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

Percentage Accurate: 58.6% → 98.5%

Time: 17.5s

Alternatives: 17

Speedup: 2.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 58.6% 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: 98.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606\\ t_1 := x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\\ \mathbf{if}\;\frac{\left(x - 2\right) \cdot t\_1}{t\_0} \leq \infty:\\ \;\;\;\;\left(x + -2\right) \cdot \frac{t\_1}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          (*
           x
           (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
          47.066876606))
        (t_1
         (+
          (*
           x
           (+
            (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
            y))
          z)))
   (if (<= (/ (* (- x 2.0) t_1) t_0) INFINITY)
     (* (+ x -2.0) (/ t_1 t_0))
     (/ (+ x -2.0) 0.24013125253755718))))

C

double code(double x, double y, double z) {
	double t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	double t_1 = (x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z;
	double tmp;
	if ((((x - 2.0) * t_1) / t_0) <= ((double) INFINITY)) {
		tmp = (x + -2.0) * (t_1 / t_0);
	} else {
		tmp = (x + -2.0) / 0.24013125253755718;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	double t_1 = (x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z;
	double tmp;
	if ((((x - 2.0) * t_1) / t_0) <= Double.POSITIVE_INFINITY) {
		tmp = (x + -2.0) * (t_1 / t_0);
	} else {
		tmp = (x + -2.0) / 0.24013125253755718;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606
	t_1 = (x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z
	tmp = 0
	if (((x - 2.0) * t_1) / t_0) <= math.inf:
		tmp = (x + -2.0) * (t_1 / t_0)
	else:
		tmp = (x + -2.0) / 0.24013125253755718
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)
	t_1 = Float64(Float64(x * Float64(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_1) / t_0) <= Inf)
		tmp = Float64(Float64(x + -2.0) * Float64(t_1 / t_0));
	else
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	t_1 = (x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z;
	tmp = 0.0;
	if ((((x - 2.0) * t_1) / t_0) <= Inf)
		tmp = (x + -2.0) * (t_1 / t_0);
	else
		tmp = (x + -2.0) / 0.24013125253755718;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x * N[(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$1), $MachinePrecision] / t$95$0), $MachinePrecision], Infinity], N[(N[(x + -2.0), $MachinePrecision] * N[(t$95$1 / t$95$0), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < +inf.0

   1. Initial program 94.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 +inf.0 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64)))

   1. Initial program 0.0%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 0.0%

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

   6. Applied egg-rr 0.0%

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

   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 99.7%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq \infty:\\ \;\;\;\;\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+51}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+24}:\\ \;\;\;\;\frac{x + -2}{\frac{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}{z + x \cdot \left(y + x \cdot 137.519416416\right)}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.8e+51)
   (/ (+ x -2.0) 0.24013125253755718)
   (if (<= x 4.4e+24)
     (/
      (+ x -2.0)
      (/
       (+
        (*
         x
         (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
        47.066876606)
       (+ z (* x (+ y (* x 137.519416416))))))
     (*
      (+ 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 <= -7.8e+51) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= 4.4e+24) {
		tmp = (x + -2.0) / (((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606) / (z + (x * (y + (x * 137.519416416)))));
	} 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 <= (-7.8d+51)) then
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    else if (x <= 4.4d+24) then
        tmp = (x + (-2.0d0)) / (((x * ((x * ((x * (x + 43.3400022514d0)) + 263.505074721d0)) + 313.399215894d0)) + 47.066876606d0) / (z + (x * (y + (x * 137.519416416d0)))))
    else
        tmp = (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 <= -7.8e+51) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= 4.4e+24) {
		tmp = (x + -2.0) / (((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606) / (z + (x * (y + (x * 137.519416416)))));
	} 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 <= -7.8e+51:
		tmp = (x + -2.0) / 0.24013125253755718
	elif x <= 4.4e+24:
		tmp = (x + -2.0) / (((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606) / (z + (x * (y + (x * 137.519416416)))))
	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 <= -7.8e+51)
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	elseif (x <= 4.4e+24)
		tmp = Float64(Float64(x + -2.0) / Float64(Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606) / Float64(z + Float64(x * Float64(y + Float64(x * 137.519416416))))));
	else
		tmp = 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 <= -7.8e+51)
		tmp = (x + -2.0) / 0.24013125253755718;
	elseif (x <= 4.4e+24)
		tmp = (x + -2.0) / (((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606) / (z + (x * (y + (x * 137.519416416)))));
	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, -7.8e+51], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision], If[LessEqual[x, 4.4e+24], N[(N[(x + -2.0), $MachinePrecision] / N[(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] / N[(z + N[(x * N[(y + N[(x * 137.519416416), $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 3 regimes

2. if x < -7.79999999999999968e51

   1. Initial program 2.0%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 3.8%

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

   6. Applied egg-rr 3.9%

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

   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 -7.79999999999999968e51 < x < 4.40000000000000003e24

   1. Initial program 98.3%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.6%

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

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 98.1%

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

   9. Simplified 98.1%

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

   if 4.40000000000000003e24 < x

   1. Initial program 10.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 17.3%

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

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

   7. Simplified 98.0%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+51}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+24}:\\ \;\;\;\;\frac{x + -2}{\frac{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}{z + x \cdot \left(y + x \cdot 137.519416416\right)}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+14}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.5e+14)
   (/ (+ x -2.0) (+ 0.24013125253755718 (/ 5.86923874282773 x)))
   (if (<= x 8.5e+24)
     (/
      (* (- x 2.0) (+ z (* x (+ y (* x 137.519416416)))))
      (+
       (*
        x
        (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
       47.066876606))
     (*
      (+ 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 <= -7.5e+14) {
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x));
	} else if (x <= 8.5e+24) {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	} else {
		tmp = (x + -2.0) * (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 <= (-7.5d+14)) then
        tmp = (x + (-2.0d0)) / (0.24013125253755718d0 + (5.86923874282773d0 / x))
    else if (x <= 8.5d+24) then
        tmp = ((x - 2.0d0) * (z + (x * (y + (x * 137.519416416d0))))) / ((x * ((x * ((x * (x + 43.3400022514d0)) + 263.505074721d0)) + 313.399215894d0)) + 47.066876606d0)
    else
        tmp = (x + (-2.0d0)) * (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 <= -7.5e+14) {
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x));
	} else if (x <= 8.5e+24) {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.5e+14:
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x))
	elif x <= 8.5e+24:
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)
	else:
		tmp = (x + -2.0) * (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 <= -7.5e+14)
		tmp = Float64(Float64(x + -2.0) / Float64(0.24013125253755718 + Float64(5.86923874282773 / x)));
	elseif (x <= 8.5e+24)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(z + Float64(x * Float64(y + Float64(x * 137.519416416))))) / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606));
	else
		tmp = Float64(Float64(x + -2.0) * 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 <= -7.5e+14)
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x));
	elseif (x <= 8.5e+24)
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	else
		tmp = (x + -2.0) * (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, -7.5e+14], N[(N[(x + -2.0), $MachinePrecision] / N[(0.24013125253755718 + N[(5.86923874282773 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e+24], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(z + N[(x * N[(y + N[(x * 137.519416416), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * 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 3 regimes

2. if x < -7.5e14

   1. Initial program 3.9%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 9.1%

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

   6. Applied egg-rr 9.2%

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

   7. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \color{blue}{\left(\frac{25000000000}{104109730557} + \frac{63615716158700684400745}{10838835996651139530249} \cdot \frac{1}{x}\right)}\right) \]
   8. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\frac{25000000000}{104109730557}, \color{blue}{\left(\frac{63615716158700684400745}{10838835996651139530249} \cdot \frac{1}{x}\right)}\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\frac{25000000000}{104109730557}, \left(\frac{\frac{63615716158700684400745}{10838835996651139530249} \cdot 1}{\color{blue}{x}}\right)\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\frac{25000000000}{104109730557}, \left(\frac{\frac{63615716158700684400745}{10838835996651139530249}}{x}\right)\right)\right) \]

      4. /-lowering-/.f64 96.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\frac{25000000000}{104109730557}, \mathsf{/.f64}\left(\frac{63615716158700684400745}{10838835996651139530249}, \color{blue}{x}\right)\right)\right) \]

   9. Simplified 96.4%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718 + \frac{5.86923874282773}{x}}} \]

   if -7.5e14 < x < 8.49999999999999959e24

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 98.9%

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

   5. Simplified 98.9%

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

   if 8.49999999999999959e24 < x

   1. Initial program 10.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 17.3%

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

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

   7. Simplified 98.0%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+14}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{if}\;x \leq -1.35:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 63:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot 313.399215894}{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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 -1.35)
     t_0
     (if (<= x 63.0)
       (/
        (+ x -2.0)
        (/
         (+ 47.066876606 (* x 313.399215894))
         (+
          (*
           x
           (+
            (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
            y))
          z)))
       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 <= -1.35) {
		tmp = t_0;
	} else if (x <= 63.0) {
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z));
	} 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 <= (-1.35d0)) then
        tmp = t_0
    else if (x <= 63.0d0) then
        tmp = (x + (-2.0d0)) / ((47.066876606d0 + (x * 313.399215894d0)) / ((x * ((x * ((x * ((x * 4.16438922228d0) + 78.6994924154d0)) + 137.519416416d0)) + y)) + z))
    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 <= -1.35) {
		tmp = t_0;
	} else if (x <= 63.0) {
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z));
	} 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 <= -1.35:
		tmp = t_0
	elif x <= 63.0:
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z))
	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 <= -1.35)
		tmp = t_0;
	elseif (x <= 63.0)
		tmp = Float64(Float64(x + -2.0) / Float64(Float64(47.066876606 + Float64(x * 313.399215894)) / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)));
	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 <= -1.35)
		tmp = t_0;
	elseif (x <= 63.0)
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z));
	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, -1.35], t$95$0, If[LessEqual[x, 63.0], N[(N[(x + -2.0), $MachinePrecision] / N[(N[(47.066876606 + N[(x * 313.399215894), $MachinePrecision]), $MachinePrecision] / 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]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3500000000000001 or 63 < x

   1. Initial program 12.4%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 18.2%

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

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

   7. Simplified 94.3%

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

   if -1.3500000000000001 < x < 63

   1. Initial program 99.7%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.7%

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

   6. Applied egg-rr 99.6%

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

   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 98.7%

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

   9. Simplified 98.7%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{elif}\;x \leq 63:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot 313.399215894}{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{if}\;x \leq -58:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 30:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + x \cdot \left(y \cdot 0.0212463641547976 + x \cdot \left(2.9217875995295866 + y \cdot -0.14147091005106402\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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 -58.0)
     t_0
     (if (<= x 30.0)
       (*
        (+ x -2.0)
        (+
         (* z 0.0212463641547976)
         (*
          x
          (+
           (* y 0.0212463641547976)
           (* x (+ 2.9217875995295866 (* y -0.14147091005106402)))))))
       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 <= -58.0) {
		tmp = t_0;
	} else if (x <= 30.0) {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) + (x * (2.9217875995295866 + (y * -0.14147091005106402))))));
	} 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 <= (-58.0d0)) then
        tmp = t_0
    else if (x <= 30.0d0) then
        tmp = (x + (-2.0d0)) * ((z * 0.0212463641547976d0) + (x * ((y * 0.0212463641547976d0) + (x * (2.9217875995295866d0 + (y * (-0.14147091005106402d0)))))))
    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 <= -58.0) {
		tmp = t_0;
	} else if (x <= 30.0) {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) + (x * (2.9217875995295866 + (y * -0.14147091005106402))))));
	} 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 <= -58.0:
		tmp = t_0
	elif x <= 30.0:
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) + (x * (2.9217875995295866 + (y * -0.14147091005106402))))))
	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 <= -58.0)
		tmp = t_0;
	elseif (x <= 30.0)
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(z * 0.0212463641547976) + Float64(x * Float64(Float64(y * 0.0212463641547976) + Float64(x * Float64(2.9217875995295866 + Float64(y * -0.14147091005106402)))))));
	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 <= -58.0)
		tmp = t_0;
	elseif (x <= 30.0)
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) + (x * (2.9217875995295866 + (y * -0.14147091005106402))))));
	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, -58.0], t$95$0, If[LessEqual[x, 30.0], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(z * 0.0212463641547976), $MachinePrecision] + N[(x * N[(N[(y * 0.0212463641547976), $MachinePrecision] + N[(x * N[(2.9217875995295866 + N[(y * -0.14147091005106402), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -58 or 30 < x

   1. Initial program 12.4%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 18.2%

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

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

   7. Simplified 94.3%

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

   if -58 < x < 30

   1. Initial program 99.7%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \color{blue}{\left(\frac{500000000}{23533438303} \cdot z + x \cdot \left(\left(\frac{500000000}{23533438303} \cdot y + x \cdot \left(\frac{68759708208}{23533438303} - \left(\frac{65876268680250000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right) \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\left(\frac{500000000}{23533438303} \cdot z\right), \color{blue}{\left(x \cdot \left(\left(\frac{500000000}{23533438303} \cdot y + x \cdot \left(\frac{68759708208}{23533438303} - \left(\frac{65876268680250000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\left(z \cdot \frac{500000000}{23533438303}\right), \left(\color{blue}{x} \cdot \left(\left(\frac{500000000}{23533438303} \cdot y + x \cdot \left(\frac{68759708208}{23533438303} - \left(\frac{65876268680250000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \left(\color{blue}{x} \cdot \left(\left(\frac{500000000}{23533438303} \cdot y + x \cdot \left(\frac{68759708208}{23533438303} - \left(\frac{65876268680250000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\left(\frac{500000000}{23533438303} \cdot y + x \cdot \left(\frac{68759708208}{23533438303} - \left(\frac{65876268680250000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)}\right)\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \left(\left(x \cdot \left(\frac{68759708208}{23533438303} - \left(\frac{65876268680250000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right) + \frac{500000000}{23533438303} \cdot y\right) - \color{blue}{\frac{78349803973500000000}{553822718361107519809}} \cdot z\right)\right)\right)\right) \]

      6. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \left(x \cdot \left(\frac{68759708208}{23533438303} - \left(\frac{65876268680250000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right) + \color{blue}{\left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(x \cdot \left(\frac{68759708208}{23533438303} - \left(\frac{65876268680250000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right), \color{blue}{\left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)}\right)\right)\right)\right) \]

   7. Simplified 98.5%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(z \cdot 0.0212463641547976 + x \cdot \left(x \cdot \left(2.9217875995295866 + \left(z \cdot -0.11894829608144908 - 6.658593866711955 \cdot \left(0.0212463641547976 \cdot y + z \cdot -0.14147091005106402\right)\right)\right) + \left(0.0212463641547976 \cdot y + z \cdot -0.14147091005106402\right)\right)\right)} \]

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \color{blue}{\left(x \cdot \left(\frac{500000000}{23533438303} \cdot y + x \cdot \left(\frac{68759708208}{23533438303} - \frac{78349803973500000000}{553822718361107519809} \cdot y\right)\right)\right)}\right)\right) \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{500000000}{23533438303} \cdot y + x \cdot \left(\frac{68759708208}{23533438303} - \frac{78349803973500000000}{553822718361107519809} \cdot y\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{500000000}{23533438303} \cdot y\right), \color{blue}{\left(x \cdot \left(\frac{68759708208}{23533438303} - \frac{78349803973500000000}{553822718361107519809} \cdot y\right)\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \left(\color{blue}{x} \cdot \left(\frac{68759708208}{23533438303} - \frac{78349803973500000000}{553822718361107519809} \cdot y\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{68759708208}{23533438303} - \frac{78349803973500000000}{553822718361107519809} \cdot y\right)}\right)\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(x, \left(\frac{68759708208}{23533438303} + \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809} \cdot y\right)\right)}\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{68759708208}{23533438303}, \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809} \cdot y\right)\right)}\right)\right)\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{68759708208}{23533438303}, \left(\mathsf{neg}\left(y \cdot \frac{78349803973500000000}{553822718361107519809}\right)\right)\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{68759708208}{23533438303}, \left(y \cdot \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809}\right)\right)}\right)\right)\right)\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{68759708208}{23533438303}, \left(y \cdot \frac{-78349803973500000000}{553822718361107519809}\right)\right)\right)\right)\right)\right)\right) \]

      10. *-lowering-*.f64 98.1%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{68759708208}{23533438303}, \mathsf{*.f64}\left(y, \color{blue}{\frac{-78349803973500000000}{553822718361107519809}}\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 98.1%

       \[\leadsto \left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + \color{blue}{x \cdot \left(0.0212463641547976 \cdot y + x \cdot \left(2.9217875995295866 + y \cdot -0.14147091005106402\right)\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -58:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{elif}\;x \leq 30:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + x \cdot \left(y \cdot 0.0212463641547976 + x \cdot \left(2.9217875995295866 + y \cdot -0.14147091005106402\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 94.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{if}\;x \leq -50:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 25:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + x \cdot \left(y \cdot 0.0212463641547976 + x \cdot 2.9217875995295866\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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 -50.0)
     t_0
     (if (<= x 25.0)
       (*
        (+ x -2.0)
        (+
         (* z 0.0212463641547976)
         (* x (+ (* y 0.0212463641547976) (* x 2.9217875995295866)))))
       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 <= -50.0) {
		tmp = t_0;
	} else if (x <= 25.0) {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) + (x * 2.9217875995295866))));
	} 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 <= (-50.0d0)) then
        tmp = t_0
    else if (x <= 25.0d0) then
        tmp = (x + (-2.0d0)) * ((z * 0.0212463641547976d0) + (x * ((y * 0.0212463641547976d0) + (x * 2.9217875995295866d0))))
    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 <= -50.0) {
		tmp = t_0;
	} else if (x <= 25.0) {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) + (x * 2.9217875995295866))));
	} 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 <= -50.0:
		tmp = t_0
	elif x <= 25.0:
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) + (x * 2.9217875995295866))))
	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 <= -50.0)
		tmp = t_0;
	elseif (x <= 25.0)
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(z * 0.0212463641547976) + Float64(x * Float64(Float64(y * 0.0212463641547976) + Float64(x * 2.9217875995295866)))));
	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 <= -50.0)
		tmp = t_0;
	elseif (x <= 25.0)
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) + (x * 2.9217875995295866))));
	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, -50.0], t$95$0, If[LessEqual[x, 25.0], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(z * 0.0212463641547976), $MachinePrecision] + N[(x * N[(N[(y * 0.0212463641547976), $MachinePrecision] + N[(x * 2.9217875995295866), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -50 or 25 < x

   1. Initial program 12.4%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 18.2%

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

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

   7. Simplified 94.3%

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

   if -50 < x < 25

   1. Initial program 99.7%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \color{blue}{\left(\frac{500000000}{23533438303} \cdot z + x \cdot \left(\left(\frac{500000000}{23533438303} \cdot y + x \cdot \left(\frac{68759708208}{23533438303} - \left(\frac{65876268680250000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right) \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\left(\frac{500000000}{23533438303} \cdot z\right), \color{blue}{\left(x \cdot \left(\left(\frac{500000000}{23533438303} \cdot y + x \cdot \left(\frac{68759708208}{23533438303} - \left(\frac{65876268680250000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\left(z \cdot \frac{500000000}{23533438303}\right), \left(\color{blue}{x} \cdot \left(\left(\frac{500000000}{23533438303} \cdot y + x \cdot \left(\frac{68759708208}{23533438303} - \left(\frac{65876268680250000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \left(\color{blue}{x} \cdot \left(\left(\frac{500000000}{23533438303} \cdot y + x \cdot \left(\frac{68759708208}{23533438303} - \left(\frac{65876268680250000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\left(\frac{500000000}{23533438303} \cdot y + x \cdot \left(\frac{68759708208}{23533438303} - \left(\frac{65876268680250000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)}\right)\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \left(\left(x \cdot \left(\frac{68759708208}{23533438303} - \left(\frac{65876268680250000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right) + \frac{500000000}{23533438303} \cdot y\right) - \color{blue}{\frac{78349803973500000000}{553822718361107519809}} \cdot z\right)\right)\right)\right) \]

      6. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \left(x \cdot \left(\frac{68759708208}{23533438303} - \left(\frac{65876268680250000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right) + \color{blue}{\left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(x \cdot \left(\frac{68759708208}{23533438303} - \left(\frac{65876268680250000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right), \color{blue}{\left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)}\right)\right)\right)\right) \]

   7. Simplified 98.5%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(z \cdot 0.0212463641547976 + x \cdot \left(x \cdot \left(2.9217875995295866 + \left(z \cdot -0.11894829608144908 - 6.658593866711955 \cdot \left(0.0212463641547976 \cdot y + z \cdot -0.14147091005106402\right)\right)\right) + \left(0.0212463641547976 \cdot y + z \cdot -0.14147091005106402\right)\right)\right)} \]

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \color{blue}{\left(x \cdot \left(\frac{500000000}{23533438303} \cdot y + x \cdot \left(\frac{68759708208}{23533438303} - \frac{78349803973500000000}{553822718361107519809} \cdot y\right)\right)\right)}\right)\right) \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{500000000}{23533438303} \cdot y + x \cdot \left(\frac{68759708208}{23533438303} - \frac{78349803973500000000}{553822718361107519809} \cdot y\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{500000000}{23533438303} \cdot y\right), \color{blue}{\left(x \cdot \left(\frac{68759708208}{23533438303} - \frac{78349803973500000000}{553822718361107519809} \cdot y\right)\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \left(\color{blue}{x} \cdot \left(\frac{68759708208}{23533438303} - \frac{78349803973500000000}{553822718361107519809} \cdot y\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{68759708208}{23533438303} - \frac{78349803973500000000}{553822718361107519809} \cdot y\right)}\right)\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(x, \left(\frac{68759708208}{23533438303} + \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809} \cdot y\right)\right)}\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{68759708208}{23533438303}, \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809} \cdot y\right)\right)}\right)\right)\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{68759708208}{23533438303}, \left(\mathsf{neg}\left(y \cdot \frac{78349803973500000000}{553822718361107519809}\right)\right)\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{68759708208}{23533438303}, \left(y \cdot \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809}\right)\right)}\right)\right)\right)\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{68759708208}{23533438303}, \left(y \cdot \frac{-78349803973500000000}{553822718361107519809}\right)\right)\right)\right)\right)\right)\right) \]

      10. *-lowering-*.f64 98.1%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{68759708208}{23533438303}, \mathsf{*.f64}\left(y, \color{blue}{\frac{-78349803973500000000}{553822718361107519809}}\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 98.1%

       \[\leadsto \left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + \color{blue}{x \cdot \left(0.0212463641547976 \cdot y + x \cdot \left(2.9217875995295866 + y \cdot -0.14147091005106402\right)\right)}\right) \]

   11. Taylor expanded in y around 0

       \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \color{blue}{\left(\frac{68759708208}{23533438303} \cdot x\right)}\right)\right)\right)\right) \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \left(x \cdot \color{blue}{\frac{68759708208}{23533438303}}\right)\right)\right)\right)\right) \]

       2. *-lowering-*.f64 97.4%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(x, \color{blue}{\frac{68759708208}{23533438303}}\right)\right)\right)\right)\right) \]

   13. Simplified 97.4%

       \[\leadsto \left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + x \cdot \left(0.0212463641547976 \cdot y + \color{blue}{x \cdot 2.9217875995295866}\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -50:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{elif}\;x \leq 25:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + x \cdot \left(y \cdot 0.0212463641547976 + x \cdot 2.9217875995295866\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 91.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1000000:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+24}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + x \cdot \left(y \cdot 0.0212463641547976 + x \cdot 2.9217875995295866\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1000000.0)
   (/ (+ x -2.0) (+ 0.24013125253755718 (/ 5.86923874282773 x)))
   (if (<= x 4.1e+24)
     (*
      (+ x -2.0)
      (+
       (* z 0.0212463641547976)
       (* x (+ (* y 0.0212463641547976) (* x 2.9217875995295866)))))
     (/ (+ x -2.0) 0.24013125253755718))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1000000.0) {
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x));
	} else if (x <= 4.1e+24) {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) + (x * 2.9217875995295866))));
	} else {
		tmp = (x + -2.0) / 0.24013125253755718;
	}
	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 <= (-1000000.0d0)) then
        tmp = (x + (-2.0d0)) / (0.24013125253755718d0 + (5.86923874282773d0 / x))
    else if (x <= 4.1d+24) then
        tmp = (x + (-2.0d0)) * ((z * 0.0212463641547976d0) + (x * ((y * 0.0212463641547976d0) + (x * 2.9217875995295866d0))))
    else
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1000000.0) {
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x));
	} else if (x <= 4.1e+24) {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) + (x * 2.9217875995295866))));
	} else {
		tmp = (x + -2.0) / 0.24013125253755718;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1000000.0:
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x))
	elif x <= 4.1e+24:
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) + (x * 2.9217875995295866))))
	else:
		tmp = (x + -2.0) / 0.24013125253755718
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1000000.0)
		tmp = Float64(Float64(x + -2.0) / Float64(0.24013125253755718 + Float64(5.86923874282773 / x)));
	elseif (x <= 4.1e+24)
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(z * 0.0212463641547976) + Float64(x * Float64(Float64(y * 0.0212463641547976) + Float64(x * 2.9217875995295866)))));
	else
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1000000.0)
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x));
	elseif (x <= 4.1e+24)
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) + (x * 2.9217875995295866))));
	else
		tmp = (x + -2.0) / 0.24013125253755718;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1000000.0], N[(N[(x + -2.0), $MachinePrecision] / N[(0.24013125253755718 + N[(5.86923874282773 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.1e+24], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(z * 0.0212463641547976), $MachinePrecision] + N[(x * N[(N[(y * 0.0212463641547976), $MachinePrecision] + N[(x * 2.9217875995295866), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1e6

   1. Initial program 8.9%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 13.8%

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

   6. Applied egg-rr 13.9%

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

   7. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \color{blue}{\left(\frac{25000000000}{104109730557} + \frac{63615716158700684400745}{10838835996651139530249} \cdot \frac{1}{x}\right)}\right) \]
   8. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\frac{25000000000}{104109730557}, \color{blue}{\left(\frac{63615716158700684400745}{10838835996651139530249} \cdot \frac{1}{x}\right)}\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\frac{25000000000}{104109730557}, \left(\frac{\frac{63615716158700684400745}{10838835996651139530249} \cdot 1}{\color{blue}{x}}\right)\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\frac{25000000000}{104109730557}, \left(\frac{\frac{63615716158700684400745}{10838835996651139530249}}{x}\right)\right)\right) \]

      4. /-lowering-/.f64 93.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\frac{25000000000}{104109730557}, \mathsf{/.f64}\left(\frac{63615716158700684400745}{10838835996651139530249}, \color{blue}{x}\right)\right)\right) \]

   9. Simplified 93.0%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718 + \frac{5.86923874282773}{x}}} \]

   if -1e6 < x < 4.1000000000000001e24

   1. Initial program 99.7%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \color{blue}{\left(\frac{500000000}{23533438303} \cdot z + x \cdot \left(\left(\frac{500000000}{23533438303} \cdot y + x \cdot \left(\frac{68759708208}{23533438303} - \left(\frac{65876268680250000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right) \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\left(\frac{500000000}{23533438303} \cdot z\right), \color{blue}{\left(x \cdot \left(\left(\frac{500000000}{23533438303} \cdot y + x \cdot \left(\frac{68759708208}{23533438303} - \left(\frac{65876268680250000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\left(z \cdot \frac{500000000}{23533438303}\right), \left(\color{blue}{x} \cdot \left(\left(\frac{500000000}{23533438303} \cdot y + x \cdot \left(\frac{68759708208}{23533438303} - \left(\frac{65876268680250000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \left(\color{blue}{x} \cdot \left(\left(\frac{500000000}{23533438303} \cdot y + x \cdot \left(\frac{68759708208}{23533438303} - \left(\frac{65876268680250000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\left(\frac{500000000}{23533438303} \cdot y + x \cdot \left(\frac{68759708208}{23533438303} - \left(\frac{65876268680250000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)}\right)\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \left(\left(x \cdot \left(\frac{68759708208}{23533438303} - \left(\frac{65876268680250000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right) + \frac{500000000}{23533438303} \cdot y\right) - \color{blue}{\frac{78349803973500000000}{553822718361107519809}} \cdot z\right)\right)\right)\right) \]

      6. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \left(x \cdot \left(\frac{68759708208}{23533438303} - \left(\frac{65876268680250000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right) + \color{blue}{\left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(x \cdot \left(\frac{68759708208}{23533438303} - \left(\frac{65876268680250000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right), \color{blue}{\left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)}\right)\right)\right)\right) \]

   7. Simplified 95.6%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(z \cdot 0.0212463641547976 + x \cdot \left(x \cdot \left(2.9217875995295866 + \left(z \cdot -0.11894829608144908 - 6.658593866711955 \cdot \left(0.0212463641547976 \cdot y + z \cdot -0.14147091005106402\right)\right)\right) + \left(0.0212463641547976 \cdot y + z \cdot -0.14147091005106402\right)\right)\right)} \]

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \color{blue}{\left(x \cdot \left(\frac{500000000}{23533438303} \cdot y + x \cdot \left(\frac{68759708208}{23533438303} - \frac{78349803973500000000}{553822718361107519809} \cdot y\right)\right)\right)}\right)\right) \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{500000000}{23533438303} \cdot y + x \cdot \left(\frac{68759708208}{23533438303} - \frac{78349803973500000000}{553822718361107519809} \cdot y\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{500000000}{23533438303} \cdot y\right), \color{blue}{\left(x \cdot \left(\frac{68759708208}{23533438303} - \frac{78349803973500000000}{553822718361107519809} \cdot y\right)\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \left(\color{blue}{x} \cdot \left(\frac{68759708208}{23533438303} - \frac{78349803973500000000}{553822718361107519809} \cdot y\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{68759708208}{23533438303} - \frac{78349803973500000000}{553822718361107519809} \cdot y\right)}\right)\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(x, \left(\frac{68759708208}{23533438303} + \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809} \cdot y\right)\right)}\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{68759708208}{23533438303}, \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809} \cdot y\right)\right)}\right)\right)\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{68759708208}{23533438303}, \left(\mathsf{neg}\left(y \cdot \frac{78349803973500000000}{553822718361107519809}\right)\right)\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{68759708208}{23533438303}, \left(y \cdot \color{blue}{\left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809}\right)\right)}\right)\right)\right)\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{68759708208}{23533438303}, \left(y \cdot \frac{-78349803973500000000}{553822718361107519809}\right)\right)\right)\right)\right)\right)\right) \]

      10. *-lowering-*.f64 95.2%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{68759708208}{23533438303}, \mathsf{*.f64}\left(y, \color{blue}{\frac{-78349803973500000000}{553822718361107519809}}\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 95.2%

       \[\leadsto \left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + \color{blue}{x \cdot \left(0.0212463641547976 \cdot y + x \cdot \left(2.9217875995295866 + y \cdot -0.14147091005106402\right)\right)}\right) \]

   11. Taylor expanded in y around 0

       \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \color{blue}{\left(\frac{68759708208}{23533438303} \cdot x\right)}\right)\right)\right)\right) \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \left(x \cdot \color{blue}{\frac{68759708208}{23533438303}}\right)\right)\right)\right)\right) \]

       2. *-lowering-*.f64 94.6%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{500000000}{23533438303}, y\right), \mathsf{*.f64}\left(x, \color{blue}{\frac{68759708208}{23533438303}}\right)\right)\right)\right)\right) \]

   13. Simplified 94.6%

       \[\leadsto \left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + x \cdot \left(0.0212463641547976 \cdot y + \color{blue}{x \cdot 2.9217875995295866}\right)\right) \]

   if 4.1000000000000001e24 < x

   1. Initial program 10.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 17.3%

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

   6. Applied egg-rr 17.2%

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

   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 96.0%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1000000:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+24}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + x \cdot \left(y \cdot 0.0212463641547976 + x \cdot 2.9217875995295866\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 88.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1000000:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+24}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(0.0212463641547976 \cdot \left(z + x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1000000.0)
   (/ (+ x -2.0) (+ 0.24013125253755718 (/ 5.86923874282773 x)))
   (if (<= x 4.1e+24)
     (* (+ x -2.0) (* 0.0212463641547976 (+ z (* x y))))
     (/ (+ x -2.0) 0.24013125253755718))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1000000.0) {
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x));
	} else if (x <= 4.1e+24) {
		tmp = (x + -2.0) * (0.0212463641547976 * (z + (x * y)));
	} else {
		tmp = (x + -2.0) / 0.24013125253755718;
	}
	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 <= (-1000000.0d0)) then
        tmp = (x + (-2.0d0)) / (0.24013125253755718d0 + (5.86923874282773d0 / x))
    else if (x <= 4.1d+24) then
        tmp = (x + (-2.0d0)) * (0.0212463641547976d0 * (z + (x * y)))
    else
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1000000.0) {
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x));
	} else if (x <= 4.1e+24) {
		tmp = (x + -2.0) * (0.0212463641547976 * (z + (x * y)));
	} else {
		tmp = (x + -2.0) / 0.24013125253755718;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1000000.0:
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x))
	elif x <= 4.1e+24:
		tmp = (x + -2.0) * (0.0212463641547976 * (z + (x * y)))
	else:
		tmp = (x + -2.0) / 0.24013125253755718
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1000000.0)
		tmp = Float64(Float64(x + -2.0) / Float64(0.24013125253755718 + Float64(5.86923874282773 / x)));
	elseif (x <= 4.1e+24)
		tmp = Float64(Float64(x + -2.0) * Float64(0.0212463641547976 * Float64(z + Float64(x * y))));
	else
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1000000.0)
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x));
	elseif (x <= 4.1e+24)
		tmp = (x + -2.0) * (0.0212463641547976 * (z + (x * y)));
	else
		tmp = (x + -2.0) / 0.24013125253755718;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1000000.0], N[(N[(x + -2.0), $MachinePrecision] / N[(0.24013125253755718 + N[(5.86923874282773 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.1e+24], N[(N[(x + -2.0), $MachinePrecision] * N[(0.0212463641547976 * N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1e6

   1. Initial program 8.9%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 13.8%

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

   6. Applied egg-rr 13.9%

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

   7. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \color{blue}{\left(\frac{25000000000}{104109730557} + \frac{63615716158700684400745}{10838835996651139530249} \cdot \frac{1}{x}\right)}\right) \]
   8. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\frac{25000000000}{104109730557}, \color{blue}{\left(\frac{63615716158700684400745}{10838835996651139530249} \cdot \frac{1}{x}\right)}\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\frac{25000000000}{104109730557}, \left(\frac{\frac{63615716158700684400745}{10838835996651139530249} \cdot 1}{\color{blue}{x}}\right)\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\frac{25000000000}{104109730557}, \left(\frac{\frac{63615716158700684400745}{10838835996651139530249}}{x}\right)\right)\right) \]

      4. /-lowering-/.f64 93.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\frac{25000000000}{104109730557}, \mathsf{/.f64}\left(\frac{63615716158700684400745}{10838835996651139530249}, \color{blue}{x}\right)\right)\right) \]

   9. Simplified 93.0%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718 + \frac{5.86923874282773}{x}}} \]

   if -1e6 < x < 4.1000000000000001e24

   1. Initial program 99.7%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \color{blue}{\left(\frac{500000000}{23533438303} \cdot z + x \cdot \left(\left(\frac{500000000}{23533438303} \cdot y + x \cdot \left(\frac{68759708208}{23533438303} - \left(\frac{65876268680250000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right) \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\left(\frac{500000000}{23533438303} \cdot z\right), \color{blue}{\left(x \cdot \left(\left(\frac{500000000}{23533438303} \cdot y + x \cdot \left(\frac{68759708208}{23533438303} - \left(\frac{65876268680250000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\left(z \cdot \frac{500000000}{23533438303}\right), \left(\color{blue}{x} \cdot \left(\left(\frac{500000000}{23533438303} \cdot y + x \cdot \left(\frac{68759708208}{23533438303} - \left(\frac{65876268680250000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \left(\color{blue}{x} \cdot \left(\left(\frac{500000000}{23533438303} \cdot y + x \cdot \left(\frac{68759708208}{23533438303} - \left(\frac{65876268680250000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\left(\frac{500000000}{23533438303} \cdot y + x \cdot \left(\frac{68759708208}{23533438303} - \left(\frac{65876268680250000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right) - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)}\right)\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \left(\left(x \cdot \left(\frac{68759708208}{23533438303} - \left(\frac{65876268680250000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right) + \frac{500000000}{23533438303} \cdot y\right) - \color{blue}{\frac{78349803973500000000}{553822718361107519809}} \cdot z\right)\right)\right)\right) \]

      6. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \left(x \cdot \left(\frac{68759708208}{23533438303} - \left(\frac{65876268680250000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right) + \color{blue}{\left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{500000000}{23533438303}\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(x \cdot \left(\frac{68759708208}{23533438303} - \left(\frac{65876268680250000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)\right)\right), \color{blue}{\left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)}\right)\right)\right)\right) \]

   7. Simplified 95.6%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(z \cdot 0.0212463641547976 + x \cdot \left(x \cdot \left(2.9217875995295866 + \left(z \cdot -0.11894829608144908 - 6.658593866711955 \cdot \left(0.0212463641547976 \cdot y + z \cdot -0.14147091005106402\right)\right)\right) + \left(0.0212463641547976 \cdot y + z \cdot -0.14147091005106402\right)\right)\right)} \]

   8. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

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

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

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

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 90.2%

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

   10. Simplified 90.2%

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

   11. Taylor expanded in x around 0

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

       1. +-commutative N/A

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

       2. distribute-lft-out N/A

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

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

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

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

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

       5. *-lowering-*.f64 89.6%

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

   13. Simplified 89.6%

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

   if 4.1000000000000001e24 < x

   1. Initial program 10.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 17.3%

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

   6. Applied egg-rr 17.2%

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

   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 96.0%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1000000:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+24}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(0.0212463641547976 \cdot \left(z + x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.7% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0021:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+24}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot z}{47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.0021)
   (/ (+ x -2.0) (+ 0.24013125253755718 (/ 5.86923874282773 x)))
   (if (<= x 4.1e+24)
     (/ (* (- x 2.0) z) 47.066876606)
     (/ (+ x -2.0) 0.24013125253755718))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.0021) {
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x));
	} else if (x <= 4.1e+24) {
		tmp = ((x - 2.0) * z) / 47.066876606;
	} else {
		tmp = (x + -2.0) / 0.24013125253755718;
	}
	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 <= (-0.0021d0)) then
        tmp = (x + (-2.0d0)) / (0.24013125253755718d0 + (5.86923874282773d0 / x))
    else if (x <= 4.1d+24) then
        tmp = ((x - 2.0d0) * z) / 47.066876606d0
    else
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.0021) {
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x));
	} else if (x <= 4.1e+24) {
		tmp = ((x - 2.0) * z) / 47.066876606;
	} else {
		tmp = (x + -2.0) / 0.24013125253755718;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.0021:
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x))
	elif x <= 4.1e+24:
		tmp = ((x - 2.0) * z) / 47.066876606
	else:
		tmp = (x + -2.0) / 0.24013125253755718
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.0021)
		tmp = Float64(Float64(x + -2.0) / Float64(0.24013125253755718 + Float64(5.86923874282773 / x)));
	elseif (x <= 4.1e+24)
		tmp = Float64(Float64(Float64(x - 2.0) * z) / 47.066876606);
	else
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.0021)
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x));
	elseif (x <= 4.1e+24)
		tmp = ((x - 2.0) * z) / 47.066876606;
	else
		tmp = (x + -2.0) / 0.24013125253755718;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.0021], N[(N[(x + -2.0), $MachinePrecision] / N[(0.24013125253755718 + N[(5.86923874282773 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.1e+24], N[(N[(N[(x - 2.0), $MachinePrecision] * z), $MachinePrecision] / 47.066876606), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.00209999999999999987

   1. Initial program 12.0%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 16.7%

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

   6. Applied egg-rr 16.8%

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

   7. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \color{blue}{\left(\frac{25000000000}{104109730557} + \frac{63615716158700684400745}{10838835996651139530249} \cdot \frac{1}{x}\right)}\right) \]
   8. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\frac{25000000000}{104109730557}, \color{blue}{\left(\frac{63615716158700684400745}{10838835996651139530249} \cdot \frac{1}{x}\right)}\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\frac{25000000000}{104109730557}, \left(\frac{\frac{63615716158700684400745}{10838835996651139530249} \cdot 1}{\color{blue}{x}}\right)\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\frac{25000000000}{104109730557}, \left(\frac{\frac{63615716158700684400745}{10838835996651139530249}}{x}\right)\right)\right) \]

      4. /-lowering-/.f64 89.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\frac{25000000000}{104109730557}, \mathsf{/.f64}\left(\frac{63615716158700684400745}{10838835996651139530249}, \color{blue}{x}\right)\right)\right) \]

   9. Simplified 89.9%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718 + \frac{5.86923874282773}{x}}} \]

   if -0.00209999999999999987 < x < 4.1000000000000001e24

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 70.0%

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

   6. Taylor expanded in x around 0

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

   8. Simplified 68.2%

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

   if 4.1000000000000001e24 < x

   1. Initial program 10.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 17.3%

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

   6. Applied egg-rr 17.2%

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

   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 96.0%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 75.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{-101.7851458539211}{x}\right)\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+24}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot z}{47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5)
   (* (+ x -2.0) (+ 4.16438922228 (/ -101.7851458539211 x)))
   (if (<= x 4.1e+24)
     (/ (* (- x 2.0) z) 47.066876606)
     (/ (+ x -2.0) 0.24013125253755718))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = (x + -2.0) * (4.16438922228 + (-101.7851458539211 / x));
	} else if (x <= 4.1e+24) {
		tmp = ((x - 2.0) * z) / 47.066876606;
	} else {
		tmp = (x + -2.0) / 0.24013125253755718;
	}
	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)) * (4.16438922228d0 + ((-101.7851458539211d0) / x))
    else if (x <= 4.1d+24) then
        tmp = ((x - 2.0d0) * z) / 47.066876606d0
    else
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    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) * (4.16438922228 + (-101.7851458539211 / x));
	} else if (x <= 4.1e+24) {
		tmp = ((x - 2.0) * z) / 47.066876606;
	} else {
		tmp = (x + -2.0) / 0.24013125253755718;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.5:
		tmp = (x + -2.0) * (4.16438922228 + (-101.7851458539211 / x))
	elif x <= 4.1e+24:
		tmp = ((x - 2.0) * z) / 47.066876606
	else:
		tmp = (x + -2.0) / 0.24013125253755718
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5)
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(-101.7851458539211 / x)));
	elseif (x <= 4.1e+24)
		tmp = Float64(Float64(Float64(x - 2.0) * z) / 47.066876606);
	else
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.5)
		tmp = (x + -2.0) * (4.16438922228 + (-101.7851458539211 / x));
	elseif (x <= 4.1e+24)
		tmp = ((x - 2.0) * z) / 47.066876606;
	else
		tmp = (x + -2.0) / 0.24013125253755718;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(-101.7851458539211 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.1e+24], N[(N[(N[(x - 2.0), $MachinePrecision] * z), $MachinePrecision] / 47.066876606), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5

   1. Initial program 10.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 15.3%

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

   5. Taylor expanded in x around inf

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

      1. sub-neg N/A

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

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

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, -2\right), \mathsf{+.f64}\left(\frac{104109730557}{25000000000}, \left(\frac{\mathsf{neg}\left(\frac{12723143231740136880149}{125000000000000000000}\right)}{\color{blue}{x}}\right)\right)\right) \]

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

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

      7. metadata-eval 90.8%

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

   7. Simplified 90.8%

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

   if -5.5 < x < 4.1000000000000001e24

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 69.5%

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

   6. Taylor expanded in x around 0

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

   8. Simplified 67.7%

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

   if 4.1000000000000001e24 < x

   1. Initial program 10.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 17.3%

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

   6. Applied egg-rr 17.2%

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

   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 96.0%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 75.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+24}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot z}{47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5)
   (* x (+ 4.16438922228 (/ -110.1139242984811 x)))
   (if (<= x 4.1e+24)
     (/ (* (- x 2.0) z) 47.066876606)
     (/ (+ x -2.0) 0.24013125253755718))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	} else if (x <= 4.1e+24) {
		tmp = ((x - 2.0) * z) / 47.066876606;
	} else {
		tmp = (x + -2.0) / 0.24013125253755718;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-5.5d0)) then
        tmp = x * (4.16438922228d0 + ((-110.1139242984811d0) / x))
    else if (x <= 4.1d+24) then
        tmp = ((x - 2.0d0) * z) / 47.066876606d0
    else
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	} else if (x <= 4.1e+24) {
		tmp = ((x - 2.0) * z) / 47.066876606;
	} else {
		tmp = (x + -2.0) / 0.24013125253755718;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.5:
		tmp = x * (4.16438922228 + (-110.1139242984811 / x))
	elif x <= 4.1e+24:
		tmp = ((x - 2.0) * z) / 47.066876606
	else:
		tmp = (x + -2.0) / 0.24013125253755718
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5)
		tmp = Float64(x * Float64(4.16438922228 + Float64(-110.1139242984811 / x)));
	elseif (x <= 4.1e+24)
		tmp = Float64(Float64(Float64(x - 2.0) * z) / 47.066876606);
	else
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.5)
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	elseif (x <= 4.1e+24)
		tmp = ((x - 2.0) * z) / 47.066876606;
	else
		tmp = (x + -2.0) / 0.24013125253755718;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5], N[(x * N[(4.16438922228 + N[(-110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.1e+24], N[(N[(N[(x - 2.0), $MachinePrecision] * z), $MachinePrecision] / 47.066876606), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5

   1. Initial program 10.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 15.3%

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

   5. Taylor expanded in x around inf

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

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

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

      2. sub-neg N/A

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

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

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. distribute-neg-frac N/A

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

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

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

      8. metadata-eval 90.7%

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

   7. Simplified 90.7%

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

   if -5.5 < x < 4.1000000000000001e24

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 69.5%

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

   6. Taylor expanded in x around 0

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

   8. Simplified 67.7%

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

   if 4.1000000000000001e24 < x

   1. Initial program 10.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 17.3%

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

   6. Applied egg-rr 17.2%

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

   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 96.0%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 75.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+24}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5)
   (* x (+ 4.16438922228 (/ -110.1139242984811 x)))
   (if (<= x 4.1e+24)
     (* (+ x -2.0) (* z 0.0212463641547976))
     (/ (+ x -2.0) 0.24013125253755718))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	} else if (x <= 4.1e+24) {
		tmp = (x + -2.0) * (z * 0.0212463641547976);
	} else {
		tmp = (x + -2.0) / 0.24013125253755718;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-5.5d0)) then
        tmp = x * (4.16438922228d0 + ((-110.1139242984811d0) / x))
    else if (x <= 4.1d+24) then
        tmp = (x + (-2.0d0)) * (z * 0.0212463641547976d0)
    else
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	} else if (x <= 4.1e+24) {
		tmp = (x + -2.0) * (z * 0.0212463641547976);
	} else {
		tmp = (x + -2.0) / 0.24013125253755718;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.5:
		tmp = x * (4.16438922228 + (-110.1139242984811 / x))
	elif x <= 4.1e+24:
		tmp = (x + -2.0) * (z * 0.0212463641547976)
	else:
		tmp = (x + -2.0) / 0.24013125253755718
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5)
		tmp = Float64(x * Float64(4.16438922228 + Float64(-110.1139242984811 / x)));
	elseif (x <= 4.1e+24)
		tmp = Float64(Float64(x + -2.0) * Float64(z * 0.0212463641547976));
	else
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.5)
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	elseif (x <= 4.1e+24)
		tmp = (x + -2.0) * (z * 0.0212463641547976);
	else
		tmp = (x + -2.0) / 0.24013125253755718;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5], N[(x * N[(4.16438922228 + N[(-110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.1e+24], N[(N[(x + -2.0), $MachinePrecision] * N[(z * 0.0212463641547976), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5

   1. Initial program 10.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 15.3%

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

   5. Taylor expanded in x around inf

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

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

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

      2. sub-neg N/A

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

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

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. distribute-neg-frac N/A

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

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

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

      8. metadata-eval 90.7%

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

   7. Simplified 90.7%

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

   if -5.5 < x < 4.1000000000000001e24

   1. Initial program 99.7%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
   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 67.4%

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

   7. Simplified 67.4%

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

   if 4.1000000000000001e24 < x

   1. Initial program 10.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 17.3%

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

   6. Applied egg-rr 17.2%

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

   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 96.0%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 75.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.17:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-29}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.17)
   (* x (+ 4.16438922228 (/ -110.1139242984811 x)))
   (if (<= x 3e-29)
     (* z -0.0424927283095952)
     (/ (+ x -2.0) 0.24013125253755718))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.17) {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	} else if (x <= 3e-29) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = (x + -2.0) / 0.24013125253755718;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-0.17d0)) then
        tmp = x * (4.16438922228d0 + ((-110.1139242984811d0) / x))
    else if (x <= 3d-29) then
        tmp = z * (-0.0424927283095952d0)
    else
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.17) {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	} else if (x <= 3e-29) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = (x + -2.0) / 0.24013125253755718;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.17:
		tmp = x * (4.16438922228 + (-110.1139242984811 / x))
	elif x <= 3e-29:
		tmp = z * -0.0424927283095952
	else:
		tmp = (x + -2.0) / 0.24013125253755718
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.17)
		tmp = Float64(x * Float64(4.16438922228 + Float64(-110.1139242984811 / x)));
	elseif (x <= 3e-29)
		tmp = Float64(z * -0.0424927283095952);
	else
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.17)
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	elseif (x <= 3e-29)
		tmp = z * -0.0424927283095952;
	else
		tmp = (x + -2.0) / 0.24013125253755718;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.17], N[(x * N[(4.16438922228 + N[(-110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3e-29], N[(z * -0.0424927283095952), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.170000000000000012

   1. Initial program 10.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 15.3%

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

   5. Taylor expanded in x around inf

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

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

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

      2. sub-neg N/A

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

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

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. distribute-neg-frac N/A

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

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

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

      8. metadata-eval 90.7%

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

   7. Simplified 90.7%

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

   if -0.170000000000000012 < x < 3.0000000000000003e-29

   1. Initial program 99.7%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 72.1%

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

   7. Simplified 72.1%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]

   if 3.0000000000000003e-29 < x

   1. Initial program 20.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 26.7%

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

   6. Applied egg-rr 26.7%

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

   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 85.5%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.17:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-29}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 75.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + -2}{0.24013125253755718}\\ \mathbf{if}\;x \leq -640:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-29}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x -2.0) 0.24013125253755718)))
   (if (<= x -640.0) t_0 (if (<= x 3e-29) (* 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 <= -640.0) {
		tmp = t_0;
	} else if (x <= 3e-29) {
		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 <= (-640.0d0)) then
        tmp = t_0
    else if (x <= 3d-29) 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 <= -640.0) {
		tmp = t_0;
	} else if (x <= 3e-29) {
		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 <= -640.0:
		tmp = t_0
	elif x <= 3e-29:
		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 <= -640.0)
		tmp = t_0;
	elseif (x <= 3e-29)
		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 <= -640.0)
		tmp = t_0;
	elseif (x <= 3e-29)
		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, -640.0], t$95$0, If[LessEqual[x, 3e-29], N[(z * -0.0424927283095952), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -640 or 3.0000000000000003e-29 < x

   1. Initial program 16.2%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 21.8%

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

   6. Applied egg-rr 21.8%

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

   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 87.7%

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

   if -640 < x < 3.0000000000000003e-29

   1. Initial program 99.7%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 72.1%

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

   7. Simplified 72.1%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -640:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-29}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 75.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4.16438922228 \cdot \left(x + -2\right)\\ \mathbf{if}\;x \leq -48:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-29}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 4.16438922228 (+ x -2.0))))
   (if (<= x -48.0) t_0 (if (<= x 3e-29) (* 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 <= -48.0) {
		tmp = t_0;
	} else if (x <= 3e-29) {
		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 <= (-48.0d0)) then
        tmp = t_0
    else if (x <= 3d-29) 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 <= -48.0) {
		tmp = t_0;
	} else if (x <= 3e-29) {
		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 <= -48.0:
		tmp = t_0
	elif x <= 3e-29:
		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 <= -48.0)
		tmp = t_0;
	elseif (x <= 3e-29)
		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 <= -48.0)
		tmp = t_0;
	elseif (x <= 3e-29)
		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, -48.0], t$95$0, If[LessEqual[x, 3e-29], N[(z * -0.0424927283095952), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -48 or 3.0000000000000003e-29 < x

   1. Initial program 16.2%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 21.8%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 87.1%

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

   if -48 < x < 3.0000000000000003e-29

   1. Initial program 99.7%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 72.1%

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

   7. Simplified 72.1%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -48:\\ \;\;\;\;4.16438922228 \cdot \left(x + -2\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-29}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot \left(x + -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 75.7% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5)
   (* 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 <= -5.5) {
		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 <= (-5.5d0)) 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 <= -5.5) {
		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 <= -5.5:
		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 <= -5.5)
		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 <= -5.5)
		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, -5.5], 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 < -5.5 or 2 < x

   1. Initial program 12.4%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 18.2%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 90.8%

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

   7. Simplified 90.8%

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

   if -5.5 < x < 2

   1. Initial program 99.7%

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

      1. associate-/l* N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

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

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 68.9%

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

   7. Simplified 68.9%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 34.5% 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 55.4%

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

   1. associate-/l* N/A

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

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

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

   3. sub-neg N/A

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

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

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

   5. metadata-eval N/A

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

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

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

3. Simplified 58.3%

   \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}} \]
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 35.3%

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

7. Simplified 35.3%

   \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]

8. Final simplification 35.3%

   \[\leadsto z \cdot -0.0424927283095952 \]
9. Add Preprocessing

Developer Target 1: 98.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\frac{y}{x \cdot x} + 4.16438922228 \cdot x\right) - 110.1139242984811\\ \mathbf{if}\;x < -3.326128725870005 \cdot 10^{+62}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x < 9.429991714554673 \cdot 10^{+55}:\\ \;\;\;\;\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(263.505074721 \cdot x + \left(43.3400022514 \cdot \left(x \cdot x\right) + x \cdot \left(x \cdot x\right)\right)\right) + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811)))
   (if (< x -3.326128725870005e+62)
     t_0
     (if (< x 9.429991714554673e+55)
       (*
        (/ (- x 2.0) 1.0)
        (/
         (+
          (*
           (+
            (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
            y)
           x)
          z)
         (+
          (*
           (+
            (+ (* 263.505074721 x) (+ (* 43.3400022514 (* x x)) (* x (* x x))))
            313.399215894)
           x)
          47.066876606)))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811;
	double tmp;
	if (x < -3.326128725870005e+62) {
		tmp = t_0;
	} else if (x < 9.429991714554673e+55) {
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * x)))) + 313.399215894) * x) + 47.066876606));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((y / (x * x)) + (4.16438922228d0 * x)) - 110.1139242984811d0
    if (x < (-3.326128725870005d+62)) then
        tmp = t_0
    else if (x < 9.429991714554673d+55) then
        tmp = ((x - 2.0d0) / 1.0d0) * (((((((((x * 4.16438922228d0) + 78.6994924154d0) * x) + 137.519416416d0) * x) + y) * x) + z) / (((((263.505074721d0 * x) + ((43.3400022514d0 * (x * x)) + (x * (x * x)))) + 313.399215894d0) * x) + 47.066876606d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811;
	double tmp;
	if (x < -3.326128725870005e+62) {
		tmp = t_0;
	} else if (x < 9.429991714554673e+55) {
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * x)))) + 313.399215894) * x) + 47.066876606));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811
	tmp = 0
	if x < -3.326128725870005e+62:
		tmp = t_0
	elif x < 9.429991714554673e+55:
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * x)))) + 313.399215894) * x) + 47.066876606))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y / Float64(x * x)) + Float64(4.16438922228 * x)) - 110.1139242984811)
	tmp = 0.0
	if (x < -3.326128725870005e+62)
		tmp = t_0;
	elseif (x < 9.429991714554673e+55)
		tmp = Float64(Float64(Float64(x - 2.0) / 1.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / Float64(Float64(Float64(Float64(Float64(263.505074721 * x) + Float64(Float64(43.3400022514 * Float64(x * x)) + Float64(x * Float64(x * x)))) + 313.399215894) * x) + 47.066876606)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811;
	tmp = 0.0;
	if (x < -3.326128725870005e+62)
		tmp = t_0;
	elseif (x < 9.429991714554673e+55)
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * x)))) + 313.399215894) * x) + 47.066876606));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y / N[(x * x), $MachinePrecision]), $MachinePrecision] + N[(4.16438922228 * x), $MachinePrecision]), $MachinePrecision] - 110.1139242984811), $MachinePrecision]}, If[Less[x, -3.326128725870005e+62], t$95$0, If[Less[x, 9.429991714554673e+55], N[(N[(N[(x - 2.0), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision] / N[(N[(N[(N[(N[(263.505074721 * x), $MachinePrecision] + N[(N[(43.3400022514 * N[(x * x), $MachinePrecision]), $MachinePrecision] + N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024155 
(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)))