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

Percentage Accurate: 59.6% → 98.3%

Time: 20.2s

Alternatives: 23

Speedup: 2.8×

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x - 2.0d0) * ((((((((x * 4.16438922228d0) + 78.6994924154d0) * x) + 137.519416416d0) * x) + y) * x) + z)) / (((((((x + 43.3400022514d0) * x) + 263.505074721d0) * x) + 313.399215894d0) * x) + 47.066876606d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 59.6% 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: 98.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(x \cdot x\right)\\ t_1 := x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606\\ t_2 := x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\\ \mathbf{if}\;\frac{\left(x - 2\right) \cdot t\_2}{t\_1} \leq 4 \cdot 10^{+299}:\\ \;\;\;\;\left(x + -2\right) \cdot \frac{t\_2}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(\left(4.16438922228 + \frac{3655.1204654076414}{x \cdot x}\right) + \left(\frac{y}{t\_0} + \frac{-110.1139242984811}{x}\right)\right) - \frac{130977.50649958357}{t\_0}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* x x)))
        (t_1
         (+
          (*
           x
           (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
          47.066876606))
        (t_2
         (+
          (*
           x
           (+
            (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
            y))
          z)))
   (if (<= (/ (* (- x 2.0) t_2) t_1) 4e+299)
     (* (+ x -2.0) (/ t_2 t_1))
     (*
      x
      (-
       (+
        (+ 4.16438922228 (/ 3655.1204654076414 (* x x)))
        (+ (/ y t_0) (/ -110.1139242984811 x)))
       (/ 130977.50649958357 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (x * x);
	double t_1 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	double t_2 = (x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z;
	double tmp;
	if ((((x - 2.0) * t_2) / t_1) <= 4e+299) {
		tmp = (x + -2.0) * (t_2 / t_1);
	} else {
		tmp = x * (((4.16438922228 + (3655.1204654076414 / (x * x))) + ((y / t_0) + (-110.1139242984811 / x))) - (130977.50649958357 / t_0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = x * (x * x)
    t_1 = (x * ((x * ((x * (x + 43.3400022514d0)) + 263.505074721d0)) + 313.399215894d0)) + 47.066876606d0
    t_2 = (x * ((x * ((x * ((x * 4.16438922228d0) + 78.6994924154d0)) + 137.519416416d0)) + y)) + z
    if ((((x - 2.0d0) * t_2) / t_1) <= 4d+299) then
        tmp = (x + (-2.0d0)) * (t_2 / t_1)
    else
        tmp = x * (((4.16438922228d0 + (3655.1204654076414d0 / (x * x))) + ((y / t_0) + ((-110.1139242984811d0) / x))) - (130977.50649958357d0 / t_0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (x * x);
	double t_1 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	double t_2 = (x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z;
	double tmp;
	if ((((x - 2.0) * t_2) / t_1) <= 4e+299) {
		tmp = (x + -2.0) * (t_2 / t_1);
	} else {
		tmp = x * (((4.16438922228 + (3655.1204654076414 / (x * x))) + ((y / t_0) + (-110.1139242984811 / x))) - (130977.50649958357 / t_0));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (x * x)
	t_1 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606
	t_2 = (x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z
	tmp = 0
	if (((x - 2.0) * t_2) / t_1) <= 4e+299:
		tmp = (x + -2.0) * (t_2 / t_1)
	else:
		tmp = x * (((4.16438922228 + (3655.1204654076414 / (x * x))) + ((y / t_0) + (-110.1139242984811 / x))) - (130977.50649958357 / t_0))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(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(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * t_2) / t_1) <= 4e+299)
		tmp = Float64(Float64(x + -2.0) * Float64(t_2 / t_1));
	else
		tmp = Float64(x * Float64(Float64(Float64(4.16438922228 + Float64(3655.1204654076414 / Float64(x * x))) + Float64(Float64(y / t_0) + Float64(-110.1139242984811 / x))) - Float64(130977.50649958357 / t_0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (x * x);
	t_1 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	t_2 = (x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z;
	tmp = 0.0;
	if ((((x - 2.0) * t_2) / t_1) <= 4e+299)
		tmp = (x + -2.0) * (t_2 / t_1);
	else
		tmp = x * (((4.16438922228 + (3655.1204654076414 / (x * x))) + ((y / t_0) + (-110.1139242984811 / x))) - (130977.50649958357 / t_0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(x * N[(N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision] + 137.519416416), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision], 4e+299], N[(N[(x + -2.0), $MachinePrecision] * N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[(4.16438922228 + N[(3655.1204654076414 / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y / t$95$0), $MachinePrecision] + N[(-110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(130977.50649958357 / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < 4.0000000000000002e299

   1. Initial program 95.5%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.5%

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

   if 4.0000000000000002e299 < (/.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 0.3%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 3.4%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(\frac{104109730557}{25000000000} + \left(\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{{x}^{2}} + \frac{y}{{x}^{3}}\right)\right) - \left(\frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{{x}^{3}}\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\left(\frac{104109730557}{25000000000} + \left(\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{{x}^{2}} + \frac{y}{{x}^{3}}\right)\right) - \left(\frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{{x}^{3}}\right)\right)}\right) \]

      2. associate--r+ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\left(\frac{104109730557}{25000000000} + \left(\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{{x}^{2}} + \frac{y}{{x}^{3}}\right)\right) - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right) - \color{blue}{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{{x}^{3}}}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(\left(\frac{104109730557}{25000000000} + \left(\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{{x}^{2}} + \frac{y}{{x}^{3}}\right)\right) - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right), \color{blue}{\left(\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{{x}^{3}}\right)}\right)\right) \]

   7. Simplified 99.2%

      \[\leadsto \color{blue}{x \cdot \left(\left(\left(4.16438922228 + \frac{3655.1204654076414}{x \cdot x}\right) + \left(\frac{y}{x \cdot \left(x \cdot x\right)} + \frac{-110.1139242984811}{x}\right)\right) - \frac{130977.50649958357}{x \cdot \left(x \cdot x\right)}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 4 \cdot 10^{+299}:\\ \;\;\;\;\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(\left(4.16438922228 + \frac{3655.1204654076414}{x \cdot x}\right) + \left(\frac{y}{x \cdot \left(x \cdot x\right)} + \frac{-110.1139242984811}{x}\right)\right) - \frac{130977.50649958357}{x \cdot \left(x \cdot x\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(x \cdot x\right)\\ t_1 := x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\\ \mathbf{if}\;x \leq -8.8 \cdot 10^{+64}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -36:\\ \;\;\;\;t\_1 \cdot \frac{1}{t\_0}\\ \mathbf{elif}\;x \leq 72:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot 313.399215894}{t\_1}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(\left(4.16438922228 + \frac{3655.1204654076414}{x \cdot x}\right) + \left(\frac{y}{t\_0} + \frac{-110.1139242984811}{x}\right)\right) - \frac{130977.50649958357}{t\_0}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* x x)))
        (t_1
         (+
          (*
           x
           (+
            (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
            y))
          z)))
   (if (<= x -8.8e+64)
     (/ (+ x -2.0) 0.24013125253755718)
     (if (<= x -36.0)
       (* t_1 (/ 1.0 t_0))
       (if (<= x 72.0)
         (/ (+ x -2.0) (/ (+ 47.066876606 (* x 313.399215894)) t_1))
         (*
          x
          (-
           (+
            (+ 4.16438922228 (/ 3655.1204654076414 (* x x)))
            (+ (/ y t_0) (/ -110.1139242984811 x)))
           (/ 130977.50649958357 t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (x * x);
	double t_1 = (x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z;
	double tmp;
	if (x <= -8.8e+64) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -36.0) {
		tmp = t_1 * (1.0 / t_0);
	} else if (x <= 72.0) {
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / t_1);
	} else {
		tmp = x * (((4.16438922228 + (3655.1204654076414 / (x * x))) + ((y / t_0) + (-110.1139242984811 / x))) - (130977.50649958357 / t_0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * (x * x)
    t_1 = (x * ((x * ((x * ((x * 4.16438922228d0) + 78.6994924154d0)) + 137.519416416d0)) + y)) + z
    if (x <= (-8.8d+64)) then
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    else if (x <= (-36.0d0)) then
        tmp = t_1 * (1.0d0 / t_0)
    else if (x <= 72.0d0) then
        tmp = (x + (-2.0d0)) / ((47.066876606d0 + (x * 313.399215894d0)) / t_1)
    else
        tmp = x * (((4.16438922228d0 + (3655.1204654076414d0 / (x * x))) + ((y / t_0) + ((-110.1139242984811d0) / x))) - (130977.50649958357d0 / t_0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (x * x);
	double t_1 = (x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z;
	double tmp;
	if (x <= -8.8e+64) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -36.0) {
		tmp = t_1 * (1.0 / t_0);
	} else if (x <= 72.0) {
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / t_1);
	} else {
		tmp = x * (((4.16438922228 + (3655.1204654076414 / (x * x))) + ((y / t_0) + (-110.1139242984811 / x))) - (130977.50649958357 / t_0));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (x * x)
	t_1 = (x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z
	tmp = 0
	if x <= -8.8e+64:
		tmp = (x + -2.0) / 0.24013125253755718
	elif x <= -36.0:
		tmp = t_1 * (1.0 / t_0)
	elif x <= 72.0:
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / t_1)
	else:
		tmp = x * (((4.16438922228 + (3655.1204654076414 / (x * x))) + ((y / t_0) + (-110.1139242984811 / x))) - (130977.50649958357 / t_0))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(x * x))
	t_1 = Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)
	tmp = 0.0
	if (x <= -8.8e+64)
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	elseif (x <= -36.0)
		tmp = Float64(t_1 * Float64(1.0 / t_0));
	elseif (x <= 72.0)
		tmp = Float64(Float64(x + -2.0) / Float64(Float64(47.066876606 + Float64(x * 313.399215894)) / t_1));
	else
		tmp = Float64(x * Float64(Float64(Float64(4.16438922228 + Float64(3655.1204654076414 / Float64(x * x))) + Float64(Float64(y / t_0) + Float64(-110.1139242984811 / x))) - Float64(130977.50649958357 / t_0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (x * x);
	t_1 = (x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z;
	tmp = 0.0;
	if (x <= -8.8e+64)
		tmp = (x + -2.0) / 0.24013125253755718;
	elseif (x <= -36.0)
		tmp = t_1 * (1.0 / t_0);
	elseif (x <= 72.0)
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / t_1);
	else
		tmp = x * (((4.16438922228 + (3655.1204654076414 / (x * x))) + ((y / t_0) + (-110.1139242984811 / x))) - (130977.50649958357 / t_0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x * N[(N[(x * N[(N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision] + 137.519416416), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]}, If[LessEqual[x, -8.8e+64], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision], If[LessEqual[x, -36.0], N[(t$95$1 * N[(1.0 / t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 72.0], N[(N[(x + -2.0), $MachinePrecision] / N[(N[(47.066876606 + N[(x * 313.399215894), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[(4.16438922228 + N[(3655.1204654076414 / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y / t$95$0), $MachinePrecision] + N[(-110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(130977.50649958357 / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -8.80000000000000007e64

   1. Initial program 0.2%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 5.5%

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

   6. Applied egg-rr 5.5%

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

   7. Taylor expanded in x around inf

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

   9. Simplified 99.8%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]

   if -8.80000000000000007e64 < x < -36

   1. Initial program 84.9%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 94.6%

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

   6. Applied egg-rr 94.4%

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

   7. Taylor expanded in x around inf

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

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

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

      2. cube-mult N/A

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

      3. unpow2 N/A

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

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

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 91.5%

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

   9. Simplified 91.5%

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

   if -36 < x < 72

   1. Initial program 99.6%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.6%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in x around 0

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 98.2%

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

   9. Simplified 98.2%

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

   if 72 < x

   1. Initial program 9.3%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 19.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(\frac{104109730557}{25000000000} + \left(\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{{x}^{2}} + \frac{y}{{x}^{3}}\right)\right) - \left(\frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{{x}^{3}}\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\left(\frac{104109730557}{25000000000} + \left(\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{{x}^{2}} + \frac{y}{{x}^{3}}\right)\right) - \left(\frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{{x}^{3}}\right)\right)}\right) \]

      2. associate--r+ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\left(\frac{104109730557}{25000000000} + \left(\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{{x}^{2}} + \frac{y}{{x}^{3}}\right)\right) - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right) - \color{blue}{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{{x}^{3}}}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(\left(\frac{104109730557}{25000000000} + \left(\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{{x}^{2}} + \frac{y}{{x}^{3}}\right)\right) - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right), \color{blue}{\left(\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{{x}^{3}}\right)}\right)\right) \]

   7. Simplified 94.4%

      \[\leadsto \color{blue}{x \cdot \left(\left(\left(4.16438922228 + \frac{3655.1204654076414}{x \cdot x}\right) + \left(\frac{y}{x \cdot \left(x \cdot x\right)} + \frac{-110.1139242984811}{x}\right)\right) - \frac{130977.50649958357}{x \cdot \left(x \cdot x\right)}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+64}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -36:\\ \;\;\;\;\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{1}{x \cdot \left(x \cdot x\right)}\\ \mathbf{elif}\;x \leq 72:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot 313.399215894}{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(\left(4.16438922228 + \frac{3655.1204654076414}{x \cdot x}\right) + \left(\frac{y}{x \cdot \left(x \cdot x\right)} + \frac{-110.1139242984811}{x}\right)\right) - \frac{130977.50649958357}{x \cdot \left(x \cdot x\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\\ \mathbf{if}\;x \leq -8.8 \cdot 10^{+64}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -36:\\ \;\;\;\;t\_0 \cdot \frac{1}{x \cdot \left(x \cdot x\right)}\\ \mathbf{elif}\;x \leq 30:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot 313.399215894}{t\_0}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          (*
           x
           (+
            (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
            y))
          z)))
   (if (<= x -8.8e+64)
     (/ (+ x -2.0) 0.24013125253755718)
     (if (<= x -36.0)
       (* t_0 (/ 1.0 (* x (* x x))))
       (if (<= x 30.0)
         (/ (+ x -2.0) (/ (+ 47.066876606 (* x 313.399215894)) t_0))
         (*
          (+ x -2.0)
          (+
           4.16438922228
           (/
            (-
             (/ (+ 3451.550173699799 (/ (- y 124074.40615218398) x)) x)
             101.7851458539211)
            x))))))))

C

double code(double x, double y, double z) {
	double t_0 = (x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z;
	double tmp;
	if (x <= -8.8e+64) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -36.0) {
		tmp = t_0 * (1.0 / (x * (x * x)));
	} else if (x <= 30.0) {
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / t_0);
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x * ((x * ((x * ((x * 4.16438922228d0) + 78.6994924154d0)) + 137.519416416d0)) + y)) + z
    if (x <= (-8.8d+64)) then
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    else if (x <= (-36.0d0)) then
        tmp = t_0 * (1.0d0 / (x * (x * x)))
    else if (x <= 30.0d0) then
        tmp = (x + (-2.0d0)) / ((47.066876606d0 + (x * 313.399215894d0)) / t_0)
    else
        tmp = (x + (-2.0d0)) * (4.16438922228d0 + ((((3451.550173699799d0 + ((y - 124074.40615218398d0) / x)) / x) - 101.7851458539211d0) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z;
	double tmp;
	if (x <= -8.8e+64) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -36.0) {
		tmp = t_0 * (1.0 / (x * (x * x)));
	} else if (x <= 30.0) {
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / t_0);
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z
	tmp = 0
	if x <= -8.8e+64:
		tmp = (x + -2.0) / 0.24013125253755718
	elif x <= -36.0:
		tmp = t_0 * (1.0 / (x * (x * x)))
	elif x <= 30.0:
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / t_0)
	else:
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)
	tmp = 0.0
	if (x <= -8.8e+64)
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	elseif (x <= -36.0)
		tmp = Float64(t_0 * Float64(1.0 / Float64(x * Float64(x * x))));
	elseif (x <= 30.0)
		tmp = Float64(Float64(x + -2.0) / Float64(Float64(47.066876606 + Float64(x * 313.399215894)) / t_0));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(Float64(y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z;
	tmp = 0.0;
	if (x <= -8.8e+64)
		tmp = (x + -2.0) / 0.24013125253755718;
	elseif (x <= -36.0)
		tmp = t_0 * (1.0 / (x * (x * x)));
	elseif (x <= 30.0)
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / t_0);
	else
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[(N[(x * N[(N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision] + 137.519416416), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]}, If[LessEqual[x, -8.8e+64], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision], If[LessEqual[x, -36.0], N[(t$95$0 * N[(1.0 / N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 30.0], N[(N[(x + -2.0), $MachinePrecision] / N[(N[(47.066876606 + N[(x * 313.399215894), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(N[(N[(N[(3451.550173699799 + N[(N[(y - 124074.40615218398), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -8.80000000000000007e64

   1. Initial program 0.2%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 5.5%

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

   6. Applied egg-rr 5.5%

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

   7. Taylor expanded in x around inf

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

   9. Simplified 99.8%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]

   if -8.80000000000000007e64 < x < -36

   1. Initial program 84.9%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 94.6%

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

   6. Applied egg-rr 94.4%

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

   7. Taylor expanded in x around inf

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

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

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

      2. cube-mult N/A

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

      3. unpow2 N/A

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

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

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 91.5%

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

   9. Simplified 91.5%

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

   if -36 < x < 30

   1. Initial program 99.6%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.6%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in x around 0

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 98.2%

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

   9. Simplified 98.2%

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

   if 30 < x

   1. Initial program 9.3%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 19.8%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 94.3%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+64}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -36:\\ \;\;\;\;\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{1}{x \cdot \left(x \cdot x\right)}\\ \mathbf{elif}\;x \leq 30:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot 313.399215894}{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(x \cdot x\right)\\ \mathbf{if}\;x \leq -1.42 \cdot 10^{+20}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{elif}\;x \leq 145000000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(\left(4.16438922228 + \frac{3655.1204654076414}{x \cdot x}\right) + \left(\frac{y}{t\_0} + \frac{-110.1139242984811}{x}\right)\right) - \frac{130977.50649958357}{t\_0}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* x x))))
   (if (<= x -1.42e+20)
     (*
      (+ x -2.0)
      (+
       4.16438922228
       (/
        (-
         (/ (+ 3451.550173699799 (/ (- y 124074.40615218398) x)) x)
         101.7851458539211)
        x)))
     (if (<= x 145000000000.0)
       (/
        (* (- x 2.0) (+ z (* x (+ y (* x 137.519416416)))))
        (+
         (*
          x
          (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
         47.066876606))
       (*
        x
        (-
         (+
          (+ 4.16438922228 (/ 3655.1204654076414 (* x x)))
          (+ (/ y t_0) (/ -110.1139242984811 x)))
         (/ 130977.50649958357 t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (x * x);
	double tmp;
	if (x <= -1.42e+20) {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	} else if (x <= 145000000000.0) {
		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 * (((4.16438922228 + (3655.1204654076414 / (x * x))) + ((y / t_0) + (-110.1139242984811 / x))) - (130977.50649958357 / 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 * (x * x)
    if (x <= (-1.42d+20)) then
        tmp = (x + (-2.0d0)) * (4.16438922228d0 + ((((3451.550173699799d0 + ((y - 124074.40615218398d0) / x)) / x) - 101.7851458539211d0) / x))
    else if (x <= 145000000000.0d0) 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 * (((4.16438922228d0 + (3655.1204654076414d0 / (x * x))) + ((y / t_0) + ((-110.1139242984811d0) / x))) - (130977.50649958357d0 / t_0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (x * x);
	double tmp;
	if (x <= -1.42e+20) {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	} else if (x <= 145000000000.0) {
		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 * (((4.16438922228 + (3655.1204654076414 / (x * x))) + ((y / t_0) + (-110.1139242984811 / x))) - (130977.50649958357 / t_0));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (x * x)
	tmp = 0
	if x <= -1.42e+20:
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x))
	elif x <= 145000000000.0:
		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 * (((4.16438922228 + (3655.1204654076414 / (x * x))) + ((y / t_0) + (-110.1139242984811 / x))) - (130977.50649958357 / t_0))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(x * x))
	tmp = 0.0
	if (x <= -1.42e+20)
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(Float64(y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)));
	elseif (x <= 145000000000.0)
		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(x * Float64(Float64(Float64(4.16438922228 + Float64(3655.1204654076414 / Float64(x * x))) + Float64(Float64(y / t_0) + Float64(-110.1139242984811 / x))) - Float64(130977.50649958357 / t_0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (x * x);
	tmp = 0.0;
	if (x <= -1.42e+20)
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	elseif (x <= 145000000000.0)
		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 * (((4.16438922228 + (3655.1204654076414 / (x * x))) + ((y / t_0) + (-110.1139242984811 / x))) - (130977.50649958357 / t_0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.42e+20], 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, 145000000000.0], 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[(x * N[(N[(N[(4.16438922228 + N[(3655.1204654076414 / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y / t$95$0), $MachinePrecision] + N[(-110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(130977.50649958357 / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.42e20

   1. Initial program 17.6%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 24.6%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 95.2%

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

   if -1.42e20 < x < 1.45e11

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 98.8%

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

   5. Simplified 98.8%

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

   if 1.45e11 < x

   1. Initial program 9.3%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 19.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(\frac{104109730557}{25000000000} + \left(\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{{x}^{2}} + \frac{y}{{x}^{3}}\right)\right) - \left(\frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{{x}^{3}}\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\left(\frac{104109730557}{25000000000} + \left(\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{{x}^{2}} + \frac{y}{{x}^{3}}\right)\right) - \left(\frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{{x}^{3}}\right)\right)}\right) \]

      2. associate--r+ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\left(\frac{104109730557}{25000000000} + \left(\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{{x}^{2}} + \frac{y}{{x}^{3}}\right)\right) - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right) - \color{blue}{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{{x}^{3}}}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(\left(\frac{104109730557}{25000000000} + \left(\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{{x}^{2}} + \frac{y}{{x}^{3}}\right)\right) - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right), \color{blue}{\left(\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{{x}^{3}}\right)}\right)\right) \]

   7. Simplified 94.4%

      \[\leadsto \color{blue}{x \cdot \left(\left(\left(4.16438922228 + \frac{3655.1204654076414}{x \cdot x}\right) + \left(\frac{y}{x \cdot \left(x \cdot x\right)} + \frac{-110.1139242984811}{x}\right)\right) - \frac{130977.50649958357}{x \cdot \left(x \cdot x\right)}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.42 \cdot 10^{+20}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{elif}\;x \leq 145000000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(\left(4.16438922228 + \frac{3655.1204654076414}{x \cdot x}\right) + \left(\frac{y}{x \cdot \left(x \cdot x\right)} + \frac{-110.1139242984811}{x}\right)\right) - \frac{130977.50649958357}{x \cdot \left(x \cdot x\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 96.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+64}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -36:\\ \;\;\;\;\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{1}{x \cdot \left(x \cdot x\right)}\\ \mathbf{elif}\;x \leq 130:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot 313.399215894}{z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot 78.6994924154\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -8.8e+64)
   (/ (+ x -2.0) 0.24013125253755718)
   (if (<= x -36.0)
     (*
      (+
       (*
        x
        (+
         (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
         y))
       z)
      (/ 1.0 (* x (* x x))))
     (if (<= x 130.0)
       (/
        (+ x -2.0)
        (/
         (+ 47.066876606 (* x 313.399215894))
         (+ z (* x (+ y (* x (+ 137.519416416 (* x 78.6994924154))))))))
       (*
        (+ x -2.0)
        (+
         4.16438922228
         (/
          (-
           (/ (+ 3451.550173699799 (/ (- y 124074.40615218398) x)) x)
           101.7851458539211)
          x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.8e+64) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -36.0) {
		tmp = ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z) * (1.0 / (x * (x * x)));
	} else if (x <= 130.0) {
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / (z + (x * (y + (x * (137.519416416 + (x * 78.6994924154)))))));
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-8.8d+64)) then
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    else if (x <= (-36.0d0)) then
        tmp = ((x * ((x * ((x * ((x * 4.16438922228d0) + 78.6994924154d0)) + 137.519416416d0)) + y)) + z) * (1.0d0 / (x * (x * x)))
    else if (x <= 130.0d0) then
        tmp = (x + (-2.0d0)) / ((47.066876606d0 + (x * 313.399215894d0)) / (z + (x * (y + (x * (137.519416416d0 + (x * 78.6994924154d0)))))))
    else
        tmp = (x + (-2.0d0)) * (4.16438922228d0 + ((((3451.550173699799d0 + ((y - 124074.40615218398d0) / x)) / x) - 101.7851458539211d0) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.8e+64) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -36.0) {
		tmp = ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z) * (1.0 / (x * (x * x)));
	} else if (x <= 130.0) {
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / (z + (x * (y + (x * (137.519416416 + (x * 78.6994924154)))))));
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -8.8e+64:
		tmp = (x + -2.0) / 0.24013125253755718
	elif x <= -36.0:
		tmp = ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z) * (1.0 / (x * (x * x)))
	elif x <= 130.0:
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / (z + (x * (y + (x * (137.519416416 + (x * 78.6994924154)))))))
	else:
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -8.8e+64)
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	elseif (x <= -36.0)
		tmp = Float64(Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z) * Float64(1.0 / Float64(x * Float64(x * x))));
	elseif (x <= 130.0)
		tmp = Float64(Float64(x + -2.0) / Float64(Float64(47.066876606 + Float64(x * 313.399215894)) / Float64(z + Float64(x * Float64(y + Float64(x * Float64(137.519416416 + Float64(x * 78.6994924154))))))));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(Float64(y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -8.8e+64)
		tmp = (x + -2.0) / 0.24013125253755718;
	elseif (x <= -36.0)
		tmp = ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z) * (1.0 / (x * (x * x)));
	elseif (x <= 130.0)
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / (z + (x * (y + (x * (137.519416416 + (x * 78.6994924154)))))));
	else
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -8.8e+64], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision], If[LessEqual[x, -36.0], N[(N[(N[(x * N[(N[(x * N[(N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision] + 137.519416416), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] * N[(1.0 / N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 130.0], N[(N[(x + -2.0), $MachinePrecision] / N[(N[(47.066876606 + N[(x * 313.399215894), $MachinePrecision]), $MachinePrecision] / N[(z + N[(x * N[(y + N[(x * N[(137.519416416 + N[(x * 78.6994924154), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(N[(N[(N[(3451.550173699799 + N[(N[(y - 124074.40615218398), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -8.80000000000000007e64

   1. Initial program 0.2%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 5.5%

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

   6. Applied egg-rr 5.5%

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

   7. Taylor expanded in x around inf

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

   9. Simplified 99.8%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]

   if -8.80000000000000007e64 < x < -36

   1. Initial program 84.9%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 94.6%

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

   6. Applied egg-rr 94.4%

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

   7. Taylor expanded in x around inf

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

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

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

      2. cube-mult N/A

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

      3. unpow2 N/A

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

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

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 91.5%

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

   9. Simplified 91.5%

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

   if -36 < x < 130

   1. Initial program 99.6%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.6%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in x around 0

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 98.2%

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

   9. Simplified 98.2%

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

   10. Taylor expanded in x around 0

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

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

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

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

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

       3. *-commutative N/A

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

       4. *-lowering-*.f64 98.2%

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

   12. Simplified 98.2%

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

   if 130 < x

   1. Initial program 9.3%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 19.8%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 94.3%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+64}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -36:\\ \;\;\;\;\left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right) \cdot \frac{1}{x \cdot \left(x \cdot x\right)}\\ \mathbf{elif}\;x \leq 130:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot 313.399215894}{z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot 78.6994924154\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 95.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{if}\;x \leq -36:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 53:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot 313.399215894}{z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot 78.6994924154\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (+ x -2.0)
          (+
           4.16438922228
           (/
            (-
             (/ (+ 3451.550173699799 (/ (- y 124074.40615218398) x)) x)
             101.7851458539211)
            x)))))
   (if (<= x -36.0)
     t_0
     (if (<= x 53.0)
       (/
        (+ x -2.0)
        (/
         (+ 47.066876606 (* x 313.399215894))
         (+ z (* x (+ y (* x (+ 137.519416416 (* x 78.6994924154))))))))
       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 <= 53.0) {
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / (z + (x * (y + (x * (137.519416416 + (x * 78.6994924154)))))));
	} 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 <= 53.0d0) then
        tmp = (x + (-2.0d0)) / ((47.066876606d0 + (x * 313.399215894d0)) / (z + (x * (y + (x * (137.519416416d0 + (x * 78.6994924154d0)))))))
    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 <= 53.0) {
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / (z + (x * (y + (x * (137.519416416 + (x * 78.6994924154)))))));
	} 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 <= 53.0:
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / (z + (x * (y + (x * (137.519416416 + (x * 78.6994924154)))))))
	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 <= 53.0)
		tmp = Float64(Float64(x + -2.0) / Float64(Float64(47.066876606 + Float64(x * 313.399215894)) / Float64(z + Float64(x * Float64(y + Float64(x * Float64(137.519416416 + Float64(x * 78.6994924154))))))));
	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 <= 53.0)
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / (z + (x * (y + (x * (137.519416416 + (x * 78.6994924154)))))));
	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, 53.0], N[(N[(x + -2.0), $MachinePrecision] / N[(N[(47.066876606 + N[(x * 313.399215894), $MachinePrecision]), $MachinePrecision] / N[(z + N[(x * N[(y + N[(x * N[(137.519416416 + N[(x * 78.6994924154), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -36 or 53 < x

   1. Initial program 17.9%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 25.9%

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

   5. Taylor expanded in x around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \color{blue}{\left(\frac{104109730557}{25000000000} + -1 \cdot \frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)}\right) \]
   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 92.2%

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

   if -36 < x < 53

   1. Initial program 99.6%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.6%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in x around 0

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 98.2%

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

   9. Simplified 98.2%

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

   10. Taylor expanded in x around 0

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

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

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

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

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

       3. *-commutative N/A

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

       4. *-lowering-*.f64 98.2%

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

   12. Simplified 98.2%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -36:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{elif}\;x \leq 53:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot 313.399215894}{z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot 78.6994924154\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{if}\;x \leq -36:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 82:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot 313.399215894}{z + x \cdot \left(y + x \cdot 137.519416416\right)}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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 -36.0)
     t_0
     (if (<= x 82.0)
       (/
        (+ x -2.0)
        (/
         (+ 47.066876606 (* x 313.399215894))
         (+ z (* x (+ y (* x 137.519416416))))))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	double tmp;
	if (x <= -36.0) {
		tmp = t_0;
	} else if (x <= 82.0) {
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / (z + (x * (y + (x * 137.519416416)))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + (-2.0d0)) * (4.16438922228d0 + ((((3451.550173699799d0 + ((y - 124074.40615218398d0) / x)) / x) - 101.7851458539211d0) / x))
    if (x <= (-36.0d0)) then
        tmp = t_0
    else if (x <= 82.0d0) then
        tmp = (x + (-2.0d0)) / ((47.066876606d0 + (x * 313.399215894d0)) / (z + (x * (y + (x * 137.519416416d0)))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	double tmp;
	if (x <= -36.0) {
		tmp = t_0;
	} else if (x <= 82.0) {
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / (z + (x * (y + (x * 137.519416416)))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x))
	tmp = 0
	if x <= -36.0:
		tmp = t_0
	elif x <= 82.0:
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / (z + (x * (y + (x * 137.519416416)))))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(Float64(y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)))
	tmp = 0.0
	if (x <= -36.0)
		tmp = t_0;
	elseif (x <= 82.0)
		tmp = Float64(Float64(x + -2.0) / Float64(Float64(47.066876606 + Float64(x * 313.399215894)) / Float64(z + Float64(x * Float64(y + Float64(x * 137.519416416))))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	tmp = 0.0;
	if (x <= -36.0)
		tmp = t_0;
	elseif (x <= 82.0)
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / (z + (x * (y + (x * 137.519416416)))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(N[(N[(N[(3451.550173699799 + N[(N[(y - 124074.40615218398), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -36.0], t$95$0, If[LessEqual[x, 82.0], N[(N[(x + -2.0), $MachinePrecision] / N[(N[(47.066876606 + N[(x * 313.399215894), $MachinePrecision]), $MachinePrecision] / N[(z + N[(x * N[(y + N[(x * 137.519416416), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -36 or 82 < x

   1. Initial program 17.9%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 25.9%

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

   5. Taylor expanded in x around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \color{blue}{\left(\frac{104109730557}{25000000000} + -1 \cdot \frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)}\right) \]
   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 92.2%

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

   if -36 < x < 82

   1. Initial program 99.6%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.6%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in x around 0

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 98.2%

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

   9. Simplified 98.2%

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

   10. Taylor expanded in x around 0

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

       1. *-commutative N/A

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

       2. *-lowering-*.f64 98.1%

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

   12. Simplified 98.1%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -36:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{elif}\;x \leq 82:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot 313.399215894}{z + x \cdot \left(y + x \cdot 137.519416416\right)}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 93.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{if}\;x \leq -36:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 30:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot 313.399215894}{z + x \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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 30.0)
       (/ (+ x -2.0) (/ (+ 47.066876606 (* x 313.399215894)) (+ z (* x y))))
       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 <= 30.0) {
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / (z + (x * y)));
	} 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 <= 30.0d0) then
        tmp = (x + (-2.0d0)) / ((47.066876606d0 + (x * 313.399215894d0)) / (z + (x * y)))
    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 <= 30.0) {
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / (z + (x * y)));
	} 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 <= 30.0:
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / (z + (x * y)))
	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 <= 30.0)
		tmp = Float64(Float64(x + -2.0) / Float64(Float64(47.066876606 + Float64(x * 313.399215894)) / Float64(z + Float64(x * y))));
	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 <= 30.0)
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / (z + (x * y)));
	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, 30.0], N[(N[(x + -2.0), $MachinePrecision] / N[(N[(47.066876606 + N[(x * 313.399215894), $MachinePrecision]), $MachinePrecision] / N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -36 or 30 < x

   1. Initial program 17.9%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 25.9%

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

   5. Taylor expanded in x around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \color{blue}{\left(\frac{104109730557}{25000000000} + -1 \cdot \frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)}\right) \]
   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 92.2%

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

   if -36 < x < 30

   1. Initial program 99.6%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.6%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in x around 0

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 98.2%

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

   9. Simplified 98.2%

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

   10. Taylor expanded in x around 0

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

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

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

       2. *-lowering-*.f64 90.5%

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

   12. Simplified 90.5%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -36:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{elif}\;x \leq 30:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot 313.399215894}{z + x \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 47.066876606 + x \cdot 313.399215894\\ \mathbf{if}\;x \leq -36:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-44}:\\ \;\;\;\;\left(y \cdot \left(x + -2\right)\right) \cdot \frac{x}{t\_0}\\ \mathbf{elif}\;x \leq 0.0152:\\ \;\;\;\;\frac{z \cdot \left(x + -2\right)}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 47.066876606 (* x 313.399215894))))
   (if (<= x -36.0)
     (/ (+ x -2.0) 0.24013125253755718)
     (if (<= x -2e-44)
       (* (* y (+ x -2.0)) (/ x t_0))
       (if (<= x 0.0152)
         (/ (* z (+ x -2.0)) t_0)
         (* x (+ 4.16438922228 (/ -110.1139242984811 x))))))))

C

double code(double x, double y, double z) {
	double t_0 = 47.066876606 + (x * 313.399215894);
	double tmp;
	if (x <= -36.0) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -2e-44) {
		tmp = (y * (x + -2.0)) * (x / t_0);
	} else if (x <= 0.0152) {
		tmp = (z * (x + -2.0)) / t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = 47.066876606d0 + (x * 313.399215894d0)
    if (x <= (-36.0d0)) then
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    else if (x <= (-2d-44)) then
        tmp = (y * (x + (-2.0d0))) * (x / t_0)
    else if (x <= 0.0152d0) then
        tmp = (z * (x + (-2.0d0))) / t_0
    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 t_0 = 47.066876606 + (x * 313.399215894);
	double tmp;
	if (x <= -36.0) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -2e-44) {
		tmp = (y * (x + -2.0)) * (x / t_0);
	} else if (x <= 0.0152) {
		tmp = (z * (x + -2.0)) / t_0;
	} else {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 47.066876606 + (x * 313.399215894)
	tmp = 0
	if x <= -36.0:
		tmp = (x + -2.0) / 0.24013125253755718
	elif x <= -2e-44:
		tmp = (y * (x + -2.0)) * (x / t_0)
	elif x <= 0.0152:
		tmp = (z * (x + -2.0)) / t_0
	else:
		tmp = x * (4.16438922228 + (-110.1139242984811 / x))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(47.066876606 + Float64(x * 313.399215894))
	tmp = 0.0
	if (x <= -36.0)
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	elseif (x <= -2e-44)
		tmp = Float64(Float64(y * Float64(x + -2.0)) * Float64(x / t_0));
	elseif (x <= 0.0152)
		tmp = Float64(Float64(z * Float64(x + -2.0)) / t_0);
	else
		tmp = Float64(x * Float64(4.16438922228 + Float64(-110.1139242984811 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 47.066876606 + (x * 313.399215894);
	tmp = 0.0;
	if (x <= -36.0)
		tmp = (x + -2.0) / 0.24013125253755718;
	elseif (x <= -2e-44)
		tmp = (y * (x + -2.0)) * (x / t_0);
	elseif (x <= 0.0152)
		tmp = (z * (x + -2.0)) / t_0;
	else
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(47.066876606 + N[(x * 313.399215894), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -36.0], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision], If[LessEqual[x, -2e-44], N[(N[(y * N[(x + -2.0), $MachinePrecision]), $MachinePrecision] * N[(x / t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.0152], N[(N[(z * N[(x + -2.0), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision], N[(x * N[(4.16438922228 + N[(-110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -36

   1. Initial program 23.1%

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

      1. 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 29.6%

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

   6. Applied egg-rr 29.5%

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

   7. Taylor expanded in x around inf

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

   9. Simplified 82.6%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]

   if -36 < x < -1.99999999999999991e-44

   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 y around inf

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

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-lowering-+.f64 65.9%

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

   5. Simplified 65.9%

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

      1. *-commutative N/A

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

      2. *-commutative N/A

         \[\leadsto \frac{\left(y \cdot \left(x + -2\right)\right) \cdot x}{x \cdot \left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\left(y \cdot \left(x + -2\right)\right) \cdot x}{x \cdot \left(x \cdot \left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left(y \cdot \left(x + -2\right)\right) \cdot x}{x \cdot \left(x \cdot \left(x \cdot \left(x + \frac{216700011257}{5000000000}\right) + \frac{263505074721}{1000000000}\right) + \frac{156699607947}{500000000}\right) + \frac{23533438303}{500000000}} \]

      5. associate-/l* N/A

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

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

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

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

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

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

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

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

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

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

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

   7. Applied egg-rr 66.0%

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

   8. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 59.4%

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

   10. Simplified 59.4%

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

   if -1.99999999999999991e-44 < x < 0.0152

   1. Initial program 99.6%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.6%

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

   6. Applied egg-rr 99.4%

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

   7. Taylor expanded in x around 0

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 99.4%

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

   9. Simplified 99.4%

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

   10. Taylor expanded in z around inf

       \[\leadsto \color{blue}{\frac{z \cdot \left(x - 2\right)}{\frac{23533438303}{500000000} + \frac{156699607947}{500000000} \cdot x}} \]
   11. Step-by-step derivation

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

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

       2. *-commutative N/A

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

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

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

       4. sub-neg N/A

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

       5. metadata-eval N/A

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

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

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

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

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

       8. *-commutative N/A

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

       9. *-lowering-*.f64 73.4%

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

   12. Simplified 73.4%

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

   if 0.0152 < x

   1. Initial program 11.3%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 21.5%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   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 86.6%

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

   7. Simplified 86.6%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -36:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-44}:\\ \;\;\;\;\left(y \cdot \left(x + -2\right)\right) \cdot \frac{x}{47.066876606 + x \cdot 313.399215894}\\ \mathbf{elif}\;x \leq 0.0152:\\ \;\;\;\;\frac{z \cdot \left(x + -2\right)}{47.066876606 + x \cdot 313.399215894}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 77.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\right)\\ \mathbf{elif}\;x \leq 0.0152:\\ \;\;\;\;\frac{z \cdot \left(x + -2\right)}{47.066876606 + x \cdot 313.399215894}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5)
   (/ (+ x -2.0) 0.24013125253755718)
   (if (<= x -1.3e-44)
     (* x (* y (+ -0.0424927283095952 (* x 0.3041881842569256))))
     (if (<= x 0.0152)
       (/ (* z (+ x -2.0)) (+ 47.066876606 (* x 313.399215894)))
       (* x (+ 4.16438922228 (/ -110.1139242984811 x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -1.3e-44) {
		tmp = x * (y * (-0.0424927283095952 + (x * 0.3041881842569256)));
	} else if (x <= 0.0152) {
		tmp = (z * (x + -2.0)) / (47.066876606 + (x * 313.399215894));
	} else {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-5.5d0)) then
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    else if (x <= (-1.3d-44)) then
        tmp = x * (y * ((-0.0424927283095952d0) + (x * 0.3041881842569256d0)))
    else if (x <= 0.0152d0) then
        tmp = (z * (x + (-2.0d0))) / (47.066876606d0 + (x * 313.399215894d0))
    else
        tmp = x * (4.16438922228d0 + ((-110.1139242984811d0) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -1.3e-44) {
		tmp = x * (y * (-0.0424927283095952 + (x * 0.3041881842569256)));
	} else if (x <= 0.0152) {
		tmp = (z * (x + -2.0)) / (47.066876606 + (x * 313.399215894));
	} else {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.5:
		tmp = (x + -2.0) / 0.24013125253755718
	elif x <= -1.3e-44:
		tmp = x * (y * (-0.0424927283095952 + (x * 0.3041881842569256)))
	elif x <= 0.0152:
		tmp = (z * (x + -2.0)) / (47.066876606 + (x * 313.399215894))
	else:
		tmp = x * (4.16438922228 + (-110.1139242984811 / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5)
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	elseif (x <= -1.3e-44)
		tmp = Float64(x * Float64(y * Float64(-0.0424927283095952 + Float64(x * 0.3041881842569256))));
	elseif (x <= 0.0152)
		tmp = Float64(Float64(z * Float64(x + -2.0)) / Float64(47.066876606 + Float64(x * 313.399215894)));
	else
		tmp = Float64(x * Float64(4.16438922228 + Float64(-110.1139242984811 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.5)
		tmp = (x + -2.0) / 0.24013125253755718;
	elseif (x <= -1.3e-44)
		tmp = x * (y * (-0.0424927283095952 + (x * 0.3041881842569256)));
	elseif (x <= 0.0152)
		tmp = (z * (x + -2.0)) / (47.066876606 + (x * 313.399215894));
	else
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision], If[LessEqual[x, -1.3e-44], N[(x * N[(y * N[(-0.0424927283095952 + N[(x * 0.3041881842569256), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.0152], N[(N[(z * N[(x + -2.0), $MachinePrecision]), $MachinePrecision] / N[(47.066876606 + N[(x * 313.399215894), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(4.16438922228 + N[(-110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.5

   1. Initial program 24.1%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 30.5%

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

   6. Applied egg-rr 30.4%

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

   7. Taylor expanded in x around inf

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

   9. Simplified 81.6%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]

   if -5.5 < x < -1.2999999999999999e-44

   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. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-lowering-+.f64 63.6%

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

   5. Simplified 63.6%

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

   6. Taylor expanded in x around 0

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

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

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

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

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

      3. *-commutative N/A

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

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

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

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

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

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

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

      7. metadata-eval N/A

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

      8. metadata-eval N/A

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

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

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

      10. metadata-eval 62.2%

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

   8. Simplified 62.2%

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

   9. Taylor expanded in y around 0

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

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

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

       2. sub-neg N/A

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

       3. metadata-eval N/A

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

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

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

       5. *-commutative N/A

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

       6. *-lowering-*.f64 62.2%

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

   11. Simplified 62.2%

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

   if -1.2999999999999999e-44 < x < 0.0152

   1. Initial program 99.6%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.6%

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

   6. Applied egg-rr 99.4%

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

   7. Taylor expanded in x around 0

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 99.4%

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

   9. Simplified 99.4%

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

   10. Taylor expanded in z around inf

       \[\leadsto \color{blue}{\frac{z \cdot \left(x - 2\right)}{\frac{23533438303}{500000000} + \frac{156699607947}{500000000} \cdot x}} \]
   11. Step-by-step derivation

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

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

       2. *-commutative N/A

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

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

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

       4. sub-neg N/A

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

       5. metadata-eval N/A

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

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

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

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

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

       8. *-commutative N/A

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

       9. *-lowering-*.f64 73.4%

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

   12. Simplified 73.4%

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

   if 0.0152 < x

   1. Initial program 11.3%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 21.5%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   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 86.6%

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

   7. Simplified 86.6%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\right)\\ \mathbf{elif}\;x \leq 0.0152:\\ \;\;\;\;\frac{z \cdot \left(x + -2\right)}{47.066876606 + x \cdot 313.399215894}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 90.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -36:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 1850:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot 313.399215894}{z + x \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -36.0)
   (/ (+ x -2.0) 0.24013125253755718)
   (if (<= x 1850.0)
     (/ (+ x -2.0) (/ (+ 47.066876606 (* x 313.399215894)) (+ z (* x y))))
     (* x (+ 4.16438922228 (/ -110.1139242984811 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -36.0) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= 1850.0) {
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / (z + (x * y)));
	} 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 <= (-36.0d0)) then
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    else if (x <= 1850.0d0) then
        tmp = (x + (-2.0d0)) / ((47.066876606d0 + (x * 313.399215894d0)) / (z + (x * y)))
    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 <= -36.0) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= 1850.0) {
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / (z + (x * y)));
	} else {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -36.0:
		tmp = (x + -2.0) / 0.24013125253755718
	elif x <= 1850.0:
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / (z + (x * y)))
	else:
		tmp = x * (4.16438922228 + (-110.1139242984811 / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -36.0)
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	elseif (x <= 1850.0)
		tmp = Float64(Float64(x + -2.0) / Float64(Float64(47.066876606 + Float64(x * 313.399215894)) / Float64(z + Float64(x * y))));
	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 <= -36.0)
		tmp = (x + -2.0) / 0.24013125253755718;
	elseif (x <= 1850.0)
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / (z + (x * y)));
	else
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -36.0], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision], If[LessEqual[x, 1850.0], N[(N[(x + -2.0), $MachinePrecision] / N[(N[(47.066876606 + N[(x * 313.399215894), $MachinePrecision]), $MachinePrecision] / N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(4.16438922228 + N[(-110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -36

   1. Initial program 23.1%

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

      1. 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 29.6%

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

   6. Applied egg-rr 29.5%

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

   7. Taylor expanded in x around inf

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

   9. Simplified 82.6%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]

   if -36 < x < 1850

   1. Initial program 99.6%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.6%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in x around 0

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 98.2%

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

   9. Simplified 98.2%

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

   10. Taylor expanded in x around 0

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

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

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

       2. *-lowering-*.f64 90.5%

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

   12. Simplified 90.5%

       \[\leadsto \frac{x + -2}{\frac{47.066876606 + x \cdot 313.399215894}{\color{blue}{z + x \cdot y}}} \]

   if 1850 < x

   1. Initial program 9.3%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 19.8%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 88.5%

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

   7. Simplified 88.5%

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

Alternative 12: 77.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\right)\\ \mathbf{elif}\;x \leq 0.0152:\\ \;\;\;\;x \cdot \left(z \cdot 0.3041881842569256\right) + z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.0)
   (/ (+ x -2.0) 0.24013125253755718)
   (if (<= x -4e-44)
     (* x (* y (+ -0.0424927283095952 (* x 0.3041881842569256))))
     (if (<= x 0.0152)
       (+ (* x (* z 0.3041881842569256)) (* z -0.0424927283095952))
       (* x (+ 4.16438922228 (/ -110.1139242984811 x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.0) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -4e-44) {
		tmp = x * (y * (-0.0424927283095952 + (x * 0.3041881842569256)));
	} else if (x <= 0.0152) {
		tmp = (x * (z * 0.3041881842569256)) + (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 <= (-1.0d0)) then
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    else if (x <= (-4d-44)) then
        tmp = x * (y * ((-0.0424927283095952d0) + (x * 0.3041881842569256d0)))
    else if (x <= 0.0152d0) then
        tmp = (x * (z * 0.3041881842569256d0)) + (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 <= -1.0) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -4e-44) {
		tmp = x * (y * (-0.0424927283095952 + (x * 0.3041881842569256)));
	} else if (x <= 0.0152) {
		tmp = (x * (z * 0.3041881842569256)) + (z * -0.0424927283095952);
	} else {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.0:
		tmp = (x + -2.0) / 0.24013125253755718
	elif x <= -4e-44:
		tmp = x * (y * (-0.0424927283095952 + (x * 0.3041881842569256)))
	elif x <= 0.0152:
		tmp = (x * (z * 0.3041881842569256)) + (z * -0.0424927283095952)
	else:
		tmp = x * (4.16438922228 + (-110.1139242984811 / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	elseif (x <= -4e-44)
		tmp = Float64(x * Float64(y * Float64(-0.0424927283095952 + Float64(x * 0.3041881842569256))));
	elseif (x <= 0.0152)
		tmp = Float64(Float64(x * Float64(z * 0.3041881842569256)) + 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 <= -1.0)
		tmp = (x + -2.0) / 0.24013125253755718;
	elseif (x <= -4e-44)
		tmp = x * (y * (-0.0424927283095952 + (x * 0.3041881842569256)));
	elseif (x <= 0.0152)
		tmp = (x * (z * 0.3041881842569256)) + (z * -0.0424927283095952);
	else
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.0], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision], If[LessEqual[x, -4e-44], N[(x * N[(y * N[(-0.0424927283095952 + N[(x * 0.3041881842569256), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.0152], N[(N[(x * N[(z * 0.3041881842569256), $MachinePrecision]), $MachinePrecision] + N[(z * -0.0424927283095952), $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

   1. Initial program 24.1%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 30.5%

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

   6. Applied egg-rr 30.4%

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

   7. Taylor expanded in x around inf

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

   9. Simplified 81.6%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]

   if -1 < x < -3.99999999999999981e-44

   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. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-lowering-+.f64 63.6%

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

   5. Simplified 63.6%

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

   6. Taylor expanded in x around 0

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

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

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

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

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

      3. *-commutative N/A

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

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

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

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

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

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

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

      7. metadata-eval N/A

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

      8. metadata-eval N/A

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

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

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

      10. metadata-eval 62.2%

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

   8. Simplified 62.2%

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

   9. Taylor expanded in y around 0

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

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

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

       2. sub-neg N/A

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

       3. metadata-eval N/A

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

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

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

       5. *-commutative N/A

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

       6. *-lowering-*.f64 62.2%

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

   11. Simplified 62.2%

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

   if -3.99999999999999981e-44 < x < 0.0152

   1. Initial program 99.6%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 73.4%

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

   8. Taylor expanded in x around 0

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

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

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. metadata-eval N/A

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

      7. *-lowering-*.f64 73.3%

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

   10. Simplified 73.3%

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

   if 0.0152 < x

   1. Initial program 11.3%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 21.5%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   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 86.6%

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

   7. Simplified 86.6%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\right)\\ \mathbf{elif}\;x \leq 0.0152:\\ \;\;\;\;x \cdot \left(z \cdot 0.3041881842569256\right) + z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 90.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2700000:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 28:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952 + z \cdot 0.3041881842569256\right) + z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2700000.0)
   (/ (+ x -2.0) 0.24013125253755718)
   (if (<= x 28.0)
     (+
      (* x (+ (* y -0.0424927283095952) (* z 0.3041881842569256)))
      (* z -0.0424927283095952))
     (* x (+ 4.16438922228 (/ -110.1139242984811 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2700000.0) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= 28.0) {
		tmp = (x * ((y * -0.0424927283095952) + (z * 0.3041881842569256))) + (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 <= (-2700000.0d0)) then
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    else if (x <= 28.0d0) then
        tmp = (x * ((y * (-0.0424927283095952d0)) + (z * 0.3041881842569256d0))) + (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 <= -2700000.0) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= 28.0) {
		tmp = (x * ((y * -0.0424927283095952) + (z * 0.3041881842569256))) + (z * -0.0424927283095952);
	} else {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2700000.0:
		tmp = (x + -2.0) / 0.24013125253755718
	elif x <= 28.0:
		tmp = (x * ((y * -0.0424927283095952) + (z * 0.3041881842569256))) + (z * -0.0424927283095952)
	else:
		tmp = x * (4.16438922228 + (-110.1139242984811 / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2700000.0)
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	elseif (x <= 28.0)
		tmp = Float64(Float64(x * Float64(Float64(y * -0.0424927283095952) + Float64(z * 0.3041881842569256))) + 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 <= -2700000.0)
		tmp = (x + -2.0) / 0.24013125253755718;
	elseif (x <= 28.0)
		tmp = (x * ((y * -0.0424927283095952) + (z * 0.3041881842569256))) + (z * -0.0424927283095952);
	else
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2700000.0], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision], If[LessEqual[x, 28.0], N[(N[(x * N[(N[(y * -0.0424927283095952), $MachinePrecision] + N[(z * 0.3041881842569256), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * -0.0424927283095952), $MachinePrecision]), $MachinePrecision], N[(x * N[(4.16438922228 + N[(-110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.7e6

   1. Initial program 22.1%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 28.6%

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

   6. Applied egg-rr 28.6%

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

   7. Taylor expanded in x around inf

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

   9. Simplified 83.7%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]

   if -2.7e6 < x < 28

   1. Initial program 99.6%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.6%

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

   6. Applied egg-rr 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. *-lowering-*.f64 N/A

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

      12. metadata-eval 89.2%

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

   9. Simplified 89.2%

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

   if 28 < x

   1. Initial program 9.3%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 19.8%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 88.5%

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

   7. Simplified 88.5%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2700000:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 28:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952 + z \cdot 0.3041881842569256\right) + z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 77.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.205:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\right)\\ \mathbf{elif}\;x \leq 0.0152:\\ \;\;\;\;\left(x + -2\right) \cdot \frac{z}{47.066876606}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.205)
   (/ (+ x -2.0) 0.24013125253755718)
   (if (<= x -5e-44)
     (* x (* y (+ -0.0424927283095952 (* x 0.3041881842569256))))
     (if (<= x 0.0152)
       (* (+ x -2.0) (/ z 47.066876606))
       (* x (+ 4.16438922228 (/ -110.1139242984811 x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.205) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -5e-44) {
		tmp = x * (y * (-0.0424927283095952 + (x * 0.3041881842569256)));
	} else if (x <= 0.0152) {
		tmp = (x + -2.0) * (z / 47.066876606);
	} else {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-0.205d0)) then
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    else if (x <= (-5d-44)) then
        tmp = x * (y * ((-0.0424927283095952d0) + (x * 0.3041881842569256d0)))
    else if (x <= 0.0152d0) then
        tmp = (x + (-2.0d0)) * (z / 47.066876606d0)
    else
        tmp = x * (4.16438922228d0 + ((-110.1139242984811d0) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.205) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -5e-44) {
		tmp = x * (y * (-0.0424927283095952 + (x * 0.3041881842569256)));
	} else if (x <= 0.0152) {
		tmp = (x + -2.0) * (z / 47.066876606);
	} else {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.205:
		tmp = (x + -2.0) / 0.24013125253755718
	elif x <= -5e-44:
		tmp = x * (y * (-0.0424927283095952 + (x * 0.3041881842569256)))
	elif x <= 0.0152:
		tmp = (x + -2.0) * (z / 47.066876606)
	else:
		tmp = x * (4.16438922228 + (-110.1139242984811 / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.205)
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	elseif (x <= -5e-44)
		tmp = Float64(x * Float64(y * Float64(-0.0424927283095952 + Float64(x * 0.3041881842569256))));
	elseif (x <= 0.0152)
		tmp = Float64(Float64(x + -2.0) * Float64(z / 47.066876606));
	else
		tmp = Float64(x * Float64(4.16438922228 + Float64(-110.1139242984811 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.205)
		tmp = (x + -2.0) / 0.24013125253755718;
	elseif (x <= -5e-44)
		tmp = x * (y * (-0.0424927283095952 + (x * 0.3041881842569256)));
	elseif (x <= 0.0152)
		tmp = (x + -2.0) * (z / 47.066876606);
	else
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.205], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision], If[LessEqual[x, -5e-44], N[(x * N[(y * N[(-0.0424927283095952 + N[(x * 0.3041881842569256), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.0152], N[(N[(x + -2.0), $MachinePrecision] * N[(z / 47.066876606), $MachinePrecision]), $MachinePrecision], N[(x * N[(4.16438922228 + N[(-110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -0.204999999999999988

   1. Initial program 24.1%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 30.5%

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

   6. Applied egg-rr 30.4%

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

   7. Taylor expanded in x around inf

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

   9. Simplified 81.6%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]

   if -0.204999999999999988 < x < -5.00000000000000039e-44

   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. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-lowering-+.f64 63.6%

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

   5. Simplified 63.6%

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

   6. Taylor expanded in x around 0

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

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

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

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

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

      3. *-commutative N/A

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

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

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

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

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

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

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

      7. metadata-eval N/A

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

      8. metadata-eval N/A

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

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

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

      10. metadata-eval 62.2%

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

   8. Simplified 62.2%

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

   9. Taylor expanded in y around 0

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

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

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

       2. sub-neg N/A

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

       3. metadata-eval N/A

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

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

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

       5. *-commutative N/A

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

       6. *-lowering-*.f64 62.2%

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

   11. Simplified 62.2%

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

   if -5.00000000000000039e-44 < x < 0.0152

   1. Initial program 99.6%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 73.4%

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

   8. Taylor expanded in x around 0

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

   10. Simplified 73.1%

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

   if 0.0152 < x

   1. Initial program 11.3%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 21.5%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   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 86.6%

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

   7. Simplified 86.6%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.205:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\right)\\ \mathbf{elif}\;x \leq 0.0152:\\ \;\;\;\;\left(x + -2\right) \cdot \frac{z}{47.066876606}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 77.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 0.0152:\\ \;\;\;\;\left(x + -2\right) \cdot \frac{z}{47.066876606}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5)
   (/ (+ x -2.0) 0.24013125253755718)
   (if (<= x -4.5e-44)
     (* x (* y -0.0424927283095952))
     (if (<= x 0.0152)
       (* (+ x -2.0) (/ z 47.066876606))
       (* x (+ 4.16438922228 (/ -110.1139242984811 x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -4.5e-44) {
		tmp = x * (y * -0.0424927283095952);
	} else if (x <= 0.0152) {
		tmp = (x + -2.0) * (z / 47.066876606);
	} else {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-5.5d0)) then
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    else if (x <= (-4.5d-44)) then
        tmp = x * (y * (-0.0424927283095952d0))
    else if (x <= 0.0152d0) then
        tmp = (x + (-2.0d0)) * (z / 47.066876606d0)
    else
        tmp = x * (4.16438922228d0 + ((-110.1139242984811d0) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -4.5e-44) {
		tmp = x * (y * -0.0424927283095952);
	} else if (x <= 0.0152) {
		tmp = (x + -2.0) * (z / 47.066876606);
	} else {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.5:
		tmp = (x + -2.0) / 0.24013125253755718
	elif x <= -4.5e-44:
		tmp = x * (y * -0.0424927283095952)
	elif x <= 0.0152:
		tmp = (x + -2.0) * (z / 47.066876606)
	else:
		tmp = x * (4.16438922228 + (-110.1139242984811 / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5)
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	elseif (x <= -4.5e-44)
		tmp = Float64(x * Float64(y * -0.0424927283095952));
	elseif (x <= 0.0152)
		tmp = Float64(Float64(x + -2.0) * Float64(z / 47.066876606));
	else
		tmp = Float64(x * Float64(4.16438922228 + Float64(-110.1139242984811 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.5)
		tmp = (x + -2.0) / 0.24013125253755718;
	elseif (x <= -4.5e-44)
		tmp = x * (y * -0.0424927283095952);
	elseif (x <= 0.0152)
		tmp = (x + -2.0) * (z / 47.066876606);
	else
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision], If[LessEqual[x, -4.5e-44], N[(x * N[(y * -0.0424927283095952), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.0152], N[(N[(x + -2.0), $MachinePrecision] * N[(z / 47.066876606), $MachinePrecision]), $MachinePrecision], N[(x * N[(4.16438922228 + N[(-110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.5

   1. Initial program 24.1%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 30.5%

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

   6. Applied egg-rr 30.4%

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

   7. Taylor expanded in x around inf

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

   9. Simplified 81.6%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]

   if -5.5 < x < -4.4999999999999999e-44

   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. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-lowering-+.f64 63.6%

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

   5. Simplified 63.6%

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

   6. Taylor expanded in x around 0

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

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

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

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

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

      3. *-commutative N/A

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

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

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

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

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

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

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

      7. metadata-eval N/A

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

      8. metadata-eval N/A

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

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

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

      10. metadata-eval 62.2%

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

   8. Simplified 62.2%

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

   9. Taylor expanded in x around 0

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

       1. *-commutative N/A

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

       2. *-lowering-*.f64 60.1%

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

   11. Simplified 60.1%

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

   if -4.4999999999999999e-44 < x < 0.0152

   1. Initial program 99.6%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 73.4%

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

   8. Taylor expanded in x around 0

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

   10. Simplified 73.1%

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

   if 0.0152 < x

   1. Initial program 11.3%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 21.5%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   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 86.6%

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

   7. Simplified 86.6%

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

Alternative 16: 76.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-45}:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 0.0152:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5)
   (/ (+ x -2.0) 0.24013125253755718)
   (if (<= x -6.2e-45)
     (* x (* y -0.0424927283095952))
     (if (<= x 0.0152)
       (* (+ x -2.0) (* z 0.0212463641547976))
       (* x (+ 4.16438922228 (/ -110.1139242984811 x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -6.2e-45) {
		tmp = x * (y * -0.0424927283095952);
	} else if (x <= 0.0152) {
		tmp = (x + -2.0) * (z * 0.0212463641547976);
	} else {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-5.5d0)) then
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    else if (x <= (-6.2d-45)) then
        tmp = x * (y * (-0.0424927283095952d0))
    else if (x <= 0.0152d0) then
        tmp = (x + (-2.0d0)) * (z * 0.0212463641547976d0)
    else
        tmp = x * (4.16438922228d0 + ((-110.1139242984811d0) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -6.2e-45) {
		tmp = x * (y * -0.0424927283095952);
	} else if (x <= 0.0152) {
		tmp = (x + -2.0) * (z * 0.0212463641547976);
	} else {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.5:
		tmp = (x + -2.0) / 0.24013125253755718
	elif x <= -6.2e-45:
		tmp = x * (y * -0.0424927283095952)
	elif x <= 0.0152:
		tmp = (x + -2.0) * (z * 0.0212463641547976)
	else:
		tmp = x * (4.16438922228 + (-110.1139242984811 / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5)
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	elseif (x <= -6.2e-45)
		tmp = Float64(x * Float64(y * -0.0424927283095952));
	elseif (x <= 0.0152)
		tmp = Float64(Float64(x + -2.0) * Float64(z * 0.0212463641547976));
	else
		tmp = Float64(x * Float64(4.16438922228 + Float64(-110.1139242984811 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.5)
		tmp = (x + -2.0) / 0.24013125253755718;
	elseif (x <= -6.2e-45)
		tmp = x * (y * -0.0424927283095952);
	elseif (x <= 0.0152)
		tmp = (x + -2.0) * (z * 0.0212463641547976);
	else
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision], If[LessEqual[x, -6.2e-45], N[(x * N[(y * -0.0424927283095952), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.0152], N[(N[(x + -2.0), $MachinePrecision] * N[(z * 0.0212463641547976), $MachinePrecision]), $MachinePrecision], N[(x * N[(4.16438922228 + N[(-110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.5

   1. Initial program 24.1%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 30.5%

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

   6. Applied egg-rr 30.4%

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

   7. Taylor expanded in x around inf

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

   9. Simplified 81.6%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]

   if -5.5 < x < -6.2000000000000002e-45

   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. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-lowering-+.f64 63.6%

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

   5. Simplified 63.6%

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

   6. Taylor expanded in x around 0

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

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

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

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

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

      3. *-commutative N/A

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

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

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

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

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

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

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

      7. metadata-eval N/A

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

      8. metadata-eval N/A

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

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

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

      10. metadata-eval 62.2%

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

   8. Simplified 62.2%

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

   9. Taylor expanded in x around 0

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

       1. *-commutative N/A

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

       2. *-lowering-*.f64 60.1%

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

   11. Simplified 60.1%

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

   if -6.2000000000000002e-45 < x < 0.0152

   1. Initial program 99.6%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 72.9%

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

   7. Simplified 72.9%

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

   if 0.0152 < x

   1. Initial program 11.3%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 21.5%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   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 86.6%

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

   7. Simplified 86.6%

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

Alternative 17: 77.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0095:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 0.0152:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.0095)
   (/ (+ x -2.0) 0.24013125253755718)
   (if (<= x -5e-44)
     (* x (* y -0.0424927283095952))
     (if (<= x 0.0152)
       (* z -0.0424927283095952)
       (* x (+ 4.16438922228 (/ -110.1139242984811 x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.0095) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -5e-44) {
		tmp = x * (y * -0.0424927283095952);
	} else if (x <= 0.0152) {
		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 <= (-0.0095d0)) then
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    else if (x <= (-5d-44)) then
        tmp = x * (y * (-0.0424927283095952d0))
    else if (x <= 0.0152d0) 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 <= -0.0095) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -5e-44) {
		tmp = x * (y * -0.0424927283095952);
	} else if (x <= 0.0152) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.0095:
		tmp = (x + -2.0) / 0.24013125253755718
	elif x <= -5e-44:
		tmp = x * (y * -0.0424927283095952)
	elif x <= 0.0152:
		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 <= -0.0095)
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	elseif (x <= -5e-44)
		tmp = Float64(x * Float64(y * -0.0424927283095952));
	elseif (x <= 0.0152)
		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 <= -0.0095)
		tmp = (x + -2.0) / 0.24013125253755718;
	elseif (x <= -5e-44)
		tmp = x * (y * -0.0424927283095952);
	elseif (x <= 0.0152)
		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, -0.0095], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision], If[LessEqual[x, -5e-44], N[(x * N[(y * -0.0424927283095952), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.0152], N[(z * -0.0424927283095952), $MachinePrecision], N[(x * N[(4.16438922228 + N[(-110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -0.00949999999999999976

   1. Initial program 24.1%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 30.5%

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

   6. Applied egg-rr 30.4%

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

   7. Taylor expanded in x around inf

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

   9. Simplified 81.6%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]

   if -0.00949999999999999976 < x < -5.00000000000000039e-44

   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. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-lowering-+.f64 63.6%

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

   5. Simplified 63.6%

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

   6. Taylor expanded in x around 0

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

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

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

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

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

      3. *-commutative N/A

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

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

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

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

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

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

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

      7. metadata-eval N/A

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

      8. metadata-eval N/A

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

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

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

      10. metadata-eval 62.2%

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

   8. Simplified 62.2%

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

   9. Taylor expanded in x around 0

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

       1. *-commutative N/A

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

       2. *-lowering-*.f64 60.1%

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

   11. Simplified 60.1%

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

   if -5.00000000000000039e-44 < x < 0.0152

   1. Initial program 99.6%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 72.9%

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

   7. Simplified 72.9%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]

   if 0.0152 < x

   1. Initial program 11.3%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 21.5%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   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 86.6%

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

   7. Simplified 86.6%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0095:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 0.0152:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 77.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + -2}{0.24013125253755718}\\ \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 0.0152:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x -2.0) 0.24013125253755718)))
   (if (<= x -5.5)
     t_0
     (if (<= x -4.8e-44)
       (* x (* y -0.0424927283095952))
       (if (<= x 0.0152) (* z -0.0424927283095952) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = (x + -2.0) / 0.24013125253755718;
	double tmp;
	if (x <= -5.5) {
		tmp = t_0;
	} else if (x <= -4.8e-44) {
		tmp = x * (y * -0.0424927283095952);
	} else if (x <= 0.0152) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + (-2.0d0)) / 0.24013125253755718d0
    if (x <= (-5.5d0)) then
        tmp = t_0
    else if (x <= (-4.8d-44)) then
        tmp = x * (y * (-0.0424927283095952d0))
    else if (x <= 0.0152d0) then
        tmp = z * (-0.0424927283095952d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + -2.0) / 0.24013125253755718;
	double tmp;
	if (x <= -5.5) {
		tmp = t_0;
	} else if (x <= -4.8e-44) {
		tmp = x * (y * -0.0424927283095952);
	} else if (x <= 0.0152) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + -2.0) / 0.24013125253755718
	tmp = 0
	if x <= -5.5:
		tmp = t_0
	elif x <= -4.8e-44:
		tmp = x * (y * -0.0424927283095952)
	elif x <= 0.0152:
		tmp = z * -0.0424927283095952
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + -2.0) / 0.24013125253755718)
	tmp = 0.0
	if (x <= -5.5)
		tmp = t_0;
	elseif (x <= -4.8e-44)
		tmp = Float64(x * Float64(y * -0.0424927283095952));
	elseif (x <= 0.0152)
		tmp = 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) / 0.24013125253755718;
	tmp = 0.0;
	if (x <= -5.5)
		tmp = t_0;
	elseif (x <= -4.8e-44)
		tmp = x * (y * -0.0424927283095952);
	elseif (x <= 0.0152)
		tmp = 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] / 0.24013125253755718), $MachinePrecision]}, If[LessEqual[x, -5.5], t$95$0, If[LessEqual[x, -4.8e-44], N[(x * N[(y * -0.0424927283095952), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.0152], N[(z * -0.0424927283095952), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5 or 0.0152 < x

   1. Initial program 19.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 27.1%

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

   6. Applied egg-rr 27.0%

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

   7. Taylor expanded in x around inf

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

   9. Simplified 83.3%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]

   if -5.5 < x < -4.80000000000000017e-44

   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. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-lowering-+.f64 63.6%

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

   5. Simplified 63.6%

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

   6. Taylor expanded in x around 0

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{-1000000000}{23533438303} \cdot y + x \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{-1000000000}{23533438303} \cdot y\right), \color{blue}{\left(x \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right)\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(y \cdot \frac{-1000000000}{23533438303}\right), \left(\color{blue}{x} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-1000000000}{23533438303}\right), \left(\color{blue}{x} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-1000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{500000000}{23533438303} \cdot y - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right)}\right)\right)\right) \]

      6. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-1000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \left(y \cdot \color{blue}{\left(\frac{500000000}{23533438303} - \frac{-156699607947000000000}{553822718361107519809}\right)}\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-1000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \left(y \cdot \frac{168466327098500000000}{553822718361107519809}\right)\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-1000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \left(y \cdot \left(\mathsf{neg}\left(\frac{-168466327098500000000}{553822718361107519809}\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-1000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(\frac{-168466327098500000000}{553822718361107519809}\right)\right)}\right)\right)\right)\right) \]

      10. metadata-eval 62.2%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-1000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \frac{168466327098500000000}{553822718361107519809}\right)\right)\right)\right) \]

   8. Simplified 62.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot -0.0424927283095952 + x \cdot \left(y \cdot 0.3041881842569256\right)\right)} \]

   9. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{-1000000000}{23533438303} \cdot y\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(y \cdot \color{blue}{\frac{-1000000000}{23533438303}}\right)\right) \]

       2. *-lowering-*.f64 60.1%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{-1000000000}{23533438303}}\right)\right) \]

   11. Simplified 60.1%

       \[\leadsto x \cdot \color{blue}{\left(y \cdot -0.0424927283095952\right)} \]

   if -4.80000000000000017e-44 < x < 0.0152

   1. Initial program 99.6%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \left(x - 2\right) \cdot \color{blue}{\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x - 2\right), \color{blue}{\left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x + \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + \color{blue}{z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{/.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}\right)}\right)\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 72.9%

         \[\leadsto \mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, \color{blue}{z}\right) \]

   7. Simplified 72.9%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 0.0152:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 76.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4.16438922228 \cdot \left(x + -2\right)\\ \mathbf{if}\;x \leq -0.15:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 0.0152:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 4.16438922228 (+ x -2.0))))
   (if (<= x -0.15)
     t_0
     (if (<= x -5e-44)
       (* x (* y -0.0424927283095952))
       (if (<= x 0.0152) (* z -0.0424927283095952) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = 4.16438922228 * (x + -2.0);
	double tmp;
	if (x <= -0.15) {
		tmp = t_0;
	} else if (x <= -5e-44) {
		tmp = x * (y * -0.0424927283095952);
	} else if (x <= 0.0152) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 4.16438922228d0 * (x + (-2.0d0))
    if (x <= (-0.15d0)) then
        tmp = t_0
    else if (x <= (-5d-44)) then
        tmp = x * (y * (-0.0424927283095952d0))
    else if (x <= 0.0152d0) then
        tmp = z * (-0.0424927283095952d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 4.16438922228 * (x + -2.0);
	double tmp;
	if (x <= -0.15) {
		tmp = t_0;
	} else if (x <= -5e-44) {
		tmp = x * (y * -0.0424927283095952);
	} else if (x <= 0.0152) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.16438922228 * (x + -2.0)
	tmp = 0
	if x <= -0.15:
		tmp = t_0
	elif x <= -5e-44:
		tmp = x * (y * -0.0424927283095952)
	elif x <= 0.0152:
		tmp = z * -0.0424927283095952
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(4.16438922228 * Float64(x + -2.0))
	tmp = 0.0
	if (x <= -0.15)
		tmp = t_0;
	elseif (x <= -5e-44)
		tmp = Float64(x * Float64(y * -0.0424927283095952));
	elseif (x <= 0.0152)
		tmp = Float64(z * -0.0424927283095952);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 4.16438922228 * (x + -2.0);
	tmp = 0.0;
	if (x <= -0.15)
		tmp = t_0;
	elseif (x <= -5e-44)
		tmp = x * (y * -0.0424927283095952);
	elseif (x <= 0.0152)
		tmp = z * -0.0424927283095952;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(4.16438922228 * N[(x + -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.15], t$95$0, If[LessEqual[x, -5e-44], N[(x * N[(y * -0.0424927283095952), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.0152], N[(z * -0.0424927283095952), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.149999999999999994 or 0.0152 < x

   1. Initial program 19.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 27.1%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \color{blue}{\frac{104109730557}{25000000000}}\right) \]
   6. Step-by-step derivation

   7. Simplified 82.8%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{4.16438922228} \]

   if -0.149999999999999994 < x < -5.00000000000000039e-44

   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. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot \left(y \cdot \left(x - 2\right)\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right), x\right), \frac{263505074721}{1000000000}\right), x\right), \frac{156699607947}{500000000}\right), x\right), \frac{23533438303}{500000000}\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y \cdot \left(x - 2\right)\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right), x\right), \frac{263505074721}{1000000000}\right), x\right), \frac{156699607947}{500000000}\right), x\right)}, \frac{23533438303}{500000000}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \left(x - 2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right), x\right), \frac{263505074721}{1000000000}\right), x\right), \frac{156699607947}{500000000}\right), \color{blue}{x}\right), \frac{23533438303}{500000000}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \left(x + \left(\mathsf{neg}\left(2\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right), x\right), \frac{263505074721}{1000000000}\right), x\right), \frac{156699607947}{500000000}\right), x\right), \frac{23533438303}{500000000}\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \left(x + -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right), x\right), \frac{263505074721}{1000000000}\right), x\right), \frac{156699607947}{500000000}\right), x\right), \frac{23533438303}{500000000}\right)\right) \]

      5. +-lowering-+.f64 63.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right), x\right), \frac{263505074721}{1000000000}\right), x\right), \frac{156699607947}{500000000}\right), x\right), \frac{23533438303}{500000000}\right)\right) \]

   5. Simplified 63.6%

      \[\leadsto \frac{\color{blue}{x \cdot \left(y \cdot \left(x + -2\right)\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{x \cdot \left(\frac{-1000000000}{23533438303} \cdot y + x \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{-1000000000}{23533438303} \cdot y + x \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{-1000000000}{23533438303} \cdot y\right), \color{blue}{\left(x \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right)\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(y \cdot \frac{-1000000000}{23533438303}\right), \left(\color{blue}{x} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-1000000000}{23533438303}\right), \left(\color{blue}{x} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-1000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{500000000}{23533438303} \cdot y - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right)}\right)\right)\right) \]

      6. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-1000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \left(y \cdot \color{blue}{\left(\frac{500000000}{23533438303} - \frac{-156699607947000000000}{553822718361107519809}\right)}\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-1000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \left(y \cdot \frac{168466327098500000000}{553822718361107519809}\right)\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-1000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \left(y \cdot \left(\mathsf{neg}\left(\frac{-168466327098500000000}{553822718361107519809}\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-1000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(\frac{-168466327098500000000}{553822718361107519809}\right)\right)}\right)\right)\right)\right) \]

      10. metadata-eval 62.2%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-1000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \frac{168466327098500000000}{553822718361107519809}\right)\right)\right)\right) \]

   8. Simplified 62.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot -0.0424927283095952 + x \cdot \left(y \cdot 0.3041881842569256\right)\right)} \]

   9. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{-1000000000}{23533438303} \cdot y\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(y \cdot \color{blue}{\frac{-1000000000}{23533438303}}\right)\right) \]

       2. *-lowering-*.f64 60.1%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{-1000000000}{23533438303}}\right)\right) \]

   11. Simplified 60.1%

       \[\leadsto x \cdot \color{blue}{\left(y \cdot -0.0424927283095952\right)} \]

   if -5.00000000000000039e-44 < x < 0.0152

   1. Initial program 99.6%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \left(x - 2\right) \cdot \color{blue}{\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x - 2\right), \color{blue}{\left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)}\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x + \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \left(\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + \color{blue}{z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{/.f64}\left(\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right), \color{blue}{\left(\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}\right)}\right)\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 72.9%

         \[\leadsto \mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, \color{blue}{z}\right) \]

   7. Simplified 72.9%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.15:\\ \;\;\;\;4.16438922228 \cdot \left(x + -2\right)\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 0.0152:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot \left(x + -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 76.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5)
   (* x 4.16438922228)
   (if (<= x -1.65e-44)
     (* x (* y -0.0424927283095952))
     (if (<= x 2.0) (* z -0.0424927283095952) (* x 4.16438922228)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = x * 4.16438922228;
	} else if (x <= -1.65e-44) {
		tmp = x * (y * -0.0424927283095952);
	} else if (x <= 2.0) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-5.5d0)) then
        tmp = x * 4.16438922228d0
    else if (x <= (-1.65d-44)) then
        tmp = x * (y * (-0.0424927283095952d0))
    else if (x <= 2.0d0) then
        tmp = z * (-0.0424927283095952d0)
    else
        tmp = x * 4.16438922228d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = x * 4.16438922228;
	} else if (x <= -1.65e-44) {
		tmp = x * (y * -0.0424927283095952);
	} else if (x <= 2.0) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.5:
		tmp = x * 4.16438922228
	elif x <= -1.65e-44:
		tmp = x * (y * -0.0424927283095952)
	elif x <= 2.0:
		tmp = z * -0.0424927283095952
	else:
		tmp = x * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= -1.65e-44)
		tmp = Float64(x * Float64(y * -0.0424927283095952));
	elseif (x <= 2.0)
		tmp = Float64(z * -0.0424927283095952);
	else
		tmp = Float64(x * 4.16438922228);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.5)
		tmp = x * 4.16438922228;
	elseif (x <= -1.65e-44)
		tmp = x * (y * -0.0424927283095952);
	elseif (x <= 2.0)
		tmp = z * -0.0424927283095952;
	else
		tmp = x * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, -1.65e-44], N[(x * N[(y * -0.0424927283095952), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.0], N[(z * -0.0424927283095952), $MachinePrecision], N[(x * 4.16438922228), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5 or 2 < 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 26.5%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x \cdot \color{blue}{\frac{104109730557}{25000000000}} \]

      2. *-lowering-*.f64 83.5%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\frac{104109730557}{25000000000}}\right) \]

   7. Simplified 83.5%

      \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

   if -5.5 < x < -1.65000000000000003e-44

   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. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot \left(y \cdot \left(x - 2\right)\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right), x\right), \frac{263505074721}{1000000000}\right), x\right), \frac{156699607947}{500000000}\right), x\right), \frac{23533438303}{500000000}\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y \cdot \left(x - 2\right)\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right), x\right), \frac{263505074721}{1000000000}\right), x\right), \frac{156699607947}{500000000}\right), x\right)}, \frac{23533438303}{500000000}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \left(x - 2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right), x\right), \frac{263505074721}{1000000000}\right), x\right), \frac{156699607947}{500000000}\right), \color{blue}{x}\right), \frac{23533438303}{500000000}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \left(x + \left(\mathsf{neg}\left(2\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right), x\right), \frac{263505074721}{1000000000}\right), x\right), \frac{156699607947}{500000000}\right), x\right), \frac{23533438303}{500000000}\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \left(x + -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right), x\right), \frac{263505074721}{1000000000}\right), x\right), \frac{156699607947}{500000000}\right), x\right), \frac{23533438303}{500000000}\right)\right) \]

      5. +-lowering-+.f64 63.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right), x\right), \frac{263505074721}{1000000000}\right), x\right), \frac{156699607947}{500000000}\right), x\right), \frac{23533438303}{500000000}\right)\right) \]

   5. Simplified 63.6%

      \[\leadsto \frac{\color{blue}{x \cdot \left(y \cdot \left(x + -2\right)\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{x \cdot \left(\frac{-1000000000}{23533438303} \cdot y + x \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{-1000000000}{23533438303} \cdot y + x \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{-1000000000}{23533438303} \cdot y\right), \color{blue}{\left(x \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right)\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(y \cdot \frac{-1000000000}{23533438303}\right), \left(\color{blue}{x} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-1000000000}{23533438303}\right), \left(\color{blue}{x} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-1000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{500000000}{23533438303} \cdot y - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right)}\right)\right)\right) \]

      6. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-1000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \left(y \cdot \color{blue}{\left(\frac{500000000}{23533438303} - \frac{-156699607947000000000}{553822718361107519809}\right)}\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-1000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \left(y \cdot \frac{168466327098500000000}{553822718361107519809}\right)\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-1000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \left(y \cdot \left(\mathsf{neg}\left(\frac{-168466327098500000000}{553822718361107519809}\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-1000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(\frac{-168466327098500000000}{553822718361107519809}\right)\right)}\right)\right)\right)\right) \]

      10. metadata-eval 62.2%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{-1000000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \frac{168466327098500000000}{553822718361107519809}\right)\right)\right)\right) \]

   8. Simplified 62.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot -0.0424927283095952 + x \cdot \left(y \cdot 0.3041881842569256\right)\right)} \]

   9. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{-1000000000}{23533438303} \cdot y\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(y \cdot \color{blue}{\frac{-1000000000}{23533438303}}\right)\right) \]

       2. *-lowering-*.f64 60.1%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{-1000000000}{23533438303}}\right)\right) \]

   11. Simplified 60.1%

       \[\leadsto x \cdot \color{blue}{\left(y \cdot -0.0424927283095952\right)} \]

   if -1.65000000000000003e-44 < x < 2

   1. Initial program 99.6%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. 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 99.6%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 72.4%

         \[\leadsto \mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, \color{blue}{z}\right) \]

   7. Simplified 72.4%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 76.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{-44}:\\ \;\;\;\;\left(x \cdot y\right) \cdot -0.0424927283095952\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5)
   (* x 4.16438922228)
   (if (<= x -4.3e-44)
     (* (* x y) -0.0424927283095952)
     (if (<= x 2.0) (* z -0.0424927283095952) (* x 4.16438922228)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = x * 4.16438922228;
	} else if (x <= -4.3e-44) {
		tmp = (x * y) * -0.0424927283095952;
	} else if (x <= 2.0) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-5.5d0)) then
        tmp = x * 4.16438922228d0
    else if (x <= (-4.3d-44)) then
        tmp = (x * y) * (-0.0424927283095952d0)
    else if (x <= 2.0d0) then
        tmp = z * (-0.0424927283095952d0)
    else
        tmp = x * 4.16438922228d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = x * 4.16438922228;
	} else if (x <= -4.3e-44) {
		tmp = (x * y) * -0.0424927283095952;
	} else if (x <= 2.0) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.5:
		tmp = x * 4.16438922228
	elif x <= -4.3e-44:
		tmp = (x * y) * -0.0424927283095952
	elif x <= 2.0:
		tmp = z * -0.0424927283095952
	else:
		tmp = x * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= -4.3e-44)
		tmp = Float64(Float64(x * y) * -0.0424927283095952);
	elseif (x <= 2.0)
		tmp = Float64(z * -0.0424927283095952);
	else
		tmp = Float64(x * 4.16438922228);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.5)
		tmp = x * 4.16438922228;
	elseif (x <= -4.3e-44)
		tmp = (x * y) * -0.0424927283095952;
	elseif (x <= 2.0)
		tmp = z * -0.0424927283095952;
	else
		tmp = x * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, -4.3e-44], N[(N[(x * y), $MachinePrecision] * -0.0424927283095952), $MachinePrecision], If[LessEqual[x, 2.0], N[(z * -0.0424927283095952), $MachinePrecision], N[(x * 4.16438922228), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5 or 2 < 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 26.5%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x \cdot \color{blue}{\frac{104109730557}{25000000000}} \]

      2. *-lowering-*.f64 83.5%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\frac{104109730557}{25000000000}}\right) \]

   7. Simplified 83.5%

      \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

   if -5.5 < x < -4.30000000000000013e-44

   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. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot \left(y \cdot \left(x - 2\right)\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right), x\right), \frac{263505074721}{1000000000}\right), x\right), \frac{156699607947}{500000000}\right), x\right), \frac{23533438303}{500000000}\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y \cdot \left(x - 2\right)\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right), x\right), \frac{263505074721}{1000000000}\right), x\right), \frac{156699607947}{500000000}\right), x\right)}, \frac{23533438303}{500000000}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \left(x - 2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right), x\right), \frac{263505074721}{1000000000}\right), x\right), \frac{156699607947}{500000000}\right), \color{blue}{x}\right), \frac{23533438303}{500000000}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \left(x + \left(\mathsf{neg}\left(2\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right), x\right), \frac{263505074721}{1000000000}\right), x\right), \frac{156699607947}{500000000}\right), x\right), \frac{23533438303}{500000000}\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \left(x + -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right), x\right), \frac{263505074721}{1000000000}\right), x\right), \frac{156699607947}{500000000}\right), x\right), \frac{23533438303}{500000000}\right)\right) \]

      5. +-lowering-+.f64 63.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, \frac{216700011257}{5000000000}\right), x\right), \frac{263505074721}{1000000000}\right), x\right), \frac{156699607947}{500000000}\right), x\right), \frac{23533438303}{500000000}\right)\right) \]

   5. Simplified 63.6%

      \[\leadsto \frac{\color{blue}{x \cdot \left(y \cdot \left(x + -2\right)\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot \left(x \cdot y\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, \color{blue}{\left(x \cdot y\right)}\right) \]

      2. *-lowering-*.f64 60.0%

         \[\leadsto \mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   8. Simplified 60.0%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot \left(x \cdot y\right)} \]

   if -4.30000000000000013e-44 < x < 2

   1. Initial program 99.6%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. 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 99.6%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 72.4%

         \[\leadsto \mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, \color{blue}{z}\right) \]

   7. Simplified 72.4%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{-44}:\\ \;\;\;\;\left(x \cdot y\right) \cdot -0.0424927283095952\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 76.9% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2400000:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2400000.0)
   (* x 4.16438922228)
   (if (<= x 2.0) (* z -0.0424927283095952) (* x 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2400000.0) {
		tmp = x * 4.16438922228;
	} else if (x <= 2.0) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-2400000.0d0)) then
        tmp = x * 4.16438922228d0
    else if (x <= 2.0d0) then
        tmp = z * (-0.0424927283095952d0)
    else
        tmp = x * 4.16438922228d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2400000.0) {
		tmp = x * 4.16438922228;
	} else if (x <= 2.0) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2400000.0:
		tmp = x * 4.16438922228
	elif x <= 2.0:
		tmp = z * -0.0424927283095952
	else:
		tmp = x * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2400000.0)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 2.0)
		tmp = Float64(z * -0.0424927283095952);
	else
		tmp = Float64(x * 4.16438922228);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2400000.0)
		tmp = x * 4.16438922228;
	elseif (x <= 2.0)
		tmp = z * -0.0424927283095952;
	else
		tmp = x * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2400000.0], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 2.0], N[(z * -0.0424927283095952), $MachinePrecision], N[(x * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.4e6 or 2 < x

   1. Initial program 17.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 25.3%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x \cdot \color{blue}{\frac{104109730557}{25000000000}} \]

      2. *-lowering-*.f64 84.8%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\frac{104109730557}{25000000000}}\right) \]

   7. Simplified 84.8%

      \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

   if -2.4e6 < x < 2

   1. Initial program 99.6%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. 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 99.6%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 67.0%

         \[\leadsto \mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, \color{blue}{z}\right) \]

   7. Simplified 67.0%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2400000:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 36.4% 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 61.6%

   \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
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 65.3%

   \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
4. Add Preprocessing

5. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z} \]
6. Step-by-step derivation

   1. *-lowering-*.f64 37.6%

      \[\leadsto \mathsf{*.f64}\left(\frac{-1000000000}{23533438303}, \color{blue}{z}\right) \]

7. Simplified 37.6%

   \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]

8. Final simplification 37.6%

   \[\leadsto z \cdot -0.0424927283095952 \]
9. Add Preprocessing

Developer Target 1: 98.7% 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 2024152 
(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)))