 * N[(N[(z * 0.0212463641547976), $MachinePrecision] + N[(0.0212463641547976 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.17499999999999999

   1. Initial program 21.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \left(x - 2\right) \cdot \color{blue}{\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x - 2\right), \color{blue}{\left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x + \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + \color{blue}{z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{/.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}\right)}\right)\right) \]

   3. Simplified 21.2%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{104109730557}{25000000000} + \color{blue}{\left(\mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{104109730557}{25000000000}, \color{blue}{\left(\mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)\right)}\right)\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{104109730557}{25000000000}, \left(\mathsf{neg}\left(\frac{\frac{13764240537310136880149}{125000000000000000000} \cdot 1}{x}\right)\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{104109730557}{25000000000}, \left(\mathsf{neg}\left(\frac{\frac{13764240537310136880149}{125000000000000000000}}{x}\right)\right)\right)\right) \]

      6. distribute-neg-frac N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000}\right)}{\color{blue}{x}}\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000}\right)\right), \color{blue}{x}\right)\right)\right) \]

      8. metadata-eval 83.7%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\frac{-13764240537310136880149}{125000000000000000000}, x\right)\right)\right) \]

   7. Simplified 83.7%

      \[\leadsto \color{blue}{x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)} \]

   if -0.17499999999999999 < 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. associate-/l* N/A

         \[\leadsto \left(x - 2\right) \cdot \color{blue}{\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x - 2\right), \color{blue}{\left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x + \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + \color{blue}{z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{/.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}\right)}\right)\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \color{blue}{\left(\frac{500000000}{23533438303} \cdot z + x \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right) \]
   6. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\left(\frac{500000000}{23533438303} \cdot z\right), \color{blue}{\left(x \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\left(z \cdot \frac{500000000}{23533438303}\right), \left(\color{blue}{x} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \left(\color{blue}{x} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)}\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \left(\frac{500000000}{23533438303} \cdot y + \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right)\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{500000000}{23533438303} \cdot y\right), \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \left(\mathsf{neg}\left(\color{blue}{\frac{78349803973500000000}{553822718361107519809} \cdot z}\right)\right)\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \left(\mathsf{neg}\left(z \cdot \frac{78349803973500000000}{553822718361107519809}\right)\right)\right)\right)\right)\right) \]

      9. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809}\right)\right)}\right)\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809}\right)\right)}\right)\right)\right)\right)\right) \]

      11. metadata-eval 91.4%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(z, \frac{-78349803973500000000}{553822718361107519809}\right)\right)\right)\right)\right) \]

   7. Simplified 91.4%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(z \cdot 0.0212463641547976 + x \cdot \left(0.0212463641547976 \cdot y + z \cdot -0.14147091005106402\right)\right)} \]

   8. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \color{blue}{\left(\frac{500000000}{23533438303} \cdot \left(x \cdot y\right)\right)}\right)\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(\frac{500000000}{23533438303}, \color{blue}{\left(x \cdot y\right)}\right)\right)\right) \]

      2. *-lowering-*.f64 91.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(\frac{500000000}{23533438303}, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right)\right) \]

   10. Simplified 91.2%

       \[\leadsto \left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + \color{blue}{0.0212463641547976 \cdot \left(x \cdot y\right)}\right) \]

   11. Taylor expanded in x around 0

       \[\leadsto \mathsf{*.f64}\left(\color{blue}{-2}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(\frac{500000000}{23533438303}, \mathsf{*.f64}\left(x, y\right)\right)\right)\right) \]
   12. Step-by-step derivation

   13. Simplified 91.2%

       \[\leadsto \color{blue}{-2} \cdot \left(z \cdot 0.0212463641547976 + 0.0212463641547976 \cdot \left(x \cdot y\right)\right) \]

   if 2 < x

   1. Initial program 11.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \left(x - 2\right) \cdot \color{blue}{\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x - 2\right), \color{blue}{\left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x + \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + \color{blue}{z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{/.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}\right)}\right)\right) \]

   3. Simplified 20.5%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 82.4%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\frac{104109730557}{25000000000}}\right) \]

   7. Simplified 82.4%

      \[\leadsto \color{blue}{x \cdot 4.16438922228} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 19: 75.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.192:\\ \;\;\;\;4.16438922228 \cdot \left(x + -2\right)\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-101}:\\ \;\;\;\;-0.0424927283095952 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 18000:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.192)
   (* 4.16438922228 (+ x -2.0))
   (if (<= x -7.2e-101)
     (* -0.0424927283095952 (* x y))
     (if (<= x 18000.0) (* z -0.0424927283095952) (* x 4.16438922228)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.192) {
		tmp = 4.16438922228 * (x + -2.0);
	} else if (x <= -7.2e-101) {
		tmp = -0.0424927283095952 * (x * y);
	} else if (x <= 18000.0) {
		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 <= (-0.192d0)) then
        tmp = 4.16438922228d0 * (x + (-2.0d0))
    else if (x <= (-7.2d-101)) then
        tmp = (-0.0424927283095952d0) * (x * y)
    else if (x <= 18000.0d0) 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 <= -0.192) {
		tmp = 4.16438922228 * (x + -2.0);
	} else if (x <= -7.2e-101) {
		tmp = -0.0424927283095952 * (x * y);
	} else if (x <= 18000.0) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.192:
		tmp = 4.16438922228 * (x + -2.0)
	elif x <= -7.2e-101:
		tmp = -0.0424927283095952 * (x * y)
	elif x <= 18000.0:
		tmp = z * -0.0424927283095952
	else:
		tmp = x * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.192)
		tmp = Float64(4.16438922228 * Float64(x + -2.0));
	elseif (x <= -7.2e-101)
		tmp = Float64(-0.0424927283095952 * Float64(x * y));
	elseif (x <= 18000.0)
		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 <= -0.192)
		tmp = 4.16438922228 * (x + -2.0);
	elseif (x <= -7.2e-101)
		tmp = -0.0424927283095952 * (x * y);
	elseif (x <= 18000.0)
		tmp = z * -0.0424927283095952;
	else
		tmp = x * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.192], N[(4.16438922228 * N[(x + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.2e-101], N[(-0.0424927283095952 * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 18000.0], N[(z * -0.0424927283095952), $MachinePrecision], N[(x * 4.16438922228), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -0.192

   1. Initial program 21.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \left(x - 2\right) \cdot \color{blue}{\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x - 2\right), \color{blue}{\left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x + \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + \color{blue}{z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{/.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}\right)}\right)\right) \]

   3. Simplified 21.2%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \color{blue}{\frac{104109730557}{25000000000}}\right) \]
   6. Step-by-step derivation

   7. Simplified 82.6%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{4.16438922228} \]

   if -0.192 < x < -7.19999999999999999e-101

   1. Initial program 99.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \left(x - 2\right) \cdot \color{blue}{\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x - 2\right), \color{blue}{\left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x + \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + \color{blue}{z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{/.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}\right)}\right)\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{/.f64}\left(\color{blue}{\left(x \cdot y\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 63.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right)}, \frac{23533438303}{500000000}\right)\right)\right) \]

   7. Simplified 63.0%

      \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{x \cdot y}}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \]

   8. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot \left(x \cdot y\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, \color{blue}{\left(x \cdot y\right)}\right) \]

      2. *-lowering-*.f64 57.3%

         \[\leadsto \mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   10. Simplified 57.3%

       \[\leadsto \color{blue}{-0.0424927283095952 \cdot \left(x \cdot y\right)} \]

   if -7.19999999999999999e-101 < x < 18000

   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. associate-/l* N/A

         \[\leadsto \left(x - 2\right) \cdot \color{blue}{\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x - 2\right), \color{blue}{\left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x + \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + \color{blue}{z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{/.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}\right)}\right)\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 76.2%

         \[\leadsto \mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, \color{blue}{z}\right) \]

   7. Simplified 76.2%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]

   if 18000 < x

   1. Initial program 8.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \left(x - 2\right) \cdot \color{blue}{\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x - 2\right), \color{blue}{\left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x + \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + \color{blue}{z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{/.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}\right)}\right)\right) \]

   3. Simplified 18.0%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 85.0%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\frac{104109730557}{25000000000}}\right) \]

   7. Simplified 85.0%

      \[\leadsto \color{blue}{x \cdot 4.16438922228} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.192:\\ \;\;\;\;4.16438922228 \cdot \left(x + -2\right)\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-101}:\\ \;\;\;\;-0.0424927283095952 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 18000:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 75.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.225:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-100}:\\ \;\;\;\;-0.0424927283095952 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 18000:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.225)
   (* x 4.16438922228)
   (if (<= x -2.9e-100)
     (* -0.0424927283095952 (* x y))
     (if (<= x 18000.0) (* z -0.0424927283095952) (* x 4.16438922228)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.225) {
		tmp = x * 4.16438922228;
	} else if (x <= -2.9e-100) {
		tmp = -0.0424927283095952 * (x * y);
	} else if (x <= 18000.0) {
		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 <= (-0.225d0)) then
        tmp = x * 4.16438922228d0
    else if (x <= (-2.9d-100)) then
        tmp = (-0.0424927283095952d0) * (x * y)
    else if (x <= 18000.0d0) 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 <= -0.225) {
		tmp = x * 4.16438922228;
	} else if (x <= -2.9e-100) {
		tmp = -0.0424927283095952 * (x * y);
	} else if (x <= 18000.0) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.225:
		tmp = x * 4.16438922228
	elif x <= -2.9e-100:
		tmp = -0.0424927283095952 * (x * y)
	elif x <= 18000.0:
		tmp = z * -0.0424927283095952
	else:
		tmp = x * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.225)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= -2.9e-100)
		tmp = Float64(-0.0424927283095952 * Float64(x * y));
	elseif (x <= 18000.0)
		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 <= -0.225)
		tmp = x * 4.16438922228;
	elseif (x <= -2.9e-100)
		tmp = -0.0424927283095952 * (x * y);
	elseif (x <= 18000.0)
		tmp = z * -0.0424927283095952;
	else
		tmp = x * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.225], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, -2.9e-100], N[(-0.0424927283095952 * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 18000.0], N[(z * -0.0424927283095952), $MachinePrecision], N[(x * 4.16438922228), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.225000000000000006 or 18000 < x

   1. Initial program 15.0%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \left(x - 2\right) \cdot \color{blue}{\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x - 2\right), \color{blue}{\left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x + \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + \color{blue}{z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{/.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}\right)}\right)\right) \]

   3. Simplified 19.6%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 83.8%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\frac{104109730557}{25000000000}}\right) \]

   7. Simplified 83.8%

      \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

   if -0.225000000000000006 < x < -2.89999999999999975e-100

   1. Initial program 99.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \left(x - 2\right) \cdot \color{blue}{\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x - 2\right), \color{blue}{\left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x + \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + \color{blue}{z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{/.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}\right)}\right)\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{/.f64}\left(\color{blue}{\left(x \cdot y\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 63.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right)}, \frac{23533438303}{500000000}\right)\right)\right) \]

   7. Simplified 63.0%

      \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{x \cdot y}}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \]

   8. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot \left(x \cdot y\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, \color{blue}{\left(x \cdot y\right)}\right) \]

      2. *-lowering-*.f64 57.3%

         \[\leadsto \mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   10. Simplified 57.3%

       \[\leadsto \color{blue}{-0.0424927283095952 \cdot \left(x \cdot y\right)} \]

   if -2.89999999999999975e-100 < x < 18000

   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. associate-/l* N/A

         \[\leadsto \left(x - 2\right) \cdot \color{blue}{\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x - 2\right), \color{blue}{\left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x + \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + \color{blue}{z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{/.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}\right)}\right)\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 76.2%

         \[\leadsto \mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, \color{blue}{z}\right) \]

   7. Simplified 76.2%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.225:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-100}:\\ \;\;\;\;-0.0424927283095952 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 18000:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 76.3% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.000106:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 18000:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.000106)
   (* x 4.16438922228)
   (if (<= x 18000.0) (* z -0.0424927283095952) (* x 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.000106) {
		tmp = x * 4.16438922228;
	} else if (x <= 18000.0) {
		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 <= (-0.000106d0)) then
        tmp = x * 4.16438922228d0
    else if (x <= 18000.0d0) 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 <= -0.000106) {
		tmp = x * 4.16438922228;
	} else if (x <= 18000.0) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.000106:
		tmp = x * 4.16438922228
	elif x <= 18000.0:
		tmp = z * -0.0424927283095952
	else:
		tmp = x * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.000106)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 18000.0)
		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 <= -0.000106)
		tmp = x * 4.16438922228;
	elseif (x <= 18000.0)
		tmp = z * -0.0424927283095952;
	else
		tmp = x * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.000106], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 18000.0], N[(z * -0.0424927283095952), $MachinePrecision], N[(x * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.06e-4 or 18000 < x

   1. Initial program 15.6%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \left(x - 2\right) \cdot \color{blue}{\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x - 2\right), \color{blue}{\left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x + \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + \color{blue}{z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{/.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}\right)}\right)\right) \]

   3. Simplified 20.2%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 83.1%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\frac{104109730557}{25000000000}}\right) \]

   7. Simplified 83.1%

      \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

   if -1.06e-4 < x < 18000

   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. associate-/l* N/A

         \[\leadsto \left(x - 2\right) \cdot \color{blue}{\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x - 2\right), \color{blue}{\left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x + \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + \color{blue}{z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{/.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}\right)}\right)\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 68.4%

         \[\leadsto \mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, \color{blue}{z}\right) \]

   7. Simplified 68.4%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.000106:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 18000:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 35.1% 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 59.3%

   \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
2. Step-by-step derivation

   1. associate-/l* N/A

      \[\leadsto \left(x - 2\right) \cdot \color{blue}{\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(x - 2\right), \color{blue}{\left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

   3. sub-neg N/A

      \[\leadsto \mathsf{*.f64}\left(\left(x + \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

   4. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

   5. metadata-eval N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + \color{blue}{z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

   6. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{/.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}\right)}\right)\right) \]

3. Simplified 61.5%

   \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
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 37.0%

      \[\leadsto \mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, \color{blue}{z}\right) \]

7. Simplified 37.0%

   \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]

8. Final simplification 37.0%

   \[\leadsto z \cdot -0.0424927283095952 \]
9. Add Preprocessing

Developer Target 1: 98.8% 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 2024160 
(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)))