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

Percentage Accurate: 57.6% → 98.1%

Time: 18.0s

Alternatives: 15

Speedup: 4.4×

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: 57.6% 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: 98.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 2 \cdot 10^{+292}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}}{\frac{1}{x + -2}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{y}{x \cdot \left(x \cdot x\right)}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (/
       (*
        (- x 2.0)
        (+
         (*
          x
          (+
           (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
           y))
         z))
       (+
        (*
         x
         (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
        47.066876606))
      2e+292)
   (/
    (/
     (fma
      x
      (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y)
      z)
     (fma
      x
      (fma x (fma x (+ x 43.3400022514) 263.505074721) 313.399215894)
      47.066876606))
    (/ 1.0 (+ x -2.0)))
   (* x (+ 4.16438922228 (/ y (* x (* x x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)) <= 2e+292) {
		tmp = (fma(x, fma(x, fma(x, fma(x, 4.16438922228, 78.6994924154), 137.519416416), y), z) / fma(x, fma(x, fma(x, (x + 43.3400022514), 263.505074721), 313.399215894), 47.066876606)) / (1.0 / (x + -2.0));
	} else {
		tmp = x * (4.16438922228 + (y / (x * (x * x))));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)) <= 2e+292)
		tmp = Float64(Float64(fma(x, fma(x, fma(x, fma(x, 4.16438922228, 78.6994924154), 137.519416416), y), z) / fma(x, fma(x, fma(x, Float64(x + 43.3400022514), 263.505074721), 313.399215894), 47.066876606)) / Float64(1.0 / Float64(x + -2.0)));
	else
		tmp = Float64(x * Float64(4.16438922228 + Float64(y / Float64(x * Float64(x * x)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(N[(x - 2.0), $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] / 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], 2e+292], N[(N[(N[(x * N[(x * N[(x * N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] + 137.519416416), $MachinePrecision] + y), $MachinePrecision] + z), $MachinePrecision] / N[(x * N[(x * N[(x * N[(x + 43.3400022514), $MachinePrecision] + 263.505074721), $MachinePrecision] + 313.399215894), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision] / N[(1.0 / N[(x + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(4.16438922228 + N[(y / N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < 2e292

   1. Initial program 97.8%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. flip3-- N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

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

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

   4. Applied egg-rr 99.6%

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

   if 2e292 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64)))

   1. Initial program 0.1%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 99.2%

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

   6. Taylor expanded in y around inf

      \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \color{blue}{\frac{y}{{x}^{3}}}\right) \]
   7. Step-by-step derivation

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

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \color{blue}{\frac{y}{{x}^{3}}}\right) \]

      2. cube-mult N/A

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \frac{y}{\color{blue}{x \cdot \left(x \cdot x\right)}}\right) \]

      3. unpow2 N/A

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \frac{y}{x \cdot \color{blue}{{x}^{2}}}\right) \]

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

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \frac{y}{\color{blue}{x \cdot {x}^{2}}}\right) \]

      5. unpow2 N/A

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \frac{y}{x \cdot \color{blue}{\left(x \cdot x\right)}}\right) \]

      6. *-lowering-*.f64 99.2

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

   8. Simplified 99.2%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 2 \cdot 10^{+292}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}}{\frac{1}{x + -2}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{y}{x \cdot \left(x \cdot x\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 2 \cdot 10^{+292}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \cdot \mathsf{fma}\left(x, x, -4\right)}{x + 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{y}{x \cdot \left(x \cdot x\right)}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (/
       (*
        (- x 2.0)
        (+
         (*
          x
          (+
           (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
           y))
         z))
       (+
        (*
         x
         (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
        47.066876606))
      2e+292)
   (/
    (*
     (/
      (fma
       x
       (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y)
       z)
      (fma
       x
       (fma x (fma x (+ x 43.3400022514) 263.505074721) 313.399215894)
       47.066876606))
     (fma x x -4.0))
    (+ x 2.0))
   (* x (+ 4.16438922228 (/ y (* x (* x x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)) <= 2e+292) {
		tmp = ((fma(x, fma(x, fma(x, fma(x, 4.16438922228, 78.6994924154), 137.519416416), y), z) / fma(x, fma(x, fma(x, (x + 43.3400022514), 263.505074721), 313.399215894), 47.066876606)) * fma(x, x, -4.0)) / (x + 2.0);
	} else {
		tmp = x * (4.16438922228 + (y / (x * (x * x))));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)) <= 2e+292)
		tmp = Float64(Float64(Float64(fma(x, fma(x, fma(x, fma(x, 4.16438922228, 78.6994924154), 137.519416416), y), z) / fma(x, fma(x, fma(x, Float64(x + 43.3400022514), 263.505074721), 313.399215894), 47.066876606)) * fma(x, x, -4.0)) / Float64(x + 2.0));
	else
		tmp = Float64(x * Float64(4.16438922228 + Float64(y / Float64(x * Float64(x * x)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(N[(x - 2.0), $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] / 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], 2e+292], N[(N[(N[(N[(x * N[(x * N[(x * N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] + 137.519416416), $MachinePrecision] + y), $MachinePrecision] + z), $MachinePrecision] / N[(x * N[(x * N[(x * N[(x + 43.3400022514), $MachinePrecision] + 263.505074721), $MachinePrecision] + 313.399215894), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision] * N[(x * x + -4.0), $MachinePrecision]), $MachinePrecision] / N[(x + 2.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(4.16438922228 + N[(y / N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < 2e292

   1. Initial program 97.8%

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

      1. associate-/l* N/A

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

      2. flip-- N/A

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

      3. associate-*l/ N/A

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

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

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

   4. Applied egg-rr 99.6%

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

   if 2e292 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64)))

   1. Initial program 0.1%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 99.2%

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

   6. Taylor expanded in y around inf

      \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \color{blue}{\frac{y}{{x}^{3}}}\right) \]
   7. Step-by-step derivation

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

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \color{blue}{\frac{y}{{x}^{3}}}\right) \]

      2. cube-mult N/A

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \frac{y}{\color{blue}{x \cdot \left(x \cdot x\right)}}\right) \]

      3. unpow2 N/A

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \frac{y}{x \cdot \color{blue}{{x}^{2}}}\right) \]

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

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \frac{y}{\color{blue}{x \cdot {x}^{2}}}\right) \]

      5. unpow2 N/A

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \frac{y}{x \cdot \color{blue}{\left(x \cdot x\right)}}\right) \]

      6. *-lowering-*.f64 99.2

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

   8. Simplified 99.2%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 2 \cdot 10^{+292}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \cdot \mathsf{fma}\left(x, x, -4\right)}{x + 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{y}{x \cdot \left(x \cdot x\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 2 \cdot 10^{+292}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right) \cdot \frac{x + -2}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{y}{x \cdot \left(x \cdot x\right)}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (/
       (*
        (- x 2.0)
        (+
         (*
          x
          (+
           (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
           y))
         z))
       (+
        (*
         x
         (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
        47.066876606))
      2e+292)
   (*
    (fma
     x
     (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y)
     z)
    (/
     (+ x -2.0)
     (fma
      x
      (fma x (fma x (+ x 43.3400022514) 263.505074721) 313.399215894)
      47.066876606)))
   (* x (+ 4.16438922228 (/ y (* x (* x x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)) <= 2e+292) {
		tmp = fma(x, fma(x, fma(x, fma(x, 4.16438922228, 78.6994924154), 137.519416416), y), z) * ((x + -2.0) / fma(x, fma(x, fma(x, (x + 43.3400022514), 263.505074721), 313.399215894), 47.066876606));
	} else {
		tmp = x * (4.16438922228 + (y / (x * (x * x))));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)) <= 2e+292)
		tmp = Float64(fma(x, fma(x, fma(x, fma(x, 4.16438922228, 78.6994924154), 137.519416416), y), z) * Float64(Float64(x + -2.0) / fma(x, fma(x, fma(x, Float64(x + 43.3400022514), 263.505074721), 313.399215894), 47.066876606)));
	else
		tmp = Float64(x * Float64(4.16438922228 + Float64(y / Float64(x * Float64(x * x)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(N[(x - 2.0), $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] / 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], 2e+292], N[(N[(x * N[(x * N[(x * N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] + 137.519416416), $MachinePrecision] + y), $MachinePrecision] + z), $MachinePrecision] * N[(N[(x + -2.0), $MachinePrecision] / N[(x * N[(x * N[(x * N[(x + 43.3400022514), $MachinePrecision] + 263.505074721), $MachinePrecision] + 313.399215894), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(4.16438922228 + N[(y / N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < 2e292

   1. Initial program 97.8%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

   4. Applied egg-rr 99.4%

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

   if 2e292 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64)))

   1. Initial program 0.1%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 99.2%

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

   6. Taylor expanded in y around inf

      \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \color{blue}{\frac{y}{{x}^{3}}}\right) \]
   7. Step-by-step derivation

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

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \color{blue}{\frac{y}{{x}^{3}}}\right) \]

      2. cube-mult N/A

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \frac{y}{\color{blue}{x \cdot \left(x \cdot x\right)}}\right) \]

      3. unpow2 N/A

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \frac{y}{x \cdot \color{blue}{{x}^{2}}}\right) \]

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

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \frac{y}{\color{blue}{x \cdot {x}^{2}}}\right) \]

      5. unpow2 N/A

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \frac{y}{x \cdot \color{blue}{\left(x \cdot x\right)}}\right) \]

      6. *-lowering-*.f64 99.2

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

   8. Simplified 99.2%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 2 \cdot 10^{+292}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right) \cdot \frac{x + -2}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{y}{x \cdot \left(x \cdot x\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(4.16438922228 + \frac{y}{x \cdot \left(x \cdot x\right)}\right)\\ \mathbf{if}\;x \leq -6.4 \cdot 10^{+32}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+14}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(x, \mathsf{fma}\left(x, 137.519416416, y\right), z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ 4.16438922228 (/ y (* x (* x x)))))))
   (if (<= x -6.4e+32)
     t_0
     (if (<= x 4e+14)
       (/
        (* (- x 2.0) (fma x (fma x 137.519416416 y) z))
        (+
         (*
          x
          (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
         47.066876606))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (4.16438922228 + (y / (x * (x * x))));
	double tmp;
	if (x <= -6.4e+32) {
		tmp = t_0;
	} else if (x <= 4e+14) {
		tmp = ((x - 2.0) * fma(x, fma(x, 137.519416416, y), z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(4.16438922228 + Float64(y / Float64(x * Float64(x * x)))))
	tmp = 0.0
	if (x <= -6.4e+32)
		tmp = t_0;
	elseif (x <= 4e+14)
		tmp = Float64(Float64(Float64(x - 2.0) * fma(x, fma(x, 137.519416416, y), z)) / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(4.16438922228 + N[(y / N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.4e+32], t$95$0, If[LessEqual[x, 4e+14], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(x * N[(x * 137.519416416 + y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.3999999999999998e32 or 4e14 < x

   1. Initial program 8.5%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 99.2%

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

   6. Taylor expanded in y around inf

      \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \color{blue}{\frac{y}{{x}^{3}}}\right) \]
   7. Step-by-step derivation

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

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \color{blue}{\frac{y}{{x}^{3}}}\right) \]

      2. cube-mult N/A

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \frac{y}{\color{blue}{x \cdot \left(x \cdot x\right)}}\right) \]

      3. unpow2 N/A

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \frac{y}{x \cdot \color{blue}{{x}^{2}}}\right) \]

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

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \frac{y}{\color{blue}{x \cdot {x}^{2}}}\right) \]

      5. unpow2 N/A

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \frac{y}{x \cdot \color{blue}{\left(x \cdot x\right)}}\right) \]

      6. *-lowering-*.f64 99.2

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

   8. Simplified 99.2%

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

   if -6.3999999999999998e32 < x < 4e14

   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

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

      1. +-commutative N/A

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

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

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. accelerator-lowering-fma.f64 97.5

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

   5. Simplified 97.5%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{y}{x \cdot \left(x \cdot x\right)}\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+14}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(x, \mathsf{fma}\left(x, 137.519416416, y\right), z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{y}{x \cdot \left(x \cdot x\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(4.16438922228 + \frac{y}{x \cdot \left(x \cdot x\right)}\right)\\ \mathbf{if}\;x \leq -1.05 \cdot 10^{+21}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 66000000000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(x, y, z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ 4.16438922228 (/ y (* x (* x x)))))))
   (if (<= x -1.05e+21)
     t_0
     (if (<= x 66000000000000.0)
       (/
        (* (- x 2.0) (fma x y z))
        (+
         (*
          x
          (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
         47.066876606))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (4.16438922228 + (y / (x * (x * x))));
	double tmp;
	if (x <= -1.05e+21) {
		tmp = t_0;
	} else if (x <= 66000000000000.0) {
		tmp = ((x - 2.0) * fma(x, y, z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(4.16438922228 + Float64(y / Float64(x * Float64(x * x)))))
	tmp = 0.0
	if (x <= -1.05e+21)
		tmp = t_0;
	elseif (x <= 66000000000000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * fma(x, y, z)) / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(4.16438922228 + N[(y / N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.05e+21], t$95$0, If[LessEqual[x, 66000000000000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(x * y + z), $MachinePrecision]), $MachinePrecision] / N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.05e21 or 6.6e13 < x

   1. Initial program 11.8%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 97.5%

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

   6. Taylor expanded in y around inf

      \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \color{blue}{\frac{y}{{x}^{3}}}\right) \]
   7. Step-by-step derivation

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

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \color{blue}{\frac{y}{{x}^{3}}}\right) \]

      2. cube-mult N/A

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \frac{y}{\color{blue}{x \cdot \left(x \cdot x\right)}}\right) \]

      3. unpow2 N/A

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \frac{y}{x \cdot \color{blue}{{x}^{2}}}\right) \]

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

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \frac{y}{\color{blue}{x \cdot {x}^{2}}}\right) \]

      5. unpow2 N/A

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \frac{y}{x \cdot \color{blue}{\left(x \cdot x\right)}}\right) \]

      6. *-lowering-*.f64 97.5

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

   8. Simplified 97.5%

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

   if -1.05e21 < x < 6.6e13

   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

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 95.5

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

   5. Simplified 95.5%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{y}{x \cdot \left(x \cdot x\right)}\right)\\ \mathbf{elif}\;x \leq 66000000000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(x, y, z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{y}{x \cdot \left(x \cdot x\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 92.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(4.16438922228 + \frac{y}{x \cdot \left(x \cdot x\right)}\right)\\ \mathbf{if}\;x \leq -22500000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3150000000000:\\ \;\;\;\;\mathsf{fma}\left(z \cdot 0.0212463641547976, x, \mathsf{fma}\left(x, \mathsf{fma}\left(z, 0.28294182010212804, y \cdot -0.0424927283095952\right), z \cdot -0.0424927283095952\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ 4.16438922228 (/ y (* x (* x x)))))))
   (if (<= x -22500000.0)
     t_0
     (if (<= x 3150000000000.0)
       (fma
        (* z 0.0212463641547976)
        x
        (fma
         x
         (fma z 0.28294182010212804 (* y -0.0424927283095952))
         (* z -0.0424927283095952)))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (4.16438922228 + (y / (x * (x * x))));
	double tmp;
	if (x <= -22500000.0) {
		tmp = t_0;
	} else if (x <= 3150000000000.0) {
		tmp = fma((z * 0.0212463641547976), x, fma(x, fma(z, 0.28294182010212804, (y * -0.0424927283095952)), (z * -0.0424927283095952)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(4.16438922228 + Float64(y / Float64(x * Float64(x * x)))))
	tmp = 0.0
	if (x <= -22500000.0)
		tmp = t_0;
	elseif (x <= 3150000000000.0)
		tmp = fma(Float64(z * 0.0212463641547976), x, fma(x, fma(z, 0.28294182010212804, Float64(y * -0.0424927283095952)), Float64(z * -0.0424927283095952)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(4.16438922228 + N[(y / N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -22500000.0], t$95$0, If[LessEqual[x, 3150000000000.0], N[(N[(z * 0.0212463641547976), $MachinePrecision] * x + N[(x * N[(z * 0.28294182010212804 + N[(y * -0.0424927283095952), $MachinePrecision]), $MachinePrecision] + N[(z * -0.0424927283095952), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.25e7 or 3.15e12 < x

   1. Initial program 14.1%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 96.7%

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

   6. Taylor expanded in y around inf

      \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \color{blue}{\frac{y}{{x}^{3}}}\right) \]
   7. Step-by-step derivation

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

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \color{blue}{\frac{y}{{x}^{3}}}\right) \]

      2. cube-mult N/A

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \frac{y}{\color{blue}{x \cdot \left(x \cdot x\right)}}\right) \]

      3. unpow2 N/A

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \frac{y}{x \cdot \color{blue}{{x}^{2}}}\right) \]

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

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \frac{y}{\color{blue}{x \cdot {x}^{2}}}\right) \]

      5. unpow2 N/A

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \frac{y}{x \cdot \color{blue}{\left(x \cdot x\right)}}\right) \]

      6. *-lowering-*.f64 96.4

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

   8. Simplified 96.4%

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

   if -2.25e7 < x < 3.15e12

   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

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

      1. +-commutative N/A

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

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

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

      3. distribute-rgt-in N/A

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

      4. associate--l+ N/A

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

      5. *-commutative N/A

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

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

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

      7. sub-neg N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. metadata-eval N/A

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

      12. accelerator-lowering-fma.f64 N/A

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

      13. *-commutative N/A

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

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

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

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

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

      16. metadata-eval N/A

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

      17. *-commutative N/A

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

      18. *-lowering-*.f64 91.4

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

   5. Simplified 91.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(z, 0.0212463641547976, \mathsf{fma}\left(y, -0.0424927283095952, z \cdot 0.28294182010212804\right)\right), z \cdot -0.0424927283095952\right)} \]
   6. Step-by-step derivation

      1. distribute-rgt-in N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. *-commutative N/A

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

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

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

      7. +-commutative N/A

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

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

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

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

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

      10. *-lowering-*.f64 91.4

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

   7. Applied egg-rr 91.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot 0.0212463641547976, x, \mathsf{fma}\left(x, \mathsf{fma}\left(z, 0.28294182010212804, y \cdot -0.0424927283095952\right), z \cdot -0.0424927283095952\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 92.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(4.16438922228 + \frac{y}{x \cdot \left(x \cdot x\right)}\right)\\ \mathbf{if}\;x \leq -22500000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3150000000000:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(z, 0.0212463641547976, \mathsf{fma}\left(y, -0.0424927283095952, z \cdot 0.28294182010212804\right)\right), z \cdot -0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ 4.16438922228 (/ y (* x (* x x)))))))
   (if (<= x -22500000.0)
     t_0
     (if (<= x 3150000000000.0)
       (fma
        x
        (fma
         z
         0.0212463641547976
         (fma y -0.0424927283095952 (* z 0.28294182010212804)))
        (* z -0.0424927283095952))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (4.16438922228 + (y / (x * (x * x))));
	double tmp;
	if (x <= -22500000.0) {
		tmp = t_0;
	} else if (x <= 3150000000000.0) {
		tmp = fma(x, fma(z, 0.0212463641547976, fma(y, -0.0424927283095952, (z * 0.28294182010212804))), (z * -0.0424927283095952));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(4.16438922228 + Float64(y / Float64(x * Float64(x * x)))))
	tmp = 0.0
	if (x <= -22500000.0)
		tmp = t_0;
	elseif (x <= 3150000000000.0)
		tmp = fma(x, fma(z, 0.0212463641547976, fma(y, -0.0424927283095952, Float64(z * 0.28294182010212804))), Float64(z * -0.0424927283095952));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(4.16438922228 + N[(y / N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -22500000.0], t$95$0, If[LessEqual[x, 3150000000000.0], N[(x * N[(z * 0.0212463641547976 + N[(y * -0.0424927283095952 + N[(z * 0.28294182010212804), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * -0.0424927283095952), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.25e7 or 3.15e12 < x

   1. Initial program 14.1%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 96.7%

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

   6. Taylor expanded in y around inf

      \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \color{blue}{\frac{y}{{x}^{3}}}\right) \]
   7. Step-by-step derivation

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

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \color{blue}{\frac{y}{{x}^{3}}}\right) \]

      2. cube-mult N/A

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \frac{y}{\color{blue}{x \cdot \left(x \cdot x\right)}}\right) \]

      3. unpow2 N/A

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \frac{y}{x \cdot \color{blue}{{x}^{2}}}\right) \]

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

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \frac{y}{\color{blue}{x \cdot {x}^{2}}}\right) \]

      5. unpow2 N/A

         \[\leadsto x \cdot \left(\frac{104109730557}{25000000000} + \frac{y}{x \cdot \color{blue}{\left(x \cdot x\right)}}\right) \]

      6. *-lowering-*.f64 96.4

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

   8. Simplified 96.4%

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

   if -2.25e7 < x < 3.15e12

   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

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

      1. +-commutative N/A

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

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

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

      3. distribute-rgt-in N/A

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

      4. associate--l+ N/A

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

      5. *-commutative N/A

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

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

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

      7. sub-neg N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. metadata-eval N/A

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

      12. accelerator-lowering-fma.f64 N/A

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

      13. *-commutative N/A

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

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

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

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

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

      16. metadata-eval N/A

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

      17. *-commutative N/A

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

      18. *-lowering-*.f64 91.4

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

   5. Simplified 91.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(z, 0.0212463641547976, \mathsf{fma}\left(y, -0.0424927283095952, z \cdot 0.28294182010212804\right)\right), z \cdot -0.0424927283095952\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 89.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -22500000:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \mathbf{elif}\;x \leq 3150000000000:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(z, 0.0212463641547976, \mathsf{fma}\left(y, -0.0424927283095952, z \cdot 0.28294182010212804\right)\right), z \cdot -0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{4.16438922228}{\frac{1}{x + -2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -22500000.0)
   (* x (+ 4.16438922228 (/ -110.1139242984811 x)))
   (if (<= x 3150000000000.0)
     (fma
      x
      (fma
       z
       0.0212463641547976
       (fma y -0.0424927283095952 (* z 0.28294182010212804)))
      (* z -0.0424927283095952))
     (/ 4.16438922228 (/ 1.0 (+ x -2.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -22500000.0) {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	} else if (x <= 3150000000000.0) {
		tmp = fma(x, fma(z, 0.0212463641547976, fma(y, -0.0424927283095952, (z * 0.28294182010212804))), (z * -0.0424927283095952));
	} else {
		tmp = 4.16438922228 / (1.0 / (x + -2.0));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -22500000.0)
		tmp = Float64(x * Float64(4.16438922228 + Float64(-110.1139242984811 / x)));
	elseif (x <= 3150000000000.0)
		tmp = fma(x, fma(z, 0.0212463641547976, fma(y, -0.0424927283095952, Float64(z * 0.28294182010212804))), Float64(z * -0.0424927283095952));
	else
		tmp = Float64(4.16438922228 / Float64(1.0 / Float64(x + -2.0)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -22500000.0], N[(x * N[(4.16438922228 + N[(-110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3150000000000.0], N[(x * N[(z * 0.0212463641547976 + N[(y * -0.0424927283095952 + N[(z * 0.28294182010212804), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * -0.0424927283095952), $MachinePrecision]), $MachinePrecision], N[(4.16438922228 / N[(1.0 / N[(x + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.25e7

   1. Initial program 20.2%

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

   3. Taylor expanded in x around inf

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. neg-sub0 N/A

         \[\leadsto x \cdot \left(\color{blue}{\left(0 - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} + \frac{104109730557}{25000000000}\right) \]

      4. associate-+l- N/A

         \[\leadsto x \cdot \color{blue}{\left(0 - \left(\frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x} - \frac{104109730557}{25000000000}\right)\right)} \]

      5. neg-sub0 N/A

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

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

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

      7. neg-sub0 N/A

         \[\leadsto x \cdot \color{blue}{\left(0 - \left(\frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x} - \frac{104109730557}{25000000000}\right)\right)} \]

      8. associate-+l- N/A

         \[\leadsto x \cdot \color{blue}{\left(\left(0 - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right) + \frac{104109730557}{25000000000}\right)} \]

      9. neg-sub0 N/A

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

      10. +-commutative N/A

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

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

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

      12. associate-*r/ N/A

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

      13. metadata-eval N/A

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

      14. distribute-neg-frac N/A

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

      15. /-lowering-/.f64 N/A

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

      16. metadata-eval 88.7

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

   5. Simplified 88.7%

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

   if -2.25e7 < x < 3.15e12

   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

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

      1. +-commutative N/A

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

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

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

      3. distribute-rgt-in N/A

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

      4. associate--l+ N/A

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

      5. *-commutative N/A

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

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

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

      7. sub-neg N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. metadata-eval N/A

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

      12. accelerator-lowering-fma.f64 N/A

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

      13. *-commutative N/A

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

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

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

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

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

      16. metadata-eval N/A

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

      17. *-commutative N/A

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

      18. *-lowering-*.f64 91.4

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

   5. Simplified 91.4%

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

   if 3.15e12 < x

   1. Initial program 8.5%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. flip3-- N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

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

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

   4. Applied egg-rr 10.1%

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

   5. Taylor expanded in x around inf

      \[\leadsto \frac{\color{blue}{\frac{104109730557}{25000000000}}}{\frac{1}{x + -2}} \]
   6. Step-by-step derivation

   7. Simplified 95.9%

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

Alternative 9: 89.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -22500000:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \mathbf{elif}\;x \leq 3150000000000:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(z, 0.0212463641547976, y \cdot -0.0424927283095952\right), z \cdot -0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{4.16438922228}{\frac{1}{x + -2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -22500000.0)
   (* x (+ 4.16438922228 (/ -110.1139242984811 x)))
   (if (<= x 3150000000000.0)
     (fma
      x
      (fma z 0.0212463641547976 (* y -0.0424927283095952))
      (* z -0.0424927283095952))
     (/ 4.16438922228 (/ 1.0 (+ x -2.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -22500000.0) {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	} else if (x <= 3150000000000.0) {
		tmp = fma(x, fma(z, 0.0212463641547976, (y * -0.0424927283095952)), (z * -0.0424927283095952));
	} else {
		tmp = 4.16438922228 / (1.0 / (x + -2.0));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -22500000.0)
		tmp = Float64(x * Float64(4.16438922228 + Float64(-110.1139242984811 / x)));
	elseif (x <= 3150000000000.0)
		tmp = fma(x, fma(z, 0.0212463641547976, Float64(y * -0.0424927283095952)), Float64(z * -0.0424927283095952));
	else
		tmp = Float64(4.16438922228 / Float64(1.0 / Float64(x + -2.0)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -22500000.0], N[(x * N[(4.16438922228 + N[(-110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3150000000000.0], N[(x * N[(z * 0.0212463641547976 + N[(y * -0.0424927283095952), $MachinePrecision]), $MachinePrecision] + N[(z * -0.0424927283095952), $MachinePrecision]), $MachinePrecision], N[(4.16438922228 / N[(1.0 / N[(x + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.25e7

   1. Initial program 20.2%

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

   3. Taylor expanded in x around inf

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. neg-sub0 N/A

         \[\leadsto x \cdot \left(\color{blue}{\left(0 - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} + \frac{104109730557}{25000000000}\right) \]

      4. associate-+l- N/A

         \[\leadsto x \cdot \color{blue}{\left(0 - \left(\frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x} - \frac{104109730557}{25000000000}\right)\right)} \]

      5. neg-sub0 N/A

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

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

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

      7. neg-sub0 N/A

         \[\leadsto x \cdot \color{blue}{\left(0 - \left(\frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x} - \frac{104109730557}{25000000000}\right)\right)} \]

      8. associate-+l- N/A

         \[\leadsto x \cdot \color{blue}{\left(\left(0 - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right) + \frac{104109730557}{25000000000}\right)} \]

      9. neg-sub0 N/A

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

      10. +-commutative N/A

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

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

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

      12. associate-*r/ N/A

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

      13. metadata-eval N/A

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

      14. distribute-neg-frac N/A

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

      15. /-lowering-/.f64 N/A

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

      16. metadata-eval 88.7

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

   5. Simplified 88.7%

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

   if -2.25e7 < x < 3.15e12

   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

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

      1. +-commutative N/A

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

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

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

      3. distribute-rgt-in N/A

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

      4. associate--l+ N/A

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

      5. *-commutative N/A

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

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

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

      7. sub-neg N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. metadata-eval N/A

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

      12. accelerator-lowering-fma.f64 N/A

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

      13. *-commutative N/A

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

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

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

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

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

      16. metadata-eval N/A

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

      17. *-commutative N/A

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

      18. *-lowering-*.f64 91.4

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

   5. Simplified 91.4%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(z, \frac{500000000}{23533438303}, \color{blue}{\frac{-1000000000}{23533438303} \cdot y}\right), z \cdot \frac{-1000000000}{23533438303}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 91.0

         \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(z, 0.0212463641547976, \color{blue}{-0.0424927283095952 \cdot y}\right), z \cdot -0.0424927283095952\right) \]

   8. Simplified 91.0%

      \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(z, 0.0212463641547976, \color{blue}{-0.0424927283095952 \cdot y}\right), z \cdot -0.0424927283095952\right) \]

   if 3.15e12 < x

   1. Initial program 8.5%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. flip3-- N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

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

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

   4. Applied egg-rr 10.1%

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

   5. Taylor expanded in x around inf

      \[\leadsto \frac{\color{blue}{\frac{104109730557}{25000000000}}}{\frac{1}{x + -2}} \]
   6. Step-by-step derivation

   7. Simplified 95.9%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -22500000:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \mathbf{elif}\;x \leq 3150000000000:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(z, 0.0212463641547976, y \cdot -0.0424927283095952\right), z \cdot -0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{4.16438922228}{\frac{1}{x + -2}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -22500000:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \mathbf{elif}\;x \leq 3150000000000:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(z, 0.0212463641547976, y \cdot -0.0424927283095952\right), z \cdot -0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -22500000.0)
   (* x (+ 4.16438922228 (/ -110.1139242984811 x)))
   (if (<= x 3150000000000.0)
     (fma
      x
      (fma z 0.0212463641547976 (* y -0.0424927283095952))
      (* z -0.0424927283095952))
     (* x 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -22500000.0) {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	} else if (x <= 3150000000000.0) {
		tmp = fma(x, fma(z, 0.0212463641547976, (y * -0.0424927283095952)), (z * -0.0424927283095952));
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -22500000.0)
		tmp = Float64(x * Float64(4.16438922228 + Float64(-110.1139242984811 / x)));
	elseif (x <= 3150000000000.0)
		tmp = fma(x, fma(z, 0.0212463641547976, Float64(y * -0.0424927283095952)), Float64(z * -0.0424927283095952));
	else
		tmp = Float64(x * 4.16438922228);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -22500000.0], N[(x * N[(4.16438922228 + N[(-110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3150000000000.0], N[(x * N[(z * 0.0212463641547976 + N[(y * -0.0424927283095952), $MachinePrecision]), $MachinePrecision] + N[(z * -0.0424927283095952), $MachinePrecision]), $MachinePrecision], N[(x * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.25e7

   1. Initial program 20.2%

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

   3. Taylor expanded in x around inf

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. neg-sub0 N/A

         \[\leadsto x \cdot \left(\color{blue}{\left(0 - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} + \frac{104109730557}{25000000000}\right) \]

      4. associate-+l- N/A

         \[\leadsto x \cdot \color{blue}{\left(0 - \left(\frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x} - \frac{104109730557}{25000000000}\right)\right)} \]

      5. neg-sub0 N/A

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

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

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

      7. neg-sub0 N/A

         \[\leadsto x \cdot \color{blue}{\left(0 - \left(\frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x} - \frac{104109730557}{25000000000}\right)\right)} \]

      8. associate-+l- N/A

         \[\leadsto x \cdot \color{blue}{\left(\left(0 - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right) + \frac{104109730557}{25000000000}\right)} \]

      9. neg-sub0 N/A

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

      10. +-commutative N/A

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

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

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

      12. associate-*r/ N/A

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

      13. metadata-eval N/A

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

      14. distribute-neg-frac N/A

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

      15. /-lowering-/.f64 N/A

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

      16. metadata-eval 88.7

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

   5. Simplified 88.7%

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

   if -2.25e7 < x < 3.15e12

   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

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

      1. +-commutative N/A

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

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

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

      3. distribute-rgt-in N/A

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

      4. associate--l+ N/A

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

      5. *-commutative N/A

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

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

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

      7. sub-neg N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. metadata-eval N/A

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

      12. accelerator-lowering-fma.f64 N/A

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

      13. *-commutative N/A

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

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

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

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

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

      16. metadata-eval N/A

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

      17. *-commutative N/A

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

      18. *-lowering-*.f64 91.4

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

   5. Simplified 91.4%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(z, \frac{500000000}{23533438303}, \color{blue}{\frac{-1000000000}{23533438303} \cdot y}\right), z \cdot \frac{-1000000000}{23533438303}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 91.0

         \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(z, 0.0212463641547976, \color{blue}{-0.0424927283095952 \cdot y}\right), z \cdot -0.0424927283095952\right) \]

   8. Simplified 91.0%

      \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(z, 0.0212463641547976, \color{blue}{-0.0424927283095952 \cdot y}\right), z \cdot -0.0424927283095952\right) \]

   if 3.15e12 < x

   1. Initial program 8.5%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 95.9

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

   5. Simplified 95.9%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -22500000:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \mathbf{elif}\;x \leq 3150000000000:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(z, 0.0212463641547976, y \cdot -0.0424927283095952\right), z \cdot -0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 89.2% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -22500000:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\mathsf{fma}\left(x, y \cdot -0.0424927283095952, z \cdot -0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -22500000.0)
   (* x (+ 4.16438922228 (/ -110.1139242984811 x)))
   (if (<= x 2.0)
     (fma x (* y -0.0424927283095952) (* z -0.0424927283095952))
     (* x 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -22500000.0) {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	} else if (x <= 2.0) {
		tmp = fma(x, (y * -0.0424927283095952), (z * -0.0424927283095952));
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -22500000.0)
		tmp = Float64(x * Float64(4.16438922228 + Float64(-110.1139242984811 / x)));
	elseif (x <= 2.0)
		tmp = fma(x, Float64(y * -0.0424927283095952), Float64(z * -0.0424927283095952));
	else
		tmp = Float64(x * 4.16438922228);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -22500000.0], N[(x * N[(4.16438922228 + N[(-110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.0], N[(x * N[(y * -0.0424927283095952), $MachinePrecision] + N[(z * -0.0424927283095952), $MachinePrecision]), $MachinePrecision], N[(x * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.25e7

   1. Initial program 20.2%

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

   3. Taylor expanded in x around inf

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. neg-sub0 N/A

         \[\leadsto x \cdot \left(\color{blue}{\left(0 - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} + \frac{104109730557}{25000000000}\right) \]

      4. associate-+l- N/A

         \[\leadsto x \cdot \color{blue}{\left(0 - \left(\frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x} - \frac{104109730557}{25000000000}\right)\right)} \]

      5. neg-sub0 N/A

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

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

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

      7. neg-sub0 N/A

         \[\leadsto x \cdot \color{blue}{\left(0 - \left(\frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x} - \frac{104109730557}{25000000000}\right)\right)} \]

      8. associate-+l- N/A

         \[\leadsto x \cdot \color{blue}{\left(\left(0 - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right) + \frac{104109730557}{25000000000}\right)} \]

      9. neg-sub0 N/A

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

      10. +-commutative N/A

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

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

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

      12. associate-*r/ N/A

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

      13. metadata-eval N/A

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

      14. distribute-neg-frac N/A

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

      15. /-lowering-/.f64 N/A

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

      16. metadata-eval 88.7

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

   5. Simplified 88.7%

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

   if -2.25e7 < 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. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

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

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

      3. distribute-rgt-in N/A

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

      4. associate--l+ N/A

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

      5. *-commutative N/A

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

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

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

      7. sub-neg N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. metadata-eval N/A

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

      12. accelerator-lowering-fma.f64 N/A

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

      13. *-commutative N/A

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

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

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

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

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

      16. metadata-eval N/A

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

      17. *-commutative N/A

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

      18. *-lowering-*.f64 92.6

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

   5. Simplified 92.6%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{\frac{-1000000000}{23533438303} \cdot y}, z \cdot \frac{-1000000000}{23533438303}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 92.2

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{-0.0424927283095952 \cdot y}, z \cdot -0.0424927283095952\right) \]

   8. Simplified 92.2%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{-0.0424927283095952 \cdot y}, z \cdot -0.0424927283095952\right) \]

   if 2 < x

   1. Initial program 11.5%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 92.8

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

   5. Simplified 92.8%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -22500000:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\mathsf{fma}\left(x, y \cdot -0.0424927283095952, z \cdot -0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 89.2% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -22500000:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\mathsf{fma}\left(x, y \cdot -0.0424927283095952, z \cdot -0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -22500000.0)
   (* x 4.16438922228)
   (if (<= x 2.0)
     (fma x (* y -0.0424927283095952) (* z -0.0424927283095952))
     (* x 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -22500000.0) {
		tmp = x * 4.16438922228;
	} else if (x <= 2.0) {
		tmp = fma(x, (y * -0.0424927283095952), (z * -0.0424927283095952));
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -22500000.0)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 2.0)
		tmp = fma(x, Float64(y * -0.0424927283095952), Float64(z * -0.0424927283095952));
	else
		tmp = Float64(x * 4.16438922228);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -22500000.0], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 2.0], N[(x * N[(y * -0.0424927283095952), $MachinePrecision] + N[(z * -0.0424927283095952), $MachinePrecision]), $MachinePrecision], N[(x * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.25e7 or 2 < x

   1. Initial program 15.6%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 90.5

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

   5. Simplified 90.5%

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

   if -2.25e7 < 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. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

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

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

      3. distribute-rgt-in N/A

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

      4. associate--l+ N/A

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

      5. *-commutative N/A

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

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

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

      7. sub-neg N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. metadata-eval N/A

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

      12. accelerator-lowering-fma.f64 N/A

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

      13. *-commutative N/A

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

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

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

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

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

      16. metadata-eval N/A

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

      17. *-commutative N/A

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

      18. *-lowering-*.f64 92.6

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

   5. Simplified 92.6%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{\frac{-1000000000}{23533438303} \cdot y}, z \cdot \frac{-1000000000}{23533438303}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 92.2

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{-0.0424927283095952 \cdot y}, z \cdot -0.0424927283095952\right) \]

   8. Simplified 92.2%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -22500000:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\mathsf{fma}\left(x, y \cdot -0.0424927283095952, z \cdot -0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 76.8% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -22500000:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 3150000000000:\\ \;\;\;\;z \cdot \mathsf{fma}\left(x, 0.3041881842569256, -0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -22500000.0)
   (* x 4.16438922228)
   (if (<= x 3150000000000.0)
     (* z (fma x 0.3041881842569256 -0.0424927283095952))
     (* x 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -22500000.0) {
		tmp = x * 4.16438922228;
	} else if (x <= 3150000000000.0) {
		tmp = z * fma(x, 0.3041881842569256, -0.0424927283095952);
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -22500000.0)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 3150000000000.0)
		tmp = Float64(z * fma(x, 0.3041881842569256, -0.0424927283095952));
	else
		tmp = Float64(x * 4.16438922228);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -22500000.0], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 3150000000000.0], N[(z * N[(x * 0.3041881842569256 + -0.0424927283095952), $MachinePrecision]), $MachinePrecision], N[(x * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.25e7 or 3.15e12 < x

   1. Initial program 14.1%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 92.1

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

   5. Simplified 92.1%

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

   if -2.25e7 < x < 3.15e12

   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

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

      1. +-commutative N/A

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

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

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

      3. distribute-rgt-in N/A

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

      4. associate--l+ N/A

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

      5. *-commutative N/A

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

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

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

      7. sub-neg N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. metadata-eval N/A

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

      12. accelerator-lowering-fma.f64 N/A

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

      13. *-commutative N/A

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

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

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

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

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

      16. metadata-eval N/A

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

      17. *-commutative N/A

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

      18. *-lowering-*.f64 91.4

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

   5. Simplified 91.4%

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

   6. Taylor expanded in z around inf

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

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

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

      2. sub-neg N/A

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

      3. *-commutative N/A

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

      4. metadata-eval N/A

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

      5. accelerator-lowering-fma.f64 63.1

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

   8. Simplified 63.1%

      \[\leadsto \color{blue}{z \cdot \mathsf{fma}\left(x, 0.3041881842569256, -0.0424927283095952\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 76.7% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -22500000:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -22500000.0)
   (* x 4.16438922228)
   (if (<= x 2.0) (* z -0.0424927283095952) (* x 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -22500000.0) {
		tmp = x * 4.16438922228;
	} else if (x <= 2.0) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-22500000.0d0)) then
        tmp = x * 4.16438922228d0
    else if (x <= 2.0d0) then
        tmp = z * (-0.0424927283095952d0)
    else
        tmp = x * 4.16438922228d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -22500000.0) {
		tmp = x * 4.16438922228;
	} else if (x <= 2.0) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -22500000.0:
		tmp = x * 4.16438922228
	elif x <= 2.0:
		tmp = z * -0.0424927283095952
	else:
		tmp = x * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -22500000.0)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 2.0)
		tmp = Float64(z * -0.0424927283095952);
	else
		tmp = Float64(x * 4.16438922228);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -22500000.0)
		tmp = x * 4.16438922228;
	elseif (x <= 2.0)
		tmp = z * -0.0424927283095952;
	else
		tmp = x * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -22500000.0], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 2.0], N[(z * -0.0424927283095952), $MachinePrecision], N[(x * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.25e7 or 2 < x

   1. Initial program 15.6%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 90.5

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

   5. Simplified 90.5%

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

   if -2.25e7 < 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. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot \frac{-1000000000}{23533438303}} \]

      2. *-lowering-*.f64 63.5

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

   5. Simplified 63.5%

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

Alternative 15: 45.7% accurate, 13.2× speedup

Math

\[\begin{array}{l} \\ x \cdot 4.16438922228 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x 4.16438922228))

C

double code(double x, double y, double z) {
	return x * 4.16438922228;
}

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 * 4.16438922228d0
end function

Java

public static double code(double x, double y, double z) {
	return x * 4.16438922228;
}

Python

def code(x, y, z):
	return x * 4.16438922228

Julia

function code(x, y, z)
	return Float64(x * 4.16438922228)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * 4.16438922228;
end

Wolfram

code[x_, y_, z_] := N[(x * 4.16438922228), $MachinePrecision]

Derivation

1. Initial program 61.6%

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

3. Taylor expanded in x around inf

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

   1. *-commutative N/A

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

   2. *-lowering-*.f64 42.8

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

5. Simplified 42.8%

   \[\leadsto \color{blue}{x \cdot 4.16438922228} \]
6. Add Preprocessing

Developer Target 1: 98.7% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024195 
(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)))