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

Percentage Accurate: 58.6% → 98.5%

Time: 22.2s

Alternatives: 23

Speedup: 2.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 58.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 10^{+302}:\\ \;\;\;\;\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{y}{{x}^{2}}}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (/
       (*
        (- x 2.0)
        (+
         (*
          x
          (+
           (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
           y))
         z))
       (+
        (*
         x
         (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
        47.066876606))
      1e+302)
   (*
    (+ x -2.0)
    (/
     (fma
      (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
      x
      z)
     (fma
      (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
      x
      47.066876606)))
   (* (+ x -2.0) (+ 4.16438922228 (/ (/ y (pow x 2.0)) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)) <= 1e+302) {
		tmp = (x + -2.0) * (fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(fma((x + 43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606));
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((y / pow(x, 2.0)) / x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)) <= 1e+302)
		tmp = Float64(Float64(x + -2.0) * Float64(fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(fma(Float64(x + 43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(y / (x ^ 2.0)) / x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(x * N[(N[(x * N[(N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision] + 137.519416416), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], 1e+302], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(N[(N[(N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(N[(y / N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < 1.0000000000000001e302

   1. Initial program 94.8%

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

      1. associate-/l* 99.6%

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

      2. sub-neg 99.6%

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

      3. metadata-eval 99.6%

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

      4. fma-define 99.6%

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

      5. fma-define 99.6%

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

      6. fma-define 99.6%

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

      7. fma-define 99.6%

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

      8. fma-define 99.6%

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

      9. fma-define 99.6%

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

      10. fma-define 99.6%

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

   3. Simplified 99.6%

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

   if 1.0000000000000001e302 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64)))

   1. Initial program 0.2%

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

      1. associate-/l* 3.5%

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

      2. sub-neg 3.5%

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

      3. metadata-eval 3.5%

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

      4. fma-define 3.5%

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

      5. fma-define 3.5%

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

      6. fma-define 3.5%

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

      7. fma-define 3.5%

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

      8. fma-define 3.5%

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

      9. fma-define 3.5%

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

      10. fma-define 3.5%

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

   3. Simplified 3.5%

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

   5. Taylor expanded in x around -inf 97.8%

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

      1. mul-1-neg 97.8%

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

      2. unsub-neg 97.8%

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

      3. mul-1-neg 97.8%

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

      4. unsub-neg 97.8%

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

      5. mul-1-neg 97.8%

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

      6. unsub-neg 97.8%

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

      7. mul-1-neg 97.8%

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

      8. unsub-neg 97.8%

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

   7. Simplified 97.8%

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

   8. Taylor expanded in y around inf 97.8%

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

      1. mul-1-neg 97.8%

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

      2. distribute-neg-frac2 97.8%

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

   10. Simplified 97.8%

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

   11. Taylor expanded in y around inf 97.9%

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

       1. associate-*r/ 97.9%

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

       2. mul-1-neg 97.9%

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

   13. Simplified 97.9%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 10^{+302}:\\ \;\;\;\;\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{y}{{x}^{2}}}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)\\ t_1 := x \cdot \left(x + 43.3400022514\right)\\ t_2 := x \cdot \left(x \cdot \left(t\_1 + 263.505074721\right) + 313.399215894\right) + 47.066876606\\ \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(t\_0 + z\right)}{t\_2} \leq 10^{+302}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{z}{47.066876606 + x \cdot \left(313.399215894 + \left(x \cdot 263.505074721 + x \cdot t\_1\right)\right)} + \frac{t\_0}{t\_2}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{y}{{x}^{2}}}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          x
          (+
           (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
           y)))
        (t_1 (* x (+ x 43.3400022514)))
        (t_2
         (+ (* x (+ (* x (+ t_1 263.505074721)) 313.399215894)) 47.066876606)))
   (if (<= (/ (* (- x 2.0) (+ t_0 z)) t_2) 1e+302)
     (*
      (+ x -2.0)
      (+
       (/
        z
        (+
         47.066876606
         (* x (+ 313.399215894 (+ (* x 263.505074721) (* x t_1))))))
       (/ t_0 t_2)))
     (* (+ x -2.0) (+ 4.16438922228 (/ (/ y (pow x 2.0)) x))))))

C

double code(double x, double y, double z) {
	double t_0 = x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y);
	double t_1 = x * (x + 43.3400022514);
	double t_2 = (x * ((x * (t_1 + 263.505074721)) + 313.399215894)) + 47.066876606;
	double tmp;
	if ((((x - 2.0) * (t_0 + z)) / t_2) <= 1e+302) {
		tmp = (x + -2.0) * ((z / (47.066876606 + (x * (313.399215894 + ((x * 263.505074721) + (x * t_1)))))) + (t_0 / t_2));
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((y / pow(x, 2.0)) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = x * ((x * ((x * ((x * 4.16438922228d0) + 78.6994924154d0)) + 137.519416416d0)) + y)
    t_1 = x * (x + 43.3400022514d0)
    t_2 = (x * ((x * (t_1 + 263.505074721d0)) + 313.399215894d0)) + 47.066876606d0
    if ((((x - 2.0d0) * (t_0 + z)) / t_2) <= 1d+302) then
        tmp = (x + (-2.0d0)) * ((z / (47.066876606d0 + (x * (313.399215894d0 + ((x * 263.505074721d0) + (x * t_1)))))) + (t_0 / t_2))
    else
        tmp = (x + (-2.0d0)) * (4.16438922228d0 + ((y / (x ** 2.0d0)) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y);
	double t_1 = x * (x + 43.3400022514);
	double t_2 = (x * ((x * (t_1 + 263.505074721)) + 313.399215894)) + 47.066876606;
	double tmp;
	if ((((x - 2.0) * (t_0 + z)) / t_2) <= 1e+302) {
		tmp = (x + -2.0) * ((z / (47.066876606 + (x * (313.399215894 + ((x * 263.505074721) + (x * t_1)))))) + (t_0 / t_2));
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((y / Math.pow(x, 2.0)) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)
	t_1 = x * (x + 43.3400022514)
	t_2 = (x * ((x * (t_1 + 263.505074721)) + 313.399215894)) + 47.066876606
	tmp = 0
	if (((x - 2.0) * (t_0 + z)) / t_2) <= 1e+302:
		tmp = (x + -2.0) * ((z / (47.066876606 + (x * (313.399215894 + ((x * 263.505074721) + (x * t_1)))))) + (t_0 / t_2))
	else:
		tmp = (x + -2.0) * (4.16438922228 + ((y / math.pow(x, 2.0)) / x))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y))
	t_1 = Float64(x * Float64(x + 43.3400022514))
	t_2 = Float64(Float64(x * Float64(Float64(x * Float64(t_1 + 263.505074721)) + 313.399215894)) + 47.066876606)
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * Float64(t_0 + z)) / t_2) <= 1e+302)
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(z / Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(Float64(x * 263.505074721) + Float64(x * t_1)))))) + Float64(t_0 / t_2)));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(y / (x ^ 2.0)) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y);
	t_1 = x * (x + 43.3400022514);
	t_2 = (x * ((x * (t_1 + 263.505074721)) + 313.399215894)) + 47.066876606;
	tmp = 0.0;
	if ((((x - 2.0) * (t_0 + z)) / t_2) <= 1e+302)
		tmp = (x + -2.0) * ((z / (47.066876606 + (x * (313.399215894 + ((x * 263.505074721) + (x * t_1)))))) + (t_0 / t_2));
	else
		tmp = (x + -2.0) * (4.16438922228 + ((y / (x ^ 2.0)) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = 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]}, Block[{t$95$1 = N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(x * N[(t$95$1 + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * N[(t$95$0 + z), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], 1e+302], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(z / N[(47.066876606 + N[(x * N[(313.399215894 + N[(N[(x * 263.505074721), $MachinePrecision] + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(N[(y / N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < 1.0000000000000001e302

   1. Initial program 94.8%

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

      1. associate-/l* 99.6%

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

      2. sub-neg 99.6%

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

      3. metadata-eval 99.6%

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

      4. fma-define 99.6%

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

      5. fma-define 99.6%

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

      6. fma-define 99.6%

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

      7. fma-define 99.6%

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

      8. fma-define 99.6%

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

      9. fma-define 99.6%

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

      10. fma-define 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around 0 99.6%

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

      1. distribute-lft-in 99.6%

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

      2. +-commutative 99.6%

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

   7. Applied egg-rr 99.6%

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

   if 1.0000000000000001e302 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64)))

   1. Initial program 0.2%

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

      1. associate-/l* 3.5%

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

      2. sub-neg 3.5%

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

      3. metadata-eval 3.5%

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

      4. fma-define 3.5%

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

      5. fma-define 3.5%

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

      6. fma-define 3.5%

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

      7. fma-define 3.5%

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

      8. fma-define 3.5%

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

      9. fma-define 3.5%

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

      10. fma-define 3.5%

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

   3. Simplified 3.5%

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

   5. Taylor expanded in x around -inf 97.8%

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

      1. mul-1-neg 97.8%

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

      2. unsub-neg 97.8%

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

      3. mul-1-neg 97.8%

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

      4. unsub-neg 97.8%

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

      5. mul-1-neg 97.8%

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

      6. unsub-neg 97.8%

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

      7. mul-1-neg 97.8%

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

      8. unsub-neg 97.8%

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

   7. Simplified 97.8%

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

   8. Taylor expanded in y around inf 97.8%

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

      1. mul-1-neg 97.8%

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

      2. distribute-neg-frac2 97.8%

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

   10. Simplified 97.8%

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

   11. Taylor expanded in y around inf 97.9%

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

       1. associate-*r/ 97.9%

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

       2. mul-1-neg 97.9%

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

   13. Simplified 97.9%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 10^{+302}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{z}{47.066876606 + x \cdot \left(313.399215894 + \left(x \cdot 263.505074721 + x \cdot \left(x \cdot \left(x + 43.3400022514\right)\right)\right)\right)} + \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{y}{{x}^{2}}}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606\\ t_1 := \frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{t\_0}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{z}{t\_0}\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+302}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{1}{\frac{x}{y - 124074.40615218398}}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          (*
           x
           (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
          47.066876606))
        (t_1
         (/
          (*
           (- x 2.0)
           (+
            (*
             x
             (+
              (*
               x
               (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
              y))
            z))
          t_0)))
   (if (<= t_1 (- INFINITY))
     (* (+ x -2.0) (+ 4.16438922228 (/ z t_0)))
     (if (<= t_1 1e+302)
       t_1
       (*
        (+ x -2.0)
        (+
         4.16438922228
         (/
          (-
           (/ (+ 3451.550173699799 (/ 1.0 (/ x (- y 124074.40615218398)))) x)
           101.7851458539211)
          x)))))))

C

double code(double x, double y, double z) {
	double t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	double t_1 = ((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / t_0;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x + -2.0) * (4.16438922228 + (z / t_0));
	} else if (t_1 <= 1e+302) {
		tmp = t_1;
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (1.0 / (x / (y - 124074.40615218398)))) / x) - 101.7851458539211) / x));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	double t_1 = ((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / t_0;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x + -2.0) * (4.16438922228 + (z / t_0));
	} else if (t_1 <= 1e+302) {
		tmp = t_1;
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (1.0 / (x / (y - 124074.40615218398)))) / x) - 101.7851458539211) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606
	t_1 = ((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / t_0
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x + -2.0) * (4.16438922228 + (z / t_0))
	elif t_1 <= 1e+302:
		tmp = t_1
	else:
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (1.0 / (x / (y - 124074.40615218398)))) / x) - 101.7851458539211) / x))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)
	t_1 = Float64(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)) / t_0)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(z / t_0)));
	elseif (t_1 <= 1e+302)
		tmp = t_1;
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(1.0 / Float64(x / Float64(y - 124074.40615218398)))) / x) - 101.7851458539211) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	t_1 = ((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / t_0;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x + -2.0) * (4.16438922228 + (z / t_0));
	elseif (t_1 <= 1e+302)
		tmp = t_1;
	else
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (1.0 / (x / (y - 124074.40615218398)))) / x) - 101.7851458539211) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]}, Block[{t$95$1 = 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] / t$95$0), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(z / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+302], t$95$1, N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(N[(N[(N[(3451.550173699799 + N[(1.0 / N[(x / N[(y - 124074.40615218398), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 4.5%

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

      1. associate-/l* 98.9%

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

      2. sub-neg 98.9%

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

      3. metadata-eval 98.9%

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

      4. fma-define 98.9%

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

      5. fma-define 98.9%

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

      6. fma-define 98.9%

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

      7. fma-define 98.9%

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

      8. fma-define 98.9%

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

      9. fma-define 98.9%

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

      10. fma-define 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in z around 0 98.9%

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

   6. Taylor expanded in x around inf 99.1%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < 1.0000000000000001e302

   1. Initial program 99.6%

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

   if 1.0000000000000001e302 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64)))

   1. Initial program 0.2%

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

      1. associate-/l* 3.5%

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

      2. sub-neg 3.5%

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

      3. metadata-eval 3.5%

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

      4. fma-define 3.5%

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

      5. fma-define 3.5%

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

      6. fma-define 3.5%

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

      7. fma-define 3.5%

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

      8. fma-define 3.5%

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

      9. fma-define 3.5%

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

      10. fma-define 3.5%

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

   3. Simplified 3.5%

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

   5. Taylor expanded in x around -inf 97.8%

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

      1. mul-1-neg 97.8%

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

      2. unsub-neg 97.8%

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

      3. mul-1-neg 97.8%

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

      4. unsub-neg 97.8%

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

      5. mul-1-neg 97.8%

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

      6. unsub-neg 97.8%

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

      7. mul-1-neg 97.8%

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

      8. unsub-neg 97.8%

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

   7. Simplified 97.8%

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

      1. clear-num 97.8%

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

      2. inv-pow 97.8%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \color{blue}{{\left(\frac{x}{124074.40615218398 - y}\right)}^{-1}}}{x}}{x}\right) \]

   9. Applied egg-rr 97.8%

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

       1. unpow-1 97.8%

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

   11. Simplified 97.8%

       \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \color{blue}{\frac{1}{\frac{x}{124074.40615218398 - y}}}}{x}}{x}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq -\infty:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\right)\\ \mathbf{elif}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 10^{+302}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{1}{\frac{x}{y - 124074.40615218398}}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)\\ t_1 := x \cdot \left(x + 43.3400022514\right)\\ t_2 := x \cdot \left(x \cdot \left(t\_1 + 263.505074721\right) + 313.399215894\right) + 47.066876606\\ \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(t\_0 + z\right)}{t\_2} \leq 10^{+302}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{z}{47.066876606 + x \cdot \left(313.399215894 + \left(x \cdot 263.505074721 + x \cdot t\_1\right)\right)} + \frac{t\_0}{t\_2}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{1}{\frac{x}{y - 124074.40615218398}}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          x
          (+
           (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
           y)))
        (t_1 (* x (+ x 43.3400022514)))
        (t_2
         (+ (* x (+ (* x (+ t_1 263.505074721)) 313.399215894)) 47.066876606)))
   (if (<= (/ (* (- x 2.0) (+ t_0 z)) t_2) 1e+302)
     (*
      (+ x -2.0)
      (+
       (/
        z
        (+
         47.066876606
         (* x (+ 313.399215894 (+ (* x 263.505074721) (* x t_1))))))
       (/ t_0 t_2)))
     (*
      (+ x -2.0)
      (+
       4.16438922228
       (/
        (-
         (/ (+ 3451.550173699799 (/ 1.0 (/ x (- y 124074.40615218398)))) x)
         101.7851458539211)
        x))))))

C

double code(double x, double y, double z) {
	double t_0 = x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y);
	double t_1 = x * (x + 43.3400022514);
	double t_2 = (x * ((x * (t_1 + 263.505074721)) + 313.399215894)) + 47.066876606;
	double tmp;
	if ((((x - 2.0) * (t_0 + z)) / t_2) <= 1e+302) {
		tmp = (x + -2.0) * ((z / (47.066876606 + (x * (313.399215894 + ((x * 263.505074721) + (x * t_1)))))) + (t_0 / t_2));
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (1.0 / (x / (y - 124074.40615218398)))) / x) - 101.7851458539211) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = x * ((x * ((x * ((x * 4.16438922228d0) + 78.6994924154d0)) + 137.519416416d0)) + y)
    t_1 = x * (x + 43.3400022514d0)
    t_2 = (x * ((x * (t_1 + 263.505074721d0)) + 313.399215894d0)) + 47.066876606d0
    if ((((x - 2.0d0) * (t_0 + z)) / t_2) <= 1d+302) then
        tmp = (x + (-2.0d0)) * ((z / (47.066876606d0 + (x * (313.399215894d0 + ((x * 263.505074721d0) + (x * t_1)))))) + (t_0 / t_2))
    else
        tmp = (x + (-2.0d0)) * (4.16438922228d0 + ((((3451.550173699799d0 + (1.0d0 / (x / (y - 124074.40615218398d0)))) / x) - 101.7851458539211d0) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y);
	double t_1 = x * (x + 43.3400022514);
	double t_2 = (x * ((x * (t_1 + 263.505074721)) + 313.399215894)) + 47.066876606;
	double tmp;
	if ((((x - 2.0) * (t_0 + z)) / t_2) <= 1e+302) {
		tmp = (x + -2.0) * ((z / (47.066876606 + (x * (313.399215894 + ((x * 263.505074721) + (x * t_1)))))) + (t_0 / t_2));
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (1.0 / (x / (y - 124074.40615218398)))) / x) - 101.7851458539211) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)
	t_1 = x * (x + 43.3400022514)
	t_2 = (x * ((x * (t_1 + 263.505074721)) + 313.399215894)) + 47.066876606
	tmp = 0
	if (((x - 2.0) * (t_0 + z)) / t_2) <= 1e+302:
		tmp = (x + -2.0) * ((z / (47.066876606 + (x * (313.399215894 + ((x * 263.505074721) + (x * t_1)))))) + (t_0 / t_2))
	else:
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (1.0 / (x / (y - 124074.40615218398)))) / x) - 101.7851458539211) / x))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y))
	t_1 = Float64(x * Float64(x + 43.3400022514))
	t_2 = Float64(Float64(x * Float64(Float64(x * Float64(t_1 + 263.505074721)) + 313.399215894)) + 47.066876606)
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * Float64(t_0 + z)) / t_2) <= 1e+302)
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(z / Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(Float64(x * 263.505074721) + Float64(x * t_1)))))) + Float64(t_0 / t_2)));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(1.0 / Float64(x / Float64(y - 124074.40615218398)))) / x) - 101.7851458539211) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y);
	t_1 = x * (x + 43.3400022514);
	t_2 = (x * ((x * (t_1 + 263.505074721)) + 313.399215894)) + 47.066876606;
	tmp = 0.0;
	if ((((x - 2.0) * (t_0 + z)) / t_2) <= 1e+302)
		tmp = (x + -2.0) * ((z / (47.066876606 + (x * (313.399215894 + ((x * 263.505074721) + (x * t_1)))))) + (t_0 / t_2));
	else
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (1.0 / (x / (y - 124074.40615218398)))) / x) - 101.7851458539211) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = 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]}, Block[{t$95$1 = N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(x * N[(t$95$1 + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * N[(t$95$0 + z), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], 1e+302], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(z / N[(47.066876606 + N[(x * N[(313.399215894 + N[(N[(x * 263.505074721), $MachinePrecision] + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(N[(N[(N[(3451.550173699799 + N[(1.0 / N[(x / N[(y - 124074.40615218398), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < 1.0000000000000001e302

   1. Initial program 94.8%

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

      1. associate-/l* 99.6%

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

      2. sub-neg 99.6%

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

      3. metadata-eval 99.6%

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

      4. fma-define 99.6%

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

      5. fma-define 99.6%

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

      6. fma-define 99.6%

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

      7. fma-define 99.6%

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

      8. fma-define 99.6%

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

      9. fma-define 99.6%

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

      10. fma-define 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around 0 99.6%

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

      1. distribute-lft-in 99.6%

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

      2. +-commutative 99.6%

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

   7. Applied egg-rr 99.6%

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

   if 1.0000000000000001e302 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64)))

   1. Initial program 0.2%

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

      1. associate-/l* 3.5%

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

      2. sub-neg 3.5%

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

      3. metadata-eval 3.5%

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

      4. fma-define 3.5%

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

      5. fma-define 3.5%

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

      6. fma-define 3.5%

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

      7. fma-define 3.5%

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

      8. fma-define 3.5%

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

      9. fma-define 3.5%

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

      10. fma-define 3.5%

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

   3. Simplified 3.5%

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

   5. Taylor expanded in x around -inf 97.8%

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

      1. mul-1-neg 97.8%

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

      2. unsub-neg 97.8%

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

      3. mul-1-neg 97.8%

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

      4. unsub-neg 97.8%

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

      5. mul-1-neg 97.8%

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

      6. unsub-neg 97.8%

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

      7. mul-1-neg 97.8%

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

      8. unsub-neg 97.8%

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

   7. Simplified 97.8%

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

      1. clear-num 97.8%

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

      2. inv-pow 97.8%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \color{blue}{{\left(\frac{x}{124074.40615218398 - y}\right)}^{-1}}}{x}}{x}\right) \]

   9. Applied egg-rr 97.8%

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

       1. unpow-1 97.8%

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

   11. Simplified 97.8%

       \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \color{blue}{\frac{1}{\frac{x}{124074.40615218398 - y}}}}{x}}{x}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 10^{+302}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{z}{47.066876606 + x \cdot \left(313.399215894 + \left(x \cdot 263.505074721 + x \cdot \left(x \cdot \left(x + 43.3400022514\right)\right)\right)\right)} + \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{1}{\frac{x}{y - 124074.40615218398}}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606\\ t_1 := x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)\\ \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(t\_1 + z\right)}{t\_0} \leq 10^{+302}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{t\_1}{t\_0} + \frac{z}{t\_0}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{1}{\frac{x}{y - 124074.40615218398}}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          (*
           x
           (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
          47.066876606))
        (t_1
         (*
          x
          (+
           (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
           y))))
   (if (<= (/ (* (- x 2.0) (+ t_1 z)) t_0) 1e+302)
     (* (+ x -2.0) (+ (/ t_1 t_0) (/ z t_0)))
     (*
      (+ x -2.0)
      (+
       4.16438922228
       (/
        (-
         (/ (+ 3451.550173699799 (/ 1.0 (/ x (- y 124074.40615218398)))) x)
         101.7851458539211)
        x))))))

C

double code(double x, double y, double z) {
	double t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	double t_1 = x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y);
	double tmp;
	if ((((x - 2.0) * (t_1 + z)) / t_0) <= 1e+302) {
		tmp = (x + -2.0) * ((t_1 / t_0) + (z / t_0));
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (1.0 / (x / (y - 124074.40615218398)))) / x) - 101.7851458539211) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (x * ((x * ((x * (x + 43.3400022514d0)) + 263.505074721d0)) + 313.399215894d0)) + 47.066876606d0
    t_1 = x * ((x * ((x * ((x * 4.16438922228d0) + 78.6994924154d0)) + 137.519416416d0)) + y)
    if ((((x - 2.0d0) * (t_1 + z)) / t_0) <= 1d+302) then
        tmp = (x + (-2.0d0)) * ((t_1 / t_0) + (z / t_0))
    else
        tmp = (x + (-2.0d0)) * (4.16438922228d0 + ((((3451.550173699799d0 + (1.0d0 / (x / (y - 124074.40615218398d0)))) / x) - 101.7851458539211d0) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	double t_1 = x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y);
	double tmp;
	if ((((x - 2.0) * (t_1 + z)) / t_0) <= 1e+302) {
		tmp = (x + -2.0) * ((t_1 / t_0) + (z / t_0));
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (1.0 / (x / (y - 124074.40615218398)))) / x) - 101.7851458539211) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606
	t_1 = x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)
	tmp = 0
	if (((x - 2.0) * (t_1 + z)) / t_0) <= 1e+302:
		tmp = (x + -2.0) * ((t_1 / t_0) + (z / t_0))
	else:
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (1.0 / (x / (y - 124074.40615218398)))) / x) - 101.7851458539211) / x))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)
	t_1 = Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y))
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * Float64(t_1 + z)) / t_0) <= 1e+302)
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(t_1 / t_0) + Float64(z / t_0)));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(1.0 / Float64(x / Float64(y - 124074.40615218398)))) / x) - 101.7851458539211) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	t_1 = x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y);
	tmp = 0.0;
	if ((((x - 2.0) * (t_1 + z)) / t_0) <= 1e+302)
		tmp = (x + -2.0) * ((t_1 / t_0) + (z / t_0));
	else
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (1.0 / (x / (y - 124074.40615218398)))) / x) - 101.7851458539211) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]}, Block[{t$95$1 = 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]}, If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * N[(t$95$1 + z), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision], 1e+302], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(t$95$1 / t$95$0), $MachinePrecision] + N[(z / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(N[(N[(N[(3451.550173699799 + N[(1.0 / N[(x / N[(y - 124074.40615218398), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < 1.0000000000000001e302

   1. Initial program 94.8%

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

      1. associate-/l* 99.6%

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

      2. sub-neg 99.6%

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

      3. metadata-eval 99.6%

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

      4. fma-define 99.6%

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

      5. fma-define 99.6%

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

      6. fma-define 99.6%

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

      7. fma-define 99.6%

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

      8. fma-define 99.6%

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

      9. fma-define 99.6%

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

      10. fma-define 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around 0 99.6%

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

   if 1.0000000000000001e302 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64)))

   1. Initial program 0.2%

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

      1. associate-/l* 3.5%

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

      2. sub-neg 3.5%

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

      3. metadata-eval 3.5%

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

      4. fma-define 3.5%

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

      5. fma-define 3.5%

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

      6. fma-define 3.5%

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

      7. fma-define 3.5%

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

      8. fma-define 3.5%

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

      9. fma-define 3.5%

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

      10. fma-define 3.5%

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

   3. Simplified 3.5%

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

   5. Taylor expanded in x around -inf 97.8%

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

      1. mul-1-neg 97.8%

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

      2. unsub-neg 97.8%

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

      3. mul-1-neg 97.8%

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

      4. unsub-neg 97.8%

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

      5. mul-1-neg 97.8%

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

      6. unsub-neg 97.8%

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

      7. mul-1-neg 97.8%

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

      8. unsub-neg 97.8%

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

   7. Simplified 97.8%

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

      1. clear-num 97.8%

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

      2. inv-pow 97.8%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \color{blue}{{\left(\frac{x}{124074.40615218398 - y}\right)}^{-1}}}{x}}{x}\right) \]

   9. Applied egg-rr 97.8%

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

       1. unpow-1 97.8%

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

   11. Simplified 97.8%

       \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \color{blue}{\frac{1}{\frac{x}{124074.40615218398 - y}}}}{x}}{x}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 10^{+302}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} + \frac{z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{1}{\frac{x}{y - 124074.40615218398}}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{+23}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{z}{t\_0}\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+18}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot 78.6994924154\right)\right)\right)}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{1}{\frac{x}{y - 124074.40615218398}}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          (*
           x
           (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
          47.066876606)))
   (if (<= x -2.3e+23)
     (* (+ x -2.0) (+ 4.16438922228 (/ z t_0)))
     (if (<= x 2.6e+18)
       (/
        (*
         (- x 2.0)
         (+ z (* x (+ y (* x (+ 137.519416416 (* x 78.6994924154)))))))
        t_0)
       (*
        (+ x -2.0)
        (+
         4.16438922228
         (/
          (-
           (/ (+ 3451.550173699799 (/ 1.0 (/ x (- y 124074.40615218398)))) x)
           101.7851458539211)
          x)))))))

C

double code(double x, double y, double z) {
	double t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	double tmp;
	if (x <= -2.3e+23) {
		tmp = (x + -2.0) * (4.16438922228 + (z / t_0));
	} else if (x <= 2.6e+18) {
		tmp = ((x - 2.0) * (z + (x * (y + (x * (137.519416416 + (x * 78.6994924154))))))) / t_0;
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (1.0 / (x / (y - 124074.40615218398)))) / x) - 101.7851458539211) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x * ((x * ((x * (x + 43.3400022514d0)) + 263.505074721d0)) + 313.399215894d0)) + 47.066876606d0
    if (x <= (-2.3d+23)) then
        tmp = (x + (-2.0d0)) * (4.16438922228d0 + (z / t_0))
    else if (x <= 2.6d+18) then
        tmp = ((x - 2.0d0) * (z + (x * (y + (x * (137.519416416d0 + (x * 78.6994924154d0))))))) / t_0
    else
        tmp = (x + (-2.0d0)) * (4.16438922228d0 + ((((3451.550173699799d0 + (1.0d0 / (x / (y - 124074.40615218398d0)))) / x) - 101.7851458539211d0) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	double tmp;
	if (x <= -2.3e+23) {
		tmp = (x + -2.0) * (4.16438922228 + (z / t_0));
	} else if (x <= 2.6e+18) {
		tmp = ((x - 2.0) * (z + (x * (y + (x * (137.519416416 + (x * 78.6994924154))))))) / t_0;
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (1.0 / (x / (y - 124074.40615218398)))) / x) - 101.7851458539211) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606
	tmp = 0
	if x <= -2.3e+23:
		tmp = (x + -2.0) * (4.16438922228 + (z / t_0))
	elif x <= 2.6e+18:
		tmp = ((x - 2.0) * (z + (x * (y + (x * (137.519416416 + (x * 78.6994924154))))))) / t_0
	else:
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (1.0 / (x / (y - 124074.40615218398)))) / x) - 101.7851458539211) / x))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)
	tmp = 0.0
	if (x <= -2.3e+23)
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(z / t_0)));
	elseif (x <= 2.6e+18)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(z + Float64(x * Float64(y + Float64(x * Float64(137.519416416 + Float64(x * 78.6994924154))))))) / t_0);
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(1.0 / Float64(x / Float64(y - 124074.40615218398)))) / x) - 101.7851458539211) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	tmp = 0.0;
	if (x <= -2.3e+23)
		tmp = (x + -2.0) * (4.16438922228 + (z / t_0));
	elseif (x <= 2.6e+18)
		tmp = ((x - 2.0) * (z + (x * (y + (x * (137.519416416 + (x * 78.6994924154))))))) / t_0;
	else
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (1.0 / (x / (y - 124074.40615218398)))) / x) - 101.7851458539211) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]}, If[LessEqual[x, -2.3e+23], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(z / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.6e+18], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(z + N[(x * N[(y + N[(x * N[(137.519416416 + N[(x * 78.6994924154), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(N[(N[(N[(3451.550173699799 + N[(1.0 / N[(x / N[(y - 124074.40615218398), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.3e23

   1. Initial program 7.1%

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

      1. associate-/l* 16.7%

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

      2. sub-neg 16.7%

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

      3. metadata-eval 16.7%

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

      4. fma-define 16.7%

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

      5. fma-define 16.7%

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

      6. fma-define 16.7%

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

      7. fma-define 16.7%

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

      8. fma-define 16.7%

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

      9. fma-define 16.7%

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

      10. fma-define 16.7%

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

   3. Simplified 16.7%

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

   5. Taylor expanded in z around 0 16.7%

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

   6. Taylor expanded in x around inf 99.1%

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

   if -2.3e23 < x < 2.6e18

   1. Initial program 98.2%

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

   3. Taylor expanded in x around 0 96.6%

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

      1. *-commutative 96.6%

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

   5. Simplified 96.6%

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

   if 2.6e18 < x

   1. Initial program 7.3%

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

      1. associate-/l* 11.3%

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

      2. sub-neg 11.3%

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

      3. metadata-eval 11.3%

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

      4. fma-define 11.3%

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

      5. fma-define 11.3%

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

      6. fma-define 11.3%

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

      7. fma-define 11.3%

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

      8. fma-define 11.3%

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

      9. fma-define 11.3%

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

      10. fma-define 11.3%

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

   3. Simplified 11.3%

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

   5. Taylor expanded in x around -inf 96.4%

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

      1. mul-1-neg 96.4%

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

      2. unsub-neg 96.4%

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

      3. mul-1-neg 96.4%

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

      4. unsub-neg 96.4%

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

      5. mul-1-neg 96.4%

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

      6. unsub-neg 96.4%

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

      7. mul-1-neg 96.4%

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

      8. unsub-neg 96.4%

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

   7. Simplified 96.4%

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

      1. clear-num 96.4%

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

      2. inv-pow 96.4%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \color{blue}{{\left(\frac{x}{124074.40615218398 - y}\right)}^{-1}}}{x}}{x}\right) \]

   9. Applied egg-rr 96.4%

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

       1. unpow-1 96.4%

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

   11. Simplified 96.4%

       \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \color{blue}{\frac{1}{\frac{x}{124074.40615218398 - y}}}}{x}}{x}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+23}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+18}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot 78.6994924154\right)\right)\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{1}{\frac{x}{y - 124074.40615218398}}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 96.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606\\ \mathbf{if}\;x \leq -3.15 \cdot 10^{+29}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{z}{t\_0}\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+16}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{1}{\frac{x}{y - 124074.40615218398}}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          (*
           x
           (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
          47.066876606)))
   (if (<= x -3.15e+29)
     (* (+ x -2.0) (+ 4.16438922228 (/ z t_0)))
     (if (<= x 3.1e+16)
       (/ (* (- x 2.0) (+ z (* x (+ y (* x 137.519416416))))) t_0)
       (*
        (+ x -2.0)
        (+
         4.16438922228
         (/
          (-
           (/ (+ 3451.550173699799 (/ 1.0 (/ x (- y 124074.40615218398)))) x)
           101.7851458539211)
          x)))))))

C

double code(double x, double y, double z) {
	double t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	double tmp;
	if (x <= -3.15e+29) {
		tmp = (x + -2.0) * (4.16438922228 + (z / t_0));
	} else if (x <= 3.1e+16) {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / t_0;
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (1.0 / (x / (y - 124074.40615218398)))) / x) - 101.7851458539211) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x * ((x * ((x * (x + 43.3400022514d0)) + 263.505074721d0)) + 313.399215894d0)) + 47.066876606d0
    if (x <= (-3.15d+29)) then
        tmp = (x + (-2.0d0)) * (4.16438922228d0 + (z / t_0))
    else if (x <= 3.1d+16) then
        tmp = ((x - 2.0d0) * (z + (x * (y + (x * 137.519416416d0))))) / t_0
    else
        tmp = (x + (-2.0d0)) * (4.16438922228d0 + ((((3451.550173699799d0 + (1.0d0 / (x / (y - 124074.40615218398d0)))) / x) - 101.7851458539211d0) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	double tmp;
	if (x <= -3.15e+29) {
		tmp = (x + -2.0) * (4.16438922228 + (z / t_0));
	} else if (x <= 3.1e+16) {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / t_0;
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (1.0 / (x / (y - 124074.40615218398)))) / x) - 101.7851458539211) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606
	tmp = 0
	if x <= -3.15e+29:
		tmp = (x + -2.0) * (4.16438922228 + (z / t_0))
	elif x <= 3.1e+16:
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / t_0
	else:
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (1.0 / (x / (y - 124074.40615218398)))) / x) - 101.7851458539211) / x))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)
	tmp = 0.0
	if (x <= -3.15e+29)
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(z / t_0)));
	elseif (x <= 3.1e+16)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(z + Float64(x * Float64(y + Float64(x * 137.519416416))))) / t_0);
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(1.0 / Float64(x / Float64(y - 124074.40615218398)))) / x) - 101.7851458539211) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	tmp = 0.0;
	if (x <= -3.15e+29)
		tmp = (x + -2.0) * (4.16438922228 + (z / t_0));
	elseif (x <= 3.1e+16)
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / t_0;
	else
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (1.0 / (x / (y - 124074.40615218398)))) / x) - 101.7851458539211) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]}, If[LessEqual[x, -3.15e+29], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(z / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.1e+16], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(z + N[(x * N[(y + N[(x * 137.519416416), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(N[(N[(N[(3451.550173699799 + N[(1.0 / N[(x / N[(y - 124074.40615218398), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.1499999999999999e29

   1. Initial program 7.1%

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

      1. associate-/l* 16.7%

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

      2. sub-neg 16.7%

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

      3. metadata-eval 16.7%

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

      4. fma-define 16.7%

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

      5. fma-define 16.7%

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

      6. fma-define 16.7%

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

      7. fma-define 16.7%

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

      8. fma-define 16.7%

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

      9. fma-define 16.7%

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

      10. fma-define 16.7%

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

   3. Simplified 16.7%

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

   5. Taylor expanded in z around 0 16.7%

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

   6. Taylor expanded in x around inf 99.1%

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

   if -3.1499999999999999e29 < x < 3.1e16

   1. Initial program 98.2%

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

   3. Taylor expanded in x around 0 95.9%

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

      1. *-commutative 95.9%

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

   5. Simplified 95.9%

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

   if 3.1e16 < x

   1. Initial program 7.3%

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

      1. associate-/l* 11.3%

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

      2. sub-neg 11.3%

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

      3. metadata-eval 11.3%

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

      4. fma-define 11.3%

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

      5. fma-define 11.3%

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

      6. fma-define 11.3%

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

      7. fma-define 11.3%

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

      8. fma-define 11.3%

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

      9. fma-define 11.3%

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

      10. fma-define 11.3%

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

   3. Simplified 11.3%

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

   5. Taylor expanded in x around -inf 96.4%

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

      1. mul-1-neg 96.4%

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

      2. unsub-neg 96.4%

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

      3. mul-1-neg 96.4%

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

      4. unsub-neg 96.4%

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

      5. mul-1-neg 96.4%

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

      6. unsub-neg 96.4%

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

      7. mul-1-neg 96.4%

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

      8. unsub-neg 96.4%

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

   7. Simplified 96.4%

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

      1. clear-num 96.4%

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

      2. inv-pow 96.4%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \color{blue}{{\left(\frac{x}{124074.40615218398 - y}\right)}^{-1}}}{x}}{x}\right) \]

   9. Applied egg-rr 96.4%

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

       1. unpow-1 96.4%

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

   11. Simplified 96.4%

       \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \color{blue}{\frac{1}{\frac{x}{124074.40615218398 - y}}}}{x}}{x}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.15 \cdot 10^{+29}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+16}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{1}{\frac{x}{y - 124074.40615218398}}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 92.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{if}\;x \leq -11500000000000:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + t\_0\right)\\ \mathbf{elif}\;x \leq 28500:\\ \;\;\;\;\left(x + -2\right) \cdot \left(t\_0 + 0.0212463641547976 \cdot \left(x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{1}{\frac{x}{y - 124074.40615218398}}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (/
          z
          (+
           (*
            x
            (+
             (* x (+ (* x (+ x 43.3400022514)) 263.505074721))
             313.399215894))
           47.066876606))))
   (if (<= x -11500000000000.0)
     (* (+ x -2.0) (+ 4.16438922228 t_0))
     (if (<= x 28500.0)
       (* (+ x -2.0) (+ t_0 (* 0.0212463641547976 (* x y))))
       (*
        (+ x -2.0)
        (+
         4.16438922228
         (/
          (-
           (/ (+ 3451.550173699799 (/ 1.0 (/ x (- y 124074.40615218398)))) x)
           101.7851458539211)
          x)))))))

C

double code(double x, double y, double z) {
	double t_0 = z / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	double tmp;
	if (x <= -11500000000000.0) {
		tmp = (x + -2.0) * (4.16438922228 + t_0);
	} else if (x <= 28500.0) {
		tmp = (x + -2.0) * (t_0 + (0.0212463641547976 * (x * y)));
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (1.0 / (x / (y - 124074.40615218398)))) / x) - 101.7851458539211) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z / ((x * ((x * ((x * (x + 43.3400022514d0)) + 263.505074721d0)) + 313.399215894d0)) + 47.066876606d0)
    if (x <= (-11500000000000.0d0)) then
        tmp = (x + (-2.0d0)) * (4.16438922228d0 + t_0)
    else if (x <= 28500.0d0) then
        tmp = (x + (-2.0d0)) * (t_0 + (0.0212463641547976d0 * (x * y)))
    else
        tmp = (x + (-2.0d0)) * (4.16438922228d0 + ((((3451.550173699799d0 + (1.0d0 / (x / (y - 124074.40615218398d0)))) / x) - 101.7851458539211d0) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	double tmp;
	if (x <= -11500000000000.0) {
		tmp = (x + -2.0) * (4.16438922228 + t_0);
	} else if (x <= 28500.0) {
		tmp = (x + -2.0) * (t_0 + (0.0212463641547976 * (x * y)));
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (1.0 / (x / (y - 124074.40615218398)))) / x) - 101.7851458539211) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)
	tmp = 0
	if x <= -11500000000000.0:
		tmp = (x + -2.0) * (4.16438922228 + t_0)
	elif x <= 28500.0:
		tmp = (x + -2.0) * (t_0 + (0.0212463641547976 * (x * y)))
	else:
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (1.0 / (x / (y - 124074.40615218398)))) / x) - 101.7851458539211) / x))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606))
	tmp = 0.0
	if (x <= -11500000000000.0)
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + t_0));
	elseif (x <= 28500.0)
		tmp = Float64(Float64(x + -2.0) * Float64(t_0 + Float64(0.0212463641547976 * Float64(x * y))));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(1.0 / Float64(x / Float64(y - 124074.40615218398)))) / x) - 101.7851458539211) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	tmp = 0.0;
	if (x <= -11500000000000.0)
		tmp = (x + -2.0) * (4.16438922228 + t_0);
	elseif (x <= 28500.0)
		tmp = (x + -2.0) * (t_0 + (0.0212463641547976 * (x * y)));
	else
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (1.0 / (x / (y - 124074.40615218398)))) / x) - 101.7851458539211) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z / 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, -11500000000000.0], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 28500.0], N[(N[(x + -2.0), $MachinePrecision] * N[(t$95$0 + N[(0.0212463641547976 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(N[(N[(N[(3451.550173699799 + N[(1.0 / N[(x / N[(y - 124074.40615218398), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.15e13

   1. Initial program 10.0%

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

      1. associate-/l* 20.7%

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

      2. sub-neg 20.7%

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

      3. metadata-eval 20.7%

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

      4. fma-define 20.7%

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

      5. fma-define 20.7%

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

      6. fma-define 20.7%

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

      7. fma-define 20.7%

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

      8. fma-define 20.7%

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

      9. fma-define 20.7%

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

      10. fma-define 20.7%

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

   3. Simplified 20.7%

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

   5. Taylor expanded in z around 0 20.7%

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

   6. Taylor expanded in x around inf 96.1%

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

   if -1.15e13 < x < 28500

   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* 99.7%

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

      2. sub-neg 99.7%

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

      3. metadata-eval 99.7%

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

      4. fma-define 99.7%

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

      5. fma-define 99.7%

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

      6. fma-define 99.7%

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

      7. fma-define 99.7%

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

      8. fma-define 99.7%

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

      9. fma-define 99.7%

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

      10. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.7%

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

   6. Taylor expanded in x around 0 91.2%

      \[\leadsto \left(x + -2\right) \cdot \left(\frac{z}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right)\right)} + \color{blue}{0.0212463641547976 \cdot \left(x \cdot y\right)}\right) \]

   if 28500 < x

   1. Initial program 10.9%

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

      1. associate-/l* 16.0%

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

      2. sub-neg 16.0%

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

      3. metadata-eval 16.0%

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

      4. fma-define 16.0%

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

      5. fma-define 16.0%

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

      6. fma-define 16.0%

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

      7. fma-define 16.0%

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

      8. fma-define 16.0%

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

      9. fma-define 16.0%

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

      10. fma-define 16.0%

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

   3. Simplified 16.0%

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

   5. Taylor expanded in x around -inf 94.1%

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

      1. mul-1-neg 94.1%

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

      2. unsub-neg 94.1%

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

      3. mul-1-neg 94.1%

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

      4. unsub-neg 94.1%

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

      5. mul-1-neg 94.1%

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

      6. unsub-neg 94.1%

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

      7. mul-1-neg 94.1%

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

      8. unsub-neg 94.1%

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

   7. Simplified 94.1%

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

      1. clear-num 94.1%

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

      2. inv-pow 94.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \color{blue}{{\left(\frac{x}{124074.40615218398 - y}\right)}^{-1}}}{x}}{x}\right) \]

   9. Applied egg-rr 94.1%

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

       1. unpow-1 94.1%

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

   11. Simplified 94.1%

       \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \color{blue}{\frac{1}{\frac{x}{124074.40615218398 - y}}}}{x}}{x}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -11500000000000:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\right)\\ \mathbf{elif}\;x \leq 28500:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} + 0.0212463641547976 \cdot \left(x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{1}{\frac{x}{y - 124074.40615218398}}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 93.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.000125:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{-1}{\frac{x}{101.7851458539211 - \frac{3451.550173699799 + \frac{y}{x}}{x}}}\right)\\ \mathbf{elif}\;x \leq 31.5:\\ \;\;\;\;\left(x + -2\right) \cdot \left(0.0212463641547976 \cdot \left(x \cdot y\right) + \frac{z}{47.066876606 + x \cdot 313.399215894}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{1}{\frac{x}{y - 124074.40615218398}}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.000125)
   (*
    (+ x -2.0)
    (+
     4.16438922228
     (/ -1.0 (/ x (- 101.7851458539211 (/ (+ 3451.550173699799 (/ y x)) x))))))
   (if (<= x 31.5)
     (*
      (+ x -2.0)
      (+
       (* 0.0212463641547976 (* x y))
       (/ z (+ 47.066876606 (* x 313.399215894)))))
     (*
      (+ x -2.0)
      (+
       4.16438922228
       (/
        (-
         (/ (+ 3451.550173699799 (/ 1.0 (/ x (- y 124074.40615218398)))) x)
         101.7851458539211)
        x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.000125) {
		tmp = (x + -2.0) * (4.16438922228 + (-1.0 / (x / (101.7851458539211 - ((3451.550173699799 + (y / x)) / x)))));
	} else if (x <= 31.5) {
		tmp = (x + -2.0) * ((0.0212463641547976 * (x * y)) + (z / (47.066876606 + (x * 313.399215894))));
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (1.0 / (x / (y - 124074.40615218398)))) / x) - 101.7851458539211) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-0.000125d0)) then
        tmp = (x + (-2.0d0)) * (4.16438922228d0 + ((-1.0d0) / (x / (101.7851458539211d0 - ((3451.550173699799d0 + (y / x)) / x)))))
    else if (x <= 31.5d0) then
        tmp = (x + (-2.0d0)) * ((0.0212463641547976d0 * (x * y)) + (z / (47.066876606d0 + (x * 313.399215894d0))))
    else
        tmp = (x + (-2.0d0)) * (4.16438922228d0 + ((((3451.550173699799d0 + (1.0d0 / (x / (y - 124074.40615218398d0)))) / x) - 101.7851458539211d0) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.000125) {
		tmp = (x + -2.0) * (4.16438922228 + (-1.0 / (x / (101.7851458539211 - ((3451.550173699799 + (y / x)) / x)))));
	} else if (x <= 31.5) {
		tmp = (x + -2.0) * ((0.0212463641547976 * (x * y)) + (z / (47.066876606 + (x * 313.399215894))));
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (1.0 / (x / (y - 124074.40615218398)))) / x) - 101.7851458539211) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.000125:
		tmp = (x + -2.0) * (4.16438922228 + (-1.0 / (x / (101.7851458539211 - ((3451.550173699799 + (y / x)) / x)))))
	elif x <= 31.5:
		tmp = (x + -2.0) * ((0.0212463641547976 * (x * y)) + (z / (47.066876606 + (x * 313.399215894))))
	else:
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (1.0 / (x / (y - 124074.40615218398)))) / x) - 101.7851458539211) / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.000125)
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(-1.0 / Float64(x / Float64(101.7851458539211 - Float64(Float64(3451.550173699799 + Float64(y / x)) / x))))));
	elseif (x <= 31.5)
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(0.0212463641547976 * Float64(x * y)) + Float64(z / Float64(47.066876606 + Float64(x * 313.399215894)))));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(1.0 / Float64(x / Float64(y - 124074.40615218398)))) / x) - 101.7851458539211) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.000125)
		tmp = (x + -2.0) * (4.16438922228 + (-1.0 / (x / (101.7851458539211 - ((3451.550173699799 + (y / x)) / x)))));
	elseif (x <= 31.5)
		tmp = (x + -2.0) * ((0.0212463641547976 * (x * y)) + (z / (47.066876606 + (x * 313.399215894))));
	else
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (1.0 / (x / (y - 124074.40615218398)))) / x) - 101.7851458539211) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.000125], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(-1.0 / N[(x / N[(101.7851458539211 - N[(N[(3451.550173699799 + N[(y / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 31.5], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(0.0212463641547976 * N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(z / N[(47.066876606 + N[(x * 313.399215894), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(N[(N[(N[(3451.550173699799 + N[(1.0 / N[(x / N[(y - 124074.40615218398), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.25e-4

   1. Initial program 15.4%

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

      1. associate-/l* 25.4%

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

      2. sub-neg 25.4%

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

      3. metadata-eval 25.4%

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

      4. fma-define 25.4%

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

      5. fma-define 25.4%

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

      6. fma-define 25.4%

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

      7. fma-define 25.4%

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

      8. fma-define 25.4%

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

      9. fma-define 25.4%

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

      10. fma-define 25.4%

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

   3. Simplified 25.4%

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

   5. Taylor expanded in x around -inf 90.4%

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

      1. mul-1-neg 90.4%

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

      2. unsub-neg 90.4%

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

      3. mul-1-neg 90.4%

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

      4. unsub-neg 90.4%

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

      5. mul-1-neg 90.4%

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

      6. unsub-neg 90.4%

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

      7. mul-1-neg 90.4%

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

      8. unsub-neg 90.4%

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

   7. Simplified 90.4%

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

   8. Taylor expanded in y around inf 90.4%

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

      1. mul-1-neg 90.4%

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

      2. distribute-neg-frac2 90.4%

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

   10. Simplified 90.4%

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

       1. clear-num 90.4%

          \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \color{blue}{\frac{1}{\frac{x}{101.7851458539211 - \frac{3451.550173699799 - \frac{y}{-x}}{x}}}}\right) \]

       2. inv-pow 90.4%

          \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \color{blue}{{\left(\frac{x}{101.7851458539211 - \frac{3451.550173699799 - \frac{y}{-x}}{x}}\right)}^{-1}}\right) \]

   12. Applied egg-rr 90.4%

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

       1. unpow-1 90.4%

          \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \color{blue}{\frac{1}{\frac{x}{101.7851458539211 - \frac{3451.550173699799 - \frac{y}{-x}}{x}}}}\right) \]

       2. *-lft-identity 90.4%

          \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{1}{\frac{x}{101.7851458539211 - \color{blue}{1 \cdot \frac{3451.550173699799 - \frac{y}{-x}}{x}}}}\right) \]

       3. *-lft-identity 90.4%

          \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{1}{\frac{x}{101.7851458539211 - \color{blue}{\frac{3451.550173699799 - \frac{y}{-x}}{x}}}}\right) \]

       4. sub-neg 90.4%

          \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{1}{\frac{x}{101.7851458539211 - \frac{\color{blue}{3451.550173699799 + \left(-\frac{y}{-x}\right)}}{x}}}\right) \]

       5. distribute-frac-neg2 90.4%

          \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{1}{\frac{x}{101.7851458539211 - \frac{3451.550173699799 + \left(-\color{blue}{\left(-\frac{y}{x}\right)}\right)}{x}}}\right) \]

       6. remove-double-neg 90.4%

          \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{1}{\frac{x}{101.7851458539211 - \frac{3451.550173699799 + \color{blue}{\frac{y}{x}}}{x}}}\right) \]

       7. +-commutative 90.4%

          \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{1}{\frac{x}{101.7851458539211 - \frac{\color{blue}{\frac{y}{x} + 3451.550173699799}}{x}}}\right) \]

   14. Simplified 90.4%

       \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \color{blue}{\frac{1}{\frac{x}{101.7851458539211 - \frac{\frac{y}{x} + 3451.550173699799}{x}}}}\right) \]

   if -1.25e-4 < x < 31.5

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

      2. sub-neg 99.7%

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

      3. metadata-eval 99.7%

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

      4. fma-define 99.7%

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

      5. fma-define 99.7%

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

      6. fma-define 99.7%

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

      7. fma-define 99.7%

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

      8. fma-define 99.7%

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

      9. fma-define 99.7%

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

      10. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.7%

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

   6. Taylor expanded in x around 0 93.3%

      \[\leadsto \left(x + -2\right) \cdot \left(\frac{z}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right)\right)} + \color{blue}{0.0212463641547976 \cdot \left(x \cdot y\right)}\right) \]

   7. Taylor expanded in x around 0 91.9%

      \[\leadsto \left(x + -2\right) \cdot \left(\frac{z}{47.066876606 + \color{blue}{313.399215894 \cdot x}} + 0.0212463641547976 \cdot \left(x \cdot y\right)\right) \]
   8. Step-by-step derivation

      1. *-commutative 91.9%

         \[\leadsto \left(x + -2\right) \cdot \left(\frac{z}{47.066876606 + \color{blue}{x \cdot 313.399215894}} + 0.0212463641547976 \cdot \left(x \cdot y\right)\right) \]

   9. Simplified 91.9%

      \[\leadsto \left(x + -2\right) \cdot \left(\frac{z}{47.066876606 + \color{blue}{x \cdot 313.399215894}} + 0.0212463641547976 \cdot \left(x \cdot y\right)\right) \]

   if 31.5 < x

   1. Initial program 10.9%

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

      1. associate-/l* 16.0%

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

      2. sub-neg 16.0%

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

      3. metadata-eval 16.0%

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

      4. fma-define 16.0%

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

      5. fma-define 16.0%

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

      6. fma-define 16.0%

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

      7. fma-define 16.0%

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

      8. fma-define 16.0%

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

      9. fma-define 16.0%

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

      10. fma-define 16.0%

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

   3. Simplified 16.0%

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

   5. Taylor expanded in x around -inf 94.1%

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

      1. mul-1-neg 94.1%

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

      2. unsub-neg 94.1%

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

      3. mul-1-neg 94.1%

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

      4. unsub-neg 94.1%

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

      5. mul-1-neg 94.1%

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

      6. unsub-neg 94.1%

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

      7. mul-1-neg 94.1%

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

      8. unsub-neg 94.1%

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

   7. Simplified 94.1%

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

      1. clear-num 94.1%

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

      2. inv-pow 94.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \color{blue}{{\left(\frac{x}{124074.40615218398 - y}\right)}^{-1}}}{x}}{x}\right) \]

   9. Applied egg-rr 94.1%

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

       1. unpow-1 94.1%

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

   11. Simplified 94.1%

       \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \color{blue}{\frac{1}{\frac{x}{124074.40615218398 - y}}}}{x}}{x}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.000125:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{-1}{\frac{x}{101.7851458539211 - \frac{3451.550173699799 + \frac{y}{x}}{x}}}\right)\\ \mathbf{elif}\;x \leq 31.5:\\ \;\;\;\;\left(x + -2\right) \cdot \left(0.0212463641547976 \cdot \left(x \cdot y\right) + \frac{z}{47.066876606 + x \cdot 313.399215894}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{1}{\frac{x}{y - 124074.40615218398}}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 92.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.4 \cdot 10^{-10}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\right)\\ \mathbf{elif}\;x \leq 36:\\ \;\;\;\;\left(x + -2\right) \cdot \left(0.0212463641547976 \cdot \left(x \cdot y\right) + \frac{z}{47.066876606 + x \cdot 313.399215894}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{1}{\frac{x}{y - 124074.40615218398}}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.4e-10)
   (*
    (+ x -2.0)
    (+
     4.16438922228
     (/
      z
      (+
       (*
        x
        (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
       47.066876606))))
   (if (<= x 36.0)
     (*
      (+ x -2.0)
      (+
       (* 0.0212463641547976 (* x y))
       (/ z (+ 47.066876606 (* x 313.399215894)))))
     (*
      (+ x -2.0)
      (+
       4.16438922228
       (/
        (-
         (/ (+ 3451.550173699799 (/ 1.0 (/ x (- y 124074.40615218398)))) x)
         101.7851458539211)
        x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.4e-10) {
		tmp = (x + -2.0) * (4.16438922228 + (z / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)));
	} else if (x <= 36.0) {
		tmp = (x + -2.0) * ((0.0212463641547976 * (x * y)) + (z / (47.066876606 + (x * 313.399215894))));
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (1.0 / (x / (y - 124074.40615218398)))) / x) - 101.7851458539211) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-7.4d-10)) then
        tmp = (x + (-2.0d0)) * (4.16438922228d0 + (z / ((x * ((x * ((x * (x + 43.3400022514d0)) + 263.505074721d0)) + 313.399215894d0)) + 47.066876606d0)))
    else if (x <= 36.0d0) then
        tmp = (x + (-2.0d0)) * ((0.0212463641547976d0 * (x * y)) + (z / (47.066876606d0 + (x * 313.399215894d0))))
    else
        tmp = (x + (-2.0d0)) * (4.16438922228d0 + ((((3451.550173699799d0 + (1.0d0 / (x / (y - 124074.40615218398d0)))) / x) - 101.7851458539211d0) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.4e-10) {
		tmp = (x + -2.0) * (4.16438922228 + (z / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)));
	} else if (x <= 36.0) {
		tmp = (x + -2.0) * ((0.0212463641547976 * (x * y)) + (z / (47.066876606 + (x * 313.399215894))));
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (1.0 / (x / (y - 124074.40615218398)))) / x) - 101.7851458539211) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.4e-10:
		tmp = (x + -2.0) * (4.16438922228 + (z / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)))
	elif x <= 36.0:
		tmp = (x + -2.0) * ((0.0212463641547976 * (x * y)) + (z / (47.066876606 + (x * 313.399215894))))
	else:
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (1.0 / (x / (y - 124074.40615218398)))) / x) - 101.7851458539211) / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.4e-10)
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(z / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606))));
	elseif (x <= 36.0)
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(0.0212463641547976 * Float64(x * y)) + Float64(z / Float64(47.066876606 + Float64(x * 313.399215894)))));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(1.0 / Float64(x / Float64(y - 124074.40615218398)))) / x) - 101.7851458539211) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -7.4e-10)
		tmp = (x + -2.0) * (4.16438922228 + (z / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)));
	elseif (x <= 36.0)
		tmp = (x + -2.0) * ((0.0212463641547976 * (x * y)) + (z / (47.066876606 + (x * 313.399215894))));
	else
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (1.0 / (x / (y - 124074.40615218398)))) / x) - 101.7851458539211) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.4e-10], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(z / 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]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 36.0], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(0.0212463641547976 * N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(z / N[(47.066876606 + N[(x * 313.399215894), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(N[(N[(N[(3451.550173699799 + N[(1.0 / N[(x / N[(y - 124074.40615218398), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.4000000000000003e-10

   1. Initial program 19.0%

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

      1. associate-/l* 28.6%

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

      2. sub-neg 28.6%

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

      3. metadata-eval 28.6%

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

      4. fma-define 28.6%

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

      5. fma-define 28.6%

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

      6. fma-define 28.6%

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

      7. fma-define 28.6%

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

      8. fma-define 28.6%

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

      9. fma-define 28.6%

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

      10. fma-define 28.6%

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

   3. Simplified 28.6%

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

   5. Taylor expanded in z around 0 28.6%

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

   6. Taylor expanded in x around inf 91.0%

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

   if -7.4000000000000003e-10 < x < 36

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

      2. sub-neg 99.8%

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

      3. metadata-eval 99.8%

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

      4. fma-define 99.8%

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

      5. fma-define 99.8%

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

      6. fma-define 99.8%

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

      7. fma-define 99.8%

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

      8. fma-define 99.8%

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

      9. fma-define 99.8%

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

      10. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in x around 0 94.0%

      \[\leadsto \left(x + -2\right) \cdot \left(\frac{z}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right)\right)} + \color{blue}{0.0212463641547976 \cdot \left(x \cdot y\right)}\right) \]

   7. Taylor expanded in x around 0 92.8%

      \[\leadsto \left(x + -2\right) \cdot \left(\frac{z}{47.066876606 + \color{blue}{313.399215894 \cdot x}} + 0.0212463641547976 \cdot \left(x \cdot y\right)\right) \]
   8. Step-by-step derivation

      1. *-commutative 92.8%

         \[\leadsto \left(x + -2\right) \cdot \left(\frac{z}{47.066876606 + \color{blue}{x \cdot 313.399215894}} + 0.0212463641547976 \cdot \left(x \cdot y\right)\right) \]

   9. Simplified 92.8%

      \[\leadsto \left(x + -2\right) \cdot \left(\frac{z}{47.066876606 + \color{blue}{x \cdot 313.399215894}} + 0.0212463641547976 \cdot \left(x \cdot y\right)\right) \]

   if 36 < x

   1. Initial program 10.9%

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

      1. associate-/l* 16.0%

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

      2. sub-neg 16.0%

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

      3. metadata-eval 16.0%

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

      4. fma-define 16.0%

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

      5. fma-define 16.0%

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

      6. fma-define 16.0%

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

      7. fma-define 16.0%

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

      8. fma-define 16.0%

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

      9. fma-define 16.0%

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

      10. fma-define 16.0%

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

   3. Simplified 16.0%

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

   5. Taylor expanded in x around -inf 94.1%

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

      1. mul-1-neg 94.1%

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

      2. unsub-neg 94.1%

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

      3. mul-1-neg 94.1%

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

      4. unsub-neg 94.1%

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

      5. mul-1-neg 94.1%

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

      6. unsub-neg 94.1%

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

      7. mul-1-neg 94.1%

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

      8. unsub-neg 94.1%

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

   7. Simplified 94.1%

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

      1. clear-num 94.1%

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

      2. inv-pow 94.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \color{blue}{{\left(\frac{x}{124074.40615218398 - y}\right)}^{-1}}}{x}}{x}\right) \]

   9. Applied egg-rr 94.1%

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

       1. unpow-1 94.1%

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

   11. Simplified 94.1%

       \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \color{blue}{\frac{1}{\frac{x}{124074.40615218398 - y}}}}{x}}{x}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.4 \cdot 10^{-10}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\right)\\ \mathbf{elif}\;x \leq 36:\\ \;\;\;\;\left(x + -2\right) \cdot \left(0.0212463641547976 \cdot \left(x \cdot y\right) + \frac{z}{47.066876606 + x \cdot 313.399215894}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{1}{\frac{x}{y - 124074.40615218398}}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 93.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.000125:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{-1}{\frac{x}{101.7851458539211 - \frac{3451.550173699799 + \frac{y}{x}}{x}}}\right)\\ \mathbf{elif}\;x \leq 38:\\ \;\;\;\;\left(x + -2\right) \cdot \left(0.0212463641547976 \cdot \left(x \cdot y\right) + \frac{z}{47.066876606 + x \cdot 313.399215894}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{\frac{124074.40615218398 - y}{x} - 3451.550173699799}{x}}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.000125)
   (*
    (+ x -2.0)
    (+
     4.16438922228
     (/ -1.0 (/ x (- 101.7851458539211 (/ (+ 3451.550173699799 (/ y x)) x))))))
   (if (<= x 38.0)
     (*
      (+ x -2.0)
      (+
       (* 0.0212463641547976 (* x y))
       (/ z (+ 47.066876606 (* x 313.399215894)))))
     (*
      (+ x -2.0)
      (-
       4.16438922228
       (/
        (+
         101.7851458539211
         (/ (- (/ (- 124074.40615218398 y) x) 3451.550173699799) x))
        x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.000125) {
		tmp = (x + -2.0) * (4.16438922228 + (-1.0 / (x / (101.7851458539211 - ((3451.550173699799 + (y / x)) / x)))));
	} else if (x <= 38.0) {
		tmp = (x + -2.0) * ((0.0212463641547976 * (x * y)) + (z / (47.066876606 + (x * 313.399215894))));
	} else {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-0.000125d0)) then
        tmp = (x + (-2.0d0)) * (4.16438922228d0 + ((-1.0d0) / (x / (101.7851458539211d0 - ((3451.550173699799d0 + (y / x)) / x)))))
    else if (x <= 38.0d0) then
        tmp = (x + (-2.0d0)) * ((0.0212463641547976d0 * (x * y)) + (z / (47.066876606d0 + (x * 313.399215894d0))))
    else
        tmp = (x + (-2.0d0)) * (4.16438922228d0 - ((101.7851458539211d0 + ((((124074.40615218398d0 - y) / x) - 3451.550173699799d0) / x)) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.000125) {
		tmp = (x + -2.0) * (4.16438922228 + (-1.0 / (x / (101.7851458539211 - ((3451.550173699799 + (y / x)) / x)))));
	} else if (x <= 38.0) {
		tmp = (x + -2.0) * ((0.0212463641547976 * (x * y)) + (z / (47.066876606 + (x * 313.399215894))));
	} else {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.000125:
		tmp = (x + -2.0) * (4.16438922228 + (-1.0 / (x / (101.7851458539211 - ((3451.550173699799 + (y / x)) / x)))))
	elif x <= 38.0:
		tmp = (x + -2.0) * ((0.0212463641547976 * (x * y)) + (z / (47.066876606 + (x * 313.399215894))))
	else:
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.000125)
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(-1.0 / Float64(x / Float64(101.7851458539211 - Float64(Float64(3451.550173699799 + Float64(y / x)) / x))))));
	elseif (x <= 38.0)
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(0.0212463641547976 * Float64(x * y)) + Float64(z / Float64(47.066876606 + Float64(x * 313.399215894)))));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 - Float64(Float64(101.7851458539211 + Float64(Float64(Float64(Float64(124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.000125)
		tmp = (x + -2.0) * (4.16438922228 + (-1.0 / (x / (101.7851458539211 - ((3451.550173699799 + (y / x)) / x)))));
	elseif (x <= 38.0)
		tmp = (x + -2.0) * ((0.0212463641547976 * (x * y)) + (z / (47.066876606 + (x * 313.399215894))));
	else
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + ((((124074.40615218398 - y) / x) - 3451.550173699799) / x)) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.000125], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(-1.0 / N[(x / N[(101.7851458539211 - N[(N[(3451.550173699799 + N[(y / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 38.0], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(0.0212463641547976 * N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(z / N[(47.066876606 + N[(x * 313.399215894), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 - N[(N[(101.7851458539211 + N[(N[(N[(N[(124074.40615218398 - y), $MachinePrecision] / x), $MachinePrecision] - 3451.550173699799), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.25e-4

   1. Initial program 15.4%

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

      1. associate-/l* 25.4%

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

      2. sub-neg 25.4%

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

      3. metadata-eval 25.4%

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

      4. fma-define 25.4%

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

      5. fma-define 25.4%

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

      6. fma-define 25.4%

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

      7. fma-define 25.4%

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

      8. fma-define 25.4%

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

      9. fma-define 25.4%

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

      10. fma-define 25.4%

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

   3. Simplified 25.4%

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

   5. Taylor expanded in x around -inf 90.4%

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

      1. mul-1-neg 90.4%

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

      2. unsub-neg 90.4%

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

      3. mul-1-neg 90.4%

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

      4. unsub-neg 90.4%

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

      5. mul-1-neg 90.4%

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

      6. unsub-neg 90.4%

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

      7. mul-1-neg 90.4%

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

      8. unsub-neg 90.4%

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

   7. Simplified 90.4%

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

   8. Taylor expanded in y around inf 90.4%

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

      1. mul-1-neg 90.4%

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

      2. distribute-neg-frac2 90.4%

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

   10. Simplified 90.4%

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

       1. clear-num 90.4%

          \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \color{blue}{\frac{1}{\frac{x}{101.7851458539211 - \frac{3451.550173699799 - \frac{y}{-x}}{x}}}}\right) \]

       2. inv-pow 90.4%

          \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \color{blue}{{\left(\frac{x}{101.7851458539211 - \frac{3451.550173699799 - \frac{y}{-x}}{x}}\right)}^{-1}}\right) \]

   12. Applied egg-rr 90.4%

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

       1. unpow-1 90.4%

          \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \color{blue}{\frac{1}{\frac{x}{101.7851458539211 - \frac{3451.550173699799 - \frac{y}{-x}}{x}}}}\right) \]

       2. *-lft-identity 90.4%

          \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{1}{\frac{x}{101.7851458539211 - \color{blue}{1 \cdot \frac{3451.550173699799 - \frac{y}{-x}}{x}}}}\right) \]

       3. *-lft-identity 90.4%

          \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{1}{\frac{x}{101.7851458539211 - \color{blue}{\frac{3451.550173699799 - \frac{y}{-x}}{x}}}}\right) \]

       4. sub-neg 90.4%

          \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{1}{\frac{x}{101.7851458539211 - \frac{\color{blue}{3451.550173699799 + \left(-\frac{y}{-x}\right)}}{x}}}\right) \]

       5. distribute-frac-neg2 90.4%

          \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{1}{\frac{x}{101.7851458539211 - \frac{3451.550173699799 + \left(-\color{blue}{\left(-\frac{y}{x}\right)}\right)}{x}}}\right) \]

       6. remove-double-neg 90.4%

          \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{1}{\frac{x}{101.7851458539211 - \frac{3451.550173699799 + \color{blue}{\frac{y}{x}}}{x}}}\right) \]

       7. +-commutative 90.4%

          \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{1}{\frac{x}{101.7851458539211 - \frac{\color{blue}{\frac{y}{x} + 3451.550173699799}}{x}}}\right) \]

   14. Simplified 90.4%

       \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \color{blue}{\frac{1}{\frac{x}{101.7851458539211 - \frac{\frac{y}{x} + 3451.550173699799}{x}}}}\right) \]

   if -1.25e-4 < x < 38

   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* 99.7%

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

      2. sub-neg 99.7%

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

      3. metadata-eval 99.7%

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

      4. fma-define 99.7%

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

      5. fma-define 99.7%

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

      6. fma-define 99.7%

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

      7. fma-define 99.7%

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

      8. fma-define 99.7%

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

      9. fma-define 99.7%

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

      10. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.7%

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

   6. Taylor expanded in x around 0 93.3%

      \[\leadsto \left(x + -2\right) \cdot \left(\frac{z}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right)\right)} + \color{blue}{0.0212463641547976 \cdot \left(x \cdot y\right)}\right) \]

   7. Taylor expanded in x around 0 91.9%

      \[\leadsto \left(x + -2\right) \cdot \left(\frac{z}{47.066876606 + \color{blue}{313.399215894 \cdot x}} + 0.0212463641547976 \cdot \left(x \cdot y\right)\right) \]
   8. Step-by-step derivation

      1. *-commutative 91.9%

         \[\leadsto \left(x + -2\right) \cdot \left(\frac{z}{47.066876606 + \color{blue}{x \cdot 313.399215894}} + 0.0212463641547976 \cdot \left(x \cdot y\right)\right) \]

   9. Simplified 91.9%

      \[\leadsto \left(x + -2\right) \cdot \left(\frac{z}{47.066876606 + \color{blue}{x \cdot 313.399215894}} + 0.0212463641547976 \cdot \left(x \cdot y\right)\right) \]

   if 38 < x

   1. Initial program 10.9%

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

      1. associate-/l* 16.0%

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

      2. sub-neg 16.0%

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

      3. metadata-eval 16.0%

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

      4. fma-define 16.0%

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

      5. fma-define 16.0%

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

      6. fma-define 16.0%

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

      7. fma-define 16.0%

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

      8. fma-define 16.0%

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

      9. fma-define 16.0%

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

      10. fma-define 16.0%

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

   3. Simplified 16.0%

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

   5. Taylor expanded in x around -inf 94.1%

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

      1. mul-1-neg 94.1%

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

      2. unsub-neg 94.1%

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

      3. mul-1-neg 94.1%

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

      4. unsub-neg 94.1%

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

      5. mul-1-neg 94.1%

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

      6. unsub-neg 94.1%

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

      7. mul-1-neg 94.1%

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

      8. unsub-neg 94.1%

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

   7. Simplified 94.1%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.000125:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{-1}{\frac{x}{101.7851458539211 - \frac{3451.550173699799 + \frac{y}{x}}{x}}}\right)\\ \mathbf{elif}\;x \leq 38:\\ \;\;\;\;\left(x + -2\right) \cdot \left(0.0212463641547976 \cdot \left(x \cdot y\right) + \frac{z}{47.066876606 + x \cdot 313.399215894}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{\frac{124074.40615218398 - y}{x} - 3451.550173699799}{x}}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 93.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.000125 \lor \neg \left(x \leq 21.5\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(0.0212463641547976 \cdot \left(x \cdot y\right) + \frac{z}{47.066876606 + x \cdot 313.399215894}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.000125) (not (<= x 21.5)))
   (*
    (+ x -2.0)
    (+
     4.16438922228
     (/ (- (/ (+ 3451.550173699799 (/ y x)) x) 101.7851458539211) x)))
   (*
    (+ x -2.0)
    (+
     (* 0.0212463641547976 (* x y))
     (/ z (+ 47.066876606 (* x 313.399215894)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.000125) || !(x <= 21.5)) {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (y / x)) / x) - 101.7851458539211) / x));
	} else {
		tmp = (x + -2.0) * ((0.0212463641547976 * (x * y)) + (z / (47.066876606 + (x * 313.399215894))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-0.000125d0)) .or. (.not. (x <= 21.5d0))) then
        tmp = (x + (-2.0d0)) * (4.16438922228d0 + ((((3451.550173699799d0 + (y / x)) / x) - 101.7851458539211d0) / x))
    else
        tmp = (x + (-2.0d0)) * ((0.0212463641547976d0 * (x * y)) + (z / (47.066876606d0 + (x * 313.399215894d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.000125) || !(x <= 21.5)) {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (y / x)) / x) - 101.7851458539211) / x));
	} else {
		tmp = (x + -2.0) * ((0.0212463641547976 * (x * y)) + (z / (47.066876606 + (x * 313.399215894))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.000125) or not (x <= 21.5):
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (y / x)) / x) - 101.7851458539211) / x))
	else:
		tmp = (x + -2.0) * ((0.0212463641547976 * (x * y)) + (z / (47.066876606 + (x * 313.399215894))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.000125) || !(x <= 21.5))
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(y / x)) / x) - 101.7851458539211) / x)));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(0.0212463641547976 * Float64(x * y)) + Float64(z / Float64(47.066876606 + Float64(x * 313.399215894)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -0.000125) || ~((x <= 21.5)))
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + (y / x)) / x) - 101.7851458539211) / x));
	else
		tmp = (x + -2.0) * ((0.0212463641547976 * (x * y)) + (z / (47.066876606 + (x * 313.399215894))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.000125], N[Not[LessEqual[x, 21.5]], $MachinePrecision]], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(N[(N[(N[(3451.550173699799 + N[(y / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(0.0212463641547976 * N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(z / N[(47.066876606 + N[(x * 313.399215894), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.25e-4 or 21.5 < x

   1. Initial program 13.0%

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

      1. associate-/l* 20.4%

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

      2. sub-neg 20.4%

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

      3. metadata-eval 20.4%

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

      4. fma-define 20.4%

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

      5. fma-define 20.4%

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

      6. fma-define 20.4%

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

      7. fma-define 20.4%

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

      8. fma-define 20.4%

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

      9. fma-define 20.4%

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

      10. fma-define 20.4%

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

   3. Simplified 20.4%

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

   5. Taylor expanded in x around -inf 92.3%

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

      1. mul-1-neg 92.3%

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

      2. unsub-neg 92.3%

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

      3. mul-1-neg 92.3%

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

      4. unsub-neg 92.3%

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

      5. mul-1-neg 92.3%

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

      6. unsub-neg 92.3%

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

      7. mul-1-neg 92.3%

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

      8. unsub-neg 92.3%

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

   7. Simplified 92.3%

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

   8. Taylor expanded in y around inf 92.3%

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

      1. mul-1-neg 92.3%

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

      2. distribute-neg-frac2 92.3%

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

   10. Simplified 92.3%

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

   11. Taylor expanded in x around inf 92.3%

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

       1. +-commutative 92.3%

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

   13. Simplified 92.3%

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

   if -1.25e-4 < x < 21.5

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

      2. sub-neg 99.7%

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

      3. metadata-eval 99.7%

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

      4. fma-define 99.7%

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

      5. fma-define 99.7%

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

      6. fma-define 99.7%

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

      7. fma-define 99.7%

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

      8. fma-define 99.7%

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

      9. fma-define 99.7%

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

      10. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.7%

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

   6. Taylor expanded in x around 0 93.3%

      \[\leadsto \left(x + -2\right) \cdot \left(\frac{z}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right)\right)} + \color{blue}{0.0212463641547976 \cdot \left(x \cdot y\right)}\right) \]

   7. Taylor expanded in x around 0 91.9%

      \[\leadsto \left(x + -2\right) \cdot \left(\frac{z}{47.066876606 + \color{blue}{313.399215894 \cdot x}} + 0.0212463641547976 \cdot \left(x \cdot y\right)\right) \]
   8. Step-by-step derivation

      1. *-commutative 91.9%

         \[\leadsto \left(x + -2\right) \cdot \left(\frac{z}{47.066876606 + \color{blue}{x \cdot 313.399215894}} + 0.0212463641547976 \cdot \left(x \cdot y\right)\right) \]

   9. Simplified 91.9%

      \[\leadsto \left(x + -2\right) \cdot \left(\frac{z}{47.066876606 + \color{blue}{x \cdot 313.399215894}} + 0.0212463641547976 \cdot \left(x \cdot y\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.000125 \lor \neg \left(x \leq 21.5\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(0.0212463641547976 \cdot \left(x \cdot y\right) + \frac{z}{47.066876606 + x \cdot 313.399215894}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 89.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+22}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 0.106:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + x \cdot \left(y \cdot 0.0212463641547976 - z \cdot 0.14147091005106402\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.4e+22)
   (* x 4.16438922228)
   (if (<= x 0.106)
     (*
      (+ x -2.0)
      (+
       (* z 0.0212463641547976)
       (* x (- (* y 0.0212463641547976) (* z 0.14147091005106402)))))
     (*
      (+ x -2.0)
      (-
       4.16438922228
       (/ (+ 101.7851458539211 (/ -3451.550173699799 x)) x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.4e+22) {
		tmp = x * 4.16438922228;
	} else if (x <= 0.106) {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) - (z * 0.14147091005106402))));
	} else {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / 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 <= (-6.4d+22)) then
        tmp = x * 4.16438922228d0
    else if (x <= 0.106d0) then
        tmp = (x + (-2.0d0)) * ((z * 0.0212463641547976d0) + (x * ((y * 0.0212463641547976d0) - (z * 0.14147091005106402d0))))
    else
        tmp = (x + (-2.0d0)) * (4.16438922228d0 - ((101.7851458539211d0 + ((-3451.550173699799d0) / x)) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.4e+22) {
		tmp = x * 4.16438922228;
	} else if (x <= 0.106) {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) - (z * 0.14147091005106402))));
	} else {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6.4e+22:
		tmp = x * 4.16438922228
	elif x <= 0.106:
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) - (z * 0.14147091005106402))))
	else:
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.4e+22)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 0.106)
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(z * 0.0212463641547976) + Float64(x * Float64(Float64(y * 0.0212463641547976) - Float64(z * 0.14147091005106402)))));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 - Float64(Float64(101.7851458539211 + Float64(-3451.550173699799 / x)) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -6.4e+22)
		tmp = x * 4.16438922228;
	elseif (x <= 0.106)
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) - (z * 0.14147091005106402))));
	else
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.4e+22], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 0.106], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(z * 0.0212463641547976), $MachinePrecision] + N[(x * N[(N[(y * 0.0212463641547976), $MachinePrecision] - N[(z * 0.14147091005106402), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 - N[(N[(101.7851458539211 + N[(-3451.550173699799 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.4e22

   1. Initial program 7.1%

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

      1. associate-/l* 16.7%

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

      2. sub-neg 16.7%

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

      3. metadata-eval 16.7%

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

      4. fma-define 16.7%

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

      5. fma-define 16.7%

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

      6. fma-define 16.7%

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

      7. fma-define 16.7%

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

      8. fma-define 16.7%

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

      9. fma-define 16.7%

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

      10. fma-define 16.7%

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

   3. Simplified 16.7%

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

   5. Taylor expanded in x around -inf 96.1%

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

      1. mul-1-neg 96.1%

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

      2. unsub-neg 96.1%

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

      3. mul-1-neg 96.1%

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

      4. unsub-neg 96.1%

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

      5. mul-1-neg 96.1%

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

      6. unsub-neg 96.1%

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

      7. mul-1-neg 96.1%

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

      8. unsub-neg 96.1%

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

   7. Simplified 96.1%

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

   8. Taylor expanded in x around inf 96.1%

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

      1. *-commutative 96.1%

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

   10. Simplified 96.1%

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

   if -6.4e22 < x < 0.105999999999999997

   1. Initial program 98.9%

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

      1. associate-/l* 99.7%

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

      2. sub-neg 99.7%

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

      3. metadata-eval 99.7%

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

      4. fma-define 99.7%

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

      5. fma-define 99.7%

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

      6. fma-define 99.7%

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

      7. fma-define 99.7%

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

      8. fma-define 99.7%

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

      9. fma-define 99.7%

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

      10. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 88.0%

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

   if 0.105999999999999997 < x

   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. Step-by-step derivation

      1. associate-/l* 18.1%

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

      2. sub-neg 18.1%

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

      3. metadata-eval 18.1%

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

      4. fma-define 18.1%

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

      5. fma-define 18.1%

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

      6. fma-define 18.1%

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

      7. fma-define 18.1%

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

      8. fma-define 18.1%

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

      9. fma-define 18.1%

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

      10. fma-define 18.1%

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

   3. Simplified 18.1%

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

   5. Taylor expanded in x around -inf 86.6%

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

      1. mul-1-neg 86.6%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 + \color{blue}{\left(-\frac{101.7851458539211 - 3451.550173699799 \cdot \frac{1}{x}}{x}\right)}\right) \]

      2. unsub-neg 86.6%

         \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - 3451.550173699799 \cdot \frac{1}{x}}{x}\right)} \]

      3. sub-neg 86.6%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{\color{blue}{101.7851458539211 + \left(-3451.550173699799 \cdot \frac{1}{x}\right)}}{x}\right) \]

      4. associate-*r/ 86.6%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \left(-\color{blue}{\frac{3451.550173699799 \cdot 1}{x}}\right)}{x}\right) \]

      5. metadata-eval 86.6%

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

      6. distribute-neg-frac 86.6%

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

      7. metadata-eval 86.6%

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

   7. Simplified 86.6%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+22}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 0.106:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + x \cdot \left(y \cdot 0.0212463641547976 - z \cdot 0.14147091005106402\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 89.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -11500000000000:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 320:\\ \;\;\;\;\left(x + -2\right) \cdot \left(0.0212463641547976 \cdot \left(x \cdot y\right) + \frac{z}{47.066876606 + x \cdot 313.399215894}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -11500000000000.0)
   (* x 4.16438922228)
   (if (<= x 320.0)
     (*
      (+ x -2.0)
      (+
       (* 0.0212463641547976 (* x y))
       (/ z (+ 47.066876606 (* x 313.399215894)))))
     (*
      (+ x -2.0)
      (-
       4.16438922228
       (/ (+ 101.7851458539211 (/ -3451.550173699799 x)) x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -11500000000000.0) {
		tmp = x * 4.16438922228;
	} else if (x <= 320.0) {
		tmp = (x + -2.0) * ((0.0212463641547976 * (x * y)) + (z / (47.066876606 + (x * 313.399215894))));
	} else {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / 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 <= (-11500000000000.0d0)) then
        tmp = x * 4.16438922228d0
    else if (x <= 320.0d0) then
        tmp = (x + (-2.0d0)) * ((0.0212463641547976d0 * (x * y)) + (z / (47.066876606d0 + (x * 313.399215894d0))))
    else
        tmp = (x + (-2.0d0)) * (4.16438922228d0 - ((101.7851458539211d0 + ((-3451.550173699799d0) / x)) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -11500000000000.0) {
		tmp = x * 4.16438922228;
	} else if (x <= 320.0) {
		tmp = (x + -2.0) * ((0.0212463641547976 * (x * y)) + (z / (47.066876606 + (x * 313.399215894))));
	} else {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -11500000000000.0:
		tmp = x * 4.16438922228
	elif x <= 320.0:
		tmp = (x + -2.0) * ((0.0212463641547976 * (x * y)) + (z / (47.066876606 + (x * 313.399215894))))
	else:
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -11500000000000.0)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 320.0)
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(0.0212463641547976 * Float64(x * y)) + Float64(z / Float64(47.066876606 + Float64(x * 313.399215894)))));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 - Float64(Float64(101.7851458539211 + Float64(-3451.550173699799 / x)) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -11500000000000.0)
		tmp = x * 4.16438922228;
	elseif (x <= 320.0)
		tmp = (x + -2.0) * ((0.0212463641547976 * (x * y)) + (z / (47.066876606 + (x * 313.399215894))));
	else
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -11500000000000.0], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 320.0], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(0.0212463641547976 * N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(z / N[(47.066876606 + N[(x * 313.399215894), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 - N[(N[(101.7851458539211 + N[(-3451.550173699799 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.15e13

   1. Initial program 10.0%

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

      1. associate-/l* 20.7%

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

      2. sub-neg 20.7%

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

      3. metadata-eval 20.7%

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

      4. fma-define 20.7%

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

      5. fma-define 20.7%

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

      6. fma-define 20.7%

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

      7. fma-define 20.7%

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

      8. fma-define 20.7%

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

      9. fma-define 20.7%

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

      10. fma-define 20.7%

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

   3. Simplified 20.7%

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

   5. Taylor expanded in x around -inf 94.4%

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

      1. mul-1-neg 94.4%

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

      2. unsub-neg 94.4%

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

      3. mul-1-neg 94.4%

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

      4. unsub-neg 94.4%

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

      5. mul-1-neg 94.4%

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

      6. unsub-neg 94.4%

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

      7. mul-1-neg 94.4%

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

      8. unsub-neg 94.4%

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

   7. Simplified 94.4%

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

   8. Taylor expanded in x around inf 91.7%

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

      1. *-commutative 91.7%

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

   10. Simplified 91.7%

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

   if -1.15e13 < x < 320

   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* 99.7%

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

      2. sub-neg 99.7%

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

      3. metadata-eval 99.7%

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

      4. fma-define 99.7%

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

      5. fma-define 99.7%

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

      6. fma-define 99.7%

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

      7. fma-define 99.7%

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

      8. fma-define 99.7%

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

      9. fma-define 99.7%

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

      10. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.7%

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

   6. Taylor expanded in x around 0 91.2%

      \[\leadsto \left(x + -2\right) \cdot \left(\frac{z}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right)\right)} + \color{blue}{0.0212463641547976 \cdot \left(x \cdot y\right)}\right) \]

   7. Taylor expanded in x around 0 89.0%

      \[\leadsto \left(x + -2\right) \cdot \left(\frac{z}{47.066876606 + \color{blue}{313.399215894 \cdot x}} + 0.0212463641547976 \cdot \left(x \cdot y\right)\right) \]
   8. Step-by-step derivation

      1. *-commutative 89.0%

         \[\leadsto \left(x + -2\right) \cdot \left(\frac{z}{47.066876606 + \color{blue}{x \cdot 313.399215894}} + 0.0212463641547976 \cdot \left(x \cdot y\right)\right) \]

   9. Simplified 89.0%

      \[\leadsto \left(x + -2\right) \cdot \left(\frac{z}{47.066876606 + \color{blue}{x \cdot 313.399215894}} + 0.0212463641547976 \cdot \left(x \cdot y\right)\right) \]

   if 320 < x

   1. Initial program 10.9%

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

      1. associate-/l* 16.0%

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

      2. sub-neg 16.0%

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

      3. metadata-eval 16.0%

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

      4. fma-define 16.0%

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

      5. fma-define 16.0%

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

      6. fma-define 16.0%

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

      7. fma-define 16.0%

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

      8. fma-define 16.0%

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

      9. fma-define 16.0%

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

      10. fma-define 16.0%

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

   3. Simplified 16.0%

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

   5. Taylor expanded in x around -inf 88.7%

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

      1. mul-1-neg 88.7%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 + \color{blue}{\left(-\frac{101.7851458539211 - 3451.550173699799 \cdot \frac{1}{x}}{x}\right)}\right) \]

      2. unsub-neg 88.7%

         \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - 3451.550173699799 \cdot \frac{1}{x}}{x}\right)} \]

      3. sub-neg 88.7%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{\color{blue}{101.7851458539211 + \left(-3451.550173699799 \cdot \frac{1}{x}\right)}}{x}\right) \]

      4. associate-*r/ 88.7%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \left(-\color{blue}{\frac{3451.550173699799 \cdot 1}{x}}\right)}{x}\right) \]

      5. metadata-eval 88.7%

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

      6. distribute-neg-frac 88.7%

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

      7. metadata-eval 88.7%

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

   7. Simplified 88.7%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -11500000000000:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 320:\\ \;\;\;\;\left(x + -2\right) \cdot \left(0.0212463641547976 \cdot \left(x \cdot y\right) + \frac{z}{47.066876606 + x \cdot 313.399215894}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 93.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{3451.550173699799 + \frac{y}{x}}{x}\\ \mathbf{if}\;x \leq -0.000125:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{-1}{\frac{x}{101.7851458539211 - t\_0}}\right)\\ \mathbf{elif}\;x \leq 12.5:\\ \;\;\;\;\left(x + -2\right) \cdot \left(0.0212463641547976 \cdot \left(x \cdot y\right) + \frac{z}{47.066876606 + x \cdot 313.399215894}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{t\_0 - 101.7851458539211}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ 3451.550173699799 (/ y x)) x)))
   (if (<= x -0.000125)
     (* (+ x -2.0) (+ 4.16438922228 (/ -1.0 (/ x (- 101.7851458539211 t_0)))))
     (if (<= x 12.5)
       (*
        (+ x -2.0)
        (+
         (* 0.0212463641547976 (* x y))
         (/ z (+ 47.066876606 (* x 313.399215894)))))
       (* (+ x -2.0) (+ 4.16438922228 (/ (- t_0 101.7851458539211) x)))))))

C

double code(double x, double y, double z) {
	double t_0 = (3451.550173699799 + (y / x)) / x;
	double tmp;
	if (x <= -0.000125) {
		tmp = (x + -2.0) * (4.16438922228 + (-1.0 / (x / (101.7851458539211 - t_0))));
	} else if (x <= 12.5) {
		tmp = (x + -2.0) * ((0.0212463641547976 * (x * y)) + (z / (47.066876606 + (x * 313.399215894))));
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((t_0 - 101.7851458539211) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (3451.550173699799d0 + (y / x)) / x
    if (x <= (-0.000125d0)) then
        tmp = (x + (-2.0d0)) * (4.16438922228d0 + ((-1.0d0) / (x / (101.7851458539211d0 - t_0))))
    else if (x <= 12.5d0) then
        tmp = (x + (-2.0d0)) * ((0.0212463641547976d0 * (x * y)) + (z / (47.066876606d0 + (x * 313.399215894d0))))
    else
        tmp = (x + (-2.0d0)) * (4.16438922228d0 + ((t_0 - 101.7851458539211d0) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (3451.550173699799 + (y / x)) / x;
	double tmp;
	if (x <= -0.000125) {
		tmp = (x + -2.0) * (4.16438922228 + (-1.0 / (x / (101.7851458539211 - t_0))));
	} else if (x <= 12.5) {
		tmp = (x + -2.0) * ((0.0212463641547976 * (x * y)) + (z / (47.066876606 + (x * 313.399215894))));
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((t_0 - 101.7851458539211) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (3451.550173699799 + (y / x)) / x
	tmp = 0
	if x <= -0.000125:
		tmp = (x + -2.0) * (4.16438922228 + (-1.0 / (x / (101.7851458539211 - t_0))))
	elif x <= 12.5:
		tmp = (x + -2.0) * ((0.0212463641547976 * (x * y)) + (z / (47.066876606 + (x * 313.399215894))))
	else:
		tmp = (x + -2.0) * (4.16438922228 + ((t_0 - 101.7851458539211) / x))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(3451.550173699799 + Float64(y / x)) / x)
	tmp = 0.0
	if (x <= -0.000125)
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(-1.0 / Float64(x / Float64(101.7851458539211 - t_0)))));
	elseif (x <= 12.5)
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(0.0212463641547976 * Float64(x * y)) + Float64(z / Float64(47.066876606 + Float64(x * 313.399215894)))));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(t_0 - 101.7851458539211) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (3451.550173699799 + (y / x)) / x;
	tmp = 0.0;
	if (x <= -0.000125)
		tmp = (x + -2.0) * (4.16438922228 + (-1.0 / (x / (101.7851458539211 - t_0))));
	elseif (x <= 12.5)
		tmp = (x + -2.0) * ((0.0212463641547976 * (x * y)) + (z / (47.066876606 + (x * 313.399215894))));
	else
		tmp = (x + -2.0) * (4.16438922228 + ((t_0 - 101.7851458539211) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(3451.550173699799 + N[(y / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]}, If[LessEqual[x, -0.000125], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(-1.0 / N[(x / N[(101.7851458539211 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 12.5], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(0.0212463641547976 * N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(z / N[(47.066876606 + N[(x * 313.399215894), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(N[(t$95$0 - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.25e-4

   1. Initial program 15.4%

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

      1. associate-/l* 25.4%

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

      2. sub-neg 25.4%

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

      3. metadata-eval 25.4%

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

      4. fma-define 25.4%

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

      5. fma-define 25.4%

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

      6. fma-define 25.4%

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

      7. fma-define 25.4%

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

      8. fma-define 25.4%

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

      9. fma-define 25.4%

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

      10. fma-define 25.4%

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

   3. Simplified 25.4%

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

   5. Taylor expanded in x around -inf 90.4%

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

      1. mul-1-neg 90.4%

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

      2. unsub-neg 90.4%

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

      3. mul-1-neg 90.4%

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

      4. unsub-neg 90.4%

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

      5. mul-1-neg 90.4%

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

      6. unsub-neg 90.4%

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

      7. mul-1-neg 90.4%

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

      8. unsub-neg 90.4%

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

   7. Simplified 90.4%

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

   8. Taylor expanded in y around inf 90.4%

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

      1. mul-1-neg 90.4%

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

      2. distribute-neg-frac2 90.4%

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

   10. Simplified 90.4%

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

       1. clear-num 90.4%

          \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \color{blue}{\frac{1}{\frac{x}{101.7851458539211 - \frac{3451.550173699799 - \frac{y}{-x}}{x}}}}\right) \]

       2. inv-pow 90.4%

          \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \color{blue}{{\left(\frac{x}{101.7851458539211 - \frac{3451.550173699799 - \frac{y}{-x}}{x}}\right)}^{-1}}\right) \]

   12. Applied egg-rr 90.4%

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

       1. unpow-1 90.4%

          \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \color{blue}{\frac{1}{\frac{x}{101.7851458539211 - \frac{3451.550173699799 - \frac{y}{-x}}{x}}}}\right) \]

       2. *-lft-identity 90.4%

          \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{1}{\frac{x}{101.7851458539211 - \color{blue}{1 \cdot \frac{3451.550173699799 - \frac{y}{-x}}{x}}}}\right) \]

       3. *-lft-identity 90.4%

          \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{1}{\frac{x}{101.7851458539211 - \color{blue}{\frac{3451.550173699799 - \frac{y}{-x}}{x}}}}\right) \]

       4. sub-neg 90.4%

          \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{1}{\frac{x}{101.7851458539211 - \frac{\color{blue}{3451.550173699799 + \left(-\frac{y}{-x}\right)}}{x}}}\right) \]

       5. distribute-frac-neg2 90.4%

          \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{1}{\frac{x}{101.7851458539211 - \frac{3451.550173699799 + \left(-\color{blue}{\left(-\frac{y}{x}\right)}\right)}{x}}}\right) \]

       6. remove-double-neg 90.4%

          \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{1}{\frac{x}{101.7851458539211 - \frac{3451.550173699799 + \color{blue}{\frac{y}{x}}}{x}}}\right) \]

       7. +-commutative 90.4%

          \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{1}{\frac{x}{101.7851458539211 - \frac{\color{blue}{\frac{y}{x} + 3451.550173699799}}{x}}}\right) \]

   14. Simplified 90.4%

       \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \color{blue}{\frac{1}{\frac{x}{101.7851458539211 - \frac{\frac{y}{x} + 3451.550173699799}{x}}}}\right) \]

   if -1.25e-4 < x < 12.5

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

      2. sub-neg 99.7%

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

      3. metadata-eval 99.7%

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

      4. fma-define 99.7%

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

      5. fma-define 99.7%

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

      6. fma-define 99.7%

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

      7. fma-define 99.7%

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

      8. fma-define 99.7%

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

      9. fma-define 99.7%

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

      10. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.7%

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

   6. Taylor expanded in x around 0 93.3%

      \[\leadsto \left(x + -2\right) \cdot \left(\frac{z}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right)\right)} + \color{blue}{0.0212463641547976 \cdot \left(x \cdot y\right)}\right) \]

   7. Taylor expanded in x around 0 91.9%

      \[\leadsto \left(x + -2\right) \cdot \left(\frac{z}{47.066876606 + \color{blue}{313.399215894 \cdot x}} + 0.0212463641547976 \cdot \left(x \cdot y\right)\right) \]
   8. Step-by-step derivation

      1. *-commutative 91.9%

         \[\leadsto \left(x + -2\right) \cdot \left(\frac{z}{47.066876606 + \color{blue}{x \cdot 313.399215894}} + 0.0212463641547976 \cdot \left(x \cdot y\right)\right) \]

   9. Simplified 91.9%

      \[\leadsto \left(x + -2\right) \cdot \left(\frac{z}{47.066876606 + \color{blue}{x \cdot 313.399215894}} + 0.0212463641547976 \cdot \left(x \cdot y\right)\right) \]

   if 12.5 < x

   1. Initial program 10.9%

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

      1. associate-/l* 16.0%

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

      2. sub-neg 16.0%

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

      3. metadata-eval 16.0%

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

      4. fma-define 16.0%

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

      5. fma-define 16.0%

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

      6. fma-define 16.0%

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

      7. fma-define 16.0%

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

      8. fma-define 16.0%

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

      9. fma-define 16.0%

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

      10. fma-define 16.0%

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

   3. Simplified 16.0%

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

   5. Taylor expanded in x around -inf 94.1%

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

      1. mul-1-neg 94.1%

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

      2. unsub-neg 94.1%

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

      3. mul-1-neg 94.1%

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

      4. unsub-neg 94.1%

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

      5. mul-1-neg 94.1%

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

      6. unsub-neg 94.1%

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

      7. mul-1-neg 94.1%

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

      8. unsub-neg 94.1%

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

   7. Simplified 94.1%

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

   8. Taylor expanded in y around inf 93.9%

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

      1. mul-1-neg 93.9%

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

      2. distribute-neg-frac2 93.9%

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

   10. Simplified 93.9%

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

   11. Taylor expanded in x around inf 93.9%

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

       1. +-commutative 93.9%

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

   13. Simplified 93.9%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.000125:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{-1}{\frac{x}{101.7851458539211 - \frac{3451.550173699799 + \frac{y}{x}}{x}}}\right)\\ \mathbf{elif}\;x \leq 12.5:\\ \;\;\;\;\left(x + -2\right) \cdot \left(0.0212463641547976 \cdot \left(x \cdot y\right) + \frac{z}{47.066876606 + x \cdot 313.399215894}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 76.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -166:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 0.106:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + x \cdot \left(z \cdot -0.14147091005106402\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -166.0)
   (* x 4.16438922228)
   (if (<= x 0.106)
     (*
      (+ x -2.0)
      (+ (* z 0.0212463641547976) (* x (* z -0.14147091005106402))))
     (* x (- 4.16438922228 (/ 110.1139242984811 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -166.0) {
		tmp = x * 4.16438922228;
	} else if (x <= 0.106) {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * (z * -0.14147091005106402)));
	} else {
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-166.0d0)) then
        tmp = x * 4.16438922228d0
    else if (x <= 0.106d0) then
        tmp = (x + (-2.0d0)) * ((z * 0.0212463641547976d0) + (x * (z * (-0.14147091005106402d0))))
    else
        tmp = x * (4.16438922228d0 - (110.1139242984811d0 / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -166.0) {
		tmp = x * 4.16438922228;
	} else if (x <= 0.106) {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * (z * -0.14147091005106402)));
	} else {
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -166.0:
		tmp = x * 4.16438922228
	elif x <= 0.106:
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * (z * -0.14147091005106402)))
	else:
		tmp = x * (4.16438922228 - (110.1139242984811 / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -166.0)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 0.106)
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(z * 0.0212463641547976) + Float64(x * Float64(z * -0.14147091005106402))));
	else
		tmp = Float64(x * Float64(4.16438922228 - Float64(110.1139242984811 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -166.0)
		tmp = x * 4.16438922228;
	elseif (x <= 0.106)
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * (z * -0.14147091005106402)));
	else
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -166.0], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 0.106], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(z * 0.0212463641547976), $MachinePrecision] + N[(x * N[(z * -0.14147091005106402), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -166

   1. Initial program 11.5%

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

      1. associate-/l* 22.0%

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

      2. sub-neg 22.0%

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

      3. metadata-eval 22.0%

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

      4. fma-define 22.0%

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

      5. fma-define 22.0%

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

      6. fma-define 22.0%

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

      7. fma-define 22.0%

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

      8. fma-define 22.0%

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

      9. fma-define 22.0%

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

      10. fma-define 22.0%

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

   3. Simplified 22.0%

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

   5. Taylor expanded in x around -inf 94.1%

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

      1. mul-1-neg 94.1%

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

      2. unsub-neg 94.1%

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

      3. mul-1-neg 94.1%

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

      4. unsub-neg 94.1%

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

      5. mul-1-neg 94.1%

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

      6. unsub-neg 94.1%

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

      7. mul-1-neg 94.1%

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

      8. unsub-neg 94.1%

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

   7. Simplified 94.1%

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

   8. Taylor expanded in x around inf 90.2%

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

      1. *-commutative 90.2%

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

   10. Simplified 90.2%

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

   if -166 < x < 0.105999999999999997

   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* 99.7%

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

      2. sub-neg 99.7%

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

      3. metadata-eval 99.7%

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

      4. fma-define 99.7%

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

      5. fma-define 99.7%

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

      6. fma-define 99.7%

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

      7. fma-define 99.7%

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

      8. fma-define 99.7%

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

      9. fma-define 99.7%

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

      10. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 90.8%

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

   6. Taylor expanded in y around 0 68.1%

      \[\leadsto \left(x + -2\right) \cdot \left(0.0212463641547976 \cdot z + \color{blue}{-0.14147091005106402 \cdot \left(x \cdot z\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative 68.1%

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

      2. associate-*l* 68.1%

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

      3. *-commutative 68.1%

         \[\leadsto \left(x + -2\right) \cdot \left(0.0212463641547976 \cdot z + x \cdot \color{blue}{\left(-0.14147091005106402 \cdot z\right)}\right) \]

   8. Simplified 68.1%

      \[\leadsto \left(x + -2\right) \cdot \left(0.0212463641547976 \cdot z + \color{blue}{x \cdot \left(-0.14147091005106402 \cdot z\right)}\right) \]

   if 0.105999999999999997 < x

   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. Step-by-step derivation

      1. associate-/l* 18.1%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 18.1%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 18.1%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 18.1%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 18.1%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 18.1%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 18.1%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 18.1%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 18.1%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 18.1%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 18.1%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 86.4%

      \[\leadsto \color{blue}{x \cdot \left(4.16438922228 - 110.1139242984811 \cdot \frac{1}{x}\right)} \]
   6. Step-by-step derivation

      1. associate-*r/ 86.4%

         \[\leadsto x \cdot \left(4.16438922228 - \color{blue}{\frac{110.1139242984811 \cdot 1}{x}}\right) \]

      2. metadata-eval 86.4%

         \[\leadsto x \cdot \left(4.16438922228 - \frac{\color{blue}{110.1139242984811}}{x}\right) \]

   7. Simplified 86.4%

      \[\leadsto \color{blue}{x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -166:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 0.106:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + x \cdot \left(z \cdot -0.14147091005106402\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 89.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+22}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 270:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + y \cdot \left(x \cdot 0.0212463641547976\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.4e+22)
   (* x 4.16438922228)
   (if (<= x 270.0)
     (* (+ x -2.0) (+ (* z 0.0212463641547976) (* y (* x 0.0212463641547976))))
     (* (+ x -2.0) (- 4.16438922228 (/ 101.7851458539211 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.4e+22) {
		tmp = x * 4.16438922228;
	} else if (x <= 270.0) {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (y * (x * 0.0212463641547976)));
	} else {
		tmp = (x + -2.0) * (4.16438922228 - (101.7851458539211 / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-6.4d+22)) then
        tmp = x * 4.16438922228d0
    else if (x <= 270.0d0) then
        tmp = (x + (-2.0d0)) * ((z * 0.0212463641547976d0) + (y * (x * 0.0212463641547976d0)))
    else
        tmp = (x + (-2.0d0)) * (4.16438922228d0 - (101.7851458539211d0 / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.4e+22) {
		tmp = x * 4.16438922228;
	} else if (x <= 270.0) {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (y * (x * 0.0212463641547976)));
	} else {
		tmp = (x + -2.0) * (4.16438922228 - (101.7851458539211 / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6.4e+22:
		tmp = x * 4.16438922228
	elif x <= 270.0:
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (y * (x * 0.0212463641547976)))
	else:
		tmp = (x + -2.0) * (4.16438922228 - (101.7851458539211 / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.4e+22)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 270.0)
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(z * 0.0212463641547976) + Float64(y * Float64(x * 0.0212463641547976))));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 - Float64(101.7851458539211 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -6.4e+22)
		tmp = x * 4.16438922228;
	elseif (x <= 270.0)
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (y * (x * 0.0212463641547976)));
	else
		tmp = (x + -2.0) * (4.16438922228 - (101.7851458539211 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.4e+22], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 270.0], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(z * 0.0212463641547976), $MachinePrecision] + N[(y * N[(x * 0.0212463641547976), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 - N[(101.7851458539211 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.4e22

   1. Initial program 7.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 16.7%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 16.7%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 16.7%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 16.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 16.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 16.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 16.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 16.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 16.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 16.7%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 16.7%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 96.1%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 96.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 + \color{blue}{\left(-\frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)}\right) \]

      2. unsub-neg 96.1%

         \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \]

      3. mul-1-neg 96.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \color{blue}{\left(-\frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}\right)}}{x}\right) \]

      4. unsub-neg 96.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{\color{blue}{101.7851458539211 - \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}}{x}\right) \]

      5. mul-1-neg 96.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 + \color{blue}{\left(-\frac{124074.40615218398 + -1 \cdot y}{x}\right)}}{x}}{x}\right) \]

      6. unsub-neg 96.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{\color{blue}{3451.550173699799 - \frac{124074.40615218398 + -1 \cdot y}{x}}}{x}}{x}\right) \]

      7. mul-1-neg 96.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 + \color{blue}{\left(-y\right)}}{x}}{x}}{x}\right) \]

      8. unsub-neg 96.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{\color{blue}{124074.40615218398 - y}}{x}}{x}}{x}\right) \]

   7. Simplified 96.1%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right)} \]

   8. Taylor expanded in x around inf 96.1%

      \[\leadsto \color{blue}{4.16438922228 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 96.1%

         \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

   10. Simplified 96.1%

       \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

   if -6.4e22 < x < 270

   1. Initial program 98.9%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 99.7%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 99.7%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 99.7%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 86.6%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(0.0212463641547976 \cdot z + x \cdot \left(0.0212463641547976 \cdot y - 0.14147091005106402 \cdot z\right)\right)} \]

   6. Taylor expanded in y around inf 85.6%

      \[\leadsto \left(x + -2\right) \cdot \left(0.0212463641547976 \cdot z + \color{blue}{0.0212463641547976 \cdot \left(x \cdot y\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative 85.6%

         \[\leadsto \left(x + -2\right) \cdot \left(0.0212463641547976 \cdot z + \color{blue}{\left(x \cdot y\right) \cdot 0.0212463641547976}\right) \]

      2. *-commutative 85.6%

         \[\leadsto \left(x + -2\right) \cdot \left(0.0212463641547976 \cdot z + \color{blue}{\left(y \cdot x\right)} \cdot 0.0212463641547976\right) \]

      3. associate-*r* 85.6%

         \[\leadsto \left(x + -2\right) \cdot \left(0.0212463641547976 \cdot z + \color{blue}{y \cdot \left(x \cdot 0.0212463641547976\right)}\right) \]

   8. Simplified 85.6%

      \[\leadsto \left(x + -2\right) \cdot \left(0.0212463641547976 \cdot z + \color{blue}{y \cdot \left(x \cdot 0.0212463641547976\right)}\right) \]

   if 270 < x

   1. Initial program 10.9%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 16.0%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 16.0%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 16.0%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 16.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 16.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 16.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 16.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 16.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 16.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 16.0%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 16.0%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 88.4%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - 101.7851458539211 \cdot \frac{1}{x}\right)} \]
   6. Step-by-step derivation

      1. associate-*r/ 88.4%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \color{blue}{\frac{101.7851458539211 \cdot 1}{x}}\right) \]

      2. metadata-eval 88.4%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{\color{blue}{101.7851458539211}}{x}\right) \]

   7. Simplified 88.4%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211}{x}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+22}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 270:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + y \cdot \left(x \cdot 0.0212463641547976\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 89.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+22}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 620:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + y \cdot \left(x \cdot 0.0212463641547976\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.4e+22)
   (* x 4.16438922228)
   (if (<= x 620.0)
     (* (+ x -2.0) (+ (* z 0.0212463641547976) (* y (* x 0.0212463641547976))))
     (*
      (+ x -2.0)
      (-
       4.16438922228
       (/ (+ 101.7851458539211 (/ -3451.550173699799 x)) x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.4e+22) {
		tmp = x * 4.16438922228;
	} else if (x <= 620.0) {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (y * (x * 0.0212463641547976)));
	} else {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / 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 <= (-6.4d+22)) then
        tmp = x * 4.16438922228d0
    else if (x <= 620.0d0) then
        tmp = (x + (-2.0d0)) * ((z * 0.0212463641547976d0) + (y * (x * 0.0212463641547976d0)))
    else
        tmp = (x + (-2.0d0)) * (4.16438922228d0 - ((101.7851458539211d0 + ((-3451.550173699799d0) / x)) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.4e+22) {
		tmp = x * 4.16438922228;
	} else if (x <= 620.0) {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (y * (x * 0.0212463641547976)));
	} else {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6.4e+22:
		tmp = x * 4.16438922228
	elif x <= 620.0:
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (y * (x * 0.0212463641547976)))
	else:
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.4e+22)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 620.0)
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(z * 0.0212463641547976) + Float64(y * Float64(x * 0.0212463641547976))));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 - Float64(Float64(101.7851458539211 + Float64(-3451.550173699799 / x)) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -6.4e+22)
		tmp = x * 4.16438922228;
	elseif (x <= 620.0)
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (y * (x * 0.0212463641547976)));
	else
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.4e+22], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 620.0], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(z * 0.0212463641547976), $MachinePrecision] + N[(y * N[(x * 0.0212463641547976), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 - N[(N[(101.7851458539211 + N[(-3451.550173699799 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.4e22

   1. Initial program 7.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 16.7%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 16.7%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 16.7%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 16.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 16.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 16.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 16.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 16.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 16.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 16.7%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 16.7%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 96.1%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 96.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 + \color{blue}{\left(-\frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)}\right) \]

      2. unsub-neg 96.1%

         \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \]

      3. mul-1-neg 96.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \color{blue}{\left(-\frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}\right)}}{x}\right) \]

      4. unsub-neg 96.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{\color{blue}{101.7851458539211 - \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}}{x}\right) \]

      5. mul-1-neg 96.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 + \color{blue}{\left(-\frac{124074.40615218398 + -1 \cdot y}{x}\right)}}{x}}{x}\right) \]

      6. unsub-neg 96.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{\color{blue}{3451.550173699799 - \frac{124074.40615218398 + -1 \cdot y}{x}}}{x}}{x}\right) \]

      7. mul-1-neg 96.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 + \color{blue}{\left(-y\right)}}{x}}{x}}{x}\right) \]

      8. unsub-neg 96.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{\color{blue}{124074.40615218398 - y}}{x}}{x}}{x}\right) \]

   7. Simplified 96.1%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right)} \]

   8. Taylor expanded in x around inf 96.1%

      \[\leadsto \color{blue}{4.16438922228 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 96.1%

         \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

   10. Simplified 96.1%

       \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

   if -6.4e22 < x < 620

   1. Initial program 98.9%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 99.7%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 99.7%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 99.7%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 86.6%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(0.0212463641547976 \cdot z + x \cdot \left(0.0212463641547976 \cdot y - 0.14147091005106402 \cdot z\right)\right)} \]

   6. Taylor expanded in y around inf 85.6%

      \[\leadsto \left(x + -2\right) \cdot \left(0.0212463641547976 \cdot z + \color{blue}{0.0212463641547976 \cdot \left(x \cdot y\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative 85.6%

         \[\leadsto \left(x + -2\right) \cdot \left(0.0212463641547976 \cdot z + \color{blue}{\left(x \cdot y\right) \cdot 0.0212463641547976}\right) \]

      2. *-commutative 85.6%

         \[\leadsto \left(x + -2\right) \cdot \left(0.0212463641547976 \cdot z + \color{blue}{\left(y \cdot x\right)} \cdot 0.0212463641547976\right) \]

      3. associate-*r* 85.6%

         \[\leadsto \left(x + -2\right) \cdot \left(0.0212463641547976 \cdot z + \color{blue}{y \cdot \left(x \cdot 0.0212463641547976\right)}\right) \]

   8. Simplified 85.6%

      \[\leadsto \left(x + -2\right) \cdot \left(0.0212463641547976 \cdot z + \color{blue}{y \cdot \left(x \cdot 0.0212463641547976\right)}\right) \]

   if 620 < x

   1. Initial program 10.9%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 16.0%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 16.0%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 16.0%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 16.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 16.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 16.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 16.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 16.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 16.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 16.0%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 16.0%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 88.7%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 - 3451.550173699799 \cdot \frac{1}{x}}{x}\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 88.7%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 + \color{blue}{\left(-\frac{101.7851458539211 - 3451.550173699799 \cdot \frac{1}{x}}{x}\right)}\right) \]

      2. unsub-neg 88.7%

         \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - 3451.550173699799 \cdot \frac{1}{x}}{x}\right)} \]

      3. sub-neg 88.7%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{\color{blue}{101.7851458539211 + \left(-3451.550173699799 \cdot \frac{1}{x}\right)}}{x}\right) \]

      4. associate-*r/ 88.7%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \left(-\color{blue}{\frac{3451.550173699799 \cdot 1}{x}}\right)}{x}\right) \]

      5. metadata-eval 88.7%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \left(-\frac{\color{blue}{3451.550173699799}}{x}\right)}{x}\right) \]

      6. distribute-neg-frac 88.7%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \color{blue}{\frac{-3451.550173699799}{x}}}{x}\right) \]

      7. metadata-eval 88.7%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{\color{blue}{-3451.550173699799}}{x}}{x}\right) \]

   7. Simplified 88.7%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+22}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 620:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + y \cdot \left(x \cdot 0.0212463641547976\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 76.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -145:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 2.8:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -145.0)
   (* x 4.16438922228)
   (if (<= x 2.8)
     (* z -0.0424927283095952)
     (* (+ x -2.0) (- 4.16438922228 (/ 101.7851458539211 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -145.0) {
		tmp = x * 4.16438922228;
	} else if (x <= 2.8) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = (x + -2.0) * (4.16438922228 - (101.7851458539211 / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-145.0d0)) then
        tmp = x * 4.16438922228d0
    else if (x <= 2.8d0) then
        tmp = z * (-0.0424927283095952d0)
    else
        tmp = (x + (-2.0d0)) * (4.16438922228d0 - (101.7851458539211d0 / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -145.0) {
		tmp = x * 4.16438922228;
	} else if (x <= 2.8) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = (x + -2.0) * (4.16438922228 - (101.7851458539211 / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -145.0:
		tmp = x * 4.16438922228
	elif x <= 2.8:
		tmp = z * -0.0424927283095952
	else:
		tmp = (x + -2.0) * (4.16438922228 - (101.7851458539211 / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -145.0)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 2.8)
		tmp = Float64(z * -0.0424927283095952);
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 - Float64(101.7851458539211 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -145.0)
		tmp = x * 4.16438922228;
	elseif (x <= 2.8)
		tmp = z * -0.0424927283095952;
	else
		tmp = (x + -2.0) * (4.16438922228 - (101.7851458539211 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -145.0], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 2.8], N[(z * -0.0424927283095952), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 - N[(101.7851458539211 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -145

   1. Initial program 11.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 22.0%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 22.0%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 22.0%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 22.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 22.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 22.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 22.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 22.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 22.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 22.0%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 22.0%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 94.1%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 94.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 + \color{blue}{\left(-\frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)}\right) \]

      2. unsub-neg 94.1%

         \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \]

      3. mul-1-neg 94.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \color{blue}{\left(-\frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}\right)}}{x}\right) \]

      4. unsub-neg 94.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{\color{blue}{101.7851458539211 - \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}}{x}\right) \]

      5. mul-1-neg 94.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 + \color{blue}{\left(-\frac{124074.40615218398 + -1 \cdot y}{x}\right)}}{x}}{x}\right) \]

      6. unsub-neg 94.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{\color{blue}{3451.550173699799 - \frac{124074.40615218398 + -1 \cdot y}{x}}}{x}}{x}\right) \]

      7. mul-1-neg 94.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 + \color{blue}{\left(-y\right)}}{x}}{x}}{x}\right) \]

      8. unsub-neg 94.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{\color{blue}{124074.40615218398 - y}}{x}}{x}}{x}\right) \]

   7. Simplified 94.1%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right)} \]

   8. Taylor expanded in x around inf 90.2%

      \[\leadsto \color{blue}{4.16438922228 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 90.2%

         \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

   10. Simplified 90.2%

       \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

   if -145 < x < 2.7999999999999998

   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* 99.7%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 99.7%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 99.7%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 99.7%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 66.0%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]
   6. Step-by-step derivation

      1. *-commutative 66.0%

         \[\leadsto \color{blue}{z \cdot -0.0424927283095952} \]

   7. Simplified 66.0%

      \[\leadsto \color{blue}{z \cdot -0.0424927283095952} \]

   if 2.7999999999999998 < x

   1. Initial program 10.9%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 16.0%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 16.0%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 16.0%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 16.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 16.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 16.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 16.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 16.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 16.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 16.0%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 16.0%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 88.4%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - 101.7851458539211 \cdot \frac{1}{x}\right)} \]
   6. Step-by-step derivation

      1. associate-*r/ 88.4%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \color{blue}{\frac{101.7851458539211 \cdot 1}{x}}\right) \]

      2. metadata-eval 88.4%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{\color{blue}{101.7851458539211}}{x}\right) \]

   7. Simplified 88.4%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211}{x}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -145:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 2.8:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 76.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -14200:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 2.3:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -14200.0)
   (* x 4.16438922228)
   (if (<= x 2.3)
     (* z -0.0424927283095952)
     (* x (- 4.16438922228 (/ 110.1139242984811 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -14200.0) {
		tmp = x * 4.16438922228;
	} else if (x <= 2.3) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-14200.0d0)) then
        tmp = x * 4.16438922228d0
    else if (x <= 2.3d0) then
        tmp = z * (-0.0424927283095952d0)
    else
        tmp = x * (4.16438922228d0 - (110.1139242984811d0 / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -14200.0) {
		tmp = x * 4.16438922228;
	} else if (x <= 2.3) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -14200.0:
		tmp = x * 4.16438922228
	elif x <= 2.3:
		tmp = z * -0.0424927283095952
	else:
		tmp = x * (4.16438922228 - (110.1139242984811 / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -14200.0)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 2.3)
		tmp = Float64(z * -0.0424927283095952);
	else
		tmp = Float64(x * Float64(4.16438922228 - Float64(110.1139242984811 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -14200.0)
		tmp = x * 4.16438922228;
	elseif (x <= 2.3)
		tmp = z * -0.0424927283095952;
	else
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -14200.0], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 2.3], N[(z * -0.0424927283095952), $MachinePrecision], N[(x * N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -14200

   1. Initial program 11.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 22.0%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 22.0%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 22.0%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 22.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 22.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 22.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 22.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 22.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 22.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 22.0%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 22.0%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 94.1%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 94.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 + \color{blue}{\left(-\frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)}\right) \]

      2. unsub-neg 94.1%

         \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \]

      3. mul-1-neg 94.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \color{blue}{\left(-\frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}\right)}}{x}\right) \]

      4. unsub-neg 94.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{\color{blue}{101.7851458539211 - \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}}{x}\right) \]

      5. mul-1-neg 94.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 + \color{blue}{\left(-\frac{124074.40615218398 + -1 \cdot y}{x}\right)}}{x}}{x}\right) \]

      6. unsub-neg 94.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{\color{blue}{3451.550173699799 - \frac{124074.40615218398 + -1 \cdot y}{x}}}{x}}{x}\right) \]

      7. mul-1-neg 94.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 + \color{blue}{\left(-y\right)}}{x}}{x}}{x}\right) \]

      8. unsub-neg 94.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{\color{blue}{124074.40615218398 - y}}{x}}{x}}{x}\right) \]

   7. Simplified 94.1%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right)} \]

   8. Taylor expanded in x around inf 90.2%

      \[\leadsto \color{blue}{4.16438922228 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 90.2%

         \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

   10. Simplified 90.2%

       \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

   if -14200 < x < 2.2999999999999998

   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* 99.7%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 99.7%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 99.7%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 99.7%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 66.0%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]
   6. Step-by-step derivation

      1. *-commutative 66.0%

         \[\leadsto \color{blue}{z \cdot -0.0424927283095952} \]

   7. Simplified 66.0%

      \[\leadsto \color{blue}{z \cdot -0.0424927283095952} \]

   if 2.2999999999999998 < x

   1. Initial program 10.9%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 16.0%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 16.0%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 16.0%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 16.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 16.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 16.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 16.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 16.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 16.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 16.0%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 16.0%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 88.4%

      \[\leadsto \color{blue}{x \cdot \left(4.16438922228 - 110.1139242984811 \cdot \frac{1}{x}\right)} \]
   6. Step-by-step derivation

      1. associate-*r/ 88.4%

         \[\leadsto x \cdot \left(4.16438922228 - \color{blue}{\frac{110.1139242984811 \cdot 1}{x}}\right) \]

      2. metadata-eval 88.4%

         \[\leadsto x \cdot \left(4.16438922228 - \frac{\color{blue}{110.1139242984811}}{x}\right) \]

   7. Simplified 88.4%

      \[\leadsto \color{blue}{x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -14200:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 2.3:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 76.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -195:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 0.106:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot \left(x + -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -195.0)
   (* x 4.16438922228)
   (if (<= x 0.106) (* z -0.0424927283095952) (* 4.16438922228 (+ x -2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -195.0) {
		tmp = x * 4.16438922228;
	} else if (x <= 0.106) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = 4.16438922228 * (x + -2.0);
	}
	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) :: tmp
    if (x <= (-195.0d0)) then
        tmp = x * 4.16438922228d0
    else if (x <= 0.106d0) then
        tmp = z * (-0.0424927283095952d0)
    else
        tmp = 4.16438922228d0 * (x + (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -195.0) {
		tmp = x * 4.16438922228;
	} else if (x <= 0.106) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = 4.16438922228 * (x + -2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -195.0:
		tmp = x * 4.16438922228
	elif x <= 0.106:
		tmp = z * -0.0424927283095952
	else:
		tmp = 4.16438922228 * (x + -2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -195.0)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 0.106)
		tmp = Float64(z * -0.0424927283095952);
	else
		tmp = Float64(4.16438922228 * Float64(x + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -195.0)
		tmp = x * 4.16438922228;
	elseif (x <= 0.106)
		tmp = z * -0.0424927283095952;
	else
		tmp = 4.16438922228 * (x + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -195.0], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 0.106], N[(z * -0.0424927283095952), $MachinePrecision], N[(4.16438922228 * N[(x + -2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -195

   1. Initial program 11.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 22.0%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 22.0%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 22.0%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 22.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 22.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 22.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 22.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 22.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 22.0%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 22.0%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 22.0%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 94.1%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 94.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 + \color{blue}{\left(-\frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)}\right) \]

      2. unsub-neg 94.1%

         \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \]

      3. mul-1-neg 94.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \color{blue}{\left(-\frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}\right)}}{x}\right) \]

      4. unsub-neg 94.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{\color{blue}{101.7851458539211 - \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}}{x}\right) \]

      5. mul-1-neg 94.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 + \color{blue}{\left(-\frac{124074.40615218398 + -1 \cdot y}{x}\right)}}{x}}{x}\right) \]

      6. unsub-neg 94.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{\color{blue}{3451.550173699799 - \frac{124074.40615218398 + -1 \cdot y}{x}}}{x}}{x}\right) \]

      7. mul-1-neg 94.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 + \color{blue}{\left(-y\right)}}{x}}{x}}{x}\right) \]

      8. unsub-neg 94.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{\color{blue}{124074.40615218398 - y}}{x}}{x}}{x}\right) \]

   7. Simplified 94.1%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right)} \]

   8. Taylor expanded in x around inf 90.2%

      \[\leadsto \color{blue}{4.16438922228 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 90.2%

         \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

   10. Simplified 90.2%

       \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

   if -195 < x < 0.105999999999999997

   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* 99.7%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 99.7%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 99.7%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 99.7%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 66.9%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]
   6. Step-by-step derivation

      1. *-commutative 66.9%

         \[\leadsto \color{blue}{z \cdot -0.0424927283095952} \]

   7. Simplified 66.9%

      \[\leadsto \color{blue}{z \cdot -0.0424927283095952} \]

   if 0.105999999999999997 < x

   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. Step-by-step derivation

      1. associate-/l* 18.1%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 18.1%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 18.1%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 18.1%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 18.1%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 18.1%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 18.1%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 18.1%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 18.1%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 18.1%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 18.1%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 86.1%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{4.16438922228} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -195:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 0.106:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot \left(x + -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 76.6% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3000 \lor \neg \left(x \leq 2\right):\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3000.0) (not (<= x 2.0)))
   (* x 4.16438922228)
   (* z -0.0424927283095952)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3000.0) || !(x <= 2.0)) {
		tmp = x * 4.16438922228;
	} 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 <= (-3000.0d0)) .or. (.not. (x <= 2.0d0))) then
        tmp = x * 4.16438922228d0
    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 <= -3000.0) || !(x <= 2.0)) {
		tmp = x * 4.16438922228;
	} else {
		tmp = z * -0.0424927283095952;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3000.0) or not (x <= 2.0):
		tmp = x * 4.16438922228
	else:
		tmp = z * -0.0424927283095952
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3000.0) || !(x <= 2.0))
		tmp = Float64(x * 4.16438922228);
	else
		tmp = Float64(z * -0.0424927283095952);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3000.0) || ~((x <= 2.0)))
		tmp = x * 4.16438922228;
	else
		tmp = z * -0.0424927283095952;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3000.0], N[Not[LessEqual[x, 2.0]], $MachinePrecision]], N[(x * 4.16438922228), $MachinePrecision], N[(z * -0.0424927283095952), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3e3 or 2 < x

   1. Initial program 11.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 18.7%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 18.7%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 18.7%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 18.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 18.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 18.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 18.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 18.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 18.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 18.7%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 18.7%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 94.1%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 94.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 + \color{blue}{\left(-\frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)}\right) \]

      2. unsub-neg 94.1%

         \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \]

      3. mul-1-neg 94.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \color{blue}{\left(-\frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}\right)}}{x}\right) \]

      4. unsub-neg 94.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{\color{blue}{101.7851458539211 - \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}}{x}\right) \]

      5. mul-1-neg 94.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 + \color{blue}{\left(-\frac{124074.40615218398 + -1 \cdot y}{x}\right)}}{x}}{x}\right) \]

      6. unsub-neg 94.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{\color{blue}{3451.550173699799 - \frac{124074.40615218398 + -1 \cdot y}{x}}}{x}}{x}\right) \]

      7. mul-1-neg 94.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 + \color{blue}{\left(-y\right)}}{x}}{x}}{x}\right) \]

      8. unsub-neg 94.1%

         \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{\color{blue}{124074.40615218398 - y}}{x}}{x}}{x}\right) \]

   7. Simplified 94.1%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right)} \]

   8. Taylor expanded in x around inf 89.1%

      \[\leadsto \color{blue}{4.16438922228 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 89.1%

         \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

   10. Simplified 89.1%

       \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

   if -3e3 < x < 2

   1. Initial program 99.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

      2. sub-neg 99.7%

         \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      3. metadata-eval 99.7%

         \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      4. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      5. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      6. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      7. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

      8. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

      9. fma-define 99.7%

         \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

      10. fma-define 99.7%

          \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 66.0%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]
   6. Step-by-step derivation

      1. *-commutative 66.0%

         \[\leadsto \color{blue}{z \cdot -0.0424927283095952} \]

   7. Simplified 66.0%

      \[\leadsto \color{blue}{z \cdot -0.0424927283095952} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3000 \lor \neg \left(x \leq 2\right):\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 44.4% accurate, 12.3× speedup

Math

\[\begin{array}{l} \\ x \cdot 4.16438922228 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x 4.16438922228))

C

double code(double x, double y, double z) {
	return x * 4.16438922228;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * 4.16438922228d0
end function

Java

public static double code(double x, double y, double z) {
	return x * 4.16438922228;
}

Python

def code(x, y, z):
	return x * 4.16438922228

Julia

function code(x, y, z)
	return Float64(x * 4.16438922228)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * 4.16438922228;
end

Wolfram

code[x_, y_, z_] := N[(x * 4.16438922228), $MachinePrecision]

Derivation

1. Initial program 52.0%

   \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
2. Step-by-step derivation

   1. associate-/l* 56.0%

      \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]

   2. sub-neg 56.0%

      \[\leadsto \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   3. metadata-eval 56.0%

      \[\leadsto \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   4. fma-define 56.0%

      \[\leadsto \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   5. fma-define 56.0%

      \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   6. fma-define 56.0%

      \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   7. fma-define 56.0%

      \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   8. fma-define 56.0%

      \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}} \]

   9. fma-define 56.0%

      \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)} \]

   10. fma-define 56.0%

       \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)} \]

3. Simplified 56.0%

   \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
4. Add Preprocessing

5. Taylor expanded in x around -inf 52.2%

   \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \]
6. Step-by-step derivation

   1. mul-1-neg 52.2%

      \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 + \color{blue}{\left(-\frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)}\right) \]

   2. unsub-neg 52.2%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \]

   3. mul-1-neg 52.2%

      \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \color{blue}{\left(-\frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}\right)}}{x}\right) \]

   4. unsub-neg 52.2%

      \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{\color{blue}{101.7851458539211 - \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}}{x}\right) \]

   5. mul-1-neg 52.2%

      \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 + \color{blue}{\left(-\frac{124074.40615218398 + -1 \cdot y}{x}\right)}}{x}}{x}\right) \]

   6. unsub-neg 52.2%

      \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{\color{blue}{3451.550173699799 - \frac{124074.40615218398 + -1 \cdot y}{x}}}{x}}{x}\right) \]

   7. mul-1-neg 52.2%

      \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 + \color{blue}{\left(-y\right)}}{x}}{x}}{x}\right) \]

   8. unsub-neg 52.2%

      \[\leadsto \left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{\color{blue}{124074.40615218398 - y}}{x}}{x}}{x}\right) \]

7. Simplified 52.2%

   \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right)} \]

8. Taylor expanded in x around inf 49.6%

   \[\leadsto \color{blue}{4.16438922228 \cdot x} \]
9. Step-by-step derivation

   1. *-commutative 49.6%

      \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

10. Simplified 49.6%

    \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

11. Final simplification 49.6%

    \[\leadsto x \cdot 4.16438922228 \]
12. Add Preprocessing

Developer target: 98.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\frac{y}{x \cdot x} + 4.16438922228 \cdot x\right) - 110.1139242984811\\ \mathbf{if}\;x < -3.326128725870005 \cdot 10^{+62}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x < 9.429991714554673 \cdot 10^{+55}:\\ \;\;\;\;\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(263.505074721 \cdot x + \left(43.3400022514 \cdot \left(x \cdot x\right) + x \cdot \left(x \cdot x\right)\right)\right) + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811)))
   (if (< x -3.326128725870005e+62)
     t_0
     (if (< x 9.429991714554673e+55)
       (*
        (/ (- x 2.0) 1.0)
        (/
         (+
          (*
           (+
            (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
            y)
           x)
          z)
         (+
          (*
           (+
            (+ (* 263.505074721 x) (+ (* 43.3400022514 (* x x)) (* x (* x x))))
            313.399215894)
           x)
          47.066876606)))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811;
	double tmp;
	if (x < -3.326128725870005e+62) {
		tmp = t_0;
	} else if (x < 9.429991714554673e+55) {
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * x)))) + 313.399215894) * x) + 47.066876606));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((y / (x * x)) + (4.16438922228d0 * x)) - 110.1139242984811d0
    if (x < (-3.326128725870005d+62)) then
        tmp = t_0
    else if (x < 9.429991714554673d+55) then
        tmp = ((x - 2.0d0) / 1.0d0) * (((((((((x * 4.16438922228d0) + 78.6994924154d0) * x) + 137.519416416d0) * x) + y) * x) + z) / (((((263.505074721d0 * x) + ((43.3400022514d0 * (x * x)) + (x * (x * x)))) + 313.399215894d0) * x) + 47.066876606d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811;
	double tmp;
	if (x < -3.326128725870005e+62) {
		tmp = t_0;
	} else if (x < 9.429991714554673e+55) {
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * x)))) + 313.399215894) * x) + 47.066876606));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811
	tmp = 0
	if x < -3.326128725870005e+62:
		tmp = t_0
	elif x < 9.429991714554673e+55:
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * x)))) + 313.399215894) * x) + 47.066876606))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y / Float64(x * x)) + Float64(4.16438922228 * x)) - 110.1139242984811)
	tmp = 0.0
	if (x < -3.326128725870005e+62)
		tmp = t_0;
	elseif (x < 9.429991714554673e+55)
		tmp = Float64(Float64(Float64(x - 2.0) / 1.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / Float64(Float64(Float64(Float64(Float64(263.505074721 * x) + Float64(Float64(43.3400022514 * Float64(x * x)) + Float64(x * Float64(x * x)))) + 313.399215894) * x) + 47.066876606)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811;
	tmp = 0.0;
	if (x < -3.326128725870005e+62)
		tmp = t_0;
	elseif (x < 9.429991714554673e+55)
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * x)))) + 313.399215894) * x) + 47.066876606));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y / N[(x * x), $MachinePrecision]), $MachinePrecision] + N[(4.16438922228 * x), $MachinePrecision]), $MachinePrecision] - 110.1139242984811), $MachinePrecision]}, If[Less[x, -3.326128725870005e+62], t$95$0, If[Less[x, 9.429991714554673e+55], N[(N[(N[(x - 2.0), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision] / N[(N[(N[(N[(N[(263.505074721 * x), $MachinePrecision] + N[(N[(43.3400022514 * N[(x * x), $MachinePrecision]), $MachinePrecision] + N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024095 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C"
  :precision binary64

  :alt
  (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)))