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

Percentage Accurate: 57.9% → 98.6%

Time: 16.1s

Alternatives: 19

Speedup: 5.2×

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: 57.9% 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: 98.6% accurate, 0.0× speedup

Math

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

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))
      INFINITY)
   (/
    (+ x -2.0)
    (/
     (fma
      (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
      x
      47.066876606)
     (fma
      (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
      x
      z)))
   (/ (+ x -2.0) 0.24013125253755718)))

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)) <= ((double) INFINITY)) {
		tmp = (x + -2.0) / (fma(fma(fma((x + 43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606) / fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z));
	} else {
		tmp = (x + -2.0) / 0.24013125253755718;
	}
	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)) <= Inf)
		tmp = Float64(Float64(x + -2.0) / Float64(fma(fma(fma(Float64(x + 43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606) / fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z)));
	else
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	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], Infinity], N[(N[(x + -2.0), $MachinePrecision] / N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision] / N[(N[(N[(N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.4%

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

      1. associate-/l* 98.1%

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

      2. sub-neg 98.1%

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

      3. metadata-eval 98.1%

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

      4. fma-def 98.1%

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

      5. fma-def 98.2%

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

      6. fma-def 98.2%

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

      7. fma-def 98.2%

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

      8. fma-def 98.1%

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

      9. fma-def 98.1%

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

      10. fma-def 98.1%

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

   3. Simplified 98.1%

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

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

   1. Initial program 0.0%

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

      1. associate-/l* 0.0%

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

      2. sub-neg 0.0%

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

      3. metadata-eval 0.0%

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

      4. fma-def 0.0%

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

      5. fma-def 0.0%

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

      6. fma-def 0.0%

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

      7. fma-def 0.0%

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

      8. fma-def 0.0%

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

      9. fma-def 0.0%

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

      10. fma-def 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in x around inf 99.7%

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

4. Final simplification 98.8%

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

Alternative 2: 98.5% accurate, 0.0× speedup

Math

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

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))
      INFINITY)
   (*
    (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 -2.0) 0.24013125253755718)))

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)) <= ((double) INFINITY)) {
		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 + -2.0) / 0.24013125253755718;
	}
	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)) <= Inf)
		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(Float64(x + -2.0) / 0.24013125253755718);
	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], Infinity], 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[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.4%

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

      1. *-commutative 93.4%

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

      2. associate-*r/ 98.0%

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

      3. *-commutative 98.0%

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

      4. fma-def 98.0%

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

      5. *-commutative 98.0%

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

      6. fma-def 98.0%

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

      7. *-commutative 98.0%

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

      8. fma-def 98.0%

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

      9. fma-def 98.0%

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

   3. Simplified 98.0%

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

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

   1. Initial program 0.0%

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

      1. associate-/l* 0.0%

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

      2. sub-neg 0.0%

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

      3. metadata-eval 0.0%

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

      4. fma-def 0.0%

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

      5. fma-def 0.0%

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

      6. fma-def 0.0%

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

      7. fma-def 0.0%

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

      8. fma-def 0.0%

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

      9. fma-def 0.0%

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

      10. fma-def 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in x around inf 99.7%

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

4. Final simplification 98.7%

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

Alternative 3: 98.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right)}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}{x \cdot \left(x + -2\right)}}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{3655.1204654076414}{x} + \mathsf{fma}\left(x, 4.16438922228, -110.1139242984811\right)\right) + \frac{y - 130977.50649958357}{x \cdot x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (/
          (*
           (- 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))))
   (if (<= t_0 (- INFINITY))
     (/
      (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y)
      (/
       (fma
        x
        (fma x (fma x (+ x 43.3400022514) 263.505074721) 313.399215894)
        47.066876606)
       (* x (+ x -2.0))))
     (if (<= t_0 5e+304)
       t_0
       (+
        (+ (/ 3655.1204654076414 x) (fma x 4.16438922228 -110.1139242984811))
        (/ (- y 130977.50649958357) (* x x)))))))

C

double code(double x, double y, double z) {
	double t_0 = ((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);
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = fma(x, fma(x, fma(x, 4.16438922228, 78.6994924154), 137.519416416), y) / (fma(x, fma(x, fma(x, (x + 43.3400022514), 263.505074721), 313.399215894), 47.066876606) / (x * (x + -2.0)));
	} else if (t_0 <= 5e+304) {
		tmp = t_0;
	} else {
		tmp = ((3655.1204654076414 / x) + fma(x, 4.16438922228, -110.1139242984811)) + ((y - 130977.50649958357) / (x * x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = 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))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = Float64(fma(x, fma(x, fma(x, 4.16438922228, 78.6994924154), 137.519416416), y) / Float64(fma(x, fma(x, fma(x, Float64(x + 43.3400022514), 263.505074721), 313.399215894), 47.066876606) / Float64(x * Float64(x + -2.0))));
	elseif (t_0 <= 5e+304)
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(3655.1204654076414 / x) + fma(x, 4.16438922228, -110.1139242984811)) + Float64(Float64(y - 130977.50649958357) / Float64(x * x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = 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]}, If[LessEqual[t$95$0, (-Infinity)], N[(N[(x * N[(x * N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] + 137.519416416), $MachinePrecision] + y), $MachinePrecision] / N[(N[(x * N[(x * N[(x * N[(x + 43.3400022514), $MachinePrecision] + 263.505074721), $MachinePrecision] + 313.399215894), $MachinePrecision] + 47.066876606), $MachinePrecision] / N[(x * N[(x + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+304], t$95$0, N[(N[(N[(3655.1204654076414 / x), $MachinePrecision] + N[(x * 4.16438922228 + -110.1139242984811), $MachinePrecision]), $MachinePrecision] + N[(N[(y - 130977.50649958357), $MachinePrecision] / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 4.4%

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

      1. *-commutative 4.4%

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

      2. associate-*r/ 67.9%

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

      3. *-commutative 67.9%

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

      4. fma-def 67.9%

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

      5. *-commutative 67.9%

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

      6. fma-def 67.9%

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

      7. *-commutative 67.9%

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

      8. fma-def 67.9%

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

      9. fma-def 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in z around 0 4.4%

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

   6. Simplified 99.7%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 x 2) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000)) < 4.9999999999999997e304

   1. Initial program 99.6%

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

   if 4.9999999999999997e304 < (/.f64 (*.f64 (-.f64 x 2) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000))

   1. Initial program 0.2%

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

      1. *-commutative 0.2%

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

      2. associate-*r/ 3.7%

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

      3. *-commutative 3.7%

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

      4. fma-def 3.7%

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

      5. *-commutative 3.7%

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

      6. fma-def 3.7%

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

      7. *-commutative 3.7%

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

      8. fma-def 3.7%

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

      9. fma-def 3.7%

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

   3. Simplified 3.7%

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

   4. Taylor expanded in x around -inf 97.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} + \left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) - 110.1139242984811} \]
   5. Step-by-step derivation

      1. associate--l+ 97.2%

         \[\leadsto \color{blue}{-1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} + \left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - 110.1139242984811\right)} \]

      2. +-commutative 97.2%

         \[\leadsto \color{blue}{\left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - 110.1139242984811\right) + -1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}} \]

      3. mul-1-neg 97.2%

         \[\leadsto \left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - 110.1139242984811\right) + \color{blue}{\left(-\frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)} \]

      4. unsub-neg 97.2%

         \[\leadsto \color{blue}{\left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - 110.1139242984811\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}} \]

      5. +-commutative 97.2%

         \[\leadsto \left(\color{blue}{\left(3655.1204654076414 \cdot \frac{1}{x} + 4.16438922228 \cdot x\right)} - 110.1139242984811\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} \]

      6. *-commutative 97.2%

         \[\leadsto \left(\left(3655.1204654076414 \cdot \frac{1}{x} + \color{blue}{x \cdot 4.16438922228}\right) - 110.1139242984811\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} \]

      7. associate--l+ 97.2%

         \[\leadsto \color{blue}{\left(3655.1204654076414 \cdot \frac{1}{x} + \left(x \cdot 4.16438922228 - 110.1139242984811\right)\right)} - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} \]

      8. associate-*r/ 97.2%

         \[\leadsto \left(\color{blue}{\frac{3655.1204654076414 \cdot 1}{x}} + \left(x \cdot 4.16438922228 - 110.1139242984811\right)\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} \]

      9. metadata-eval 97.2%

         \[\leadsto \left(\frac{\color{blue}{3655.1204654076414}}{x} + \left(x \cdot 4.16438922228 - 110.1139242984811\right)\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} \]

      10. fma-neg 97.2%

          \[\leadsto \left(\frac{3655.1204654076414}{x} + \color{blue}{\mathsf{fma}\left(x, 4.16438922228, -110.1139242984811\right)}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} \]

      11. metadata-eval 97.2%

          \[\leadsto \left(\frac{3655.1204654076414}{x} + \mathsf{fma}\left(x, 4.16438922228, \color{blue}{-110.1139242984811}\right)\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} \]

      12. mul-1-neg 97.2%

          \[\leadsto \left(\frac{3655.1204654076414}{x} + \mathsf{fma}\left(x, 4.16438922228, -110.1139242984811\right)\right) - \frac{130977.50649958357 + \color{blue}{\left(-y\right)}}{{x}^{2}} \]

      13. unsub-neg 97.2%

          \[\leadsto \left(\frac{3655.1204654076414}{x} + \mathsf{fma}\left(x, 4.16438922228, -110.1139242984811\right)\right) - \frac{\color{blue}{130977.50649958357 - y}}{{x}^{2}} \]

      14. unpow2 97.2%

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

   6. Simplified 97.2%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq -\infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right)}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}{x \cdot \left(x + -2\right)}}\\ \mathbf{elif}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 5 \cdot 10^{+304}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{3655.1204654076414}{x} + \mathsf{fma}\left(x, 4.16438922228, -110.1139242984811\right)\right) + \frac{y - 130977.50649958357}{x \cdot x}\\ \end{array} \]

Alternative 4: 98.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{if}\;t_0 \leq -\infty \lor \neg \left(t_0 \leq 5 \cdot 10^{+304}\right):\\ \;\;\;\;\left(\frac{3655.1204654076414}{x} + \mathsf{fma}\left(x, 4.16438922228, -110.1139242984811\right)\right) + \frac{y - 130977.50649958357}{x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (/
          (*
           (- 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))))
   (if (or (<= t_0 (- INFINITY)) (not (<= t_0 5e+304)))
     (+
      (+ (/ 3655.1204654076414 x) (fma x 4.16438922228 -110.1139242984811))
      (/ (- y 130977.50649958357) (* x x)))
     t_0)))

C

double code(double x, double y, double z) {
	double t_0 = ((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);
	double tmp;
	if ((t_0 <= -((double) INFINITY)) || !(t_0 <= 5e+304)) {
		tmp = ((3655.1204654076414 / x) + fma(x, 4.16438922228, -110.1139242984811)) + ((y - 130977.50649958357) / (x * x));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = 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))
	tmp = 0.0
	if ((t_0 <= Float64(-Inf)) || !(t_0 <= 5e+304))
		tmp = Float64(Float64(Float64(3655.1204654076414 / x) + fma(x, 4.16438922228, -110.1139242984811)) + Float64(Float64(y - 130977.50649958357) / Float64(x * x)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = 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]}, If[Or[LessEqual[t$95$0, (-Infinity)], N[Not[LessEqual[t$95$0, 5e+304]], $MachinePrecision]], N[(N[(N[(3655.1204654076414 / x), $MachinePrecision] + N[(x * 4.16438922228 + -110.1139242984811), $MachinePrecision]), $MachinePrecision] + N[(N[(y - 130977.50649958357), $MachinePrecision] / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x 2) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000)) < -inf.0 or 4.9999999999999997e304 < (/.f64 (*.f64 (-.f64 x 2) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000))

   1. Initial program 0.4%

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

      1. *-commutative 0.4%

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

      2. associate-*r/ 7.1%

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

      3. *-commutative 7.1%

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

      4. fma-def 7.1%

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

      5. *-commutative 7.1%

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

      6. fma-def 7.1%

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

      7. *-commutative 7.1%

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

      8. fma-def 7.1%

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

      9. fma-def 7.1%

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

   3. Simplified 7.1%

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

   4. Taylor expanded in x around -inf 97.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} + \left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) - 110.1139242984811} \]
   5. Step-by-step derivation

      1. associate--l+ 97.3%

         \[\leadsto \color{blue}{-1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} + \left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - 110.1139242984811\right)} \]

      2. +-commutative 97.3%

         \[\leadsto \color{blue}{\left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - 110.1139242984811\right) + -1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}} \]

      3. mul-1-neg 97.3%

         \[\leadsto \left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - 110.1139242984811\right) + \color{blue}{\left(-\frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)} \]

      4. unsub-neg 97.3%

         \[\leadsto \color{blue}{\left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - 110.1139242984811\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}} \]

      5. +-commutative 97.3%

         \[\leadsto \left(\color{blue}{\left(3655.1204654076414 \cdot \frac{1}{x} + 4.16438922228 \cdot x\right)} - 110.1139242984811\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} \]

      6. *-commutative 97.3%

         \[\leadsto \left(\left(3655.1204654076414 \cdot \frac{1}{x} + \color{blue}{x \cdot 4.16438922228}\right) - 110.1139242984811\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} \]

      7. associate--l+ 97.3%

         \[\leadsto \color{blue}{\left(3655.1204654076414 \cdot \frac{1}{x} + \left(x \cdot 4.16438922228 - 110.1139242984811\right)\right)} - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} \]

      8. associate-*r/ 97.3%

         \[\leadsto \left(\color{blue}{\frac{3655.1204654076414 \cdot 1}{x}} + \left(x \cdot 4.16438922228 - 110.1139242984811\right)\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} \]

      9. metadata-eval 97.3%

         \[\leadsto \left(\frac{\color{blue}{3655.1204654076414}}{x} + \left(x \cdot 4.16438922228 - 110.1139242984811\right)\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} \]

      10. fma-neg 97.3%

          \[\leadsto \left(\frac{3655.1204654076414}{x} + \color{blue}{\mathsf{fma}\left(x, 4.16438922228, -110.1139242984811\right)}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} \]

      11. metadata-eval 97.3%

          \[\leadsto \left(\frac{3655.1204654076414}{x} + \mathsf{fma}\left(x, 4.16438922228, \color{blue}{-110.1139242984811}\right)\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} \]

      12. mul-1-neg 97.3%

          \[\leadsto \left(\frac{3655.1204654076414}{x} + \mathsf{fma}\left(x, 4.16438922228, -110.1139242984811\right)\right) - \frac{130977.50649958357 + \color{blue}{\left(-y\right)}}{{x}^{2}} \]

      13. unsub-neg 97.3%

          \[\leadsto \left(\frac{3655.1204654076414}{x} + \mathsf{fma}\left(x, 4.16438922228, -110.1139242984811\right)\right) - \frac{\color{blue}{130977.50649958357 - y}}{{x}^{2}} \]

      14. unpow2 97.3%

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

   6. Simplified 97.3%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 x 2) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000)) < 4.9999999999999997e304

   1. Initial program 99.6%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq -\infty \lor \neg \left(\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 5 \cdot 10^{+304}\right):\\ \;\;\;\;\left(\frac{3655.1204654076414}{x} + \mathsf{fma}\left(x, 4.16438922228, -110.1139242984811\right)\right) + \frac{y - 130977.50649958357}{x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \end{array} \]

Alternative 5: 96.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{if}\;t_0 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (/
          (*
           (- 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))))
   (if (<= t_0 5e+304) t_0 (/ (+ x -2.0) 0.24013125253755718))))

C

double code(double x, double y, double z) {
	double t_0 = ((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);
	double tmp;
	if (t_0 <= 5e+304) {
		tmp = t_0;
	} else {
		tmp = (x + -2.0) / 0.24013125253755718;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((x - 2.0d0) * ((x * ((x * ((x * ((x * 4.16438922228d0) + 78.6994924154d0)) + 137.519416416d0)) + y)) + z)) / ((x * ((x * ((x * (x + 43.3400022514d0)) + 263.505074721d0)) + 313.399215894d0)) + 47.066876606d0)
    if (t_0 <= 5d+304) then
        tmp = t_0
    else
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((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);
	double tmp;
	if (t_0 <= 5e+304) {
		tmp = t_0;
	} else {
		tmp = (x + -2.0) / 0.24013125253755718;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((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)
	tmp = 0
	if t_0 <= 5e+304:
		tmp = t_0
	else:
		tmp = (x + -2.0) / 0.24013125253755718
	return tmp

Julia

function code(x, y, z)
	t_0 = 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))
	tmp = 0.0
	if (t_0 <= 5e+304)
		tmp = t_0;
	else
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((x - 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);
	tmp = 0.0;
	if (t_0 <= 5e+304)
		tmp = t_0;
	else
		tmp = (x + -2.0) / 0.24013125253755718;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(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]}, If[LessEqual[t$95$0, 5e+304], t$95$0, N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x 2) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000)) < 4.9999999999999997e304

   1. Initial program 95.8%

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

   if 4.9999999999999997e304 < (/.f64 (*.f64 (-.f64 x 2) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000))

   1. Initial program 0.2%

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

      1. associate-/l* 3.7%

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

      2. sub-neg 3.7%

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

      3. metadata-eval 3.7%

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

      4. fma-def 3.7%

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

      5. fma-def 3.7%

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

      6. fma-def 3.7%

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

      7. fma-def 3.7%

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

      8. fma-def 3.7%

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

      9. fma-def 3.7%

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

      10. fma-def 3.7%

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

   3. Simplified 3.7%

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

   4. Taylor expanded in x around inf 96.9%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 5 \cdot 10^{+304}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]

Alternative 6: 95.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{47.066876606 + x \cdot \left(313.399215894 + \left(x + 43.3400022514\right) \cdot \left(x \cdot x\right)\right)}\\ t_1 := \frac{x + -2}{0.24013125253755718}\\ \mathbf{if}\;x \leq -1 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{y}{x \cdot x}\\ \mathbf{elif}\;x \leq -900000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 3900000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{+49}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (/
          (*
           (- x 2.0)
           (+
            (*
             x
             (+
              (*
               x
               (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
              y))
            z))
          (+
           47.066876606
           (* x (+ 313.399215894 (* (+ x 43.3400022514) (* x x)))))))
        (t_1 (/ (+ x -2.0) 0.24013125253755718)))
   (if (<= x -1e+65)
     t_1
     (if (<= x -5.5e+24)
       (/ y (* x x))
       (if (<= x -900000.0)
         t_0
         (if (<= x 3900000.0)
           (/
            (* (- x 2.0) (+ z (* x (+ y (* x 137.519416416)))))
            (+
             (*
              x
              (+
               (* x (+ (* x (+ x 43.3400022514)) 263.505074721))
               313.399215894))
             47.066876606))
           (if (<= x 1.26e+49) t_0 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = ((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / (47.066876606 + (x * (313.399215894 + ((x + 43.3400022514) * (x * x)))));
	double t_1 = (x + -2.0) / 0.24013125253755718;
	double tmp;
	if (x <= -1e+65) {
		tmp = t_1;
	} else if (x <= -5.5e+24) {
		tmp = y / (x * x);
	} else if (x <= -900000.0) {
		tmp = t_0;
	} else if (x <= 3900000.0) {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	} else if (x <= 1.26e+49) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ((x - 2.0d0) * ((x * ((x * ((x * ((x * 4.16438922228d0) + 78.6994924154d0)) + 137.519416416d0)) + y)) + z)) / (47.066876606d0 + (x * (313.399215894d0 + ((x + 43.3400022514d0) * (x * x)))))
    t_1 = (x + (-2.0d0)) / 0.24013125253755718d0
    if (x <= (-1d+65)) then
        tmp = t_1
    else if (x <= (-5.5d+24)) then
        tmp = y / (x * x)
    else if (x <= (-900000.0d0)) then
        tmp = t_0
    else if (x <= 3900000.0d0) then
        tmp = ((x - 2.0d0) * (z + (x * (y + (x * 137.519416416d0))))) / ((x * ((x * ((x * (x + 43.3400022514d0)) + 263.505074721d0)) + 313.399215894d0)) + 47.066876606d0)
    else if (x <= 1.26d+49) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / (47.066876606 + (x * (313.399215894 + ((x + 43.3400022514) * (x * x)))));
	double t_1 = (x + -2.0) / 0.24013125253755718;
	double tmp;
	if (x <= -1e+65) {
		tmp = t_1;
	} else if (x <= -5.5e+24) {
		tmp = y / (x * x);
	} else if (x <= -900000.0) {
		tmp = t_0;
	} else if (x <= 3900000.0) {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	} else if (x <= 1.26e+49) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / (47.066876606 + (x * (313.399215894 + ((x + 43.3400022514) * (x * x)))))
	t_1 = (x + -2.0) / 0.24013125253755718
	tmp = 0
	if x <= -1e+65:
		tmp = t_1
	elif x <= -5.5e+24:
		tmp = y / (x * x)
	elif x <= -900000.0:
		tmp = t_0
	elif x <= 3900000.0:
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)
	elif x <= 1.26e+49:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = 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(47.066876606 + Float64(x * Float64(313.399215894 + Float64(Float64(x + 43.3400022514) * Float64(x * x))))))
	t_1 = Float64(Float64(x + -2.0) / 0.24013125253755718)
	tmp = 0.0
	if (x <= -1e+65)
		tmp = t_1;
	elseif (x <= -5.5e+24)
		tmp = Float64(y / Float64(x * x));
	elseif (x <= -900000.0)
		tmp = t_0;
	elseif (x <= 3900000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(z + Float64(x * Float64(y + Float64(x * 137.519416416))))) / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606));
	elseif (x <= 1.26e+49)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / (47.066876606 + (x * (313.399215894 + ((x + 43.3400022514) * (x * x)))));
	t_1 = (x + -2.0) / 0.24013125253755718;
	tmp = 0.0;
	if (x <= -1e+65)
		tmp = t_1;
	elseif (x <= -5.5e+24)
		tmp = y / (x * x);
	elseif (x <= -900000.0)
		tmp = t_0;
	elseif (x <= 3900000.0)
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	elseif (x <= 1.26e+49)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = 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[(47.066876606 + N[(x * N[(313.399215894 + N[(N[(x + 43.3400022514), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]}, If[LessEqual[x, -1e+65], t$95$1, If[LessEqual[x, -5.5e+24], N[(y / N[(x * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -900000.0], t$95$0, If[LessEqual[x, 3900000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(z + N[(x * N[(y + N[(x * 137.519416416), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.26e+49], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.9999999999999999e64 or 1.2599999999999999e49 < x

   1. Initial program 1.1%

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

      1. associate-/l* 5.5%

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

      2. sub-neg 5.5%

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

      3. metadata-eval 5.5%

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

      4. fma-def 5.5%

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

      5. fma-def 5.5%

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

      6. fma-def 5.5%

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

      7. fma-def 5.5%

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

      8. fma-def 5.5%

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

      9. fma-def 5.5%

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

      10. fma-def 5.5%

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

   3. Simplified 5.5%

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

   4. Taylor expanded in x around inf 98.7%

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

   if -9.9999999999999999e64 < x < -5.5000000000000002e24

   1. Initial program 42.0%

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

   2. Taylor expanded in y around inf 42.0%

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

   3. Taylor expanded in x around inf 99.4%

      \[\leadsto \color{blue}{\frac{y}{{x}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 99.4%

         \[\leadsto \frac{y}{\color{blue}{x \cdot x}} \]

   5. Simplified 99.4%

      \[\leadsto \color{blue}{\frac{y}{x \cdot x}} \]

   if -5.5000000000000002e24 < x < -9e5 or 3.9e6 < x < 1.2599999999999999e49

   1. Initial program 85.9%

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

   2. Taylor expanded in x around inf 84.0%

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

      1. +-commutative 84.0%

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\color{blue}{\left({x}^{3} + 43.3400022514 \cdot {x}^{2}\right)} + 313.399215894\right) \cdot x + 47.066876606} \]

      2. cube-mult 83.9%

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

      3. unpow2 83.9%

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

      4. distribute-rgt-out 84.0%

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

      5. unpow2 84.0%

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

   4. Simplified 84.0%

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

   if -9e5 < x < 3.9e6

   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. Taylor expanded in x around 0 99.7%

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

      1. *-commutative 99.7%

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

   4. Simplified 99.7%

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\color{blue}{x \cdot 137.519416416} + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
3. Recombined 4 regimes into one program.

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+65}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{y}{x \cdot x}\\ \mathbf{elif}\;x \leq -900000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{47.066876606 + x \cdot \left(313.399215894 + \left(x + 43.3400022514\right) \cdot \left(x \cdot x\right)\right)}\\ \mathbf{elif}\;x \leq 3900000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{+49}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{47.066876606 + x \cdot \left(313.399215894 + \left(x + 43.3400022514\right) \cdot \left(x \cdot x\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]

Alternative 7: 92.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + -2}{0.24013125253755718}\\ \mathbf{if}\;x \leq -1 \cdot 10^{+65}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{+24}:\\ \;\;\;\;\frac{y}{x \cdot x}\\ \mathbf{elif}\;x \leq -1050000:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} - \frac{55.572073733743466}{x \cdot x}\right)}\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+47}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x -2.0) 0.24013125253755718)))
   (if (<= x -1e+65)
     t_0
     (if (<= x -4.9e+24)
       (/ y (* x x))
       (if (<= x -1050000.0)
         (/
          (+ x -2.0)
          (+
           0.24013125253755718
           (- (/ 5.86923874282773 x) (/ 55.572073733743466 (* x x)))))
         (if (<= x 8.2e+47)
           (/
            (* (- x 2.0) (+ z (* x (+ y (* x 137.519416416)))))
            (+
             (*
              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 + -2.0) / 0.24013125253755718;
	double tmp;
	if (x <= -1e+65) {
		tmp = t_0;
	} else if (x <= -4.9e+24) {
		tmp = y / (x * x);
	} else if (x <= -1050000.0) {
		tmp = (x + -2.0) / (0.24013125253755718 + ((5.86923874282773 / x) - (55.572073733743466 / (x * x))));
	} else if (x <= 8.2e+47) {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 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 = (x + (-2.0d0)) / 0.24013125253755718d0
    if (x <= (-1d+65)) then
        tmp = t_0
    else if (x <= (-4.9d+24)) then
        tmp = y / (x * x)
    else if (x <= (-1050000.0d0)) then
        tmp = (x + (-2.0d0)) / (0.24013125253755718d0 + ((5.86923874282773d0 / x) - (55.572073733743466d0 / (x * x))))
    else if (x <= 8.2d+47) then
        tmp = ((x - 2.0d0) * (z + (x * (y + (x * 137.519416416d0))))) / ((x * ((x * ((x * (x + 43.3400022514d0)) + 263.505074721d0)) + 313.399215894d0)) + 47.066876606d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + -2.0) / 0.24013125253755718;
	double tmp;
	if (x <= -1e+65) {
		tmp = t_0;
	} else if (x <= -4.9e+24) {
		tmp = y / (x * x);
	} else if (x <= -1050000.0) {
		tmp = (x + -2.0) / (0.24013125253755718 + ((5.86923874282773 / x) - (55.572073733743466 / (x * x))));
	} else if (x <= 8.2e+47) {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + -2.0) / 0.24013125253755718
	tmp = 0
	if x <= -1e+65:
		tmp = t_0
	elif x <= -4.9e+24:
		tmp = y / (x * x)
	elif x <= -1050000.0:
		tmp = (x + -2.0) / (0.24013125253755718 + ((5.86923874282773 / x) - (55.572073733743466 / (x * x))))
	elif x <= 8.2e+47:
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / ((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(Float64(x + -2.0) / 0.24013125253755718)
	tmp = 0.0
	if (x <= -1e+65)
		tmp = t_0;
	elseif (x <= -4.9e+24)
		tmp = Float64(y / Float64(x * x));
	elseif (x <= -1050000.0)
		tmp = Float64(Float64(x + -2.0) / Float64(0.24013125253755718 + Float64(Float64(5.86923874282773 / x) - Float64(55.572073733743466 / Float64(x * x)))));
	elseif (x <= 8.2e+47)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(z + Float64(x * Float64(y + Float64(x * 137.519416416))))) / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + -2.0) / 0.24013125253755718;
	tmp = 0.0;
	if (x <= -1e+65)
		tmp = t_0;
	elseif (x <= -4.9e+24)
		tmp = y / (x * x);
	elseif (x <= -1050000.0)
		tmp = (x + -2.0) / (0.24013125253755718 + ((5.86923874282773 / x) - (55.572073733743466 / (x * x))));
	elseif (x <= 8.2e+47)
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]}, If[LessEqual[x, -1e+65], t$95$0, If[LessEqual[x, -4.9e+24], N[(y / N[(x * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1050000.0], N[(N[(x + -2.0), $MachinePrecision] / N[(0.24013125253755718 + N[(N[(5.86923874282773 / x), $MachinePrecision] - N[(55.572073733743466 / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.2e+47], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(z + N[(x * N[(y + N[(x * 137.519416416), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.9999999999999999e64 or 8.2000000000000002e47 < x

   1. Initial program 1.1%

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

      1. associate-/l* 5.5%

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

      2. sub-neg 5.5%

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

      3. metadata-eval 5.5%

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

      4. fma-def 5.5%

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

      5. fma-def 5.5%

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

      6. fma-def 5.5%

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

      7. fma-def 5.5%

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

      8. fma-def 5.5%

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

      9. fma-def 5.5%

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

      10. fma-def 5.5%

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

   3. Simplified 5.5%

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

   4. Taylor expanded in x around inf 98.7%

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

   if -9.9999999999999999e64 < x < -4.90000000000000029e24

   1. Initial program 42.0%

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

   2. Taylor expanded in y around inf 42.0%

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

   3. Taylor expanded in x around inf 99.4%

      \[\leadsto \color{blue}{\frac{y}{{x}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 99.4%

         \[\leadsto \frac{y}{\color{blue}{x \cdot x}} \]

   5. Simplified 99.4%

      \[\leadsto \color{blue}{\frac{y}{x \cdot x}} \]

   if -4.90000000000000029e24 < x < -1.05e6

   1. Initial program 99.6%

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

      1. associate-/l* 99.2%

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

      2. sub-neg 99.2%

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

      3. metadata-eval 99.2%

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

      4. fma-def 99.2%

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

      5. fma-def 99.6%

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

      6. fma-def 99.6%

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

      7. fma-def 99.6%

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

      8. fma-def 99.6%

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

      9. fma-def 99.6%

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

      10. fma-def 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around inf 74.2%

      \[\leadsto \frac{x + -2}{\color{blue}{\left(0.24013125253755718 + 5.86923874282773 \cdot \frac{1}{x}\right) - 55.572073733743466 \cdot \frac{1}{{x}^{2}}}} \]
   5. Step-by-step derivation

      1. associate--l+ 74.2%

         \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718 + \left(5.86923874282773 \cdot \frac{1}{x} - 55.572073733743466 \cdot \frac{1}{{x}^{2}}\right)}} \]

      2. associate-*r/ 74.2%

         \[\leadsto \frac{x + -2}{0.24013125253755718 + \left(\color{blue}{\frac{5.86923874282773 \cdot 1}{x}} - 55.572073733743466 \cdot \frac{1}{{x}^{2}}\right)} \]

      3. metadata-eval 74.2%

         \[\leadsto \frac{x + -2}{0.24013125253755718 + \left(\frac{\color{blue}{5.86923874282773}}{x} - 55.572073733743466 \cdot \frac{1}{{x}^{2}}\right)} \]

      4. associate-*r/ 74.2%

         \[\leadsto \frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} - \color{blue}{\frac{55.572073733743466 \cdot 1}{{x}^{2}}}\right)} \]

      5. metadata-eval 74.2%

         \[\leadsto \frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} - \frac{\color{blue}{55.572073733743466}}{{x}^{2}}\right)} \]

      6. unpow2 74.2%

         \[\leadsto \frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} - \frac{55.572073733743466}{\color{blue}{x \cdot x}}\right)} \]

   6. Simplified 74.2%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} - \frac{55.572073733743466}{x \cdot x}\right)}} \]

   if -1.05e6 < x < 8.2000000000000002e47

   1. Initial program 98.3%

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

   2. Taylor expanded in x around 0 96.8%

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

      1. *-commutative 96.8%

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

   4. Simplified 96.8%

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\color{blue}{x \cdot 137.519416416} + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
3. Recombined 4 regimes into one program.

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+65}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{+24}:\\ \;\;\;\;\frac{y}{x \cdot x}\\ \mathbf{elif}\;x \leq -1050000:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} - \frac{55.572073733743466}{x \cdot x}\right)}\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+47}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]

Alternative 8: 89.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+65}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{+24}:\\ \;\;\;\;\frac{y}{x \cdot x}\\ \mathbf{elif}\;x \leq -240 \lor \neg \left(x \leq 5000\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} - \frac{55.572073733743466}{x \cdot x}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.0212463641547976 \cdot \left(z + y \cdot -2\right) - z \cdot -0.28294182010212804\right) + z \cdot -0.0424927283095952\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1e+65)
   (/ (+ x -2.0) 0.24013125253755718)
   (if (<= x -4.4e+24)
     (/ y (* x x))
     (if (or (<= x -240.0) (not (<= x 5000.0)))
       (/
        (+ x -2.0)
        (+
         0.24013125253755718
         (- (/ 5.86923874282773 x) (/ 55.572073733743466 (* x x)))))
       (+
        (*
         x
         (-
          (* 0.0212463641547976 (+ z (* y -2.0)))
          (* z -0.28294182010212804)))
        (* z -0.0424927283095952))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1e+65) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -4.4e+24) {
		tmp = y / (x * x);
	} else if ((x <= -240.0) || !(x <= 5000.0)) {
		tmp = (x + -2.0) / (0.24013125253755718 + ((5.86923874282773 / x) - (55.572073733743466 / (x * x))));
	} else {
		tmp = (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804))) + (z * -0.0424927283095952);
	}
	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 <= (-1d+65)) then
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    else if (x <= (-4.4d+24)) then
        tmp = y / (x * x)
    else if ((x <= (-240.0d0)) .or. (.not. (x <= 5000.0d0))) then
        tmp = (x + (-2.0d0)) / (0.24013125253755718d0 + ((5.86923874282773d0 / x) - (55.572073733743466d0 / (x * x))))
    else
        tmp = (x * ((0.0212463641547976d0 * (z + (y * (-2.0d0)))) - (z * (-0.28294182010212804d0)))) + (z * (-0.0424927283095952d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1e+65) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -4.4e+24) {
		tmp = y / (x * x);
	} else if ((x <= -240.0) || !(x <= 5000.0)) {
		tmp = (x + -2.0) / (0.24013125253755718 + ((5.86923874282773 / x) - (55.572073733743466 / (x * x))));
	} else {
		tmp = (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804))) + (z * -0.0424927283095952);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1e+65:
		tmp = (x + -2.0) / 0.24013125253755718
	elif x <= -4.4e+24:
		tmp = y / (x * x)
	elif (x <= -240.0) or not (x <= 5000.0):
		tmp = (x + -2.0) / (0.24013125253755718 + ((5.86923874282773 / x) - (55.572073733743466 / (x * x))))
	else:
		tmp = (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804))) + (z * -0.0424927283095952)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1e+65)
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	elseif (x <= -4.4e+24)
		tmp = Float64(y / Float64(x * x));
	elseif ((x <= -240.0) || !(x <= 5000.0))
		tmp = Float64(Float64(x + -2.0) / Float64(0.24013125253755718 + Float64(Float64(5.86923874282773 / x) - Float64(55.572073733743466 / Float64(x * x)))));
	else
		tmp = Float64(Float64(x * Float64(Float64(0.0212463641547976 * Float64(z + Float64(y * -2.0))) - Float64(z * -0.28294182010212804))) + Float64(z * -0.0424927283095952));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1e+65)
		tmp = (x + -2.0) / 0.24013125253755718;
	elseif (x <= -4.4e+24)
		tmp = y / (x * x);
	elseif ((x <= -240.0) || ~((x <= 5000.0)))
		tmp = (x + -2.0) / (0.24013125253755718 + ((5.86923874282773 / x) - (55.572073733743466 / (x * x))));
	else
		tmp = (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804))) + (z * -0.0424927283095952);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1e+65], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision], If[LessEqual[x, -4.4e+24], N[(y / N[(x * x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -240.0], N[Not[LessEqual[x, 5000.0]], $MachinePrecision]], N[(N[(x + -2.0), $MachinePrecision] / N[(0.24013125253755718 + N[(N[(5.86923874282773 / x), $MachinePrecision] - N[(55.572073733743466 / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(0.0212463641547976 * N[(z + N[(y * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * -0.28294182010212804), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * -0.0424927283095952), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.9999999999999999e64

   1. Initial program 0.3%

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

      1. associate-/l* 7.8%

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

      2. sub-neg 7.8%

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

      3. metadata-eval 7.8%

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

      4. fma-def 7.8%

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

      5. fma-def 7.8%

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

      6. fma-def 7.8%

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

      7. fma-def 7.8%

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

      8. fma-def 7.8%

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

      9. fma-def 7.8%

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

      10. fma-def 7.8%

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

   3. Simplified 7.8%

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

   4. Taylor expanded in x around inf 97.6%

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

   if -9.9999999999999999e64 < x < -4.40000000000000003e24

   1. Initial program 42.0%

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

   2. Taylor expanded in y around inf 42.0%

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

   3. Taylor expanded in x around inf 99.4%

      \[\leadsto \color{blue}{\frac{y}{{x}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 99.4%

         \[\leadsto \frac{y}{\color{blue}{x \cdot x}} \]

   5. Simplified 99.4%

      \[\leadsto \color{blue}{\frac{y}{x \cdot x}} \]

   if -4.40000000000000003e24 < x < -240 or 5e3 < x

   1. Initial program 18.1%

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

      1. associate-/l* 20.7%

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

      2. sub-neg 20.7%

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

      3. metadata-eval 20.7%

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

      4. fma-def 20.7%

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

      5. fma-def 20.7%

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

      6. fma-def 20.7%

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

      7. fma-def 20.7%

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

      8. fma-def 20.7%

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

      9. fma-def 20.7%

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

      10. fma-def 20.7%

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

   3. Simplified 20.7%

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

   4. Taylor expanded in x around inf 87.7%

      \[\leadsto \frac{x + -2}{\color{blue}{\left(0.24013125253755718 + 5.86923874282773 \cdot \frac{1}{x}\right) - 55.572073733743466 \cdot \frac{1}{{x}^{2}}}} \]
   5. Step-by-step derivation

      1. associate--l+ 87.7%

         \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718 + \left(5.86923874282773 \cdot \frac{1}{x} - 55.572073733743466 \cdot \frac{1}{{x}^{2}}\right)}} \]

      2. associate-*r/ 87.7%

         \[\leadsto \frac{x + -2}{0.24013125253755718 + \left(\color{blue}{\frac{5.86923874282773 \cdot 1}{x}} - 55.572073733743466 \cdot \frac{1}{{x}^{2}}\right)} \]

      3. metadata-eval 87.7%

         \[\leadsto \frac{x + -2}{0.24013125253755718 + \left(\frac{\color{blue}{5.86923874282773}}{x} - 55.572073733743466 \cdot \frac{1}{{x}^{2}}\right)} \]

      4. associate-*r/ 87.7%

         \[\leadsto \frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} - \color{blue}{\frac{55.572073733743466 \cdot 1}{{x}^{2}}}\right)} \]

      5. metadata-eval 87.7%

         \[\leadsto \frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} - \frac{\color{blue}{55.572073733743466}}{{x}^{2}}\right)} \]

      6. unpow2 87.7%

         \[\leadsto \frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} - \frac{55.572073733743466}{\color{blue}{x \cdot x}}\right)} \]

   6. Simplified 87.7%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} - \frac{55.572073733743466}{x \cdot x}\right)}} \]

   if -240 < x < 5e3

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*r/ 99.3%

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

      3. *-commutative 99.3%

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

      4. fma-def 99.3%

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

      5. *-commutative 99.3%

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

      6. fma-def 99.3%

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

      7. *-commutative 99.3%

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

      8. fma-def 99.3%

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

      9. fma-def 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 91.7%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+65}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{+24}:\\ \;\;\;\;\frac{y}{x \cdot x}\\ \mathbf{elif}\;x \leq -240 \lor \neg \left(x \leq 5000\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} - \frac{55.572073733743466}{x \cdot x}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.0212463641547976 \cdot \left(z + y \cdot -2\right) - z \cdot -0.28294182010212804\right) + z \cdot -0.0424927283095952\\ \end{array} \]

Alternative 9: 76.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+65}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{y}{x \cdot x}\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-8} \lor \neg \left(x \leq 11200\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} - \frac{55.572073733743466}{x \cdot x}\right)}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1e+65)
   (/ (+ x -2.0) 0.24013125253755718)
   (if (<= x -3.5e+24)
     (/ y (* x x))
     (if (or (<= x -7.2e-8) (not (<= x 11200.0)))
       (/
        (+ x -2.0)
        (+
         0.24013125253755718
         (- (/ 5.86923874282773 x) (/ 55.572073733743466 (* x x)))))
       (* z (+ -0.0424927283095952 (* x 0.3041881842569256)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1e+65) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -3.5e+24) {
		tmp = y / (x * x);
	} else if ((x <= -7.2e-8) || !(x <= 11200.0)) {
		tmp = (x + -2.0) / (0.24013125253755718 + ((5.86923874282773 / x) - (55.572073733743466 / (x * x))));
	} else {
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256));
	}
	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 <= (-1d+65)) then
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    else if (x <= (-3.5d+24)) then
        tmp = y / (x * x)
    else if ((x <= (-7.2d-8)) .or. (.not. (x <= 11200.0d0))) then
        tmp = (x + (-2.0d0)) / (0.24013125253755718d0 + ((5.86923874282773d0 / x) - (55.572073733743466d0 / (x * x))))
    else
        tmp = z * ((-0.0424927283095952d0) + (x * 0.3041881842569256d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1e+65) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -3.5e+24) {
		tmp = y / (x * x);
	} else if ((x <= -7.2e-8) || !(x <= 11200.0)) {
		tmp = (x + -2.0) / (0.24013125253755718 + ((5.86923874282773 / x) - (55.572073733743466 / (x * x))));
	} else {
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1e+65:
		tmp = (x + -2.0) / 0.24013125253755718
	elif x <= -3.5e+24:
		tmp = y / (x * x)
	elif (x <= -7.2e-8) or not (x <= 11200.0):
		tmp = (x + -2.0) / (0.24013125253755718 + ((5.86923874282773 / x) - (55.572073733743466 / (x * x))))
	else:
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1e+65)
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	elseif (x <= -3.5e+24)
		tmp = Float64(y / Float64(x * x));
	elseif ((x <= -7.2e-8) || !(x <= 11200.0))
		tmp = Float64(Float64(x + -2.0) / Float64(0.24013125253755718 + Float64(Float64(5.86923874282773 / x) - Float64(55.572073733743466 / Float64(x * x)))));
	else
		tmp = Float64(z * Float64(-0.0424927283095952 + Float64(x * 0.3041881842569256)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1e+65)
		tmp = (x + -2.0) / 0.24013125253755718;
	elseif (x <= -3.5e+24)
		tmp = y / (x * x);
	elseif ((x <= -7.2e-8) || ~((x <= 11200.0)))
		tmp = (x + -2.0) / (0.24013125253755718 + ((5.86923874282773 / x) - (55.572073733743466 / (x * x))));
	else
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1e+65], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision], If[LessEqual[x, -3.5e+24], N[(y / N[(x * x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -7.2e-8], N[Not[LessEqual[x, 11200.0]], $MachinePrecision]], N[(N[(x + -2.0), $MachinePrecision] / N[(0.24013125253755718 + N[(N[(5.86923874282773 / x), $MachinePrecision] - N[(55.572073733743466 / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(-0.0424927283095952 + N[(x * 0.3041881842569256), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.9999999999999999e64

   1. Initial program 0.3%

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

      1. associate-/l* 7.8%

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

      2. sub-neg 7.8%

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

      3. metadata-eval 7.8%

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

      4. fma-def 7.8%

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

      5. fma-def 7.8%

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

      6. fma-def 7.8%

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

      7. fma-def 7.8%

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

      8. fma-def 7.8%

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

      9. fma-def 7.8%

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

      10. fma-def 7.8%

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

   3. Simplified 7.8%

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

   4. Taylor expanded in x around inf 97.6%

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

   if -9.9999999999999999e64 < x < -3.5000000000000002e24

   1. Initial program 42.0%

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

   2. Taylor expanded in y around inf 42.0%

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

   3. Taylor expanded in x around inf 99.4%

      \[\leadsto \color{blue}{\frac{y}{{x}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 99.4%

         \[\leadsto \frac{y}{\color{blue}{x \cdot x}} \]

   5. Simplified 99.4%

      \[\leadsto \color{blue}{\frac{y}{x \cdot x}} \]

   if -3.5000000000000002e24 < x < -7.19999999999999962e-8 or 11200 < x

   1. Initial program 20.3%

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

      1. associate-/l* 22.8%

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

      2. sub-neg 22.8%

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

      3. metadata-eval 22.8%

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

      4. fma-def 22.8%

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

      5. fma-def 22.8%

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

      6. fma-def 22.8%

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

      7. fma-def 22.8%

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

      8. fma-def 22.8%

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

      9. fma-def 22.8%

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

      10. fma-def 22.8%

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

   3. Simplified 22.8%

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

   4. Taylor expanded in x around inf 85.5%

      \[\leadsto \frac{x + -2}{\color{blue}{\left(0.24013125253755718 + 5.86923874282773 \cdot \frac{1}{x}\right) - 55.572073733743466 \cdot \frac{1}{{x}^{2}}}} \]
   5. Step-by-step derivation

      1. associate--l+ 85.5%

         \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718 + \left(5.86923874282773 \cdot \frac{1}{x} - 55.572073733743466 \cdot \frac{1}{{x}^{2}}\right)}} \]

      2. associate-*r/ 85.5%

         \[\leadsto \frac{x + -2}{0.24013125253755718 + \left(\color{blue}{\frac{5.86923874282773 \cdot 1}{x}} - 55.572073733743466 \cdot \frac{1}{{x}^{2}}\right)} \]

      3. metadata-eval 85.5%

         \[\leadsto \frac{x + -2}{0.24013125253755718 + \left(\frac{\color{blue}{5.86923874282773}}{x} - 55.572073733743466 \cdot \frac{1}{{x}^{2}}\right)} \]

      4. associate-*r/ 85.5%

         \[\leadsto \frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} - \color{blue}{\frac{55.572073733743466 \cdot 1}{{x}^{2}}}\right)} \]

      5. metadata-eval 85.5%

         \[\leadsto \frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} - \frac{\color{blue}{55.572073733743466}}{{x}^{2}}\right)} \]

      6. unpow2 85.5%

         \[\leadsto \frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} - \frac{55.572073733743466}{\color{blue}{x \cdot x}}\right)} \]

   6. Simplified 85.5%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} - \frac{55.572073733743466}{x \cdot x}\right)}} \]

   if -7.19999999999999962e-8 < x < 11200

   1. Initial program 99.7%

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

      1. associate-/l* 99.5%

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

      2. sub-neg 99.5%

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

      3. metadata-eval 99.5%

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

      4. fma-def 99.5%

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

      5. fma-def 99.5%

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

      6. fma-def 99.5%

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

      7. fma-def 99.5%

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

      8. fma-def 99.4%

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

      9. fma-def 99.4%

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

      10. fma-def 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around inf 69.9%

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

   5. Taylor expanded in x around 0 69.1%

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

      1. +-commutative 69.1%

         \[\leadsto \color{blue}{-0.0424927283095952 \cdot z + \left(0.0212463641547976 \cdot z - -0.28294182010212804 \cdot z\right) \cdot x} \]

      2. *-commutative 69.1%

         \[\leadsto \color{blue}{z \cdot -0.0424927283095952} + \left(0.0212463641547976 \cdot z - -0.28294182010212804 \cdot z\right) \cdot x \]

      3. distribute-rgt-out-- 69.1%

         \[\leadsto z \cdot -0.0424927283095952 + \color{blue}{\left(z \cdot \left(0.0212463641547976 - -0.28294182010212804\right)\right)} \cdot x \]

      4. associate-*l* 69.1%

         \[\leadsto z \cdot -0.0424927283095952 + \color{blue}{z \cdot \left(\left(0.0212463641547976 - -0.28294182010212804\right) \cdot x\right)} \]

      5. distribute-lft-out 69.1%

         \[\leadsto \color{blue}{z \cdot \left(-0.0424927283095952 + \left(0.0212463641547976 - -0.28294182010212804\right) \cdot x\right)} \]

      6. metadata-eval 69.1%

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

   7. Simplified 69.1%

      \[\leadsto \color{blue}{z \cdot \left(-0.0424927283095952 + 0.3041881842569256 \cdot x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+65}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{y}{x \cdot x}\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-8} \lor \neg \left(x \leq 11200\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} - \frac{55.572073733743466}{x \cdot x}\right)}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\\ \end{array} \]

Alternative 10: 76.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+65}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -3 \cdot 10^{+24}:\\ \;\;\;\;\frac{y}{x \cdot x}\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-8} \lor \neg \left(x \leq 5000\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} - \frac{55.572073733743466}{x \cdot x}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1e+65)
   (/ (+ x -2.0) 0.24013125253755718)
   (if (<= x -3e+24)
     (/ y (* x x))
     (if (or (<= x -7.2e-8) (not (<= x 5000.0)))
       (/
        (+ x -2.0)
        (+
         0.24013125253755718
         (- (/ 5.86923874282773 x) (/ 55.572073733743466 (* x x)))))
       (/
        (+ x -2.0)
        (/ (+ 47.066876606 (* x (+ 313.399215894 (* x 263.505074721)))) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1e+65) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -3e+24) {
		tmp = y / (x * x);
	} else if ((x <= -7.2e-8) || !(x <= 5000.0)) {
		tmp = (x + -2.0) / (0.24013125253755718 + ((5.86923874282773 / x) - (55.572073733743466 / (x * x))));
	} else {
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + (x * 263.505074721)))) / z);
	}
	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 <= (-1d+65)) then
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    else if (x <= (-3d+24)) then
        tmp = y / (x * x)
    else if ((x <= (-7.2d-8)) .or. (.not. (x <= 5000.0d0))) then
        tmp = (x + (-2.0d0)) / (0.24013125253755718d0 + ((5.86923874282773d0 / x) - (55.572073733743466d0 / (x * x))))
    else
        tmp = (x + (-2.0d0)) / ((47.066876606d0 + (x * (313.399215894d0 + (x * 263.505074721d0)))) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1e+65) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -3e+24) {
		tmp = y / (x * x);
	} else if ((x <= -7.2e-8) || !(x <= 5000.0)) {
		tmp = (x + -2.0) / (0.24013125253755718 + ((5.86923874282773 / x) - (55.572073733743466 / (x * x))));
	} else {
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + (x * 263.505074721)))) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1e+65:
		tmp = (x + -2.0) / 0.24013125253755718
	elif x <= -3e+24:
		tmp = y / (x * x)
	elif (x <= -7.2e-8) or not (x <= 5000.0):
		tmp = (x + -2.0) / (0.24013125253755718 + ((5.86923874282773 / x) - (55.572073733743466 / (x * x))))
	else:
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + (x * 263.505074721)))) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1e+65)
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	elseif (x <= -3e+24)
		tmp = Float64(y / Float64(x * x));
	elseif ((x <= -7.2e-8) || !(x <= 5000.0))
		tmp = Float64(Float64(x + -2.0) / Float64(0.24013125253755718 + Float64(Float64(5.86923874282773 / x) - Float64(55.572073733743466 / Float64(x * x)))));
	else
		tmp = Float64(Float64(x + -2.0) / Float64(Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(x * 263.505074721)))) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1e+65)
		tmp = (x + -2.0) / 0.24013125253755718;
	elseif (x <= -3e+24)
		tmp = y / (x * x);
	elseif ((x <= -7.2e-8) || ~((x <= 5000.0)))
		tmp = (x + -2.0) / (0.24013125253755718 + ((5.86923874282773 / x) - (55.572073733743466 / (x * x))));
	else
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + (x * 263.505074721)))) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1e+65], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision], If[LessEqual[x, -3e+24], N[(y / N[(x * x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -7.2e-8], N[Not[LessEqual[x, 5000.0]], $MachinePrecision]], N[(N[(x + -2.0), $MachinePrecision] / N[(0.24013125253755718 + N[(N[(5.86923874282773 / x), $MachinePrecision] - N[(55.572073733743466 / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] / N[(N[(47.066876606 + N[(x * N[(313.399215894 + N[(x * 263.505074721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.9999999999999999e64

   1. Initial program 0.3%

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

      1. associate-/l* 7.8%

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

      2. sub-neg 7.8%

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

      3. metadata-eval 7.8%

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

      4. fma-def 7.8%

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

      5. fma-def 7.8%

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

      6. fma-def 7.8%

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

      7. fma-def 7.8%

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

      8. fma-def 7.8%

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

      9. fma-def 7.8%

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

      10. fma-def 7.8%

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

   3. Simplified 7.8%

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

   4. Taylor expanded in x around inf 97.6%

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

   if -9.9999999999999999e64 < x < -2.99999999999999995e24

   1. Initial program 42.0%

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

   2. Taylor expanded in y around inf 42.0%

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

   3. Taylor expanded in x around inf 99.4%

      \[\leadsto \color{blue}{\frac{y}{{x}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 99.4%

         \[\leadsto \frac{y}{\color{blue}{x \cdot x}} \]

   5. Simplified 99.4%

      \[\leadsto \color{blue}{\frac{y}{x \cdot x}} \]

   if -2.99999999999999995e24 < x < -7.19999999999999962e-8 or 5e3 < x

   1. Initial program 20.3%

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

      1. associate-/l* 22.8%

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

      2. sub-neg 22.8%

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

      3. metadata-eval 22.8%

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

      4. fma-def 22.8%

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

      5. fma-def 22.8%

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

      6. fma-def 22.8%

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

      7. fma-def 22.8%

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

      8. fma-def 22.8%

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

      9. fma-def 22.8%

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

      10. fma-def 22.8%

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

   3. Simplified 22.8%

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

   4. Taylor expanded in x around inf 85.5%

      \[\leadsto \frac{x + -2}{\color{blue}{\left(0.24013125253755718 + 5.86923874282773 \cdot \frac{1}{x}\right) - 55.572073733743466 \cdot \frac{1}{{x}^{2}}}} \]
   5. Step-by-step derivation

      1. associate--l+ 85.5%

         \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718 + \left(5.86923874282773 \cdot \frac{1}{x} - 55.572073733743466 \cdot \frac{1}{{x}^{2}}\right)}} \]

      2. associate-*r/ 85.5%

         \[\leadsto \frac{x + -2}{0.24013125253755718 + \left(\color{blue}{\frac{5.86923874282773 \cdot 1}{x}} - 55.572073733743466 \cdot \frac{1}{{x}^{2}}\right)} \]

      3. metadata-eval 85.5%

         \[\leadsto \frac{x + -2}{0.24013125253755718 + \left(\frac{\color{blue}{5.86923874282773}}{x} - 55.572073733743466 \cdot \frac{1}{{x}^{2}}\right)} \]

      4. associate-*r/ 85.5%

         \[\leadsto \frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} - \color{blue}{\frac{55.572073733743466 \cdot 1}{{x}^{2}}}\right)} \]

      5. metadata-eval 85.5%

         \[\leadsto \frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} - \frac{\color{blue}{55.572073733743466}}{{x}^{2}}\right)} \]

      6. unpow2 85.5%

         \[\leadsto \frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} - \frac{55.572073733743466}{\color{blue}{x \cdot x}}\right)} \]

   6. Simplified 85.5%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} - \frac{55.572073733743466}{x \cdot x}\right)}} \]

   if -7.19999999999999962e-8 < x < 5e3

   1. Initial program 99.7%

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

      1. associate-/l* 99.5%

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

      2. sub-neg 99.5%

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

      3. metadata-eval 99.5%

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

      4. fma-def 99.5%

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

      5. fma-def 99.5%

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

      6. fma-def 99.5%

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

      7. fma-def 99.5%

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

      8. fma-def 99.4%

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

      9. fma-def 99.4%

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

      10. fma-def 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around inf 69.9%

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

   5. Taylor expanded in x around 0 69.2%

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

      1. *-commutative 69.2%

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

   7. Simplified 69.2%

      \[\leadsto \frac{x + -2}{\frac{47.066876606 + \left(313.399215894 + \color{blue}{x \cdot 263.505074721}\right) \cdot x}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+65}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -3 \cdot 10^{+24}:\\ \;\;\;\;\frac{y}{x \cdot x}\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-8} \lor \neg \left(x \leq 5000\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} - \frac{55.572073733743466}{x \cdot x}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}{z}}\\ \end{array} \]

Alternative 11: 76.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+65}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{y}{x \cdot x}\\ \mathbf{elif}\;x \leq -1350 \lor \neg \left(x \leq 5000\right):\\ \;\;\;\;\left(x \cdot 4.16438922228 + \frac{3655.1204654076414}{x}\right) - 110.1139242984811\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1e+65)
   (/ (+ x -2.0) 0.24013125253755718)
   (if (<= x -3.5e+24)
     (/ y (* x x))
     (if (or (<= x -1350.0) (not (<= x 5000.0)))
       (- (+ (* x 4.16438922228) (/ 3655.1204654076414 x)) 110.1139242984811)
       (* z (+ -0.0424927283095952 (* x 0.3041881842569256)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1e+65) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -3.5e+24) {
		tmp = y / (x * x);
	} else if ((x <= -1350.0) || !(x <= 5000.0)) {
		tmp = ((x * 4.16438922228) + (3655.1204654076414 / x)) - 110.1139242984811;
	} else {
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256));
	}
	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 <= (-1d+65)) then
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    else if (x <= (-3.5d+24)) then
        tmp = y / (x * x)
    else if ((x <= (-1350.0d0)) .or. (.not. (x <= 5000.0d0))) then
        tmp = ((x * 4.16438922228d0) + (3655.1204654076414d0 / x)) - 110.1139242984811d0
    else
        tmp = z * ((-0.0424927283095952d0) + (x * 0.3041881842569256d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1e+65) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -3.5e+24) {
		tmp = y / (x * x);
	} else if ((x <= -1350.0) || !(x <= 5000.0)) {
		tmp = ((x * 4.16438922228) + (3655.1204654076414 / x)) - 110.1139242984811;
	} else {
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1e+65:
		tmp = (x + -2.0) / 0.24013125253755718
	elif x <= -3.5e+24:
		tmp = y / (x * x)
	elif (x <= -1350.0) or not (x <= 5000.0):
		tmp = ((x * 4.16438922228) + (3655.1204654076414 / x)) - 110.1139242984811
	else:
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1e+65)
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	elseif (x <= -3.5e+24)
		tmp = Float64(y / Float64(x * x));
	elseif ((x <= -1350.0) || !(x <= 5000.0))
		tmp = Float64(Float64(Float64(x * 4.16438922228) + Float64(3655.1204654076414 / x)) - 110.1139242984811);
	else
		tmp = Float64(z * Float64(-0.0424927283095952 + Float64(x * 0.3041881842569256)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1e+65)
		tmp = (x + -2.0) / 0.24013125253755718;
	elseif (x <= -3.5e+24)
		tmp = y / (x * x);
	elseif ((x <= -1350.0) || ~((x <= 5000.0)))
		tmp = ((x * 4.16438922228) + (3655.1204654076414 / x)) - 110.1139242984811;
	else
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1e+65], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision], If[LessEqual[x, -3.5e+24], N[(y / N[(x * x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -1350.0], N[Not[LessEqual[x, 5000.0]], $MachinePrecision]], N[(N[(N[(x * 4.16438922228), $MachinePrecision] + N[(3655.1204654076414 / x), $MachinePrecision]), $MachinePrecision] - 110.1139242984811), $MachinePrecision], N[(z * N[(-0.0424927283095952 + N[(x * 0.3041881842569256), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.9999999999999999e64

   1. Initial program 0.3%

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

      1. associate-/l* 7.8%

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

      2. sub-neg 7.8%

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

      3. metadata-eval 7.8%

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

      4. fma-def 7.8%

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

      5. fma-def 7.8%

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

      6. fma-def 7.8%

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

      7. fma-def 7.8%

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

      8. fma-def 7.8%

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

      9. fma-def 7.8%

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

      10. fma-def 7.8%

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

   3. Simplified 7.8%

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

   4. Taylor expanded in x around inf 97.6%

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

   if -9.9999999999999999e64 < x < -3.5000000000000002e24

   1. Initial program 42.0%

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

   2. Taylor expanded in y around inf 42.0%

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

   3. Taylor expanded in x around inf 99.4%

      \[\leadsto \color{blue}{\frac{y}{{x}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 99.4%

         \[\leadsto \frac{y}{\color{blue}{x \cdot x}} \]

   5. Simplified 99.4%

      \[\leadsto \color{blue}{\frac{y}{x \cdot x}} \]

   if -3.5000000000000002e24 < x < -1350 or 5e3 < x

   1. Initial program 18.1%

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

      1. *-commutative 18.1%

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

      2. associate-*r/ 20.7%

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

      3. *-commutative 20.7%

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

      4. fma-def 20.7%

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

      5. *-commutative 20.7%

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

      6. fma-def 20.7%

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

      7. *-commutative 20.7%

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

      8. fma-def 20.7%

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

      9. fma-def 20.7%

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

   3. Simplified 20.7%

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

   4. Taylor expanded in x around inf 87.1%

      \[\leadsto \color{blue}{\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - 110.1139242984811} \]

   5. Taylor expanded in x around 0 87.1%

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

   if -1350 < x < 5e3

   1. Initial program 99.7%

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

      1. associate-/l* 99.4%

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

      2. sub-neg 99.4%

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

      3. metadata-eval 99.4%

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

      4. fma-def 99.4%

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

      5. fma-def 99.4%

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

      6. fma-def 99.4%

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

      7. fma-def 99.4%

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

      8. fma-def 99.4%

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

      9. fma-def 99.4%

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

      10. fma-def 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around inf 68.8%

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

   5. Taylor expanded in x around 0 68.1%

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

      1. +-commutative 68.1%

         \[\leadsto \color{blue}{-0.0424927283095952 \cdot z + \left(0.0212463641547976 \cdot z - -0.28294182010212804 \cdot z\right) \cdot x} \]

      2. *-commutative 68.1%

         \[\leadsto \color{blue}{z \cdot -0.0424927283095952} + \left(0.0212463641547976 \cdot z - -0.28294182010212804 \cdot z\right) \cdot x \]

      3. distribute-rgt-out-- 68.1%

         \[\leadsto z \cdot -0.0424927283095952 + \color{blue}{\left(z \cdot \left(0.0212463641547976 - -0.28294182010212804\right)\right)} \cdot x \]

      4. associate-*l* 68.1%

         \[\leadsto z \cdot -0.0424927283095952 + \color{blue}{z \cdot \left(\left(0.0212463641547976 - -0.28294182010212804\right) \cdot x\right)} \]

      5. distribute-lft-out 68.1%

         \[\leadsto \color{blue}{z \cdot \left(-0.0424927283095952 + \left(0.0212463641547976 - -0.28294182010212804\right) \cdot x\right)} \]

      6. metadata-eval 68.1%

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

   7. Simplified 68.1%

      \[\leadsto \color{blue}{z \cdot \left(-0.0424927283095952 + 0.3041881842569256 \cdot x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+65}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{y}{x \cdot x}\\ \mathbf{elif}\;x \leq -1350 \lor \neg \left(x \leq 5000\right):\\ \;\;\;\;\left(x \cdot 4.16438922228 + \frac{3655.1204654076414}{x}\right) - 110.1139242984811\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\\ \end{array} \]

Alternative 12: 76.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+65}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{+24}:\\ \;\;\;\;\frac{y}{x \cdot x}\\ \mathbf{elif}\;x \leq -190:\\ \;\;\;\;\left(x \cdot 4.16438922228 + \frac{3655.1204654076414}{x}\right) - 110.1139242984811\\ \mathbf{elif}\;x \leq 36000:\\ \;\;\;\;z \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1e+65)
   (/ (+ x -2.0) 0.24013125253755718)
   (if (<= x -4.8e+24)
     (/ y (* x x))
     (if (<= x -190.0)
       (- (+ (* x 4.16438922228) (/ 3655.1204654076414 x)) 110.1139242984811)
       (if (<= x 36000.0)
         (* z (+ -0.0424927283095952 (* x 0.3041881842569256)))
         (/ (+ x -2.0) (+ 0.24013125253755718 (/ 5.86923874282773 x))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1e+65) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -4.8e+24) {
		tmp = y / (x * x);
	} else if (x <= -190.0) {
		tmp = ((x * 4.16438922228) + (3655.1204654076414 / x)) - 110.1139242984811;
	} else if (x <= 36000.0) {
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256));
	} else {
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1d+65)) then
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    else if (x <= (-4.8d+24)) then
        tmp = y / (x * x)
    else if (x <= (-190.0d0)) then
        tmp = ((x * 4.16438922228d0) + (3655.1204654076414d0 / x)) - 110.1139242984811d0
    else if (x <= 36000.0d0) then
        tmp = z * ((-0.0424927283095952d0) + (x * 0.3041881842569256d0))
    else
        tmp = (x + (-2.0d0)) / (0.24013125253755718d0 + (5.86923874282773d0 / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1e+65) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -4.8e+24) {
		tmp = y / (x * x);
	} else if (x <= -190.0) {
		tmp = ((x * 4.16438922228) + (3655.1204654076414 / x)) - 110.1139242984811;
	} else if (x <= 36000.0) {
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256));
	} else {
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1e+65:
		tmp = (x + -2.0) / 0.24013125253755718
	elif x <= -4.8e+24:
		tmp = y / (x * x)
	elif x <= -190.0:
		tmp = ((x * 4.16438922228) + (3655.1204654076414 / x)) - 110.1139242984811
	elif x <= 36000.0:
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256))
	else:
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1e+65)
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	elseif (x <= -4.8e+24)
		tmp = Float64(y / Float64(x * x));
	elseif (x <= -190.0)
		tmp = Float64(Float64(Float64(x * 4.16438922228) + Float64(3655.1204654076414 / x)) - 110.1139242984811);
	elseif (x <= 36000.0)
		tmp = Float64(z * Float64(-0.0424927283095952 + Float64(x * 0.3041881842569256)));
	else
		tmp = Float64(Float64(x + -2.0) / Float64(0.24013125253755718 + Float64(5.86923874282773 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1e+65)
		tmp = (x + -2.0) / 0.24013125253755718;
	elseif (x <= -4.8e+24)
		tmp = y / (x * x);
	elseif (x <= -190.0)
		tmp = ((x * 4.16438922228) + (3655.1204654076414 / x)) - 110.1139242984811;
	elseif (x <= 36000.0)
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256));
	else
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1e+65], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision], If[LessEqual[x, -4.8e+24], N[(y / N[(x * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -190.0], N[(N[(N[(x * 4.16438922228), $MachinePrecision] + N[(3655.1204654076414 / x), $MachinePrecision]), $MachinePrecision] - 110.1139242984811), $MachinePrecision], If[LessEqual[x, 36000.0], N[(z * N[(-0.0424927283095952 + N[(x * 0.3041881842569256), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] / N[(0.24013125253755718 + N[(5.86923874282773 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -9.9999999999999999e64

   1. Initial program 0.3%

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

      1. associate-/l* 7.8%

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

      2. sub-neg 7.8%

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

      3. metadata-eval 7.8%

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

      4. fma-def 7.8%

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

      5. fma-def 7.8%

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

      6. fma-def 7.8%

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

      7. fma-def 7.8%

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

      8. fma-def 7.8%

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

      9. fma-def 7.8%

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

      10. fma-def 7.8%

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

   3. Simplified 7.8%

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

   4. Taylor expanded in x around inf 97.6%

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

   if -9.9999999999999999e64 < x < -4.8000000000000001e24

   1. Initial program 42.0%

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

   2. Taylor expanded in y around inf 42.0%

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

   3. Taylor expanded in x around inf 99.4%

      \[\leadsto \color{blue}{\frac{y}{{x}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 99.4%

         \[\leadsto \frac{y}{\color{blue}{x \cdot x}} \]

   5. Simplified 99.4%

      \[\leadsto \color{blue}{\frac{y}{x \cdot x}} \]

   if -4.8000000000000001e24 < x < -190

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*r/ 99.2%

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

      3. *-commutative 99.2%

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

      4. fma-def 99.2%

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

      5. *-commutative 99.2%

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

      6. fma-def 99.2%

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

      7. *-commutative 99.2%

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

      8. fma-def 99.2%

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

      9. fma-def 99.2%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around inf 73.0%

      \[\leadsto \color{blue}{\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - 110.1139242984811} \]

   5. Taylor expanded in x around 0 73.0%

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

   if -190 < x < 36000

   1. Initial program 99.7%

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

      1. associate-/l* 99.4%

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

      2. sub-neg 99.4%

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

      3. metadata-eval 99.4%

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

      4. fma-def 99.4%

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

      5. fma-def 99.4%

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

      6. fma-def 99.4%

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

      7. fma-def 99.4%

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

      8. fma-def 99.4%

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

      9. fma-def 99.4%

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

      10. fma-def 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around inf 68.8%

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

   5. Taylor expanded in x around 0 68.1%

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

      1. +-commutative 68.1%

         \[\leadsto \color{blue}{-0.0424927283095952 \cdot z + \left(0.0212463641547976 \cdot z - -0.28294182010212804 \cdot z\right) \cdot x} \]

      2. *-commutative 68.1%

         \[\leadsto \color{blue}{z \cdot -0.0424927283095952} + \left(0.0212463641547976 \cdot z - -0.28294182010212804 \cdot z\right) \cdot x \]

      3. distribute-rgt-out-- 68.1%

         \[\leadsto z \cdot -0.0424927283095952 + \color{blue}{\left(z \cdot \left(0.0212463641547976 - -0.28294182010212804\right)\right)} \cdot x \]

      4. associate-*l* 68.1%

         \[\leadsto z \cdot -0.0424927283095952 + \color{blue}{z \cdot \left(\left(0.0212463641547976 - -0.28294182010212804\right) \cdot x\right)} \]

      5. distribute-lft-out 68.1%

         \[\leadsto \color{blue}{z \cdot \left(-0.0424927283095952 + \left(0.0212463641547976 - -0.28294182010212804\right) \cdot x\right)} \]

      6. metadata-eval 68.1%

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

   7. Simplified 68.1%

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

   if 36000 < x

   1. Initial program 13.3%

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

      1. associate-/l* 16.1%

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

      2. sub-neg 16.1%

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

      3. metadata-eval 16.1%

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

      4. fma-def 16.1%

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

      5. fma-def 16.1%

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

      6. fma-def 16.1%

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

      7. fma-def 16.1%

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

      8. fma-def 16.1%

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

      9. fma-def 16.1%

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

      10. fma-def 16.1%

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

   3. Simplified 16.1%

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

   4. Taylor expanded in x around inf 88.5%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718 + 5.86923874282773 \cdot \frac{1}{x}}} \]
   5. Step-by-step derivation

      1. associate-*r/ 88.5%

         \[\leadsto \frac{x + -2}{0.24013125253755718 + \color{blue}{\frac{5.86923874282773 \cdot 1}{x}}} \]

      2. metadata-eval 88.5%

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

   6. Simplified 88.5%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718 + \frac{5.86923874282773}{x}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+65}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{+24}:\\ \;\;\;\;\frac{y}{x \cdot x}\\ \mathbf{elif}\;x \leq -190:\\ \;\;\;\;\left(x \cdot 4.16438922228 + \frac{3655.1204654076414}{x}\right) - 110.1139242984811\\ \mathbf{elif}\;x \leq 36000:\\ \;\;\;\;z \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \end{array} \]

Alternative 13: 76.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+65}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{+24}:\\ \;\;\;\;\frac{y}{x \cdot x}\\ \mathbf{elif}\;x \leq -330 \lor \neg \left(x \leq 6200\right):\\ \;\;\;\;x \cdot 4.16438922228 - 110.1139242984811\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1e+65)
   (/ (+ x -2.0) 0.24013125253755718)
   (if (<= x -2.3e+24)
     (/ y (* x x))
     (if (or (<= x -330.0) (not (<= x 6200.0)))
       (- (* x 4.16438922228) 110.1139242984811)
       (* z (+ -0.0424927283095952 (* x 0.3041881842569256)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1e+65) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -2.3e+24) {
		tmp = y / (x * x);
	} else if ((x <= -330.0) || !(x <= 6200.0)) {
		tmp = (x * 4.16438922228) - 110.1139242984811;
	} else {
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256));
	}
	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 <= (-1d+65)) then
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    else if (x <= (-2.3d+24)) then
        tmp = y / (x * x)
    else if ((x <= (-330.0d0)) .or. (.not. (x <= 6200.0d0))) then
        tmp = (x * 4.16438922228d0) - 110.1139242984811d0
    else
        tmp = z * ((-0.0424927283095952d0) + (x * 0.3041881842569256d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1e+65) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -2.3e+24) {
		tmp = y / (x * x);
	} else if ((x <= -330.0) || !(x <= 6200.0)) {
		tmp = (x * 4.16438922228) - 110.1139242984811;
	} else {
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1e+65:
		tmp = (x + -2.0) / 0.24013125253755718
	elif x <= -2.3e+24:
		tmp = y / (x * x)
	elif (x <= -330.0) or not (x <= 6200.0):
		tmp = (x * 4.16438922228) - 110.1139242984811
	else:
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1e+65)
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	elseif (x <= -2.3e+24)
		tmp = Float64(y / Float64(x * x));
	elseif ((x <= -330.0) || !(x <= 6200.0))
		tmp = Float64(Float64(x * 4.16438922228) - 110.1139242984811);
	else
		tmp = Float64(z * Float64(-0.0424927283095952 + Float64(x * 0.3041881842569256)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1e+65)
		tmp = (x + -2.0) / 0.24013125253755718;
	elseif (x <= -2.3e+24)
		tmp = y / (x * x);
	elseif ((x <= -330.0) || ~((x <= 6200.0)))
		tmp = (x * 4.16438922228) - 110.1139242984811;
	else
		tmp = z * (-0.0424927283095952 + (x * 0.3041881842569256));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1e+65], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision], If[LessEqual[x, -2.3e+24], N[(y / N[(x * x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -330.0], N[Not[LessEqual[x, 6200.0]], $MachinePrecision]], N[(N[(x * 4.16438922228), $MachinePrecision] - 110.1139242984811), $MachinePrecision], N[(z * N[(-0.0424927283095952 + N[(x * 0.3041881842569256), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.9999999999999999e64

   1. Initial program 0.3%

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

      1. associate-/l* 7.8%

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

      2. sub-neg 7.8%

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

      3. metadata-eval 7.8%

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

      4. fma-def 7.8%

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

      5. fma-def 7.8%

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

      6. fma-def 7.8%

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

      7. fma-def 7.8%

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

      8. fma-def 7.8%

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

      9. fma-def 7.8%

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

      10. fma-def 7.8%

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

   3. Simplified 7.8%

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

   4. Taylor expanded in x around inf 97.6%

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

   if -9.9999999999999999e64 < x < -2.2999999999999999e24

   1. Initial program 42.0%

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

   2. Taylor expanded in y around inf 42.0%

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

   3. Taylor expanded in x around inf 99.4%

      \[\leadsto \color{blue}{\frac{y}{{x}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 99.4%

         \[\leadsto \frac{y}{\color{blue}{x \cdot x}} \]

   5. Simplified 99.4%

      \[\leadsto \color{blue}{\frac{y}{x \cdot x}} \]

   if -2.2999999999999999e24 < x < -330 or 6200 < x

   1. Initial program 18.1%

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

      1. *-commutative 18.1%

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

      2. associate-*r/ 20.7%

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

      3. *-commutative 20.7%

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

      4. fma-def 20.7%

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

      5. *-commutative 20.7%

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

      6. fma-def 20.7%

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

      7. *-commutative 20.7%

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

      8. fma-def 20.7%

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

      9. fma-def 20.7%

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

   3. Simplified 20.7%

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

   4. Taylor expanded in x around inf 86.8%

      \[\leadsto \color{blue}{4.16438922228 \cdot x - 110.1139242984811} \]

   if -330 < x < 6200

   1. Initial program 99.7%

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

      1. associate-/l* 99.4%

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

      2. sub-neg 99.4%

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

      3. metadata-eval 99.4%

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

      4. fma-def 99.4%

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

      5. fma-def 99.4%

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

      6. fma-def 99.4%

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

      7. fma-def 99.4%

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

      8. fma-def 99.4%

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

      9. fma-def 99.4%

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

      10. fma-def 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around inf 68.8%

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

   5. Taylor expanded in x around 0 68.1%

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

      1. +-commutative 68.1%

         \[\leadsto \color{blue}{-0.0424927283095952 \cdot z + \left(0.0212463641547976 \cdot z - -0.28294182010212804 \cdot z\right) \cdot x} \]

      2. *-commutative 68.1%

         \[\leadsto \color{blue}{z \cdot -0.0424927283095952} + \left(0.0212463641547976 \cdot z - -0.28294182010212804 \cdot z\right) \cdot x \]

      3. distribute-rgt-out-- 68.1%

         \[\leadsto z \cdot -0.0424927283095952 + \color{blue}{\left(z \cdot \left(0.0212463641547976 - -0.28294182010212804\right)\right)} \cdot x \]

      4. associate-*l* 68.1%

         \[\leadsto z \cdot -0.0424927283095952 + \color{blue}{z \cdot \left(\left(0.0212463641547976 - -0.28294182010212804\right) \cdot x\right)} \]

      5. distribute-lft-out 68.1%

         \[\leadsto \color{blue}{z \cdot \left(-0.0424927283095952 + \left(0.0212463641547976 - -0.28294182010212804\right) \cdot x\right)} \]

      6. metadata-eval 68.1%

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

   7. Simplified 68.1%

      \[\leadsto \color{blue}{z \cdot \left(-0.0424927283095952 + 0.3041881842569256 \cdot x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+65}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{+24}:\\ \;\;\;\;\frac{y}{x \cdot x}\\ \mathbf{elif}\;x \leq -330 \lor \neg \left(x \leq 6200\right):\\ \;\;\;\;x \cdot 4.16438922228 - 110.1139242984811\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\\ \end{array} \]

Alternative 14: 76.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+65}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq -2.35 \cdot 10^{+24}:\\ \;\;\;\;\frac{y}{x \cdot x}\\ \mathbf{elif}\;x \leq -1350 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;x \cdot 4.16438922228 - 110.1139242984811\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1e+65)
   (* x 4.16438922228)
   (if (<= x -2.35e+24)
     (/ y (* x x))
     (if (or (<= x -1350.0) (not (<= x 3.0)))
       (- (* x 4.16438922228) 110.1139242984811)
       (* z -0.0424927283095952)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1e+65) {
		tmp = x * 4.16438922228;
	} else if (x <= -2.35e+24) {
		tmp = y / (x * x);
	} else if ((x <= -1350.0) || !(x <= 3.0)) {
		tmp = (x * 4.16438922228) - 110.1139242984811;
	} else {
		tmp = z * -0.0424927283095952;
	}
	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 <= (-1d+65)) then
        tmp = x * 4.16438922228d0
    else if (x <= (-2.35d+24)) then
        tmp = y / (x * x)
    else if ((x <= (-1350.0d0)) .or. (.not. (x <= 3.0d0))) then
        tmp = (x * 4.16438922228d0) - 110.1139242984811d0
    else
        tmp = z * (-0.0424927283095952d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1e+65) {
		tmp = x * 4.16438922228;
	} else if (x <= -2.35e+24) {
		tmp = y / (x * x);
	} else if ((x <= -1350.0) || !(x <= 3.0)) {
		tmp = (x * 4.16438922228) - 110.1139242984811;
	} else {
		tmp = z * -0.0424927283095952;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1e+65:
		tmp = x * 4.16438922228
	elif x <= -2.35e+24:
		tmp = y / (x * x)
	elif (x <= -1350.0) or not (x <= 3.0):
		tmp = (x * 4.16438922228) - 110.1139242984811
	else:
		tmp = z * -0.0424927283095952
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1e+65)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= -2.35e+24)
		tmp = Float64(y / Float64(x * x));
	elseif ((x <= -1350.0) || !(x <= 3.0))
		tmp = Float64(Float64(x * 4.16438922228) - 110.1139242984811);
	else
		tmp = Float64(z * -0.0424927283095952);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1e+65)
		tmp = x * 4.16438922228;
	elseif (x <= -2.35e+24)
		tmp = y / (x * x);
	elseif ((x <= -1350.0) || ~((x <= 3.0)))
		tmp = (x * 4.16438922228) - 110.1139242984811;
	else
		tmp = z * -0.0424927283095952;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1e+65], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, -2.35e+24], N[(y / N[(x * x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -1350.0], N[Not[LessEqual[x, 3.0]], $MachinePrecision]], N[(N[(x * 4.16438922228), $MachinePrecision] - 110.1139242984811), $MachinePrecision], N[(z * -0.0424927283095952), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.9999999999999999e64

   1. Initial program 0.3%

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

      1. *-commutative 0.3%

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

      2. associate-*r/ 7.8%

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

      3. *-commutative 7.8%

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

      4. fma-def 7.8%

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

      5. *-commutative 7.8%

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

      6. fma-def 7.8%

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

      7. *-commutative 7.8%

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

      8. fma-def 7.8%

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

      9. fma-def 7.8%

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

   3. Simplified 7.8%

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

   4. Taylor expanded in x around inf 97.0%

      \[\leadsto \color{blue}{4.16438922228 \cdot x} \]
   5. Step-by-step derivation

      1. *-commutative 97.0%

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

   6. Simplified 97.0%

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

   if -9.9999999999999999e64 < x < -2.35e24

   1. Initial program 42.0%

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

   2. Taylor expanded in y around inf 42.0%

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

   3. Taylor expanded in x around inf 99.4%

      \[\leadsto \color{blue}{\frac{y}{{x}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 99.4%

         \[\leadsto \frac{y}{\color{blue}{x \cdot x}} \]

   5. Simplified 99.4%

      \[\leadsto \color{blue}{\frac{y}{x \cdot x}} \]

   if -2.35e24 < x < -1350 or 3 < x

   1. Initial program 19.2%

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

      1. *-commutative 19.2%

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

      2. associate-*r/ 21.8%

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

      3. *-commutative 21.8%

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

      4. fma-def 21.8%

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

      5. *-commutative 21.8%

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

      6. fma-def 21.8%

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

      7. *-commutative 21.8%

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

      8. fma-def 21.8%

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

      9. fma-def 21.8%

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

   3. Simplified 21.8%

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

   4. Taylor expanded in x around inf 85.6%

      \[\leadsto \color{blue}{4.16438922228 \cdot x - 110.1139242984811} \]

   if -1350 < x < 3

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*r/ 99.3%

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

      3. *-commutative 99.3%

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

      4. fma-def 99.3%

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

      5. *-commutative 99.3%

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

      6. fma-def 99.3%

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

      7. *-commutative 99.3%

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

      8. fma-def 99.3%

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

      9. fma-def 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 68.0%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+65}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq -2.35 \cdot 10^{+24}:\\ \;\;\;\;\frac{y}{x \cdot x}\\ \mathbf{elif}\;x \leq -1350 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;x \cdot 4.16438922228 - 110.1139242984811\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \end{array} \]

Alternative 15: 76.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+65}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{+24}:\\ \;\;\;\;\frac{y}{x \cdot x}\\ \mathbf{elif}\;x \leq -135 \lor \neg \left(x \leq 9.5\right):\\ \;\;\;\;x \cdot 4.16438922228 - 110.1139242984811\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1e+65)
   (/ (+ x -2.0) 0.24013125253755718)
   (if (<= x -3.6e+24)
     (/ y (* x x))
     (if (or (<= x -135.0) (not (<= x 9.5)))
       (- (* x 4.16438922228) 110.1139242984811)
       (* z -0.0424927283095952)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1e+65) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -3.6e+24) {
		tmp = y / (x * x);
	} else if ((x <= -135.0) || !(x <= 9.5)) {
		tmp = (x * 4.16438922228) - 110.1139242984811;
	} else {
		tmp = z * -0.0424927283095952;
	}
	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 <= (-1d+65)) then
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    else if (x <= (-3.6d+24)) then
        tmp = y / (x * x)
    else if ((x <= (-135.0d0)) .or. (.not. (x <= 9.5d0))) then
        tmp = (x * 4.16438922228d0) - 110.1139242984811d0
    else
        tmp = z * (-0.0424927283095952d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1e+65) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= -3.6e+24) {
		tmp = y / (x * x);
	} else if ((x <= -135.0) || !(x <= 9.5)) {
		tmp = (x * 4.16438922228) - 110.1139242984811;
	} else {
		tmp = z * -0.0424927283095952;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1e+65:
		tmp = (x + -2.0) / 0.24013125253755718
	elif x <= -3.6e+24:
		tmp = y / (x * x)
	elif (x <= -135.0) or not (x <= 9.5):
		tmp = (x * 4.16438922228) - 110.1139242984811
	else:
		tmp = z * -0.0424927283095952
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1e+65)
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	elseif (x <= -3.6e+24)
		tmp = Float64(y / Float64(x * x));
	elseif ((x <= -135.0) || !(x <= 9.5))
		tmp = Float64(Float64(x * 4.16438922228) - 110.1139242984811);
	else
		tmp = Float64(z * -0.0424927283095952);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1e+65)
		tmp = (x + -2.0) / 0.24013125253755718;
	elseif (x <= -3.6e+24)
		tmp = y / (x * x);
	elseif ((x <= -135.0) || ~((x <= 9.5)))
		tmp = (x * 4.16438922228) - 110.1139242984811;
	else
		tmp = z * -0.0424927283095952;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1e+65], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision], If[LessEqual[x, -3.6e+24], N[(y / N[(x * x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -135.0], N[Not[LessEqual[x, 9.5]], $MachinePrecision]], N[(N[(x * 4.16438922228), $MachinePrecision] - 110.1139242984811), $MachinePrecision], N[(z * -0.0424927283095952), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.9999999999999999e64

   1. Initial program 0.3%

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

      1. associate-/l* 7.8%

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

      2. sub-neg 7.8%

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

      3. metadata-eval 7.8%

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

      4. fma-def 7.8%

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

      5. fma-def 7.8%

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

      6. fma-def 7.8%

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

      7. fma-def 7.8%

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

      8. fma-def 7.8%

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

      9. fma-def 7.8%

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

      10. fma-def 7.8%

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

   3. Simplified 7.8%

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

   4. Taylor expanded in x around inf 97.6%

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

   if -9.9999999999999999e64 < x < -3.59999999999999983e24

   1. Initial program 42.0%

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

   2. Taylor expanded in y around inf 42.0%

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

   3. Taylor expanded in x around inf 99.4%

      \[\leadsto \color{blue}{\frac{y}{{x}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 99.4%

         \[\leadsto \frac{y}{\color{blue}{x \cdot x}} \]

   5. Simplified 99.4%

      \[\leadsto \color{blue}{\frac{y}{x \cdot x}} \]

   if -3.59999999999999983e24 < x < -135 or 9.5 < x

   1. Initial program 19.2%

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

      1. *-commutative 19.2%

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

      2. associate-*r/ 21.8%

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

      3. *-commutative 21.8%

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

      4. fma-def 21.8%

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

      5. *-commutative 21.8%

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

      6. fma-def 21.8%

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

      7. *-commutative 21.8%

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

      8. fma-def 21.8%

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

      9. fma-def 21.8%

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

   3. Simplified 21.8%

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

   4. Taylor expanded in x around inf 85.6%

      \[\leadsto \color{blue}{4.16438922228 \cdot x - 110.1139242984811} \]

   if -135 < x < 9.5

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*r/ 99.3%

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

      3. *-commutative 99.3%

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

      4. fma-def 99.3%

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

      5. *-commutative 99.3%

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

      6. fma-def 99.3%

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

      7. *-commutative 99.3%

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

      8. fma-def 99.3%

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

      9. fma-def 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 68.0%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+65}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{+24}:\\ \;\;\;\;\frac{y}{x \cdot x}\\ \mathbf{elif}\;x \leq -135 \lor \neg \left(x \leq 9.5\right):\\ \;\;\;\;x \cdot 4.16438922228 - 110.1139242984811\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \end{array} \]

Alternative 16: 77.2% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -135 \lor \neg \left(x \leq 2.4\right):\\ \;\;\;\;x \cdot 4.16438922228 - 110.1139242984811\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -135.0) (not (<= x 2.4)))
   (- (* x 4.16438922228) 110.1139242984811)
   (* z -0.0424927283095952)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -135.0) || !(x <= 2.4)) {
		tmp = (x * 4.16438922228) - 110.1139242984811;
	} else {
		tmp = z * -0.0424927283095952;
	}
	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 <= (-135.0d0)) .or. (.not. (x <= 2.4d0))) then
        tmp = (x * 4.16438922228d0) - 110.1139242984811d0
    else
        tmp = z * (-0.0424927283095952d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -135.0) || !(x <= 2.4)) {
		tmp = (x * 4.16438922228) - 110.1139242984811;
	} else {
		tmp = z * -0.0424927283095952;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -135.0) or not (x <= 2.4):
		tmp = (x * 4.16438922228) - 110.1139242984811
	else:
		tmp = z * -0.0424927283095952
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -135.0) || !(x <= 2.4))
		tmp = Float64(Float64(x * 4.16438922228) - 110.1139242984811);
	else
		tmp = Float64(z * -0.0424927283095952);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -135.0) || ~((x <= 2.4)))
		tmp = (x * 4.16438922228) - 110.1139242984811;
	else
		tmp = z * -0.0424927283095952;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -135.0], N[Not[LessEqual[x, 2.4]], $MachinePrecision]], N[(N[(x * 4.16438922228), $MachinePrecision] - 110.1139242984811), $MachinePrecision], N[(z * -0.0424927283095952), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -135 or 2.39999999999999991 < x

   1. Initial program 12.6%

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

      1. *-commutative 12.6%

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

      2. associate-*r/ 18.5%

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

      3. *-commutative 18.5%

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

      4. fma-def 18.5%

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

      5. *-commutative 18.5%

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

      6. fma-def 18.5%

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

      7. *-commutative 18.5%

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

      8. fma-def 18.5%

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

      9. fma-def 18.5%

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

   3. Simplified 18.5%

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

   4. Taylor expanded in x around inf 86.9%

      \[\leadsto \color{blue}{4.16438922228 \cdot x - 110.1139242984811} \]

   if -135 < x < 2.39999999999999991

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*r/ 99.3%

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

      3. *-commutative 99.3%

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

      4. fma-def 99.3%

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

      5. *-commutative 99.3%

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

      6. fma-def 99.3%

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

      7. *-commutative 99.3%

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

      8. fma-def 99.3%

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

      9. fma-def 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 68.0%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -135 \lor \neg \left(x \leq 2.4\right):\\ \;\;\;\;x \cdot 4.16438922228 - 110.1139242984811\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \end{array} \]

Alternative 17: 77.0% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1750:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1750.0)
   (* 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 <= -1750.0) {
		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 <= (-1750.0d0)) 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 <= -1750.0) {
		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 <= -1750.0:
		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 <= -1750.0)
		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 <= -1750.0)
		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, -1750.0], 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 < -1750 or 2 < x

   1. Initial program 12.6%

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

      1. *-commutative 12.6%

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

      2. associate-*r/ 18.5%

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

      3. *-commutative 18.5%

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

      4. fma-def 18.5%

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

      5. *-commutative 18.5%

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

      6. fma-def 18.5%

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

      7. *-commutative 18.5%

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

      8. fma-def 18.5%

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

      9. fma-def 18.5%

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

   3. Simplified 18.5%

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

   4. Taylor expanded in x around inf 86.2%

      \[\leadsto \color{blue}{4.16438922228 \cdot x} \]
   5. Step-by-step derivation

      1. *-commutative 86.2%

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

   6. Simplified 86.2%

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

   if -1750 < x < 2

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*r/ 99.3%

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

      3. *-commutative 99.3%

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

      4. fma-def 99.3%

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

      5. *-commutative 99.3%

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

      6. fma-def 99.3%

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

      7. *-commutative 99.3%

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

      8. fma-def 99.3%

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

      9. fma-def 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 68.0%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1750:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

Alternative 18: 77.0% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-8}:\\ \;\;\;\;x \cdot 4.16438922228 + 70.37071397084\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.2e-8)
   (+ (* x 4.16438922228) 70.37071397084)
   (if (<= x 2.0) (* z -0.0424927283095952) (* x 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.2e-8) {
		tmp = (x * 4.16438922228) + 70.37071397084;
	} 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 <= (-7.2d-8)) then
        tmp = (x * 4.16438922228d0) + 70.37071397084d0
    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 <= -7.2e-8) {
		tmp = (x * 4.16438922228) + 70.37071397084;
	} 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 <= -7.2e-8:
		tmp = (x * 4.16438922228) + 70.37071397084
	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 <= -7.2e-8)
		tmp = Float64(Float64(x * 4.16438922228) + 70.37071397084);
	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 <= -7.2e-8)
		tmp = (x * 4.16438922228) + 70.37071397084;
	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, -7.2e-8], N[(N[(x * 4.16438922228), $MachinePrecision] + 70.37071397084), $MachinePrecision], If[LessEqual[x, 2.0], N[(z * -0.0424927283095952), $MachinePrecision], N[(x * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.19999999999999962e-8

   1. Initial program 13.2%

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

   2. Taylor expanded in x around inf 9.8%

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\color{blue}{{x}^{3}} + 313.399215894\right) \cdot x + 47.066876606} \]

   3. Taylor expanded in x around inf 83.7%

      \[\leadsto \color{blue}{70.37071397084 + 4.16438922228 \cdot x} \]
   4. Step-by-step derivation

      1. +-commutative 83.7%

         \[\leadsto \color{blue}{4.16438922228 \cdot x + 70.37071397084} \]

      2. *-commutative 83.7%

         \[\leadsto \color{blue}{x \cdot 4.16438922228} + 70.37071397084 \]

   5. Simplified 83.7%

      \[\leadsto \color{blue}{x \cdot 4.16438922228 + 70.37071397084} \]

   if -7.19999999999999962e-8 < x < 2

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*r/ 99.3%

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

      3. *-commutative 99.3%

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

      4. fma-def 99.3%

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

      5. *-commutative 99.3%

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

      6. fma-def 99.3%

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

      7. *-commutative 99.3%

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

      8. fma-def 99.3%

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

      9. fma-def 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 69.0%

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

   if 2 < x

   1. Initial program 14.6%

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

      1. *-commutative 14.6%

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

      2. associate-*r/ 17.3%

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

      3. *-commutative 17.3%

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

      4. fma-def 17.3%

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

      5. *-commutative 17.3%

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

      6. fma-def 17.3%

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

      7. *-commutative 17.3%

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

      8. fma-def 17.3%

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

      9. fma-def 17.3%

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

   3. Simplified 17.3%

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

   4. Taylor expanded in x around inf 86.1%

      \[\leadsto \color{blue}{4.16438922228 \cdot x} \]
   5. Step-by-step derivation

      1. *-commutative 86.1%

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

   6. Simplified 86.1%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-8}:\\ \;\;\;\;x \cdot 4.16438922228 + 70.37071397084\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

Alternative 19: 34.6% accurate, 12.3× speedup

Math

\[\begin{array}{l} \\ z \cdot -0.0424927283095952 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* z -0.0424927283095952))

C

double code(double x, double y, double z) {
	return z * -0.0424927283095952;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = z * (-0.0424927283095952d0)
end function

Java

public static double code(double x, double y, double z) {
	return z * -0.0424927283095952;
}

Python

def code(x, y, z):
	return z * -0.0424927283095952

Julia

function code(x, y, z)
	return Float64(z * -0.0424927283095952)
end

MATLAB

function tmp = code(x, y, z)
	tmp = z * -0.0424927283095952;
end

Wolfram

code[x_, y_, z_] := N[(z * -0.0424927283095952), $MachinePrecision]

Derivation

1. Initial program 55.8%

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

   1. *-commutative 55.8%

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

   2. associate-*r/ 58.6%

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

   3. *-commutative 58.6%

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

   4. fma-def 58.6%

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

   5. *-commutative 58.6%

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

   6. fma-def 58.6%

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

   7. *-commutative 58.6%

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

   8. fma-def 58.6%

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

   9. fma-def 58.6%

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

3. Simplified 58.6%

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

4. Taylor expanded in x around 0 35.2%

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

5. Final simplification 35.2%

   \[\leadsto z \cdot -0.0424927283095952 \]

Developer target: 98.9% accurate, 0.8× 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 2023268 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C"
  :precision binary64

  :herbie-target
  (if (< x -3.326128725870005e+62) (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811) (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))) (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811)))

  (/ (* (- 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)))