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

Percentage Accurate: 58.2% → 98.5%

Time: 19.8s

Alternatives: 20

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: 58.2% 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: 98.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x}\\ t_1 := x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606\\ t_2 := z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)\\ t_3 := \frac{101.7851458539211 - t\_0}{x}\\ \mathbf{if}\;\frac{\left(x - 2\right) \cdot t\_2}{t\_1} \leq \infty:\\ \;\;\;\;\frac{\left(x \cdot x + -4\right) \cdot \frac{t\_2}{t\_1}}{x + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(17.342137594641823 + t\_3 \cdot \frac{t\_0 - 101.7851458539211}{x}\right) \cdot \left(x + -2\right)}{4.16438922228 + t\_3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ 3451.550173699799 (/ (- y 124074.40615218398) x)) x))
        (t_1
         (+
          (*
           x
           (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
          47.066876606))
        (t_2
         (+
          z
          (*
           x
           (+
            y
            (*
             x
             (+ 137.519416416 (* x (+ (* x 4.16438922228) 78.6994924154))))))))
        (t_3 (/ (- 101.7851458539211 t_0) x)))
   (if (<= (/ (* (- x 2.0) t_2) t_1) INFINITY)
     (/ (* (+ (* x x) -4.0) (/ t_2 t_1)) (+ x 2.0))
     (/
      (*
       (+ 17.342137594641823 (* t_3 (/ (- t_0 101.7851458539211) x)))
       (+ x -2.0))
      (+ 4.16438922228 t_3)))))

C

double code(double x, double y, double z) {
	double t_0 = (3451.550173699799 + ((y - 124074.40615218398) / x)) / x;
	double t_1 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	double t_2 = z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))));
	double t_3 = (101.7851458539211 - t_0) / x;
	double tmp;
	if ((((x - 2.0) * t_2) / t_1) <= ((double) INFINITY)) {
		tmp = (((x * x) + -4.0) * (t_2 / t_1)) / (x + 2.0);
	} else {
		tmp = ((17.342137594641823 + (t_3 * ((t_0 - 101.7851458539211) / x))) * (x + -2.0)) / (4.16438922228 + t_3);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = (3451.550173699799 + ((y - 124074.40615218398) / x)) / x;
	double t_1 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	double t_2 = z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))));
	double t_3 = (101.7851458539211 - t_0) / x;
	double tmp;
	if ((((x - 2.0) * t_2) / t_1) <= Double.POSITIVE_INFINITY) {
		tmp = (((x * x) + -4.0) * (t_2 / t_1)) / (x + 2.0);
	} else {
		tmp = ((17.342137594641823 + (t_3 * ((t_0 - 101.7851458539211) / x))) * (x + -2.0)) / (4.16438922228 + t_3);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (3451.550173699799 + ((y - 124074.40615218398) / x)) / x
	t_1 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606
	t_2 = z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))
	t_3 = (101.7851458539211 - t_0) / x
	tmp = 0
	if (((x - 2.0) * t_2) / t_1) <= math.inf:
		tmp = (((x * x) + -4.0) * (t_2 / t_1)) / (x + 2.0)
	else:
		tmp = ((17.342137594641823 + (t_3 * ((t_0 - 101.7851458539211) / x))) * (x + -2.0)) / (4.16438922228 + t_3)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(3451.550173699799 + Float64(Float64(y - 124074.40615218398) / x)) / x)
	t_1 = Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)
	t_2 = Float64(z + Float64(x * Float64(y + Float64(x * Float64(137.519416416 + Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)))))))
	t_3 = Float64(Float64(101.7851458539211 - t_0) / x)
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * t_2) / t_1) <= Inf)
		tmp = Float64(Float64(Float64(Float64(x * x) + -4.0) * Float64(t_2 / t_1)) / Float64(x + 2.0));
	else
		tmp = Float64(Float64(Float64(17.342137594641823 + Float64(t_3 * Float64(Float64(t_0 - 101.7851458539211) / x))) * Float64(x + -2.0)) / Float64(4.16438922228 + t_3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (3451.550173699799 + ((y - 124074.40615218398) / x)) / x;
	t_1 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	t_2 = z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))));
	t_3 = (101.7851458539211 - t_0) / x;
	tmp = 0.0;
	if ((((x - 2.0) * t_2) / t_1) <= Inf)
		tmp = (((x * x) + -4.0) * (t_2 / t_1)) / (x + 2.0);
	else
		tmp = ((17.342137594641823 + (t_3 * ((t_0 - 101.7851458539211) / x))) * (x + -2.0)) / (4.16438922228 + t_3);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(3451.550173699799 + N[(N[(y - 124074.40615218398), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]}, Block[{t$95$2 = N[(z + N[(x * N[(y + N[(x * N[(137.519416416 + N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(101.7851458539211 - t$95$0), $MachinePrecision] / x), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision], Infinity], N[(N[(N[(N[(x * x), $MachinePrecision] + -4.0), $MachinePrecision] * N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(17.342137594641823 + N[(t$95$3 * N[(N[(t$95$0 - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x + -2.0), $MachinePrecision]), $MachinePrecision] / N[(4.16438922228 + t$95$3), $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))) < +inf.0

   1. Initial program 93.4%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 98.8%

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

   6. Applied egg-rr 98.9%

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

   if +inf.0 < (/.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 0.0%

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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \color{blue}{\left(\frac{104109730557}{25000000000} + -1 \cdot \frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)}\right) \]
   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 99.0%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right)} \]
   8. Step-by-step derivation

      1. *-commutative N/A

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

      2. flip-- N/A

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

      3. associate-*l/ N/A

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

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

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

   9. Applied egg-rr 99.5%

      \[\leadsto \color{blue}{\frac{\left(17.342137594641823 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x} \cdot \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right) \cdot \left(x + -2\right)}{4.16438922228 + \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq \infty:\\ \;\;\;\;\frac{\left(x \cdot x + -4\right) \cdot \frac{z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}}{x + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(17.342137594641823 + \frac{101.7851458539211 - \frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x}}{x} \cdot \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right) \cdot \left(x + -2\right)}{4.16438922228 + \frac{101.7851458539211 - \frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x}}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.5% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          (*
           x
           (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
          47.066876606))
        (t_1
         (+
          z
          (*
           x
           (+
            y
            (*
             x
             (+
              137.519416416
              (* x (+ (* x 4.16438922228) 78.6994924154)))))))))
   (if (<= (/ (* (- x 2.0) t_1) t_0) INFINITY)
     (/ (* (+ (* x x) -4.0) (/ t_1 t_0)) (+ x 2.0))
     (*
      (+ x -2.0)
      (+ 4.16438922228 (/ (- y 124074.40615218398) (* x (* x 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 = z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))));
	double tmp;
	if ((((x - 2.0) * t_1) / t_0) <= ((double) INFINITY)) {
		tmp = (((x * x) + -4.0) * (t_1 / t_0)) / (x + 2.0);
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((y - 124074.40615218398) / (x * (x * x))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	double t_1 = z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))));
	double tmp;
	if ((((x - 2.0) * t_1) / t_0) <= Double.POSITIVE_INFINITY) {
		tmp = (((x * x) + -4.0) * (t_1 / t_0)) / (x + 2.0);
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((y - 124074.40615218398) / (x * (x * 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 = z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))
	tmp = 0
	if (((x - 2.0) * t_1) / t_0) <= math.inf:
		tmp = (((x * x) + -4.0) * (t_1 / t_0)) / (x + 2.0)
	else:
		tmp = (x + -2.0) * (4.16438922228 + ((y - 124074.40615218398) / (x * (x * 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(z + Float64(x * Float64(y + Float64(x * Float64(137.519416416 + Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)))))))
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * t_1) / t_0) <= Inf)
		tmp = Float64(Float64(Float64(Float64(x * x) + -4.0) * Float64(t_1 / t_0)) / Float64(x + 2.0));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(y - 124074.40615218398) / Float64(x * Float64(x * 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 = z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))));
	tmp = 0.0;
	if ((((x - 2.0) * t_1) / t_0) <= Inf)
		tmp = (((x * x) + -4.0) * (t_1 / t_0)) / (x + 2.0);
	else
		tmp = (x + -2.0) * (4.16438922228 + ((y - 124074.40615218398) / (x * (x * 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[(z + N[(x * N[(y + N[(x * N[(137.519416416 + N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * t$95$1), $MachinePrecision] / t$95$0), $MachinePrecision], Infinity], N[(N[(N[(N[(x * x), $MachinePrecision] + -4.0), $MachinePrecision] * N[(t$95$1 / t$95$0), $MachinePrecision]), $MachinePrecision] / N[(x + 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(N[(y - 124074.40615218398), $MachinePrecision] / N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]), $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))) < +inf.0

   1. Initial program 93.4%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 98.8%

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

   6. Applied egg-rr 98.9%

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

   if +inf.0 < (/.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 0.0%

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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \color{blue}{\left(\frac{104109730557}{25000000000} + -1 \cdot \frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)}\right) \]
   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 99.0%

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

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \color{blue}{\left(\frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}}\right)}\right)\right) \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} - y\right), \color{blue}{\left({x}^{3}\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), \left({\color{blue}{x}}^{3}\right)\right)\right)\right) \]

      3. cube-mult N/A

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

      4. unpow2 N/A

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

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

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

      6. unpow2 N/A

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

      7. *-lowering-*.f64 99.0%

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

   10. Simplified 99.0%

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

4. Final simplification 98.9%

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

Alternative 3: 98.5% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          (*
           x
           (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
          47.066876606))
        (t_1
         (+
          z
          (*
           x
           (+
            y
            (*
             x
             (+
              137.519416416
              (* x (+ (* x 4.16438922228) 78.6994924154)))))))))
   (if (<= (/ (* (- x 2.0) t_1) t_0) INFINITY)
     (* (+ x -2.0) (/ t_1 t_0))
     (*
      (+ x -2.0)
      (+ 4.16438922228 (/ (- y 124074.40615218398) (* x (* x 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 = z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))));
	double tmp;
	if ((((x - 2.0) * t_1) / t_0) <= ((double) INFINITY)) {
		tmp = (x + -2.0) * (t_1 / t_0);
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((y - 124074.40615218398) / (x * (x * x))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	double t_1 = z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))));
	double tmp;
	if ((((x - 2.0) * t_1) / t_0) <= Double.POSITIVE_INFINITY) {
		tmp = (x + -2.0) * (t_1 / t_0);
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((y - 124074.40615218398) / (x * (x * 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 = z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))))
	tmp = 0
	if (((x - 2.0) * t_1) / t_0) <= math.inf:
		tmp = (x + -2.0) * (t_1 / t_0)
	else:
		tmp = (x + -2.0) * (4.16438922228 + ((y - 124074.40615218398) / (x * (x * 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(z + Float64(x * Float64(y + Float64(x * Float64(137.519416416 + Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)))))))
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * t_1) / t_0) <= Inf)
		tmp = Float64(Float64(x + -2.0) * Float64(t_1 / t_0));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(y - 124074.40615218398) / Float64(x * Float64(x * 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 = z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))))));
	tmp = 0.0;
	if ((((x - 2.0) * t_1) / t_0) <= Inf)
		tmp = (x + -2.0) * (t_1 / t_0);
	else
		tmp = (x + -2.0) * (4.16438922228 + ((y - 124074.40615218398) / (x * (x * 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[(z + N[(x * N[(y + N[(x * N[(137.519416416 + N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * t$95$1), $MachinePrecision] / t$95$0), $MachinePrecision], Infinity], N[(N[(x + -2.0), $MachinePrecision] * N[(t$95$1 / t$95$0), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(N[(y - 124074.40615218398), $MachinePrecision] / N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]), $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))) < +inf.0

   1. Initial program 93.4%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 98.8%

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

   if +inf.0 < (/.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 0.0%

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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \color{blue}{\left(\frac{104109730557}{25000000000} + -1 \cdot \frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)}\right) \]
   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 99.0%

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

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \color{blue}{\left(\frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}}\right)}\right)\right) \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} - y\right), \color{blue}{\left({x}^{3}\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), \left({\color{blue}{x}}^{3}\right)\right)\right)\right) \]

      3. cube-mult N/A

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

      4. unpow2 N/A

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

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

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

      6. unpow2 N/A

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

      7. *-lowering-*.f64 99.0%

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

   10. Simplified 99.0%

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

4. Final simplification 98.9%

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

Alternative 4: 96.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\\ \mathbf{if}\;x \leq -1.4 \cdot 10^{+14}:\\ \;\;\;\;\frac{t\_0}{\frac{1}{x + -2}}\\ \mathbf{elif}\;x \leq 4100000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          4.16438922228
          (/
           (-
            (/ (+ 3451.550173699799 (/ (- y 124074.40615218398) x)) x)
            101.7851458539211)
           x))))
   (if (<= x -1.4e+14)
     (/ t_0 (/ 1.0 (+ x -2.0)))
     (if (<= x 4100000000.0)
       (/
        (* (- x 2.0) (+ z (* x (+ y (* x 137.519416416)))))
        (+
         (*
          x
          (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
         47.066876606))
       (* (+ x -2.0) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = 4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x);
	double tmp;
	if (x <= -1.4e+14) {
		tmp = t_0 / (1.0 / (x + -2.0));
	} else if (x <= 4100000000.0) {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	} else {
		tmp = (x + -2.0) * t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 4.16438922228d0 + ((((3451.550173699799d0 + ((y - 124074.40615218398d0) / x)) / x) - 101.7851458539211d0) / x)
    if (x <= (-1.4d+14)) then
        tmp = t_0 / (1.0d0 / (x + (-2.0d0)))
    else if (x <= 4100000000.0d0) then
        tmp = ((x - 2.0d0) * (z + (x * (y + (x * 137.519416416d0))))) / ((x * ((x * ((x * (x + 43.3400022514d0)) + 263.505074721d0)) + 313.399215894d0)) + 47.066876606d0)
    else
        tmp = (x + (-2.0d0)) * t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x);
	double tmp;
	if (x <= -1.4e+14) {
		tmp = t_0 / (1.0 / (x + -2.0));
	} else if (x <= 4100000000.0) {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	} else {
		tmp = (x + -2.0) * t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)
	tmp = 0
	if x <= -1.4e+14:
		tmp = t_0 / (1.0 / (x + -2.0))
	elif x <= 4100000000.0:
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)
	else:
		tmp = (x + -2.0) * t_0
	return tmp

Julia

function code(x, y, z)
	t_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 <= -1.4e+14)
		tmp = Float64(t_0 / Float64(1.0 / Float64(x + -2.0)));
	elseif (x <= 4100000000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(z + Float64(x * Float64(y + Float64(x * 137.519416416))))) / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606));
	else
		tmp = Float64(Float64(x + -2.0) * t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x);
	tmp = 0.0;
	if (x <= -1.4e+14)
		tmp = t_0 / (1.0 / (x + -2.0));
	elseif (x <= 4100000000.0)
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	else
		tmp = (x + -2.0) * t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = 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]}, If[LessEqual[x, -1.4e+14], N[(t$95$0 / N[(1.0 / N[(x + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4100000000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(z + N[(x * N[(y + N[(x * 137.519416416), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * t$95$0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.4e14

   1. Initial program 12.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 20.6%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 99.0%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right)} \]
   8. Step-by-step derivation

      1. flip3-+ N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{{x}^{3} + {-2}^{3}}{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}\right), \mathsf{\_.f64}\left(\color{blue}{\frac{104109730557}{25000000000}}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      2. cube-unmult N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x \cdot \left(x \cdot x\right) + {-2}^{3}}{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x \cdot \left(x \cdot x\right) + -8}{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x \cdot \left(x \cdot x\right) + -8}{x \cdot x + \left(4 - x \cdot -2\right)}\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      5. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x \cdot \left(x \cdot x\right) + -8}{\left(x \cdot x + 4\right) - x \cdot -2}\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\frac{\left(x \cdot x + 4\right) - x \cdot -2}{x \cdot \left(x \cdot x\right) + -8}}\right), \mathsf{\_.f64}\left(\color{blue}{\frac{104109730557}{25000000000}}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{\left(x \cdot x + 4\right) - x \cdot -2}{x \cdot \left(x \cdot x\right) + -8}\right)\right), \mathsf{\_.f64}\left(\color{blue}{\frac{104109730557}{25000000000}}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      8. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{1}{\frac{x \cdot \left(x \cdot x\right) + -8}{\left(x \cdot x + 4\right) - x \cdot -2}}\right)\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      9. cube-unmult N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{1}{\frac{{x}^{3} + -8}{\left(x \cdot x + 4\right) - x \cdot -2}}\right)\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{1}{\frac{{x}^{3} + {-2}^{3}}{\left(x \cdot x + 4\right) - x \cdot -2}}\right)\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      11. associate--l+ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{1}{\frac{{x}^{3} + {-2}^{3}}{x \cdot x + \left(4 - x \cdot -2\right)}}\right)\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{1}{\frac{{x}^{3} + {-2}^{3}}{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}}\right)\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      13. flip3-+ N/A

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

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

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

      15. +-lowering-+.f64 99.0%

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

   9. Applied egg-rr 99.0%

      \[\leadsto \color{blue}{\frac{1}{\frac{1}{x + -2}}} \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right) \]
   10. Step-by-step derivation

       1. associate-*l/ N/A

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

       2. *-lft-identity N/A

          \[\leadsto \frac{\frac{104109730557}{25000000000} - \frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} - \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} - y}{x}}{x}}{x}}{\frac{\color{blue}{1}}{x + -2}} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

       12. +-lowering-+.f64 99.1%

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

   11. Applied egg-rr 99.1%

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

   if -1.4e14 < x < 4.1e9

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{4297481763}{31250000} \cdot x\right)}, y\right), x\right), z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right), x\right), \frac{263505074721}{1000000000}\right), x\right), \frac{156699607947}{500000000}\right), x\right), \frac{23533438303}{500000000}\right)\right) \]
   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 99.7%

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

   5. Simplified 99.7%

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

   if 4.1e9 < x

   1. Initial program 18.6%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 23.3%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 92.7%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+14}:\\ \;\;\;\;\frac{4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}}{\frac{1}{x + -2}}\\ \mathbf{elif}\;x \leq 4100000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\\ \mathbf{if}\;x \leq -330:\\ \;\;\;\;\frac{t\_0}{\frac{1}{x + -2}}\\ \mathbf{elif}\;x \leq 80000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          4.16438922228
          (/
           (-
            (/ (+ 3451.550173699799 (/ (- y 124074.40615218398) x)) x)
            101.7851458539211)
           x))))
   (if (<= x -330.0)
     (/ t_0 (/ 1.0 (+ x -2.0)))
     (if (<= x 80000000.0)
       (/
        (* (- x 2.0) (+ z (* x (+ y (* x 137.519416416)))))
        (+ 47.066876606 (* x (+ 313.399215894 (* x 263.505074721)))))
       (* (+ x -2.0) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = 4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x);
	double tmp;
	if (x <= -330.0) {
		tmp = t_0 / (1.0 / (x + -2.0));
	} else if (x <= 80000000.0) {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	} else {
		tmp = (x + -2.0) * t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 4.16438922228d0 + ((((3451.550173699799d0 + ((y - 124074.40615218398d0) / x)) / x) - 101.7851458539211d0) / x)
    if (x <= (-330.0d0)) then
        tmp = t_0 / (1.0d0 / (x + (-2.0d0)))
    else if (x <= 80000000.0d0) then
        tmp = ((x - 2.0d0) * (z + (x * (y + (x * 137.519416416d0))))) / (47.066876606d0 + (x * (313.399215894d0 + (x * 263.505074721d0))))
    else
        tmp = (x + (-2.0d0)) * t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x);
	double tmp;
	if (x <= -330.0) {
		tmp = t_0 / (1.0 / (x + -2.0));
	} else if (x <= 80000000.0) {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	} else {
		tmp = (x + -2.0) * t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)
	tmp = 0
	if x <= -330.0:
		tmp = t_0 / (1.0 / (x + -2.0))
	elif x <= 80000000.0:
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))))
	else:
		tmp = (x + -2.0) * t_0
	return tmp

Julia

function code(x, y, z)
	t_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 <= -330.0)
		tmp = Float64(t_0 / Float64(1.0 / Float64(x + -2.0)));
	elseif (x <= 80000000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(z + Float64(x * Float64(y + Float64(x * 137.519416416))))) / Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(x * 263.505074721)))));
	else
		tmp = Float64(Float64(x + -2.0) * t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x);
	tmp = 0.0;
	if (x <= -330.0)
		tmp = t_0 / (1.0 / (x + -2.0));
	elseif (x <= 80000000.0)
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	else
		tmp = (x + -2.0) * t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = 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]}, If[LessEqual[x, -330.0], N[(t$95$0 / N[(1.0 / N[(x + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 80000000.0], 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 * N[(313.399215894 + N[(x * 263.505074721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * t$95$0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -330

   1. Initial program 12.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 20.6%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 99.0%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right)} \]
   8. Step-by-step derivation

      1. flip3-+ N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{{x}^{3} + {-2}^{3}}{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}\right), \mathsf{\_.f64}\left(\color{blue}{\frac{104109730557}{25000000000}}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      2. cube-unmult N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x \cdot \left(x \cdot x\right) + {-2}^{3}}{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x \cdot \left(x \cdot x\right) + -8}{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x \cdot \left(x \cdot x\right) + -8}{x \cdot x + \left(4 - x \cdot -2\right)}\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      5. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x \cdot \left(x \cdot x\right) + -8}{\left(x \cdot x + 4\right) - x \cdot -2}\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\frac{\left(x \cdot x + 4\right) - x \cdot -2}{x \cdot \left(x \cdot x\right) + -8}}\right), \mathsf{\_.f64}\left(\color{blue}{\frac{104109730557}{25000000000}}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{\left(x \cdot x + 4\right) - x \cdot -2}{x \cdot \left(x \cdot x\right) + -8}\right)\right), \mathsf{\_.f64}\left(\color{blue}{\frac{104109730557}{25000000000}}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      8. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{1}{\frac{x \cdot \left(x \cdot x\right) + -8}{\left(x \cdot x + 4\right) - x \cdot -2}}\right)\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      9. cube-unmult N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{1}{\frac{{x}^{3} + -8}{\left(x \cdot x + 4\right) - x \cdot -2}}\right)\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{1}{\frac{{x}^{3} + {-2}^{3}}{\left(x \cdot x + 4\right) - x \cdot -2}}\right)\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      11. associate--l+ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{1}{\frac{{x}^{3} + {-2}^{3}}{x \cdot x + \left(4 - x \cdot -2\right)}}\right)\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{1}{\frac{{x}^{3} + {-2}^{3}}{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}}\right)\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      13. flip3-+ N/A

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

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

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

      15. +-lowering-+.f64 99.0%

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

   9. Applied egg-rr 99.0%

      \[\leadsto \color{blue}{\frac{1}{\frac{1}{x + -2}}} \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right) \]
   10. Step-by-step derivation

       1. associate-*l/ N/A

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

       2. *-lft-identity N/A

          \[\leadsto \frac{\frac{104109730557}{25000000000} - \frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} - \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} - y}{x}}{x}}{x}}{\frac{\color{blue}{1}}{x + -2}} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

       12. +-lowering-+.f64 99.1%

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

   11. Applied egg-rr 99.1%

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

   if -330 < x < 8e7

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{4297481763}{31250000} \cdot x\right)}, y\right), x\right), z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right), x\right), \frac{263505074721}{1000000000}\right), x\right), \frac{156699607947}{500000000}\right), x\right), \frac{23533438303}{500000000}\right)\right) \]
   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 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 97.2%

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

   8. Simplified 97.2%

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

   if 8e7 < x

   1. Initial program 18.6%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 23.3%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 92.7%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -330:\\ \;\;\;\;\frac{4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}}{\frac{1}{x + -2}}\\ \mathbf{elif}\;x \leq 80000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\\ \mathbf{if}\;x \leq -330:\\ \;\;\;\;\frac{t\_0}{\frac{1}{x + -2}}\\ \mathbf{elif}\;x \leq 80000000:\\ \;\;\;\;\frac{z \cdot -2 + x \cdot \left(z + y \cdot -2\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          4.16438922228
          (/
           (-
            (/ (+ 3451.550173699799 (/ (- y 124074.40615218398) x)) x)
            101.7851458539211)
           x))))
   (if (<= x -330.0)
     (/ t_0 (/ 1.0 (+ x -2.0)))
     (if (<= x 80000000.0)
       (/
        (+ (* z -2.0) (* x (+ z (* y -2.0))))
        (+ 47.066876606 (* x (+ 313.399215894 (* x 263.505074721)))))
       (* (+ x -2.0) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = 4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x);
	double tmp;
	if (x <= -330.0) {
		tmp = t_0 / (1.0 / (x + -2.0));
	} else if (x <= 80000000.0) {
		tmp = ((z * -2.0) + (x * (z + (y * -2.0)))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	} else {
		tmp = (x + -2.0) * t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 4.16438922228d0 + ((((3451.550173699799d0 + ((y - 124074.40615218398d0) / x)) / x) - 101.7851458539211d0) / x)
    if (x <= (-330.0d0)) then
        tmp = t_0 / (1.0d0 / (x + (-2.0d0)))
    else if (x <= 80000000.0d0) then
        tmp = ((z * (-2.0d0)) + (x * (z + (y * (-2.0d0))))) / (47.066876606d0 + (x * (313.399215894d0 + (x * 263.505074721d0))))
    else
        tmp = (x + (-2.0d0)) * t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x);
	double tmp;
	if (x <= -330.0) {
		tmp = t_0 / (1.0 / (x + -2.0));
	} else if (x <= 80000000.0) {
		tmp = ((z * -2.0) + (x * (z + (y * -2.0)))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	} else {
		tmp = (x + -2.0) * t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)
	tmp = 0
	if x <= -330.0:
		tmp = t_0 / (1.0 / (x + -2.0))
	elif x <= 80000000.0:
		tmp = ((z * -2.0) + (x * (z + (y * -2.0)))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))))
	else:
		tmp = (x + -2.0) * t_0
	return tmp

Julia

function code(x, y, z)
	t_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 <= -330.0)
		tmp = Float64(t_0 / Float64(1.0 / Float64(x + -2.0)));
	elseif (x <= 80000000.0)
		tmp = Float64(Float64(Float64(z * -2.0) + Float64(x * Float64(z + Float64(y * -2.0)))) / Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(x * 263.505074721)))));
	else
		tmp = Float64(Float64(x + -2.0) * t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x);
	tmp = 0.0;
	if (x <= -330.0)
		tmp = t_0 / (1.0 / (x + -2.0));
	elseif (x <= 80000000.0)
		tmp = ((z * -2.0) + (x * (z + (y * -2.0)))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	else
		tmp = (x + -2.0) * t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = 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]}, If[LessEqual[x, -330.0], N[(t$95$0 / N[(1.0 / N[(x + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 80000000.0], N[(N[(N[(z * -2.0), $MachinePrecision] + N[(x * N[(z + N[(y * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(47.066876606 + N[(x * N[(313.399215894 + N[(x * 263.505074721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * t$95$0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -330

   1. Initial program 12.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 20.6%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 99.0%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right)} \]
   8. Step-by-step derivation

      1. flip3-+ N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{{x}^{3} + {-2}^{3}}{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}\right), \mathsf{\_.f64}\left(\color{blue}{\frac{104109730557}{25000000000}}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      2. cube-unmult N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x \cdot \left(x \cdot x\right) + {-2}^{3}}{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x \cdot \left(x \cdot x\right) + -8}{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x \cdot \left(x \cdot x\right) + -8}{x \cdot x + \left(4 - x \cdot -2\right)}\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      5. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x \cdot \left(x \cdot x\right) + -8}{\left(x \cdot x + 4\right) - x \cdot -2}\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\frac{\left(x \cdot x + 4\right) - x \cdot -2}{x \cdot \left(x \cdot x\right) + -8}}\right), \mathsf{\_.f64}\left(\color{blue}{\frac{104109730557}{25000000000}}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{\left(x \cdot x + 4\right) - x \cdot -2}{x \cdot \left(x \cdot x\right) + -8}\right)\right), \mathsf{\_.f64}\left(\color{blue}{\frac{104109730557}{25000000000}}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      8. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{1}{\frac{x \cdot \left(x \cdot x\right) + -8}{\left(x \cdot x + 4\right) - x \cdot -2}}\right)\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      9. cube-unmult N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{1}{\frac{{x}^{3} + -8}{\left(x \cdot x + 4\right) - x \cdot -2}}\right)\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{1}{\frac{{x}^{3} + {-2}^{3}}{\left(x \cdot x + 4\right) - x \cdot -2}}\right)\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      11. associate--l+ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{1}{\frac{{x}^{3} + {-2}^{3}}{x \cdot x + \left(4 - x \cdot -2\right)}}\right)\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{1}{\frac{{x}^{3} + {-2}^{3}}{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}}\right)\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{12723143231740136880149}{125000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), x\right)\right), x\right)\right), x\right)\right)\right) \]

      13. flip3-+ N/A

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

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

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

      15. +-lowering-+.f64 99.0%

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

   9. Applied egg-rr 99.0%

      \[\leadsto \color{blue}{\frac{1}{\frac{1}{x + -2}}} \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right) \]
   10. Step-by-step derivation

       1. associate-*l/ N/A

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

       2. *-lft-identity N/A

          \[\leadsto \frac{\frac{104109730557}{25000000000} - \frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} - \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} - y}{x}}{x}}{x}}{\frac{\color{blue}{1}}{x + -2}} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

       12. +-lowering-+.f64 99.1%

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

   11. Applied egg-rr 99.1%

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

   if -330 < x < 8e7

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{4297481763}{31250000} \cdot x\right)}, y\right), x\right), z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right), x\right), \frac{263505074721}{1000000000}\right), x\right), \frac{156699607947}{500000000}\right), x\right), \frac{23533438303}{500000000}\right)\right) \]
   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 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in x around 0

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

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

      7. *-lowering-*.f64 89.5%

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

   8. Simplified 89.5%

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

   9. Taylor expanded in x around 0

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

       1. *-commutative N/A

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

       2. *-lowering-*.f64 87.3%

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

   11. Simplified 87.3%

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

   if 8e7 < x

   1. Initial program 18.6%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 23.3%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 92.7%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -330:\\ \;\;\;\;\frac{4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}}{\frac{1}{x + -2}}\\ \mathbf{elif}\;x \leq 80000000:\\ \;\;\;\;\frac{z \cdot -2 + x \cdot \left(z + y \cdot -2\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 93.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{if}\;x \leq -350:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 80000000:\\ \;\;\;\;\frac{z \cdot -2 + x \cdot \left(z + y \cdot -2\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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 -350.0)
     t_0
     (if (<= x 80000000.0)
       (/
        (+ (* z -2.0) (* x (+ z (* y -2.0))))
        (+ 47.066876606 (* x (+ 313.399215894 (* x 263.505074721)))))
       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 <= -350.0) {
		tmp = t_0;
	} else if (x <= 80000000.0) {
		tmp = ((z * -2.0) + (x * (z + (y * -2.0)))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	} 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 <= (-350.0d0)) then
        tmp = t_0
    else if (x <= 80000000.0d0) then
        tmp = ((z * (-2.0d0)) + (x * (z + (y * (-2.0d0))))) / (47.066876606d0 + (x * (313.399215894d0 + (x * 263.505074721d0))))
    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 <= -350.0) {
		tmp = t_0;
	} else if (x <= 80000000.0) {
		tmp = ((z * -2.0) + (x * (z + (y * -2.0)))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	} 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 <= -350.0:
		tmp = t_0
	elif x <= 80000000.0:
		tmp = ((z * -2.0) + (x * (z + (y * -2.0)))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))))
	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 <= -350.0)
		tmp = t_0;
	elseif (x <= 80000000.0)
		tmp = Float64(Float64(Float64(z * -2.0) + Float64(x * Float64(z + Float64(y * -2.0)))) / Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(x * 263.505074721)))));
	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 <= -350.0)
		tmp = t_0;
	elseif (x <= 80000000.0)
		tmp = ((z * -2.0) + (x * (z + (y * -2.0)))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	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, -350.0], t$95$0, If[LessEqual[x, 80000000.0], N[(N[(N[(z * -2.0), $MachinePrecision] + N[(x * N[(z + N[(y * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(47.066876606 + N[(x * N[(313.399215894 + N[(x * 263.505074721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -350 or 8e7 < x

   1. Initial program 15.3%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 21.8%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 96.2%

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

   if -350 < x < 8e7

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{4297481763}{31250000} \cdot x\right)}, y\right), x\right), z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right), x\right), \frac{263505074721}{1000000000}\right), x\right), \frac{156699607947}{500000000}\right), x\right), \frac{23533438303}{500000000}\right)\right) \]
   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 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in x around 0

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

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

      7. *-lowering-*.f64 89.5%

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

   8. Simplified 89.5%

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

   9. Taylor expanded in x around 0

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

       1. *-commutative N/A

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

       2. *-lowering-*.f64 87.3%

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

   11. Simplified 87.3%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -350:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{elif}\;x \leq 80000000:\\ \;\;\;\;\frac{z \cdot -2 + x \cdot \left(z + y \cdot -2\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 92.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{if}\;x \leq -36:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 80000000:\\ \;\;\;\;\frac{z \cdot -0.0849854566191904 + x \cdot \left(y \cdot -0.0849854566191904 + z \cdot 0.5658836402042561\right)}{x + 2}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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 -36.0)
     t_0
     (if (<= x 80000000.0)
       (/
        (+
         (* z -0.0849854566191904)
         (* x (+ (* y -0.0849854566191904) (* z 0.5658836402042561))))
        (+ x 2.0))
       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 <= -36.0) {
		tmp = t_0;
	} else if (x <= 80000000.0) {
		tmp = ((z * -0.0849854566191904) + (x * ((y * -0.0849854566191904) + (z * 0.5658836402042561)))) / (x + 2.0);
	} 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 <= (-36.0d0)) then
        tmp = t_0
    else if (x <= 80000000.0d0) then
        tmp = ((z * (-0.0849854566191904d0)) + (x * ((y * (-0.0849854566191904d0)) + (z * 0.5658836402042561d0)))) / (x + 2.0d0)
    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 <= -36.0) {
		tmp = t_0;
	} else if (x <= 80000000.0) {
		tmp = ((z * -0.0849854566191904) + (x * ((y * -0.0849854566191904) + (z * 0.5658836402042561)))) / (x + 2.0);
	} 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 <= -36.0:
		tmp = t_0
	elif x <= 80000000.0:
		tmp = ((z * -0.0849854566191904) + (x * ((y * -0.0849854566191904) + (z * 0.5658836402042561)))) / (x + 2.0)
	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 <= -36.0)
		tmp = t_0;
	elseif (x <= 80000000.0)
		tmp = Float64(Float64(Float64(z * -0.0849854566191904) + Float64(x * Float64(Float64(y * -0.0849854566191904) + Float64(z * 0.5658836402042561)))) / Float64(x + 2.0));
	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 <= -36.0)
		tmp = t_0;
	elseif (x <= 80000000.0)
		tmp = ((z * -0.0849854566191904) + (x * ((y * -0.0849854566191904) + (z * 0.5658836402042561)))) / (x + 2.0);
	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, -36.0], t$95$0, If[LessEqual[x, 80000000.0], N[(N[(N[(z * -0.0849854566191904), $MachinePrecision] + N[(x * N[(N[(y * -0.0849854566191904), $MachinePrecision] + N[(z * 0.5658836402042561), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 2.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -36 or 8e7 < x

   1. Initial program 16.0%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 22.4%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 95.5%

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

   if -36 < x < 8e7

   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 99.7%

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

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{-2000000000}{23533438303} \cdot z + x \cdot \left(\frac{-2000000000}{23533438303} \cdot y - \frac{-313399215894000000000}{553822718361107519809} \cdot z\right)\right)}, \mathsf{+.f64}\left(x, 2\right)\right) \]
   8. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{-2000000000}{23533438303} \cdot z\right), \left(x \cdot \left(\frac{-2000000000}{23533438303} \cdot y - \frac{-313399215894000000000}{553822718361107519809} \cdot z\right)\right)\right), \mathsf{+.f64}\left(\color{blue}{x}, 2\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(z \cdot \frac{-2000000000}{23533438303}\right), \left(x \cdot \left(\frac{-2000000000}{23533438303} \cdot y - \frac{-313399215894000000000}{553822718361107519809} \cdot z\right)\right)\right), \mathsf{+.f64}\left(x, 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-2000000000}{23533438303}\right), \left(x \cdot \left(\frac{-2000000000}{23533438303} \cdot y - \frac{-313399215894000000000}{553822718361107519809} \cdot z\right)\right)\right), \mathsf{+.f64}\left(x, 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-2000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \left(\frac{-2000000000}{23533438303} \cdot y - \frac{-313399215894000000000}{553822718361107519809} \cdot z\right)\right)\right), \mathsf{+.f64}\left(x, 2\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-2000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \left(\frac{-2000000000}{23533438303} \cdot y + \left(\mathsf{neg}\left(\frac{-313399215894000000000}{553822718361107519809} \cdot z\right)\right)\right)\right)\right), \mathsf{+.f64}\left(x, 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-2000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{-2000000000}{23533438303} \cdot y\right), \left(\mathsf{neg}\left(\frac{-313399215894000000000}{553822718361107519809} \cdot z\right)\right)\right)\right)\right), \mathsf{+.f64}\left(x, 2\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-2000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(y \cdot \frac{-2000000000}{23533438303}\right), \left(\mathsf{neg}\left(\frac{-313399215894000000000}{553822718361107519809} \cdot z\right)\right)\right)\right)\right), \mathsf{+.f64}\left(x, 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-2000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-2000000000}{23533438303}\right), \left(\mathsf{neg}\left(\frac{-313399215894000000000}{553822718361107519809} \cdot z\right)\right)\right)\right)\right), \mathsf{+.f64}\left(x, 2\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-2000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-2000000000}{23533438303}\right), \left(\mathsf{neg}\left(z \cdot \frac{-313399215894000000000}{553822718361107519809}\right)\right)\right)\right)\right), \mathsf{+.f64}\left(x, 2\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-2000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-2000000000}{23533438303}\right), \left(z \cdot \left(\mathsf{neg}\left(\frac{-313399215894000000000}{553822718361107519809}\right)\right)\right)\right)\right)\right), \mathsf{+.f64}\left(x, 2\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-2000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-2000000000}{23533438303}\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\frac{-313399215894000000000}{553822718361107519809}\right)\right)\right)\right)\right)\right), \mathsf{+.f64}\left(x, 2\right)\right) \]

      12. metadata-eval 87.6%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-2000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-2000000000}{23533438303}\right), \mathsf{*.f64}\left(z, \frac{313399215894000000000}{553822718361107519809}\right)\right)\right)\right), \mathsf{+.f64}\left(x, 2\right)\right) \]

   9. Simplified 87.6%

      \[\leadsto \frac{\color{blue}{z \cdot -0.0849854566191904 + x \cdot \left(y \cdot -0.0849854566191904 + z \cdot 0.5658836402042561\right)}}{x + 2} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -36:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{elif}\;x \leq 80000000:\\ \;\;\;\;\frac{z \cdot -0.0849854566191904 + x \cdot \left(y \cdot -0.0849854566191904 + z \cdot 0.5658836402042561\right)}{x + 2}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 92.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + -2\right) \cdot \left(4.16438922228 + \frac{y - 124074.40615218398}{x \cdot \left(x \cdot x\right)}\right)\\ \mathbf{if}\;x \leq -36:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 80000000:\\ \;\;\;\;\frac{z \cdot -0.0849854566191904 + x \cdot \left(y \cdot -0.0849854566191904 + z \cdot 0.5658836402042561\right)}{x + 2}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (+ x -2.0)
          (+ 4.16438922228 (/ (- y 124074.40615218398) (* x (* x x)))))))
   (if (<= x -36.0)
     t_0
     (if (<= x 80000000.0)
       (/
        (+
         (* z -0.0849854566191904)
         (* x (+ (* y -0.0849854566191904) (* z 0.5658836402042561))))
        (+ x 2.0))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x + -2.0) * (4.16438922228 + ((y - 124074.40615218398) / (x * (x * x))));
	double tmp;
	if (x <= -36.0) {
		tmp = t_0;
	} else if (x <= 80000000.0) {
		tmp = ((z * -0.0849854566191904) + (x * ((y * -0.0849854566191904) + (z * 0.5658836402042561)))) / (x + 2.0);
	} 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 + ((y - 124074.40615218398d0) / (x * (x * x))))
    if (x <= (-36.0d0)) then
        tmp = t_0
    else if (x <= 80000000.0d0) then
        tmp = ((z * (-0.0849854566191904d0)) + (x * ((y * (-0.0849854566191904d0)) + (z * 0.5658836402042561d0)))) / (x + 2.0d0)
    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 + ((y - 124074.40615218398) / (x * (x * x))));
	double tmp;
	if (x <= -36.0) {
		tmp = t_0;
	} else if (x <= 80000000.0) {
		tmp = ((z * -0.0849854566191904) + (x * ((y * -0.0849854566191904) + (z * 0.5658836402042561)))) / (x + 2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + -2.0) * (4.16438922228 + ((y - 124074.40615218398) / (x * (x * x))))
	tmp = 0
	if x <= -36.0:
		tmp = t_0
	elif x <= 80000000.0:
		tmp = ((z * -0.0849854566191904) + (x * ((y * -0.0849854566191904) + (z * 0.5658836402042561)))) / (x + 2.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(y - 124074.40615218398) / Float64(x * Float64(x * x)))))
	tmp = 0.0
	if (x <= -36.0)
		tmp = t_0;
	elseif (x <= 80000000.0)
		tmp = Float64(Float64(Float64(z * -0.0849854566191904) + Float64(x * Float64(Float64(y * -0.0849854566191904) + Float64(z * 0.5658836402042561)))) / Float64(x + 2.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + -2.0) * (4.16438922228 + ((y - 124074.40615218398) / (x * (x * x))));
	tmp = 0.0;
	if (x <= -36.0)
		tmp = t_0;
	elseif (x <= 80000000.0)
		tmp = ((z * -0.0849854566191904) + (x * ((y * -0.0849854566191904) + (z * 0.5658836402042561)))) / (x + 2.0);
	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[(y - 124074.40615218398), $MachinePrecision] / N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -36.0], t$95$0, If[LessEqual[x, 80000000.0], N[(N[(N[(z * -0.0849854566191904), $MachinePrecision] + N[(x * N[(N[(y * -0.0849854566191904), $MachinePrecision] + N[(z * 0.5658836402042561), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 2.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -36 or 8e7 < x

   1. Initial program 16.0%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 22.4%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 95.5%

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

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \color{blue}{\left(\frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}}\right)}\right)\right) \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} - y\right), \color{blue}{\left({x}^{3}\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), \left({\color{blue}{x}}^{3}\right)\right)\right)\right) \]

      3. cube-mult N/A

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

      4. unpow2 N/A

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

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

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

      6. unpow2 N/A

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

      7. *-lowering-*.f64 95.0%

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

   10. Simplified 95.0%

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

   if -36 < x < 8e7

   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 99.7%

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

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{-2000000000}{23533438303} \cdot z + x \cdot \left(\frac{-2000000000}{23533438303} \cdot y - \frac{-313399215894000000000}{553822718361107519809} \cdot z\right)\right)}, \mathsf{+.f64}\left(x, 2\right)\right) \]
   8. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{-2000000000}{23533438303} \cdot z\right), \left(x \cdot \left(\frac{-2000000000}{23533438303} \cdot y - \frac{-313399215894000000000}{553822718361107519809} \cdot z\right)\right)\right), \mathsf{+.f64}\left(\color{blue}{x}, 2\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(z \cdot \frac{-2000000000}{23533438303}\right), \left(x \cdot \left(\frac{-2000000000}{23533438303} \cdot y - \frac{-313399215894000000000}{553822718361107519809} \cdot z\right)\right)\right), \mathsf{+.f64}\left(x, 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-2000000000}{23533438303}\right), \left(x \cdot \left(\frac{-2000000000}{23533438303} \cdot y - \frac{-313399215894000000000}{553822718361107519809} \cdot z\right)\right)\right), \mathsf{+.f64}\left(x, 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-2000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \left(\frac{-2000000000}{23533438303} \cdot y - \frac{-313399215894000000000}{553822718361107519809} \cdot z\right)\right)\right), \mathsf{+.f64}\left(x, 2\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-2000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \left(\frac{-2000000000}{23533438303} \cdot y + \left(\mathsf{neg}\left(\frac{-313399215894000000000}{553822718361107519809} \cdot z\right)\right)\right)\right)\right), \mathsf{+.f64}\left(x, 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-2000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{-2000000000}{23533438303} \cdot y\right), \left(\mathsf{neg}\left(\frac{-313399215894000000000}{553822718361107519809} \cdot z\right)\right)\right)\right)\right), \mathsf{+.f64}\left(x, 2\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-2000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(y \cdot \frac{-2000000000}{23533438303}\right), \left(\mathsf{neg}\left(\frac{-313399215894000000000}{553822718361107519809} \cdot z\right)\right)\right)\right)\right), \mathsf{+.f64}\left(x, 2\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-2000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-2000000000}{23533438303}\right), \left(\mathsf{neg}\left(\frac{-313399215894000000000}{553822718361107519809} \cdot z\right)\right)\right)\right)\right), \mathsf{+.f64}\left(x, 2\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-2000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-2000000000}{23533438303}\right), \left(\mathsf{neg}\left(z \cdot \frac{-313399215894000000000}{553822718361107519809}\right)\right)\right)\right)\right), \mathsf{+.f64}\left(x, 2\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-2000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-2000000000}{23533438303}\right), \left(z \cdot \left(\mathsf{neg}\left(\frac{-313399215894000000000}{553822718361107519809}\right)\right)\right)\right)\right)\right), \mathsf{+.f64}\left(x, 2\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-2000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-2000000000}{23533438303}\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\frac{-313399215894000000000}{553822718361107519809}\right)\right)\right)\right)\right)\right), \mathsf{+.f64}\left(x, 2\right)\right) \]

      12. metadata-eval 87.6%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-2000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-2000000000}{23533438303}\right), \mathsf{*.f64}\left(z, \frac{313399215894000000000}{553822718361107519809}\right)\right)\right)\right), \mathsf{+.f64}\left(x, 2\right)\right) \]

   9. Simplified 87.6%

      \[\leadsto \frac{\color{blue}{z \cdot -0.0849854566191904 + x \cdot \left(y \cdot -0.0849854566191904 + z \cdot 0.5658836402042561\right)}}{x + 2} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -36:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{y - 124074.40615218398}{x \cdot \left(x \cdot x\right)}\right)\\ \mathbf{elif}\;x \leq 80000000:\\ \;\;\;\;\frac{z \cdot -0.0849854566191904 + x \cdot \left(y \cdot -0.0849854566191904 + z \cdot 0.5658836402042561\right)}{x + 2}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{y - 124074.40615218398}{x \cdot \left(x \cdot x\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+24}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952 - x \cdot \left(y \cdot -0.3041881842569256 + 5.843575199059173\right)\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-5}:\\ \;\;\;\;z \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{\frac{3655.1204654076414}{x} + -110.1139242984811}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.45e+24)
   (* x 4.16438922228)
   (if (<= x -1.85e-110)
     (*
      x
      (-
       (* y -0.0424927283095952)
       (* x (+ (* y -0.3041881842569256) 5.843575199059173))))
     (if (<= x 1.85e-5)
       (* z (+ -0.0424927283095952 (* x 0.3041881842569256)))
       (*
        x
        (+
         4.16438922228
         (/ (+ (/ 3655.1204654076414 x) -110.1139242984811) x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.45e+24) {
		tmp = x * 4.16438922228;
	} else if (x <= -1.85e-110) {
		tmp = x * ((y * -0.0424927283095952) - (x * ((y * -0.3041881842569256) + 5.843575199059173)));
	} else if (x <= 1.85e-5) {
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256));
	} else {
		tmp = x * (4.16438922228 + (((3655.1204654076414 / x) + -110.1139242984811) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.45d+24)) then
        tmp = x * 4.16438922228d0
    else if (x <= (-1.85d-110)) then
        tmp = x * ((y * (-0.0424927283095952d0)) - (x * ((y * (-0.3041881842569256d0)) + 5.843575199059173d0)))
    else if (x <= 1.85d-5) then
        tmp = z * ((-0.0424927283095952d0) + (x * 0.3041881842569256d0))
    else
        tmp = x * (4.16438922228d0 + (((3655.1204654076414d0 / x) + (-110.1139242984811d0)) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.45e+24) {
		tmp = x * 4.16438922228;
	} else if (x <= -1.85e-110) {
		tmp = x * ((y * -0.0424927283095952) - (x * ((y * -0.3041881842569256) + 5.843575199059173)));
	} else if (x <= 1.85e-5) {
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256));
	} else {
		tmp = x * (4.16438922228 + (((3655.1204654076414 / x) + -110.1139242984811) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.45e+24:
		tmp = x * 4.16438922228
	elif x <= -1.85e-110:
		tmp = x * ((y * -0.0424927283095952) - (x * ((y * -0.3041881842569256) + 5.843575199059173)))
	elif x <= 1.85e-5:
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256))
	else:
		tmp = x * (4.16438922228 + (((3655.1204654076414 / x) + -110.1139242984811) / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.45e+24)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= -1.85e-110)
		tmp = Float64(x * Float64(Float64(y * -0.0424927283095952) - Float64(x * Float64(Float64(y * -0.3041881842569256) + 5.843575199059173))));
	elseif (x <= 1.85e-5)
		tmp = Float64(z * Float64(-0.0424927283095952 + Float64(x * 0.3041881842569256)));
	else
		tmp = Float64(x * Float64(4.16438922228 + Float64(Float64(Float64(3655.1204654076414 / x) + -110.1139242984811) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.45e+24)
		tmp = x * 4.16438922228;
	elseif (x <= -1.85e-110)
		tmp = x * ((y * -0.0424927283095952) - (x * ((y * -0.3041881842569256) + 5.843575199059173)));
	elseif (x <= 1.85e-5)
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256));
	else
		tmp = x * (4.16438922228 + (((3655.1204654076414 / x) + -110.1139242984811) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.45e+24], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, -1.85e-110], N[(x * N[(N[(y * -0.0424927283095952), $MachinePrecision] - N[(x * N[(N[(y * -0.3041881842569256), $MachinePrecision] + 5.843575199059173), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.85e-5], N[(z * N[(-0.0424927283095952 + N[(x * 0.3041881842569256), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(4.16438922228 + N[(N[(N[(3655.1204654076414 / x), $MachinePrecision] + -110.1139242984811), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.4499999999999999e24

   1. Initial program 8.9%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 17.2%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 95.9%

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

   7. Simplified 95.9%

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

   if -1.4499999999999999e24 < x < -1.85000000000000008e-110

   1. Initial program 99.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 99.3%

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

      1. flip3-+ N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{{x}^{3} + {-2}^{3}}{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}\right), \mathsf{/.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\frac{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}{{x}^{3} + {-2}^{3}}}\right), \mathsf{/.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}{{x}^{3} + {-2}^{3}}\right)\right), \mathsf{/.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}{{x}^{3} + -8}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}{{x}^{3} + \left(\mathsf{neg}\left(8\right)\right)}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}{{x}^{3} + \left(\mathsf{neg}\left({2}^{3}\right)\right)}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}{{x}^{3} - {2}^{3}}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)\right), \left({x}^{3} - {2}^{3}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), \color{blue}{z}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      9. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\left(x \cdot x + -2 \cdot -2\right) - x \cdot -2\right), \left({x}^{3} - {2}^{3}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(x \cdot x + -2 \cdot -2\right), \left(x \cdot -2\right)\right), \left({x}^{3} - {2}^{3}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(x \cdot x\right), \left(-2 \cdot -2\right)\right), \left(x \cdot -2\right)\right), \left({x}^{3} - {2}^{3}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), \left(-2 \cdot -2\right)\right), \left(x \cdot -2\right)\right), \left({x}^{3} - {2}^{3}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \left(x \cdot -2\right)\right), \left({x}^{3} - {2}^{3}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \mathsf{*.f64}\left(x, -2\right)\right), \left({x}^{3} - {2}^{3}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \mathsf{*.f64}\left(x, -2\right)\right), \left({x}^{3} + \left(\mathsf{neg}\left({2}^{3}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \mathsf{*.f64}\left(x, -2\right)\right), \left({x}^{3} + \left(\mathsf{neg}\left(8\right)\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \mathsf{*.f64}\left(x, -2\right)\right), \left({x}^{3} + -8\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      18. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \mathsf{*.f64}\left(x, -2\right)\right), \left({x}^{3} + {-2}^{3}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \mathsf{*.f64}\left(x, -2\right)\right), \mathsf{+.f64}\left(\left({x}^{3}\right), \left({-2}^{3}\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      20. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \mathsf{*.f64}\left(x, -2\right)\right), \mathsf{+.f64}\left(\left(x \cdot \left(x \cdot x\right)\right), \left({-2}^{3}\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \mathsf{*.f64}\left(x, -2\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(x \cdot x\right)\right), \left({-2}^{3}\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \mathsf{*.f64}\left(x, -2\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right), \left({-2}^{3}\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      23. metadata-eval 99.4%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \mathsf{*.f64}\left(x, -2\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right), -8\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

   6. Applied egg-rr 99.4%

      \[\leadsto \color{blue}{\frac{1}{\frac{\left(x \cdot x + 4\right) - x \cdot -2}{x \cdot \left(x \cdot x\right) + -8}}} \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \]

   7. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z + x \cdot \left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-215985700909750000000}{553822718361107519809} \cdot z + \frac{336932654197}{47066876606} \cdot \left(\frac{-1000000000}{23533438303} \cdot y - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{-1000000000}{23533438303} \cdot y\right) - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)} \]
   8. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{-1000000000}{23533438303} \cdot z\right), \color{blue}{\left(x \cdot \left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-215985700909750000000}{553822718361107519809} \cdot z + \frac{336932654197}{47066876606} \cdot \left(\frac{-1000000000}{23533438303} \cdot y - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{-1000000000}{23533438303} \cdot y\right) - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, z\right), \left(\color{blue}{x} \cdot \left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-215985700909750000000}{553822718361107519809} \cdot z + \frac{336932654197}{47066876606} \cdot \left(\frac{-1000000000}{23533438303} \cdot y - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{-1000000000}{23533438303} \cdot y\right) - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, z\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-215985700909750000000}{553822718361107519809} \cdot z + \frac{336932654197}{47066876606} \cdot \left(\frac{-1000000000}{23533438303} \cdot y - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{-1000000000}{23533438303} \cdot y\right) - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)}\right)\right) \]

      4. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, z\right), \mathsf{*.f64}\left(x, \left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-215985700909750000000}{553822718361107519809} \cdot z + \frac{336932654197}{47066876606} \cdot \left(\frac{-1000000000}{23533438303} \cdot y - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{-1000000000}{23533438303} \cdot y\right) + \color{blue}{\left(\mathsf{neg}\left(\frac{-168466327098500000000}{553822718361107519809}\right)\right) \cdot z}\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, z\right), \mathsf{*.f64}\left(x, \left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-215985700909750000000}{553822718361107519809} \cdot z + \frac{336932654197}{47066876606} \cdot \left(\frac{-1000000000}{23533438303} \cdot y - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{-1000000000}{23533438303} \cdot y\right) + \frac{168466327098500000000}{553822718361107519809} \cdot z\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, z\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-215985700909750000000}{553822718361107519809} \cdot z + \frac{336932654197}{47066876606} \cdot \left(\frac{-1000000000}{23533438303} \cdot y - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{-1000000000}{23533438303} \cdot y\right), \color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} \cdot z\right)}\right)\right)\right) \]

   9. Simplified 77.2%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z + x \cdot \left(\left(-0.0424927283095952 \cdot y - x \cdot \left(5.843575199059173 + \left(z \cdot -0.38999068429136097 + \left(-0.0424927283095952 \cdot y + z \cdot 0.3041881842569256\right) \cdot 7.158593866711955\right)\right)\right) + z \cdot 0.3041881842569256\right)} \]

   10. Taylor expanded in z around 0

       \[\leadsto \color{blue}{x \cdot \left(\frac{-1000000000}{23533438303} \cdot y - x \cdot \left(\frac{137519416416}{23533438303} + \frac{-168466327098500000000}{553822718361107519809} \cdot y\right)\right)} \]
   11. Step-by-step derivation

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

          \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{-1000000000}{23533438303} \cdot y - x \cdot \left(\frac{137519416416}{23533438303} + \frac{-168466327098500000000}{553822718361107519809} \cdot y\right)\right)}\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{-1000000000}{23533438303} \cdot y\right), \color{blue}{\left(x \cdot \left(\frac{137519416416}{23533438303} + \frac{-168466327098500000000}{553822718361107519809} \cdot y\right)\right)}\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, y\right), \left(\color{blue}{x} \cdot \left(\frac{137519416416}{23533438303} + \frac{-168466327098500000000}{553822718361107519809} \cdot y\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, y\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{137519416416}{23533438303} + \frac{-168466327098500000000}{553822718361107519809} \cdot y\right)}\right)\right)\right) \]

       5. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, y\right), \mathsf{*.f64}\left(x, \left(\frac{-168466327098500000000}{553822718361107519809} \cdot y + \color{blue}{\frac{137519416416}{23533438303}}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, y\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{-168466327098500000000}{553822718361107519809} \cdot y\right), \color{blue}{\frac{137519416416}{23533438303}}\right)\right)\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, y\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(y \cdot \frac{-168466327098500000000}{553822718361107519809}\right), \frac{137519416416}{23533438303}\right)\right)\right)\right) \]

       8. *-lowering-*.f64 58.0%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, y\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-168466327098500000000}{553822718361107519809}\right), \frac{137519416416}{23533438303}\right)\right)\right)\right) \]

   12. Simplified 58.0%

       \[\leadsto \color{blue}{x \cdot \left(-0.0424927283095952 \cdot y - x \cdot \left(y \cdot -0.3041881842569256 + 5.843575199059173\right)\right)} \]

   if -1.85000000000000008e-110 < x < 1.84999999999999991e-5

   1. Initial program 99.8%

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

      1. 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 99.8%

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

   5. Taylor expanded in x around 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 92.4%

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

   7. Simplified 92.4%

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

   8. Taylor expanded in z around inf

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

      1. associate-*r* N/A

         \[\leadsto \left(z \cdot \left(\frac{500000000}{23533438303} + \frac{-78349803973500000000}{553822718361107519809} \cdot x\right)\right) \cdot \color{blue}{\left(x - 2\right)} \]

      2. distribute-rgt-in N/A

         \[\leadsto \left(\frac{500000000}{23533438303} \cdot z + \left(\frac{-78349803973500000000}{553822718361107519809} \cdot x\right) \cdot z\right) \cdot \left(\color{blue}{x} - 2\right) \]

      3. associate-*r* N/A

         \[\leadsto \left(\frac{500000000}{23533438303} \cdot z + \frac{-78349803973500000000}{553822718361107519809} \cdot \left(x \cdot z\right)\right) \cdot \left(x - 2\right) \]

      4. +-commutative N/A

         \[\leadsto \left(\frac{-78349803973500000000}{553822718361107519809} \cdot \left(x \cdot z\right) + \frac{500000000}{23533438303} \cdot z\right) \cdot \left(\color{blue}{x} - 2\right) \]

      5. *-commutative N/A

         \[\leadsto \left(x - 2\right) \cdot \color{blue}{\left(\frac{-78349803973500000000}{553822718361107519809} \cdot \left(x \cdot z\right) + \frac{500000000}{23533438303} \cdot z\right)} \]

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

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

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

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

      10. +-commutative N/A

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

      11. associate-*r* N/A

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

      12. distribute-rgt-in N/A

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

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

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

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

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

      15. *-commutative N/A

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

      16. *-lowering-*.f64 73.2%

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

   10. Simplified 73.2%

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

   11. Taylor expanded in x around 0

       \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z + \frac{168466327098500000000}{553822718361107519809} \cdot \left(x \cdot z\right)} \]
   12. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \frac{168466327098500000000}{553822718361107519809} \cdot \left(x \cdot z\right) + \color{blue}{\frac{-1000000000}{23533438303} \cdot z} \]

       2. associate-*r* N/A

          \[\leadsto \left(\frac{168466327098500000000}{553822718361107519809} \cdot x\right) \cdot z + \color{blue}{\frac{-1000000000}{23533438303}} \cdot z \]

       3. distribute-rgt-out N/A

          \[\leadsto z \cdot \color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} \cdot x + \frac{-1000000000}{23533438303}\right)} \]

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

          \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} \cdot x + \frac{-1000000000}{23533438303}\right)}\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(\frac{168466327098500000000}{553822718361107519809} \cdot x\right), \color{blue}{\frac{-1000000000}{23533438303}}\right)\right) \]

       6. *-lowering-*.f64 73.2%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{168466327098500000000}{553822718361107519809}, x\right), \frac{-1000000000}{23533438303}\right)\right) \]

   13. Simplified 73.2%

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

   if 1.84999999999999991e-5 < x

   1. Initial program 22.5%

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

      1. 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 27.0%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(\frac{104109730557}{25000000000} + \frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{{x}^{2}}\right) - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   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 87.0%

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

   7. Simplified 87.0%

      \[\leadsto \color{blue}{x \cdot \left(4.16438922228 + \frac{\frac{3655.1204654076414}{x} + -110.1139242984811}{x}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+24}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952 - x \cdot \left(y \cdot -0.3041881842569256 + 5.843575199059173\right)\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-5}:\\ \;\;\;\;z \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{\frac{3655.1204654076414}{x} + -110.1139242984811}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 75.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+24}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-63}:\\ \;\;\;\;x \cdot \left(y \cdot \left(0 - \left(0.0424927283095952 + x \cdot -0.3041881842569256\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-5}:\\ \;\;\;\;z \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{\frac{3655.1204654076414}{x} + -110.1139242984811}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.45e+24)
   (* x 4.16438922228)
   (if (<= x -7.5e-63)
     (* x (* y (- 0.0 (+ 0.0424927283095952 (* x -0.3041881842569256)))))
     (if (<= x 1.85e-5)
       (* z (+ -0.0424927283095952 (* x 0.3041881842569256)))
       (*
        x
        (+
         4.16438922228
         (/ (+ (/ 3655.1204654076414 x) -110.1139242984811) x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.45e+24) {
		tmp = x * 4.16438922228;
	} else if (x <= -7.5e-63) {
		tmp = x * (y * (0.0 - (0.0424927283095952 + (x * -0.3041881842569256))));
	} else if (x <= 1.85e-5) {
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256));
	} else {
		tmp = x * (4.16438922228 + (((3655.1204654076414 / x) + -110.1139242984811) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.45d+24)) then
        tmp = x * 4.16438922228d0
    else if (x <= (-7.5d-63)) then
        tmp = x * (y * (0.0d0 - (0.0424927283095952d0 + (x * (-0.3041881842569256d0)))))
    else if (x <= 1.85d-5) then
        tmp = z * ((-0.0424927283095952d0) + (x * 0.3041881842569256d0))
    else
        tmp = x * (4.16438922228d0 + (((3655.1204654076414d0 / x) + (-110.1139242984811d0)) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.45e+24) {
		tmp = x * 4.16438922228;
	} else if (x <= -7.5e-63) {
		tmp = x * (y * (0.0 - (0.0424927283095952 + (x * -0.3041881842569256))));
	} else if (x <= 1.85e-5) {
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256));
	} else {
		tmp = x * (4.16438922228 + (((3655.1204654076414 / x) + -110.1139242984811) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.45e+24:
		tmp = x * 4.16438922228
	elif x <= -7.5e-63:
		tmp = x * (y * (0.0 - (0.0424927283095952 + (x * -0.3041881842569256))))
	elif x <= 1.85e-5:
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256))
	else:
		tmp = x * (4.16438922228 + (((3655.1204654076414 / x) + -110.1139242984811) / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.45e+24)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= -7.5e-63)
		tmp = Float64(x * Float64(y * Float64(0.0 - Float64(0.0424927283095952 + Float64(x * -0.3041881842569256)))));
	elseif (x <= 1.85e-5)
		tmp = Float64(z * Float64(-0.0424927283095952 + Float64(x * 0.3041881842569256)));
	else
		tmp = Float64(x * Float64(4.16438922228 + Float64(Float64(Float64(3655.1204654076414 / x) + -110.1139242984811) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.45e+24)
		tmp = x * 4.16438922228;
	elseif (x <= -7.5e-63)
		tmp = x * (y * (0.0 - (0.0424927283095952 + (x * -0.3041881842569256))));
	elseif (x <= 1.85e-5)
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256));
	else
		tmp = x * (4.16438922228 + (((3655.1204654076414 / x) + -110.1139242984811) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.45e+24], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, -7.5e-63], N[(x * N[(y * N[(0.0 - N[(0.0424927283095952 + N[(x * -0.3041881842569256), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.85e-5], N[(z * N[(-0.0424927283095952 + N[(x * 0.3041881842569256), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(4.16438922228 + N[(N[(N[(3655.1204654076414 / x), $MachinePrecision] + -110.1139242984811), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.4499999999999999e24

   1. Initial program 8.9%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 17.2%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 95.9%

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

   7. Simplified 95.9%

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

   if -1.4499999999999999e24 < x < -7.5000000000000003e-63

   1. Initial program 99.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 99.3%

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

      1. flip3-+ N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{{x}^{3} + {-2}^{3}}{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}\right), \mathsf{/.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\frac{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}{{x}^{3} + {-2}^{3}}}\right), \mathsf{/.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}{{x}^{3} + {-2}^{3}}\right)\right), \mathsf{/.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}{{x}^{3} + -8}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}{{x}^{3} + \left(\mathsf{neg}\left(8\right)\right)}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}{{x}^{3} + \left(\mathsf{neg}\left({2}^{3}\right)\right)}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}{{x}^{3} - {2}^{3}}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)\right), \left({x}^{3} - {2}^{3}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), \color{blue}{z}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      9. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\left(x \cdot x + -2 \cdot -2\right) - x \cdot -2\right), \left({x}^{3} - {2}^{3}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(x \cdot x + -2 \cdot -2\right), \left(x \cdot -2\right)\right), \left({x}^{3} - {2}^{3}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(x \cdot x\right), \left(-2 \cdot -2\right)\right), \left(x \cdot -2\right)\right), \left({x}^{3} - {2}^{3}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), \left(-2 \cdot -2\right)\right), \left(x \cdot -2\right)\right), \left({x}^{3} - {2}^{3}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \left(x \cdot -2\right)\right), \left({x}^{3} - {2}^{3}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \mathsf{*.f64}\left(x, -2\right)\right), \left({x}^{3} - {2}^{3}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \mathsf{*.f64}\left(x, -2\right)\right), \left({x}^{3} + \left(\mathsf{neg}\left({2}^{3}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \mathsf{*.f64}\left(x, -2\right)\right), \left({x}^{3} + \left(\mathsf{neg}\left(8\right)\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \mathsf{*.f64}\left(x, -2\right)\right), \left({x}^{3} + -8\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      18. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \mathsf{*.f64}\left(x, -2\right)\right), \left({x}^{3} + {-2}^{3}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \mathsf{*.f64}\left(x, -2\right)\right), \mathsf{+.f64}\left(\left({x}^{3}\right), \left({-2}^{3}\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      20. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \mathsf{*.f64}\left(x, -2\right)\right), \mathsf{+.f64}\left(\left(x \cdot \left(x \cdot x\right)\right), \left({-2}^{3}\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \mathsf{*.f64}\left(x, -2\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(x \cdot x\right)\right), \left({-2}^{3}\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \mathsf{*.f64}\left(x, -2\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right), \left({-2}^{3}\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      23. metadata-eval 99.4%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \mathsf{*.f64}\left(x, -2\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right), -8\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

   6. Applied egg-rr 99.4%

      \[\leadsto \color{blue}{\frac{1}{\frac{\left(x \cdot x + 4\right) - x \cdot -2}{x \cdot \left(x \cdot x\right) + -8}}} \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \]

   7. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z + x \cdot \left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-215985700909750000000}{553822718361107519809} \cdot z + \frac{336932654197}{47066876606} \cdot \left(\frac{-1000000000}{23533438303} \cdot y - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{-1000000000}{23533438303} \cdot y\right) - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)} \]
   8. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{-1000000000}{23533438303} \cdot z\right), \color{blue}{\left(x \cdot \left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-215985700909750000000}{553822718361107519809} \cdot z + \frac{336932654197}{47066876606} \cdot \left(\frac{-1000000000}{23533438303} \cdot y - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{-1000000000}{23533438303} \cdot y\right) - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, z\right), \left(\color{blue}{x} \cdot \left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-215985700909750000000}{553822718361107519809} \cdot z + \frac{336932654197}{47066876606} \cdot \left(\frac{-1000000000}{23533438303} \cdot y - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{-1000000000}{23533438303} \cdot y\right) - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, z\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-215985700909750000000}{553822718361107519809} \cdot z + \frac{336932654197}{47066876606} \cdot \left(\frac{-1000000000}{23533438303} \cdot y - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{-1000000000}{23533438303} \cdot y\right) - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)}\right)\right) \]

      4. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, z\right), \mathsf{*.f64}\left(x, \left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-215985700909750000000}{553822718361107519809} \cdot z + \frac{336932654197}{47066876606} \cdot \left(\frac{-1000000000}{23533438303} \cdot y - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{-1000000000}{23533438303} \cdot y\right) + \color{blue}{\left(\mathsf{neg}\left(\frac{-168466327098500000000}{553822718361107519809}\right)\right) \cdot z}\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, z\right), \mathsf{*.f64}\left(x, \left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-215985700909750000000}{553822718361107519809} \cdot z + \frac{336932654197}{47066876606} \cdot \left(\frac{-1000000000}{23533438303} \cdot y - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{-1000000000}{23533438303} \cdot y\right) + \frac{168466327098500000000}{553822718361107519809} \cdot z\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, z\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-215985700909750000000}{553822718361107519809} \cdot z + \frac{336932654197}{47066876606} \cdot \left(\frac{-1000000000}{23533438303} \cdot y - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{-1000000000}{23533438303} \cdot y\right), \color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} \cdot z\right)}\right)\right)\right) \]

   9. Simplified 70.2%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z + x \cdot \left(\left(-0.0424927283095952 \cdot y - x \cdot \left(5.843575199059173 + \left(z \cdot -0.38999068429136097 + \left(-0.0424927283095952 \cdot y + z \cdot 0.3041881842569256\right) \cdot 7.158593866711955\right)\right)\right) + z \cdot 0.3041881842569256\right)} \]

   10. Taylor expanded in y around inf

       \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(y \cdot \left(\frac{1000000000}{23533438303} + \frac{-168466327098500000000}{553822718361107519809} \cdot x\right)\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \left(x \cdot \left(y \cdot \left(\frac{1000000000}{23533438303} + \frac{-168466327098500000000}{553822718361107519809} \cdot x\right)\right)\right) \cdot \color{blue}{-1} \]

       2. metadata-eval N/A

          \[\leadsto \left(x \cdot \left(y \cdot \left(\frac{1000000000}{23533438303} + \left(\mathsf{neg}\left(\frac{168466327098500000000}{553822718361107519809}\right)\right) \cdot x\right)\right)\right) \cdot -1 \]

       3. cancel-sign-sub-inv N/A

          \[\leadsto \left(x \cdot \left(y \cdot \left(\frac{1000000000}{23533438303} - \frac{168466327098500000000}{553822718361107519809} \cdot x\right)\right)\right) \cdot -1 \]

       4. associate-*l* N/A

          \[\leadsto x \cdot \color{blue}{\left(\left(y \cdot \left(\frac{1000000000}{23533438303} - \frac{168466327098500000000}{553822718361107519809} \cdot x\right)\right) \cdot -1\right)} \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\left(y \cdot \left(\frac{1000000000}{23533438303} - \frac{168466327098500000000}{553822718361107519809} \cdot x\right)\right) \cdot -1\right)}\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(y \cdot \left(\frac{1000000000}{23533438303} - \frac{168466327098500000000}{553822718361107519809} \cdot x\right)\right), \color{blue}{-1}\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{1000000000}{23533438303} - \frac{168466327098500000000}{553822718361107519809} \cdot x\right)\right), -1\right)\right) \]

       8. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{1000000000}{23533438303} + \left(\mathsf{neg}\left(\frac{168466327098500000000}{553822718361107519809}\right)\right) \cdot x\right)\right), -1\right)\right) \]

       9. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{1000000000}{23533438303} + \frac{-168466327098500000000}{553822718361107519809} \cdot x\right)\right), -1\right)\right) \]

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

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{1000000000}{23533438303}, \left(\frac{-168466327098500000000}{553822718361107519809} \cdot x\right)\right)\right), -1\right)\right) \]

       11. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{1000000000}{23533438303}, \left(x \cdot \frac{-168466327098500000000}{553822718361107519809}\right)\right)\right), -1\right)\right) \]

       12. *-lowering-*.f64 40.0%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{1000000000}{23533438303}, \mathsf{*.f64}\left(x, \frac{-168466327098500000000}{553822718361107519809}\right)\right)\right), -1\right)\right) \]

   12. Simplified 40.0%

       \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(0.0424927283095952 + x \cdot -0.3041881842569256\right)\right) \cdot -1\right)} \]

   if -7.5000000000000003e-63 < x < 1.84999999999999991e-5

   1. Initial program 99.8%

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

      1. 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 99.8%

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

   5. Taylor expanded in x around 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 91.8%

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

   7. Simplified 91.8%

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

   8. Taylor expanded in z around inf

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

      1. associate-*r* N/A

         \[\leadsto \left(z \cdot \left(\frac{500000000}{23533438303} + \frac{-78349803973500000000}{553822718361107519809} \cdot x\right)\right) \cdot \color{blue}{\left(x - 2\right)} \]

      2. distribute-rgt-in N/A

         \[\leadsto \left(\frac{500000000}{23533438303} \cdot z + \left(\frac{-78349803973500000000}{553822718361107519809} \cdot x\right) \cdot z\right) \cdot \left(\color{blue}{x} - 2\right) \]

      3. associate-*r* N/A

         \[\leadsto \left(\frac{500000000}{23533438303} \cdot z + \frac{-78349803973500000000}{553822718361107519809} \cdot \left(x \cdot z\right)\right) \cdot \left(x - 2\right) \]

      4. +-commutative N/A

         \[\leadsto \left(\frac{-78349803973500000000}{553822718361107519809} \cdot \left(x \cdot z\right) + \frac{500000000}{23533438303} \cdot z\right) \cdot \left(\color{blue}{x} - 2\right) \]

      5. *-commutative N/A

         \[\leadsto \left(x - 2\right) \cdot \color{blue}{\left(\frac{-78349803973500000000}{553822718361107519809} \cdot \left(x \cdot z\right) + \frac{500000000}{23533438303} \cdot z\right)} \]

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

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

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

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

      10. +-commutative N/A

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

      11. associate-*r* N/A

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

      12. distribute-rgt-in N/A

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

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

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

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

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

      15. *-commutative N/A

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

      16. *-lowering-*.f64 71.8%

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

   10. Simplified 71.8%

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

   11. Taylor expanded in x around 0

       \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z + \frac{168466327098500000000}{553822718361107519809} \cdot \left(x \cdot z\right)} \]
   12. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \frac{168466327098500000000}{553822718361107519809} \cdot \left(x \cdot z\right) + \color{blue}{\frac{-1000000000}{23533438303} \cdot z} \]

       2. associate-*r* N/A

          \[\leadsto \left(\frac{168466327098500000000}{553822718361107519809} \cdot x\right) \cdot z + \color{blue}{\frac{-1000000000}{23533438303}} \cdot z \]

       3. distribute-rgt-out N/A

          \[\leadsto z \cdot \color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} \cdot x + \frac{-1000000000}{23533438303}\right)} \]

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

          \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} \cdot x + \frac{-1000000000}{23533438303}\right)}\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(\frac{168466327098500000000}{553822718361107519809} \cdot x\right), \color{blue}{\frac{-1000000000}{23533438303}}\right)\right) \]

       6. *-lowering-*.f64 71.8%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{168466327098500000000}{553822718361107519809}, x\right), \frac{-1000000000}{23533438303}\right)\right) \]

   13. Simplified 71.8%

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

   if 1.84999999999999991e-5 < x

   1. Initial program 22.5%

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

      1. 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 27.0%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(\frac{104109730557}{25000000000} + \frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{{x}^{2}}\right) - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   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 87.0%

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

   7. Simplified 87.0%

      \[\leadsto \color{blue}{x \cdot \left(4.16438922228 + \frac{\frac{3655.1204654076414}{x} + -110.1139242984811}{x}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+24}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-63}:\\ \;\;\;\;x \cdot \left(y \cdot \left(0 - \left(0.0424927283095952 + x \cdot -0.3041881842569256\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-5}:\\ \;\;\;\;z \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{\frac{3655.1204654076414}{x} + -110.1139242984811}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 92.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + -2\right) \cdot \left(4.16438922228 + \frac{y - 124074.40615218398}{x \cdot \left(x \cdot x\right)}\right)\\ \mathbf{if}\;x \leq -330:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 80000000:\\ \;\;\;\;x \cdot \left(z \cdot 0.3041881842569256 + y \cdot -0.0424927283095952\right) + z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (+ x -2.0)
          (+ 4.16438922228 (/ (- y 124074.40615218398) (* x (* x x)))))))
   (if (<= x -330.0)
     t_0
     (if (<= x 80000000.0)
       (+
        (* x (+ (* z 0.3041881842569256) (* y -0.0424927283095952)))
        (* z -0.0424927283095952))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x + -2.0) * (4.16438922228 + ((y - 124074.40615218398) / (x * (x * x))));
	double tmp;
	if (x <= -330.0) {
		tmp = t_0;
	} else if (x <= 80000000.0) {
		tmp = (x * ((z * 0.3041881842569256) + (y * -0.0424927283095952))) + (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 + ((y - 124074.40615218398d0) / (x * (x * x))))
    if (x <= (-330.0d0)) then
        tmp = t_0
    else if (x <= 80000000.0d0) then
        tmp = (x * ((z * 0.3041881842569256d0) + (y * (-0.0424927283095952d0)))) + (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 + ((y - 124074.40615218398) / (x * (x * x))));
	double tmp;
	if (x <= -330.0) {
		tmp = t_0;
	} else if (x <= 80000000.0) {
		tmp = (x * ((z * 0.3041881842569256) + (y * -0.0424927283095952))) + (z * -0.0424927283095952);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + -2.0) * (4.16438922228 + ((y - 124074.40615218398) / (x * (x * x))))
	tmp = 0
	if x <= -330.0:
		tmp = t_0
	elif x <= 80000000.0:
		tmp = (x * ((z * 0.3041881842569256) + (y * -0.0424927283095952))) + (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(y - 124074.40615218398) / Float64(x * Float64(x * x)))))
	tmp = 0.0
	if (x <= -330.0)
		tmp = t_0;
	elseif (x <= 80000000.0)
		tmp = Float64(Float64(x * Float64(Float64(z * 0.3041881842569256) + Float64(y * -0.0424927283095952))) + Float64(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 + ((y - 124074.40615218398) / (x * (x * x))));
	tmp = 0.0;
	if (x <= -330.0)
		tmp = t_0;
	elseif (x <= 80000000.0)
		tmp = (x * ((z * 0.3041881842569256) + (y * -0.0424927283095952))) + (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[(y - 124074.40615218398), $MachinePrecision] / N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -330.0], t$95$0, If[LessEqual[x, 80000000.0], N[(N[(x * N[(N[(z * 0.3041881842569256), $MachinePrecision] + N[(y * -0.0424927283095952), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * -0.0424927283095952), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -330 or 8e7 < x

   1. Initial program 15.3%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 21.8%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 96.2%

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

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \color{blue}{\left(\frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}}\right)}\right)\right) \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} - y\right), \color{blue}{\left({x}^{3}\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{\_.f64}\left(\frac{104109730557}{25000000000}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000}, y\right), \left({\color{blue}{x}}^{3}\right)\right)\right)\right) \]

      3. cube-mult N/A

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

      4. unpow2 N/A

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

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

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

      6. unpow2 N/A

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

      7. *-lowering-*.f64 95.7%

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

   10. Simplified 95.7%

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

   if -330 < x < 8e7

   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 99.7%

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

   7. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z + x \cdot \left(\frac{-1000000000}{23533438303} \cdot y - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)} \]
   8. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{-1000000000}{23533438303} \cdot z\right), \color{blue}{\left(x \cdot \left(\frac{-1000000000}{23533438303} \cdot y - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \frac{-1000000000}{23533438303}\right), \left(\color{blue}{x} \cdot \left(\frac{-1000000000}{23533438303} \cdot y - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)\right) \]

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

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

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

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

      5. sub-neg N/A

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

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

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

      7. *-commutative N/A

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

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

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

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-1000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-1000000000}{23533438303}\right), \left(\mathsf{neg}\left(z \cdot \frac{-168466327098500000000}{553822718361107519809}\right)\right)\right)\right)\right) \]

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

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

      11. metadata-eval N/A

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

      12. *-lowering-*.f64 86.9%

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

   9. Simplified 86.9%

      \[\leadsto \color{blue}{z \cdot -0.0424927283095952 + x \cdot \left(y \cdot -0.0424927283095952 + z \cdot 0.3041881842569256\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -330:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{y - 124074.40615218398}{x \cdot \left(x \cdot x\right)}\right)\\ \mathbf{elif}\;x \leq 80000000:\\ \;\;\;\;x \cdot \left(z \cdot 0.3041881842569256 + y \cdot -0.0424927283095952\right) + z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{y - 124074.40615218398}{x \cdot \left(x \cdot x\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 89.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+24}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 80000000:\\ \;\;\;\;x \cdot \left(z \cdot 0.3041881842569256 + y \cdot -0.0424927283095952\right) + z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{\frac{3655.1204654076414}{x} + -110.1139242984811}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.45e+24)
   (* x 4.16438922228)
   (if (<= x 80000000.0)
     (+
      (* x (+ (* z 0.3041881842569256) (* y -0.0424927283095952)))
      (* z -0.0424927283095952))
     (*
      x
      (+
       4.16438922228
       (/ (+ (/ 3655.1204654076414 x) -110.1139242984811) x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.45e+24) {
		tmp = x * 4.16438922228;
	} else if (x <= 80000000.0) {
		tmp = (x * ((z * 0.3041881842569256) + (y * -0.0424927283095952))) + (z * -0.0424927283095952);
	} else {
		tmp = x * (4.16438922228 + (((3655.1204654076414 / x) + -110.1139242984811) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.45d+24)) then
        tmp = x * 4.16438922228d0
    else if (x <= 80000000.0d0) then
        tmp = (x * ((z * 0.3041881842569256d0) + (y * (-0.0424927283095952d0)))) + (z * (-0.0424927283095952d0))
    else
        tmp = x * (4.16438922228d0 + (((3655.1204654076414d0 / x) + (-110.1139242984811d0)) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.45e+24) {
		tmp = x * 4.16438922228;
	} else if (x <= 80000000.0) {
		tmp = (x * ((z * 0.3041881842569256) + (y * -0.0424927283095952))) + (z * -0.0424927283095952);
	} else {
		tmp = x * (4.16438922228 + (((3655.1204654076414 / x) + -110.1139242984811) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.45e+24:
		tmp = x * 4.16438922228
	elif x <= 80000000.0:
		tmp = (x * ((z * 0.3041881842569256) + (y * -0.0424927283095952))) + (z * -0.0424927283095952)
	else:
		tmp = x * (4.16438922228 + (((3655.1204654076414 / x) + -110.1139242984811) / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.45e+24)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 80000000.0)
		tmp = Float64(Float64(x * Float64(Float64(z * 0.3041881842569256) + Float64(y * -0.0424927283095952))) + Float64(z * -0.0424927283095952));
	else
		tmp = Float64(x * Float64(4.16438922228 + Float64(Float64(Float64(3655.1204654076414 / x) + -110.1139242984811) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.45e+24)
		tmp = x * 4.16438922228;
	elseif (x <= 80000000.0)
		tmp = (x * ((z * 0.3041881842569256) + (y * -0.0424927283095952))) + (z * -0.0424927283095952);
	else
		tmp = x * (4.16438922228 + (((3655.1204654076414 / x) + -110.1139242984811) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.45e+24], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 80000000.0], N[(N[(x * N[(N[(z * 0.3041881842569256), $MachinePrecision] + N[(y * -0.0424927283095952), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * -0.0424927283095952), $MachinePrecision]), $MachinePrecision], N[(x * N[(4.16438922228 + N[(N[(N[(3655.1204654076414 / x), $MachinePrecision] + -110.1139242984811), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.4499999999999999e24

   1. Initial program 8.9%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 17.2%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 95.9%

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

   7. Simplified 95.9%

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

   if -1.4499999999999999e24 < x < 8e7

   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 99.6%

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

   7. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z + x \cdot \left(\frac{-1000000000}{23533438303} \cdot y - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)} \]
   8. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{-1000000000}{23533438303} \cdot z\right), \color{blue}{\left(x \cdot \left(\frac{-1000000000}{23533438303} \cdot y - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \frac{-1000000000}{23533438303}\right), \left(\color{blue}{x} \cdot \left(\frac{-1000000000}{23533438303} \cdot y - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)\right) \]

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

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

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

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

      5. sub-neg N/A

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

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

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

      7. *-commutative N/A

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

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

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

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{-1000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-1000000000}{23533438303}\right), \left(\mathsf{neg}\left(z \cdot \frac{-168466327098500000000}{553822718361107519809}\right)\right)\right)\right)\right) \]

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

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

      11. metadata-eval N/A

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

      12. *-lowering-*.f64 85.0%

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

   9. Simplified 85.0%

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

   if 8e7 < x

   1. Initial program 18.6%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 23.3%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 91.2%

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

   7. Simplified 91.2%

      \[\leadsto \color{blue}{x \cdot \left(4.16438922228 + \frac{\frac{3655.1204654076414}{x} + -110.1139242984811}{x}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+24}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 80000000:\\ \;\;\;\;x \cdot \left(z \cdot 0.3041881842569256 + y \cdot -0.0424927283095952\right) + z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{\frac{3655.1204654076414}{x} + -110.1139242984811}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 88.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+24}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 80000000:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + 0.0212463641547976 \cdot \left(x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{\frac{3655.1204654076414}{x} + -110.1139242984811}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.45e+24)
   (* x 4.16438922228)
   (if (<= x 80000000.0)
     (* (+ x -2.0) (+ (* z 0.0212463641547976) (* 0.0212463641547976 (* x y))))
     (*
      x
      (+
       4.16438922228
       (/ (+ (/ 3655.1204654076414 x) -110.1139242984811) x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.45e+24) {
		tmp = x * 4.16438922228;
	} else if (x <= 80000000.0) {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (0.0212463641547976 * (x * y)));
	} else {
		tmp = x * (4.16438922228 + (((3655.1204654076414 / x) + -110.1139242984811) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.45d+24)) then
        tmp = x * 4.16438922228d0
    else if (x <= 80000000.0d0) then
        tmp = (x + (-2.0d0)) * ((z * 0.0212463641547976d0) + (0.0212463641547976d0 * (x * y)))
    else
        tmp = x * (4.16438922228d0 + (((3655.1204654076414d0 / x) + (-110.1139242984811d0)) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.45e+24) {
		tmp = x * 4.16438922228;
	} else if (x <= 80000000.0) {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (0.0212463641547976 * (x * y)));
	} else {
		tmp = x * (4.16438922228 + (((3655.1204654076414 / x) + -110.1139242984811) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.45e+24:
		tmp = x * 4.16438922228
	elif x <= 80000000.0:
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (0.0212463641547976 * (x * y)))
	else:
		tmp = x * (4.16438922228 + (((3655.1204654076414 / x) + -110.1139242984811) / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.45e+24)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 80000000.0)
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(z * 0.0212463641547976) + Float64(0.0212463641547976 * Float64(x * y))));
	else
		tmp = Float64(x * Float64(4.16438922228 + Float64(Float64(Float64(3655.1204654076414 / x) + -110.1139242984811) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.45e+24)
		tmp = x * 4.16438922228;
	elseif (x <= 80000000.0)
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (0.0212463641547976 * (x * y)));
	else
		tmp = x * (4.16438922228 + (((3655.1204654076414 / x) + -110.1139242984811) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.45e+24], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 80000000.0], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(z * 0.0212463641547976), $MachinePrecision] + N[(0.0212463641547976 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(4.16438922228 + N[(N[(N[(3655.1204654076414 / x), $MachinePrecision] + -110.1139242984811), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.4499999999999999e24

   1. Initial program 8.9%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 17.2%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 95.9%

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

   7. Simplified 95.9%

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

   if -1.4499999999999999e24 < x < 8e7

   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 84.9%

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

   7. Simplified 84.9%

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

   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 84.7%

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

   10. Simplified 84.7%

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

   if 8e7 < x

   1. Initial program 18.6%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 23.3%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 91.2%

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

   7. Simplified 91.2%

      \[\leadsto \color{blue}{x \cdot \left(4.16438922228 + \frac{\frac{3655.1204654076414}{x} + -110.1139242984811}{x}\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 75.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+24}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-62}:\\ \;\;\;\;x \cdot \left(y \cdot \left(0 - \left(0.0424927283095952 + x \cdot -0.3041881842569256\right)\right)\right)\\ \mathbf{elif}\;x \leq 80000000:\\ \;\;\;\;z \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.45e+24)
   (* x 4.16438922228)
   (if (<= x -2.7e-62)
     (* x (* y (- 0.0 (+ 0.0424927283095952 (* x -0.3041881842569256)))))
     (if (<= x 80000000.0)
       (* z (+ -0.0424927283095952 (* x 0.3041881842569256)))
       (* x (+ 4.16438922228 (/ -110.1139242984811 x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.45e+24) {
		tmp = x * 4.16438922228;
	} else if (x <= -2.7e-62) {
		tmp = x * (y * (0.0 - (0.0424927283095952 + (x * -0.3041881842569256))));
	} else if (x <= 80000000.0) {
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256));
	} else {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.45d+24)) then
        tmp = x * 4.16438922228d0
    else if (x <= (-2.7d-62)) then
        tmp = x * (y * (0.0d0 - (0.0424927283095952d0 + (x * (-0.3041881842569256d0)))))
    else if (x <= 80000000.0d0) then
        tmp = z * ((-0.0424927283095952d0) + (x * 0.3041881842569256d0))
    else
        tmp = x * (4.16438922228d0 + ((-110.1139242984811d0) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.45e+24) {
		tmp = x * 4.16438922228;
	} else if (x <= -2.7e-62) {
		tmp = x * (y * (0.0 - (0.0424927283095952 + (x * -0.3041881842569256))));
	} else if (x <= 80000000.0) {
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256));
	} else {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.45e+24:
		tmp = x * 4.16438922228
	elif x <= -2.7e-62:
		tmp = x * (y * (0.0 - (0.0424927283095952 + (x * -0.3041881842569256))))
	elif x <= 80000000.0:
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256))
	else:
		tmp = x * (4.16438922228 + (-110.1139242984811 / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.45e+24)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= -2.7e-62)
		tmp = Float64(x * Float64(y * Float64(0.0 - Float64(0.0424927283095952 + Float64(x * -0.3041881842569256)))));
	elseif (x <= 80000000.0)
		tmp = Float64(z * Float64(-0.0424927283095952 + Float64(x * 0.3041881842569256)));
	else
		tmp = Float64(x * Float64(4.16438922228 + Float64(-110.1139242984811 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.45e+24)
		tmp = x * 4.16438922228;
	elseif (x <= -2.7e-62)
		tmp = x * (y * (0.0 - (0.0424927283095952 + (x * -0.3041881842569256))));
	elseif (x <= 80000000.0)
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256));
	else
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.45e+24], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, -2.7e-62], N[(x * N[(y * N[(0.0 - N[(0.0424927283095952 + N[(x * -0.3041881842569256), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 80000000.0], N[(z * N[(-0.0424927283095952 + N[(x * 0.3041881842569256), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(4.16438922228 + N[(-110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.4499999999999999e24

   1. Initial program 8.9%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 17.2%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 95.9%

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

   7. Simplified 95.9%

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

   if -1.4499999999999999e24 < x < -2.70000000000000019e-62

   1. Initial program 99.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 99.3%

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

      1. flip3-+ N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{{x}^{3} + {-2}^{3}}{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}\right), \mathsf{/.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\frac{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}{{x}^{3} + {-2}^{3}}}\right), \mathsf{/.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}{{x}^{3} + {-2}^{3}}\right)\right), \mathsf{/.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}{{x}^{3} + -8}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}{{x}^{3} + \left(\mathsf{neg}\left(8\right)\right)}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}{{x}^{3} + \left(\mathsf{neg}\left({2}^{3}\right)\right)}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}{{x}^{3} - {2}^{3}}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)\right), \left({x}^{3} - {2}^{3}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), \color{blue}{z}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      9. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\left(x \cdot x + -2 \cdot -2\right) - x \cdot -2\right), \left({x}^{3} - {2}^{3}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(x \cdot x + -2 \cdot -2\right), \left(x \cdot -2\right)\right), \left({x}^{3} - {2}^{3}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(x \cdot x\right), \left(-2 \cdot -2\right)\right), \left(x \cdot -2\right)\right), \left({x}^{3} - {2}^{3}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), \left(-2 \cdot -2\right)\right), \left(x \cdot -2\right)\right), \left({x}^{3} - {2}^{3}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \left(x \cdot -2\right)\right), \left({x}^{3} - {2}^{3}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \mathsf{*.f64}\left(x, -2\right)\right), \left({x}^{3} - {2}^{3}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \mathsf{*.f64}\left(x, -2\right)\right), \left({x}^{3} + \left(\mathsf{neg}\left({2}^{3}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \mathsf{*.f64}\left(x, -2\right)\right), \left({x}^{3} + \left(\mathsf{neg}\left(8\right)\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \mathsf{*.f64}\left(x, -2\right)\right), \left({x}^{3} + -8\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      18. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \mathsf{*.f64}\left(x, -2\right)\right), \left({x}^{3} + {-2}^{3}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \mathsf{*.f64}\left(x, -2\right)\right), \mathsf{+.f64}\left(\left({x}^{3}\right), \left({-2}^{3}\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      20. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \mathsf{*.f64}\left(x, -2\right)\right), \mathsf{+.f64}\left(\left(x \cdot \left(x \cdot x\right)\right), \left({-2}^{3}\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \mathsf{*.f64}\left(x, -2\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(x \cdot x\right)\right), \left({-2}^{3}\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \mathsf{*.f64}\left(x, -2\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right), \left({-2}^{3}\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

      23. metadata-eval 99.4%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, x\right), 4\right), \mathsf{*.f64}\left(x, -2\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right), -8\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{104109730557}{25000000000}\right), \frac{393497462077}{5000000000}\right)\right), \frac{4297481763}{31250000}\right)\right), y\right)\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right)\right), \frac{263505074721}{1000000000}\right)\right), \frac{156699607947}{500000000}\right)\right), \frac{23533438303}{500000000}\right)\right)\right) \]

   6. Applied egg-rr 99.4%

      \[\leadsto \color{blue}{\frac{1}{\frac{\left(x \cdot x + 4\right) - x \cdot -2}{x \cdot \left(x \cdot x\right) + -8}}} \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \]

   7. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z + x \cdot \left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-215985700909750000000}{553822718361107519809} \cdot z + \frac{336932654197}{47066876606} \cdot \left(\frac{-1000000000}{23533438303} \cdot y - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{-1000000000}{23533438303} \cdot y\right) - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)} \]
   8. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{-1000000000}{23533438303} \cdot z\right), \color{blue}{\left(x \cdot \left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-215985700909750000000}{553822718361107519809} \cdot z + \frac{336932654197}{47066876606} \cdot \left(\frac{-1000000000}{23533438303} \cdot y - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{-1000000000}{23533438303} \cdot y\right) - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, z\right), \left(\color{blue}{x} \cdot \left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-215985700909750000000}{553822718361107519809} \cdot z + \frac{336932654197}{47066876606} \cdot \left(\frac{-1000000000}{23533438303} \cdot y - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{-1000000000}{23533438303} \cdot y\right) - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, z\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-215985700909750000000}{553822718361107519809} \cdot z + \frac{336932654197}{47066876606} \cdot \left(\frac{-1000000000}{23533438303} \cdot y - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{-1000000000}{23533438303} \cdot y\right) - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)}\right)\right) \]

      4. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, z\right), \mathsf{*.f64}\left(x, \left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-215985700909750000000}{553822718361107519809} \cdot z + \frac{336932654197}{47066876606} \cdot \left(\frac{-1000000000}{23533438303} \cdot y - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{-1000000000}{23533438303} \cdot y\right) + \color{blue}{\left(\mathsf{neg}\left(\frac{-168466327098500000000}{553822718361107519809}\right)\right) \cdot z}\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, z\right), \mathsf{*.f64}\left(x, \left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-215985700909750000000}{553822718361107519809} \cdot z + \frac{336932654197}{47066876606} \cdot \left(\frac{-1000000000}{23533438303} \cdot y - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{-1000000000}{23533438303} \cdot y\right) + \frac{168466327098500000000}{553822718361107519809} \cdot z\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, z\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-215985700909750000000}{553822718361107519809} \cdot z + \frac{336932654197}{47066876606} \cdot \left(\frac{-1000000000}{23533438303} \cdot y - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{-1000000000}{23533438303} \cdot y\right), \color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} \cdot z\right)}\right)\right)\right) \]

   9. Simplified 70.2%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z + x \cdot \left(\left(-0.0424927283095952 \cdot y - x \cdot \left(5.843575199059173 + \left(z \cdot -0.38999068429136097 + \left(-0.0424927283095952 \cdot y + z \cdot 0.3041881842569256\right) \cdot 7.158593866711955\right)\right)\right) + z \cdot 0.3041881842569256\right)} \]

   10. Taylor expanded in y around inf

       \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(y \cdot \left(\frac{1000000000}{23533438303} + \frac{-168466327098500000000}{553822718361107519809} \cdot x\right)\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \left(x \cdot \left(y \cdot \left(\frac{1000000000}{23533438303} + \frac{-168466327098500000000}{553822718361107519809} \cdot x\right)\right)\right) \cdot \color{blue}{-1} \]

       2. metadata-eval N/A

          \[\leadsto \left(x \cdot \left(y \cdot \left(\frac{1000000000}{23533438303} + \left(\mathsf{neg}\left(\frac{168466327098500000000}{553822718361107519809}\right)\right) \cdot x\right)\right)\right) \cdot -1 \]

       3. cancel-sign-sub-inv N/A

          \[\leadsto \left(x \cdot \left(y \cdot \left(\frac{1000000000}{23533438303} - \frac{168466327098500000000}{553822718361107519809} \cdot x\right)\right)\right) \cdot -1 \]

       4. associate-*l* N/A

          \[\leadsto x \cdot \color{blue}{\left(\left(y \cdot \left(\frac{1000000000}{23533438303} - \frac{168466327098500000000}{553822718361107519809} \cdot x\right)\right) \cdot -1\right)} \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\left(y \cdot \left(\frac{1000000000}{23533438303} - \frac{168466327098500000000}{553822718361107519809} \cdot x\right)\right) \cdot -1\right)}\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(y \cdot \left(\frac{1000000000}{23533438303} - \frac{168466327098500000000}{553822718361107519809} \cdot x\right)\right), \color{blue}{-1}\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{1000000000}{23533438303} - \frac{168466327098500000000}{553822718361107519809} \cdot x\right)\right), -1\right)\right) \]

       8. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{1000000000}{23533438303} + \left(\mathsf{neg}\left(\frac{168466327098500000000}{553822718361107519809}\right)\right) \cdot x\right)\right), -1\right)\right) \]

       9. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{1000000000}{23533438303} + \frac{-168466327098500000000}{553822718361107519809} \cdot x\right)\right), -1\right)\right) \]

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

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{1000000000}{23533438303}, \left(\frac{-168466327098500000000}{553822718361107519809} \cdot x\right)\right)\right), -1\right)\right) \]

       11. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{1000000000}{23533438303}, \left(x \cdot \frac{-168466327098500000000}{553822718361107519809}\right)\right)\right), -1\right)\right) \]

       12. *-lowering-*.f64 40.0%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{1000000000}{23533438303}, \mathsf{*.f64}\left(x, \frac{-168466327098500000000}{553822718361107519809}\right)\right)\right), -1\right)\right) \]

   12. Simplified 40.0%

       \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(0.0424927283095952 + x \cdot -0.3041881842569256\right)\right) \cdot -1\right)} \]

   if -2.70000000000000019e-62 < x < 8e7

   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 90.0%

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

   7. Simplified 90.0%

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

   8. Taylor expanded in z around inf

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

      1. associate-*r* N/A

         \[\leadsto \left(z \cdot \left(\frac{500000000}{23533438303} + \frac{-78349803973500000000}{553822718361107519809} \cdot x\right)\right) \cdot \color{blue}{\left(x - 2\right)} \]

      2. distribute-rgt-in N/A

         \[\leadsto \left(\frac{500000000}{23533438303} \cdot z + \left(\frac{-78349803973500000000}{553822718361107519809} \cdot x\right) \cdot z\right) \cdot \left(\color{blue}{x} - 2\right) \]

      3. associate-*r* N/A

         \[\leadsto \left(\frac{500000000}{23533438303} \cdot z + \frac{-78349803973500000000}{553822718361107519809} \cdot \left(x \cdot z\right)\right) \cdot \left(x - 2\right) \]

      4. +-commutative N/A

         \[\leadsto \left(\frac{-78349803973500000000}{553822718361107519809} \cdot \left(x \cdot z\right) + \frac{500000000}{23533438303} \cdot z\right) \cdot \left(\color{blue}{x} - 2\right) \]

      5. *-commutative N/A

         \[\leadsto \left(x - 2\right) \cdot \color{blue}{\left(\frac{-78349803973500000000}{553822718361107519809} \cdot \left(x \cdot z\right) + \frac{500000000}{23533438303} \cdot z\right)} \]

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

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

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

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

      10. +-commutative N/A

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

      11. associate-*r* N/A

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

      12. distribute-rgt-in N/A

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

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

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

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

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

      15. *-commutative N/A

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

      16. *-lowering-*.f64 69.9%

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

   10. Simplified 69.9%

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

   11. Taylor expanded in x around 0

       \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z + \frac{168466327098500000000}{553822718361107519809} \cdot \left(x \cdot z\right)} \]
   12. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \frac{168466327098500000000}{553822718361107519809} \cdot \left(x \cdot z\right) + \color{blue}{\frac{-1000000000}{23533438303} \cdot z} \]

       2. associate-*r* N/A

          \[\leadsto \left(\frac{168466327098500000000}{553822718361107519809} \cdot x\right) \cdot z + \color{blue}{\frac{-1000000000}{23533438303}} \cdot z \]

       3. distribute-rgt-out N/A

          \[\leadsto z \cdot \color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} \cdot x + \frac{-1000000000}{23533438303}\right)} \]

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

          \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} \cdot x + \frac{-1000000000}{23533438303}\right)}\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(\frac{168466327098500000000}{553822718361107519809} \cdot x\right), \color{blue}{\frac{-1000000000}{23533438303}}\right)\right) \]

       6. *-lowering-*.f64 70.0%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{168466327098500000000}{553822718361107519809}, x\right), \frac{-1000000000}{23533438303}\right)\right) \]

   13. Simplified 70.0%

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

   if 8e7 < x

   1. Initial program 18.6%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 23.3%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 91.2%

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

   7. Simplified 91.2%

      \[\leadsto \color{blue}{x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+24}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-62}:\\ \;\;\;\;x \cdot \left(y \cdot \left(0 - \left(0.0424927283095952 + x \cdot -0.3041881842569256\right)\right)\right)\\ \mathbf{elif}\;x \leq 80000000:\\ \;\;\;\;z \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 75.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+24}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-61}:\\ \;\;\;\;0.0212463641547976 \cdot \left(x \cdot \left(y \cdot \left(x + -2\right)\right)\right)\\ \mathbf{elif}\;x \leq 80000000:\\ \;\;\;\;z \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.45e+24)
   (* x 4.16438922228)
   (if (<= x -2e-61)
     (* 0.0212463641547976 (* x (* y (+ x -2.0))))
     (if (<= x 80000000.0)
       (* z (+ -0.0424927283095952 (* x 0.3041881842569256)))
       (* x (+ 4.16438922228 (/ -110.1139242984811 x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.45e+24) {
		tmp = x * 4.16438922228;
	} else if (x <= -2e-61) {
		tmp = 0.0212463641547976 * (x * (y * (x + -2.0)));
	} else if (x <= 80000000.0) {
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256));
	} else {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.45d+24)) then
        tmp = x * 4.16438922228d0
    else if (x <= (-2d-61)) then
        tmp = 0.0212463641547976d0 * (x * (y * (x + (-2.0d0))))
    else if (x <= 80000000.0d0) then
        tmp = z * ((-0.0424927283095952d0) + (x * 0.3041881842569256d0))
    else
        tmp = x * (4.16438922228d0 + ((-110.1139242984811d0) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.45e+24) {
		tmp = x * 4.16438922228;
	} else if (x <= -2e-61) {
		tmp = 0.0212463641547976 * (x * (y * (x + -2.0)));
	} else if (x <= 80000000.0) {
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256));
	} else {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.45e+24:
		tmp = x * 4.16438922228
	elif x <= -2e-61:
		tmp = 0.0212463641547976 * (x * (y * (x + -2.0)))
	elif x <= 80000000.0:
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256))
	else:
		tmp = x * (4.16438922228 + (-110.1139242984811 / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.45e+24)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= -2e-61)
		tmp = Float64(0.0212463641547976 * Float64(x * Float64(y * Float64(x + -2.0))));
	elseif (x <= 80000000.0)
		tmp = Float64(z * Float64(-0.0424927283095952 + Float64(x * 0.3041881842569256)));
	else
		tmp = Float64(x * Float64(4.16438922228 + Float64(-110.1139242984811 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.45e+24)
		tmp = x * 4.16438922228;
	elseif (x <= -2e-61)
		tmp = 0.0212463641547976 * (x * (y * (x + -2.0)));
	elseif (x <= 80000000.0)
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256));
	else
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.45e+24], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, -2e-61], N[(0.0212463641547976 * N[(x * N[(y * N[(x + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 80000000.0], N[(z * N[(-0.0424927283095952 + N[(x * 0.3041881842569256), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(4.16438922228 + N[(-110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.4499999999999999e24

   1. Initial program 8.9%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 17.2%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 95.9%

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

   7. Simplified 95.9%

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

   if -1.4499999999999999e24 < x < -2.0000000000000001e-61

   1. Initial program 99.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 99.3%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 49.5%

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

   7. Simplified 49.5%

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

   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 39.9%

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

   10. Simplified 39.9%

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

   if -2.0000000000000001e-61 < x < 8e7

   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 90.0%

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

   7. Simplified 90.0%

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

   8. Taylor expanded in z around inf

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

      1. associate-*r* N/A

         \[\leadsto \left(z \cdot \left(\frac{500000000}{23533438303} + \frac{-78349803973500000000}{553822718361107519809} \cdot x\right)\right) \cdot \color{blue}{\left(x - 2\right)} \]

      2. distribute-rgt-in N/A

         \[\leadsto \left(\frac{500000000}{23533438303} \cdot z + \left(\frac{-78349803973500000000}{553822718361107519809} \cdot x\right) \cdot z\right) \cdot \left(\color{blue}{x} - 2\right) \]

      3. associate-*r* N/A

         \[\leadsto \left(\frac{500000000}{23533438303} \cdot z + \frac{-78349803973500000000}{553822718361107519809} \cdot \left(x \cdot z\right)\right) \cdot \left(x - 2\right) \]

      4. +-commutative N/A

         \[\leadsto \left(\frac{-78349803973500000000}{553822718361107519809} \cdot \left(x \cdot z\right) + \frac{500000000}{23533438303} \cdot z\right) \cdot \left(\color{blue}{x} - 2\right) \]

      5. *-commutative N/A

         \[\leadsto \left(x - 2\right) \cdot \color{blue}{\left(\frac{-78349803973500000000}{553822718361107519809} \cdot \left(x \cdot z\right) + \frac{500000000}{23533438303} \cdot z\right)} \]

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

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

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

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

      10. +-commutative N/A

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

      11. associate-*r* N/A

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

      12. distribute-rgt-in N/A

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

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

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

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

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

      15. *-commutative N/A

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

      16. *-lowering-*.f64 69.9%

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

   10. Simplified 69.9%

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

   11. Taylor expanded in x around 0

       \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z + \frac{168466327098500000000}{553822718361107519809} \cdot \left(x \cdot z\right)} \]
   12. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \frac{168466327098500000000}{553822718361107519809} \cdot \left(x \cdot z\right) + \color{blue}{\frac{-1000000000}{23533438303} \cdot z} \]

       2. associate-*r* N/A

          \[\leadsto \left(\frac{168466327098500000000}{553822718361107519809} \cdot x\right) \cdot z + \color{blue}{\frac{-1000000000}{23533438303}} \cdot z \]

       3. distribute-rgt-out N/A

          \[\leadsto z \cdot \color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} \cdot x + \frac{-1000000000}{23533438303}\right)} \]

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

          \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} \cdot x + \frac{-1000000000}{23533438303}\right)}\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(\frac{168466327098500000000}{553822718361107519809} \cdot x\right), \color{blue}{\frac{-1000000000}{23533438303}}\right)\right) \]

       6. *-lowering-*.f64 70.0%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{168466327098500000000}{553822718361107519809}, x\right), \frac{-1000000000}{23533438303}\right)\right) \]

   13. Simplified 70.0%

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

   if 8e7 < x

   1. Initial program 18.6%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 23.3%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 91.2%

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

   7. Simplified 91.2%

      \[\leadsto \color{blue}{x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+24}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-61}:\\ \;\;\;\;0.0212463641547976 \cdot \left(x \cdot \left(y \cdot \left(x + -2\right)\right)\right)\\ \mathbf{elif}\;x \leq 80000000:\\ \;\;\;\;z \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 76.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+24}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 80000000:\\ \;\;\;\;z \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.45e+24)
   (* x 4.16438922228)
   (if (<= x 80000000.0)
     (* z (+ -0.0424927283095952 (* x 0.3041881842569256)))
     (* x (+ 4.16438922228 (/ -110.1139242984811 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.45e+24) {
		tmp = x * 4.16438922228;
	} else if (x <= 80000000.0) {
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256));
	} else {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.45d+24)) then
        tmp = x * 4.16438922228d0
    else if (x <= 80000000.0d0) then
        tmp = z * ((-0.0424927283095952d0) + (x * 0.3041881842569256d0))
    else
        tmp = x * (4.16438922228d0 + ((-110.1139242984811d0) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.45e+24) {
		tmp = x * 4.16438922228;
	} else if (x <= 80000000.0) {
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256));
	} else {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.45e+24:
		tmp = x * 4.16438922228
	elif x <= 80000000.0:
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256))
	else:
		tmp = x * (4.16438922228 + (-110.1139242984811 / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.45e+24)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 80000000.0)
		tmp = Float64(z * Float64(-0.0424927283095952 + Float64(x * 0.3041881842569256)));
	else
		tmp = Float64(x * Float64(4.16438922228 + Float64(-110.1139242984811 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.45e+24)
		tmp = x * 4.16438922228;
	elseif (x <= 80000000.0)
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256));
	else
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.45e+24], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 80000000.0], N[(z * N[(-0.0424927283095952 + N[(x * 0.3041881842569256), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(4.16438922228 + N[(-110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.4499999999999999e24

   1. Initial program 8.9%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 17.2%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 95.9%

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

   7. Simplified 95.9%

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

   if -1.4499999999999999e24 < x < 8e7

   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 84.9%

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

   7. Simplified 84.9%

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

   8. Taylor expanded in z around inf

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

      1. associate-*r* N/A

         \[\leadsto \left(z \cdot \left(\frac{500000000}{23533438303} + \frac{-78349803973500000000}{553822718361107519809} \cdot x\right)\right) \cdot \color{blue}{\left(x - 2\right)} \]

      2. distribute-rgt-in N/A

         \[\leadsto \left(\frac{500000000}{23533438303} \cdot z + \left(\frac{-78349803973500000000}{553822718361107519809} \cdot x\right) \cdot z\right) \cdot \left(\color{blue}{x} - 2\right) \]

      3. associate-*r* N/A

         \[\leadsto \left(\frac{500000000}{23533438303} \cdot z + \frac{-78349803973500000000}{553822718361107519809} \cdot \left(x \cdot z\right)\right) \cdot \left(x - 2\right) \]

      4. +-commutative N/A

         \[\leadsto \left(\frac{-78349803973500000000}{553822718361107519809} \cdot \left(x \cdot z\right) + \frac{500000000}{23533438303} \cdot z\right) \cdot \left(\color{blue}{x} - 2\right) \]

      5. *-commutative N/A

         \[\leadsto \left(x - 2\right) \cdot \color{blue}{\left(\frac{-78349803973500000000}{553822718361107519809} \cdot \left(x \cdot z\right) + \frac{500000000}{23533438303} \cdot z\right)} \]

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

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

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

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

      10. +-commutative N/A

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

      11. associate-*r* N/A

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

      12. distribute-rgt-in N/A

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

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

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

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

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

      15. *-commutative N/A

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

      16. *-lowering-*.f64 62.4%

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

   10. Simplified 62.4%

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

   11. Taylor expanded in x around 0

       \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z + \frac{168466327098500000000}{553822718361107519809} \cdot \left(x \cdot z\right)} \]
   12. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \frac{168466327098500000000}{553822718361107519809} \cdot \left(x \cdot z\right) + \color{blue}{\frac{-1000000000}{23533438303} \cdot z} \]

       2. associate-*r* N/A

          \[\leadsto \left(\frac{168466327098500000000}{553822718361107519809} \cdot x\right) \cdot z + \color{blue}{\frac{-1000000000}{23533438303}} \cdot z \]

       3. distribute-rgt-out N/A

          \[\leadsto z \cdot \color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} \cdot x + \frac{-1000000000}{23533438303}\right)} \]

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

          \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} \cdot x + \frac{-1000000000}{23533438303}\right)}\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(\frac{168466327098500000000}{553822718361107519809} \cdot x\right), \color{blue}{\frac{-1000000000}{23533438303}}\right)\right) \]

       6. *-lowering-*.f64 62.4%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{168466327098500000000}{553822718361107519809}, x\right), \frac{-1000000000}{23533438303}\right)\right) \]

   13. Simplified 62.4%

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

   if 8e7 < x

   1. Initial program 18.6%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 23.3%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 91.2%

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

   7. Simplified 91.2%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+24}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 80000000:\\ \;\;\;\;z \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 76.2% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+24}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 0.0013:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.45e+24)
   (* x 4.16438922228)
   (if (<= x 0.0013)
     (* z -0.0424927283095952)
     (* x (+ 4.16438922228 (/ -110.1139242984811 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.45e+24) {
		tmp = x * 4.16438922228;
	} else if (x <= 0.0013) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.45d+24)) then
        tmp = x * 4.16438922228d0
    else if (x <= 0.0013d0) then
        tmp = z * (-0.0424927283095952d0)
    else
        tmp = x * (4.16438922228d0 + ((-110.1139242984811d0) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.45e+24) {
		tmp = x * 4.16438922228;
	} else if (x <= 0.0013) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.45e+24:
		tmp = x * 4.16438922228
	elif x <= 0.0013:
		tmp = z * -0.0424927283095952
	else:
		tmp = x * (4.16438922228 + (-110.1139242984811 / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.45e+24)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 0.0013)
		tmp = Float64(z * -0.0424927283095952);
	else
		tmp = Float64(x * Float64(4.16438922228 + Float64(-110.1139242984811 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.45e+24)
		tmp = x * 4.16438922228;
	elseif (x <= 0.0013)
		tmp = z * -0.0424927283095952;
	else
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.45e+24], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 0.0013], N[(z * -0.0424927283095952), $MachinePrecision], N[(x * N[(4.16438922228 + N[(-110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.4499999999999999e24

   1. Initial program 8.9%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 17.2%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 95.9%

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

   7. Simplified 95.9%

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

   if -1.4499999999999999e24 < x < 0.0012999999999999999

   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 63.0%

         \[\leadsto \mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, \color{blue}{z}\right) \]

   7. Simplified 63.0%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]

   if 0.0012999999999999999 < x

   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 25.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   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 88.4%

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

   7. Simplified 88.4%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+24}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 0.0013:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 76.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+24}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-5}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.45e+24)
   (* x 4.16438922228)
   (if (<= x 1.85e-5) (* z -0.0424927283095952) (* x 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.45e+24) {
		tmp = x * 4.16438922228;
	} else if (x <= 1.85e-5) {
		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 <= (-1.45d+24)) then
        tmp = x * 4.16438922228d0
    else if (x <= 1.85d-5) 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 <= -1.45e+24) {
		tmp = x * 4.16438922228;
	} else if (x <= 1.85e-5) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.45e+24:
		tmp = x * 4.16438922228
	elif x <= 1.85e-5:
		tmp = z * -0.0424927283095952
	else:
		tmp = x * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.45e+24)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 1.85e-5)
		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 <= -1.45e+24)
		tmp = x * 4.16438922228;
	elseif (x <= 1.85e-5)
		tmp = z * -0.0424927283095952;
	else
		tmp = x * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.45e+24], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 1.85e-5], N[(z * -0.0424927283095952), $MachinePrecision], N[(x * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4499999999999999e24 or 1.84999999999999991e-5 < x

   1. Initial program 15.4%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 21.8%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 91.2%

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

   7. Simplified 91.2%

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

   if -1.4499999999999999e24 < x < 1.84999999999999991e-5

   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 63.5%

         \[\leadsto \mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, \color{blue}{z}\right) \]

   7. Simplified 63.5%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+24}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-5}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 34.9% 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 56.5%

   \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
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 59.8%

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

5. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z} \]
6. Step-by-step derivation

   1. *-lowering-*.f64 32.4%

      \[\leadsto \mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, \color{blue}{z}\right) \]

7. Simplified 32.4%

   \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]

8. Final simplification 32.4%

   \[\leadsto z \cdot -0.0424927283095952 \]
9. Add Preprocessing

Developer Target 1: 98.6% 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 2024161 
(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)))