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

Percentage Accurate: 58.8% → 98.2%

Time: 17.6s

Alternatives: 19

Speedup: 4.4×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 58.8% 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: 98.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}}{x + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{-1}{4.16438922228 \cdot \left(x + -2\right)}}\\ \end{array} \end{array} \]

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))
      INFINITY)
   (/
    (*
     (fma x x -4.0)
     (/
      (fma
       x
       (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y)
       z)
      (fma
       x
       (fma x (fma x (+ x 43.3400022514) 263.505074721) 313.399215894)
       47.066876606)))
    (+ x 2.0))
   (/ -1.0 (/ -1.0 (* 4.16438922228 (+ x -2.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)) <= ((double) INFINITY)) {
		tmp = (fma(x, x, -4.0) * (fma(x, fma(x, fma(x, fma(x, 4.16438922228, 78.6994924154), 137.519416416), y), z) / fma(x, fma(x, fma(x, (x + 43.3400022514), 263.505074721), 313.399215894), 47.066876606))) / (x + 2.0);
	} else {
		tmp = -1.0 / (-1.0 / (4.16438922228 * (x + -2.0)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)) <= Inf)
		tmp = Float64(Float64(fma(x, x, -4.0) * Float64(fma(x, fma(x, fma(x, fma(x, 4.16438922228, 78.6994924154), 137.519416416), y), z) / fma(x, fma(x, fma(x, Float64(x + 43.3400022514), 263.505074721), 313.399215894), 47.066876606))) / Float64(x + 2.0));
	else
		tmp = Float64(-1.0 / Float64(-1.0 / Float64(4.16438922228 * Float64(x + -2.0))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(x * N[(N[(x * N[(N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision] + 137.519416416), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(x * x + -4.0), $MachinePrecision] * N[(N[(x * N[(x * N[(x * N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] + 137.519416416), $MachinePrecision] + y), $MachinePrecision] + z), $MachinePrecision] / N[(x * N[(x * N[(x * N[(x + 43.3400022514), $MachinePrecision] + 263.505074721), $MachinePrecision] + 313.399215894), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 2.0), $MachinePrecision]), $MachinePrecision], N[(-1.0 / N[(-1.0 / N[(4.16438922228 * N[(x + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.1%

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

   4. Applied egg-rr 99.5%

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

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

   1. Initial program 0.0%

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

   4. Applied egg-rr 0.0%

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

   5. Taylor expanded in x around inf

      \[\leadsto \frac{\mathsf{fma}\left(x, x, -4\right) \cdot \color{blue}{\frac{104109730557}{25000000000}}}{x + 2} \]
   6. Step-by-step derivation

   7. Simplified 34.3%

      \[\leadsto \frac{\mathsf{fma}\left(x, x, -4\right) \cdot \color{blue}{4.16438922228}}{x + 2} \]
   8. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, x, -4\right)} \cdot \frac{104109730557}{25000000000}}{x + 2} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}}{x + 2} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{\color{blue}{x + 2}} \]

      4. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{x + 2}{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}}} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{x + 2}{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}}} \]

      6. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{x + 2}}}} \]

      7. lift-/.f64 N/A

         \[\leadsto \frac{1}{\frac{1}{\color{blue}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{x + 2}}}} \]

      8. lower-/.f64 34.3

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot 4.16438922228}{x + 2}}}} \]

      9. lift-/.f64 N/A

         \[\leadsto \frac{1}{\frac{1}{\color{blue}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{x + 2}}}} \]

      10. lift-+.f64 N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{\color{blue}{x + 2}}}} \]

      11. metadata-eval N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{x + \color{blue}{\left(\mathsf{neg}\left(-2\right)\right)}}}} \]

      12. sub-neg N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{\color{blue}{x - -2}}}} \]

      13. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\color{blue}{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}}{x - -2}}} \]

      14. *-commutative N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\color{blue}{\frac{104109730557}{25000000000} \cdot \mathsf{fma}\left(x, x, -4\right)}}{x - -2}}} \]

      15. lift-fma.f64 N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\frac{104109730557}{25000000000} \cdot \color{blue}{\left(x \cdot x + -4\right)}}{x - -2}}} \]

      16. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\frac{104109730557}{25000000000} \cdot \left(\color{blue}{x \cdot x} + -4\right)}{x - -2}}} \]

      17. metadata-eval N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\frac{104109730557}{25000000000} \cdot \left(x \cdot x + \color{blue}{\left(\mathsf{neg}\left(4\right)\right)}\right)}{x - -2}}} \]

      18. metadata-eval N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\frac{104109730557}{25000000000} \cdot \left(x \cdot x + \left(\mathsf{neg}\left(\color{blue}{2 \cdot 2}\right)\right)\right)}{x - -2}}} \]

      19. sub-neg N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\frac{104109730557}{25000000000} \cdot \color{blue}{\left(x \cdot x - 2 \cdot 2\right)}}{x - -2}}} \]

      20. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\frac{104109730557}{25000000000} \cdot \left(\color{blue}{x \cdot x} - 2 \cdot 2\right)}{x - -2}}} \]

      21. associate-/l* N/A

          \[\leadsto \frac{1}{\frac{1}{\color{blue}{\frac{104109730557}{25000000000} \cdot \frac{x \cdot x - 2 \cdot 2}{x - -2}}}} \]

   9. Applied egg-rr 99.1%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}}{x + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{-1}{4.16438922228 \cdot \left(x + -2\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.3% accurate, 0.5× speedup

Math

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

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))
      INFINITY)
   (*
    (+ x -2.0)
    (/
     (fma
      x
      (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y)
      z)
     (fma
      x
      (fma (+ x 43.3400022514) (* x x) (fma x 263.505074721 313.399215894))
      47.066876606)))
   (/ -1.0 (/ -1.0 (* 4.16438922228 (+ x -2.0))))))

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.1%

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

   4. Applied egg-rr 99.5%

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

      1. lift-+.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. distribute-rgt-in N/A

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

      5. associate-+l+ N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 99.5

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

   6. Applied egg-rr 99.5%

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

   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. Initial program 0.0%

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

   4. Applied egg-rr 0.0%

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

   5. Taylor expanded in x around inf

      \[\leadsto \frac{\mathsf{fma}\left(x, x, -4\right) \cdot \color{blue}{\frac{104109730557}{25000000000}}}{x + 2} \]
   6. Step-by-step derivation

   7. Simplified 34.3%

      \[\leadsto \frac{\mathsf{fma}\left(x, x, -4\right) \cdot \color{blue}{4.16438922228}}{x + 2} \]
   8. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, x, -4\right)} \cdot \frac{104109730557}{25000000000}}{x + 2} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}}{x + 2} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{\color{blue}{x + 2}} \]

      4. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{x + 2}{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}}} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{x + 2}{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}}} \]

      6. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{x + 2}}}} \]

      7. lift-/.f64 N/A

         \[\leadsto \frac{1}{\frac{1}{\color{blue}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{x + 2}}}} \]

      8. lower-/.f64 34.3

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot 4.16438922228}{x + 2}}}} \]

      9. lift-/.f64 N/A

         \[\leadsto \frac{1}{\frac{1}{\color{blue}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{x + 2}}}} \]

      10. lift-+.f64 N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{\color{blue}{x + 2}}}} \]

      11. metadata-eval N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{x + \color{blue}{\left(\mathsf{neg}\left(-2\right)\right)}}}} \]

      12. sub-neg N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{\color{blue}{x - -2}}}} \]

      13. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\color{blue}{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}}{x - -2}}} \]

      14. *-commutative N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\color{blue}{\frac{104109730557}{25000000000} \cdot \mathsf{fma}\left(x, x, -4\right)}}{x - -2}}} \]

      15. lift-fma.f64 N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\frac{104109730557}{25000000000} \cdot \color{blue}{\left(x \cdot x + -4\right)}}{x - -2}}} \]

      16. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\frac{104109730557}{25000000000} \cdot \left(\color{blue}{x \cdot x} + -4\right)}{x - -2}}} \]

      17. metadata-eval N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\frac{104109730557}{25000000000} \cdot \left(x \cdot x + \color{blue}{\left(\mathsf{neg}\left(4\right)\right)}\right)}{x - -2}}} \]

      18. metadata-eval N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\frac{104109730557}{25000000000} \cdot \left(x \cdot x + \left(\mathsf{neg}\left(\color{blue}{2 \cdot 2}\right)\right)\right)}{x - -2}}} \]

      19. sub-neg N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\frac{104109730557}{25000000000} \cdot \color{blue}{\left(x \cdot x - 2 \cdot 2\right)}}{x - -2}}} \]

      20. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\frac{104109730557}{25000000000} \cdot \left(\color{blue}{x \cdot x} - 2 \cdot 2\right)}{x - -2}}} \]

      21. associate-/l* N/A

          \[\leadsto \frac{1}{\frac{1}{\color{blue}{\frac{104109730557}{25000000000} \cdot \frac{x \cdot x - 2 \cdot 2}{x - -2}}}} \]

   9. Applied egg-rr 99.1%

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

4. Final simplification 99.4%

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

Alternative 3: 98.3% accurate, 0.5× speedup

Math

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

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))
      INFINITY)
   (*
    (/
     (fma
      x
      (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y)
      z)
     (fma
      x
      (fma x (fma x (+ x 43.3400022514) 263.505074721) 313.399215894)
      47.066876606))
    (+ x -2.0))
   (/ -1.0 (/ -1.0 (* 4.16438922228 (+ x -2.0))))))

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.1%

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

   4. Applied egg-rr 99.5%

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

   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. Initial program 0.0%

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

   4. Applied egg-rr 0.0%

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

   5. Taylor expanded in x around inf

      \[\leadsto \frac{\mathsf{fma}\left(x, x, -4\right) \cdot \color{blue}{\frac{104109730557}{25000000000}}}{x + 2} \]
   6. Step-by-step derivation

   7. Simplified 34.3%

      \[\leadsto \frac{\mathsf{fma}\left(x, x, -4\right) \cdot \color{blue}{4.16438922228}}{x + 2} \]
   8. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, x, -4\right)} \cdot \frac{104109730557}{25000000000}}{x + 2} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}}{x + 2} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{\color{blue}{x + 2}} \]

      4. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{x + 2}{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}}} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{x + 2}{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}}} \]

      6. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{x + 2}}}} \]

      7. lift-/.f64 N/A

         \[\leadsto \frac{1}{\frac{1}{\color{blue}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{x + 2}}}} \]

      8. lower-/.f64 34.3

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot 4.16438922228}{x + 2}}}} \]

      9. lift-/.f64 N/A

         \[\leadsto \frac{1}{\frac{1}{\color{blue}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{x + 2}}}} \]

      10. lift-+.f64 N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{\color{blue}{x + 2}}}} \]

      11. metadata-eval N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{x + \color{blue}{\left(\mathsf{neg}\left(-2\right)\right)}}}} \]

      12. sub-neg N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{\color{blue}{x - -2}}}} \]

      13. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\color{blue}{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}}{x - -2}}} \]

      14. *-commutative N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\color{blue}{\frac{104109730557}{25000000000} \cdot \mathsf{fma}\left(x, x, -4\right)}}{x - -2}}} \]

      15. lift-fma.f64 N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\frac{104109730557}{25000000000} \cdot \color{blue}{\left(x \cdot x + -4\right)}}{x - -2}}} \]

      16. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\frac{104109730557}{25000000000} \cdot \left(\color{blue}{x \cdot x} + -4\right)}{x - -2}}} \]

      17. metadata-eval N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\frac{104109730557}{25000000000} \cdot \left(x \cdot x + \color{blue}{\left(\mathsf{neg}\left(4\right)\right)}\right)}{x - -2}}} \]

      18. metadata-eval N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\frac{104109730557}{25000000000} \cdot \left(x \cdot x + \left(\mathsf{neg}\left(\color{blue}{2 \cdot 2}\right)\right)\right)}{x - -2}}} \]

      19. sub-neg N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\frac{104109730557}{25000000000} \cdot \color{blue}{\left(x \cdot x - 2 \cdot 2\right)}}{x - -2}}} \]

      20. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\frac{104109730557}{25000000000} \cdot \left(\color{blue}{x \cdot x} - 2 \cdot 2\right)}{x - -2}}} \]

      21. associate-/l* N/A

          \[\leadsto \frac{1}{\frac{1}{\color{blue}{\frac{104109730557}{25000000000} \cdot \frac{x \cdot x - 2 \cdot 2}{x - -2}}}} \]

   9. Applied egg-rr 99.1%

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

4. Final simplification 99.4%

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

Alternative 4: 95.2% accurate, 0.5× speedup

Math

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

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))
      INFINITY)
   (*
    (+ x -2.0)
    (/
     (fma x (fma x (* x (* x 4.16438922228)) y) z)
     (fma
      x
      (fma x (fma x (+ x 43.3400022514) 263.505074721) 313.399215894)
      47.066876606)))
   (/ -1.0 (/ -1.0 (* 4.16438922228 (+ x -2.0))))))

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.1%

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in x around inf

      \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{\frac{104109730557}{25000000000} \cdot {x}^{2}}, y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(x + -2\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. unpow2 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 96.9

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

   7. Simplified 96.9%

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

   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. Initial program 0.0%

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

   4. Applied egg-rr 0.0%

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

   5. Taylor expanded in x around inf

      \[\leadsto \frac{\mathsf{fma}\left(x, x, -4\right) \cdot \color{blue}{\frac{104109730557}{25000000000}}}{x + 2} \]
   6. Step-by-step derivation

   7. Simplified 34.3%

      \[\leadsto \frac{\mathsf{fma}\left(x, x, -4\right) \cdot \color{blue}{4.16438922228}}{x + 2} \]
   8. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, x, -4\right)} \cdot \frac{104109730557}{25000000000}}{x + 2} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}}{x + 2} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{\color{blue}{x + 2}} \]

      4. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{x + 2}{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}}} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{x + 2}{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}}} \]

      6. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{x + 2}}}} \]

      7. lift-/.f64 N/A

         \[\leadsto \frac{1}{\frac{1}{\color{blue}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{x + 2}}}} \]

      8. lower-/.f64 34.3

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot 4.16438922228}{x + 2}}}} \]

      9. lift-/.f64 N/A

         \[\leadsto \frac{1}{\frac{1}{\color{blue}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{x + 2}}}} \]

      10. lift-+.f64 N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{\color{blue}{x + 2}}}} \]

      11. metadata-eval N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{x + \color{blue}{\left(\mathsf{neg}\left(-2\right)\right)}}}} \]

      12. sub-neg N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{\color{blue}{x - -2}}}} \]

      13. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\color{blue}{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}}{x - -2}}} \]

      14. *-commutative N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\color{blue}{\frac{104109730557}{25000000000} \cdot \mathsf{fma}\left(x, x, -4\right)}}{x - -2}}} \]

      15. lift-fma.f64 N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\frac{104109730557}{25000000000} \cdot \color{blue}{\left(x \cdot x + -4\right)}}{x - -2}}} \]

      16. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\frac{104109730557}{25000000000} \cdot \left(\color{blue}{x \cdot x} + -4\right)}{x - -2}}} \]

      17. metadata-eval N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\frac{104109730557}{25000000000} \cdot \left(x \cdot x + \color{blue}{\left(\mathsf{neg}\left(4\right)\right)}\right)}{x - -2}}} \]

      18. metadata-eval N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\frac{104109730557}{25000000000} \cdot \left(x \cdot x + \left(\mathsf{neg}\left(\color{blue}{2 \cdot 2}\right)\right)\right)}{x - -2}}} \]

      19. sub-neg N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\frac{104109730557}{25000000000} \cdot \color{blue}{\left(x \cdot x - 2 \cdot 2\right)}}{x - -2}}} \]

      20. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\frac{104109730557}{25000000000} \cdot \left(\color{blue}{x \cdot x} - 2 \cdot 2\right)}{x - -2}}} \]

      21. associate-/l* N/A

          \[\leadsto \frac{1}{\frac{1}{\color{blue}{\frac{104109730557}{25000000000} \cdot \frac{x \cdot x - 2 \cdot 2}{x - -2}}}} \]

   9. Applied egg-rr 99.1%

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

4. Final simplification 97.7%

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

Alternative 5: 96.0% accurate, 0.5× speedup

Math

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

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))
      INFINITY)
   (*
    (+ x -2.0)
    (/
     (fma
      x
      (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y)
      z)
     (fma x (* x (* x x)) 47.066876606)))
   (/ -1.0 (/ -1.0 (* 4.16438922228 (+ x -2.0))))))

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.1%

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in x around inf

      \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \color{blue}{{x}^{3}}, \frac{23533438303}{500000000}\right)} \cdot \left(x + -2\right) \]
   6. Step-by-step derivation

      1. cube-mult N/A

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

      2. unpow2 N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 94.6

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

   7. Simplified 94.6%

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

   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. Initial program 0.0%

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

   4. Applied egg-rr 0.0%

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

   5. Taylor expanded in x around inf

      \[\leadsto \frac{\mathsf{fma}\left(x, x, -4\right) \cdot \color{blue}{\frac{104109730557}{25000000000}}}{x + 2} \]
   6. Step-by-step derivation

   7. Simplified 34.3%

      \[\leadsto \frac{\mathsf{fma}\left(x, x, -4\right) \cdot \color{blue}{4.16438922228}}{x + 2} \]
   8. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, x, -4\right)} \cdot \frac{104109730557}{25000000000}}{x + 2} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}}{x + 2} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{\color{blue}{x + 2}} \]

      4. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{x + 2}{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}}} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{x + 2}{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}}} \]

      6. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{x + 2}}}} \]

      7. lift-/.f64 N/A

         \[\leadsto \frac{1}{\frac{1}{\color{blue}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{x + 2}}}} \]

      8. lower-/.f64 34.3

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot 4.16438922228}{x + 2}}}} \]

      9. lift-/.f64 N/A

         \[\leadsto \frac{1}{\frac{1}{\color{blue}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{x + 2}}}} \]

      10. lift-+.f64 N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{\color{blue}{x + 2}}}} \]

      11. metadata-eval N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{x + \color{blue}{\left(\mathsf{neg}\left(-2\right)\right)}}}} \]

      12. sub-neg N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}{\color{blue}{x - -2}}}} \]

      13. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\color{blue}{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{104109730557}{25000000000}}}{x - -2}}} \]

      14. *-commutative N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\color{blue}{\frac{104109730557}{25000000000} \cdot \mathsf{fma}\left(x, x, -4\right)}}{x - -2}}} \]

      15. lift-fma.f64 N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\frac{104109730557}{25000000000} \cdot \color{blue}{\left(x \cdot x + -4\right)}}{x - -2}}} \]

      16. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\frac{104109730557}{25000000000} \cdot \left(\color{blue}{x \cdot x} + -4\right)}{x - -2}}} \]

      17. metadata-eval N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\frac{104109730557}{25000000000} \cdot \left(x \cdot x + \color{blue}{\left(\mathsf{neg}\left(4\right)\right)}\right)}{x - -2}}} \]

      18. metadata-eval N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\frac{104109730557}{25000000000} \cdot \left(x \cdot x + \left(\mathsf{neg}\left(\color{blue}{2 \cdot 2}\right)\right)\right)}{x - -2}}} \]

      19. sub-neg N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\frac{104109730557}{25000000000} \cdot \color{blue}{\left(x \cdot x - 2 \cdot 2\right)}}{x - -2}}} \]

      20. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{1}{\frac{\frac{104109730557}{25000000000} \cdot \left(\color{blue}{x \cdot x} - 2 \cdot 2\right)}{x - -2}}} \]

      21. associate-/l* N/A

          \[\leadsto \frac{1}{\frac{1}{\color{blue}{\frac{104109730557}{25000000000} \cdot \frac{x \cdot x - 2 \cdot 2}{x - -2}}}} \]

   9. Applied egg-rr 99.1%

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

4. Final simplification 96.2%

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

Alternative 6: 96.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \left(\frac{-188.81341671388108 + \frac{\frac{y + -258651.98023111798}{x} - -7085.836212289914}{x}}{x} - -4.16438922228\right)\\ \mathbf{elif}\;x \leq 14500000000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(x, \mathsf{fma}\left(x, 137.519416416, y\right), z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y + -124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.5e+35)
   (*
    x
    (-
     (/
      (+
       -188.81341671388108
       (/ (- (/ (+ y -258651.98023111798) x) -7085.836212289914) x))
      x)
     -4.16438922228))
   (if (<= x 14500000000000.0)
     (/
      (* (- x 2.0) (fma x (fma x 137.519416416 y) z))
      (+
       (*
        x
        (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
       47.066876606))
     (*
      (+ x -2.0)
      (+
       4.16438922228
       (/
        (-
         (/ (+ 3451.550173699799 (/ (+ y -124074.40615218398) x)) x)
         101.7851458539211)
        x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.5e+35) {
		tmp = x * (((-188.81341671388108 + ((((y + -258651.98023111798) / x) - -7085.836212289914) / x)) / x) - -4.16438922228);
	} else if (x <= 14500000000000.0) {
		tmp = ((x - 2.0) * fma(x, fma(x, 137.519416416, y), z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y + -124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.5e+35)
		tmp = Float64(x * Float64(Float64(Float64(-188.81341671388108 + Float64(Float64(Float64(Float64(y + -258651.98023111798) / x) - -7085.836212289914) / x)) / x) - -4.16438922228));
	elseif (x <= 14500000000000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * fma(x, fma(x, 137.519416416, y), z)) / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(Float64(y + -124074.40615218398) / x)) / x) - 101.7851458539211) / x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.5e+35], N[(x * N[(N[(N[(-188.81341671388108 + N[(N[(N[(N[(y + -258651.98023111798), $MachinePrecision] / x), $MachinePrecision] - -7085.836212289914), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - -4.16438922228), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 14500000000000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(x * N[(x * 137.519416416 + y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(N[(N[(N[(3451.550173699799 + N[(N[(y + -124074.40615218398), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.5000000000000001e35

   1. Initial program 7.9%

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

   4. Applied egg-rr 18.6%

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

   5. Taylor expanded in x around inf

      \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{\frac{104109730557}{25000000000} \cdot {x}^{2}}, y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(x + -2\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. unpow2 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 18.6

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

   7. Simplified 18.6%

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

      1. flip-+ N/A

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

      2. metadata-eval N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \frac{x \cdot x - \color{blue}{4}}{x - -2} \]

      3. metadata-eval N/A

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

      4. div-inv N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \color{blue}{\left(\left(x \cdot x - 2 \cdot 2\right) \cdot \frac{1}{x - -2}\right)} \]

      5. sub-neg N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\left(x \cdot x - 2 \cdot 2\right) \cdot \frac{1}{\color{blue}{x + \left(\mathsf{neg}\left(-2\right)\right)}}\right) \]

      6. metadata-eval N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\left(x \cdot x - 2 \cdot 2\right) \cdot \frac{1}{x + \color{blue}{2}}\right) \]

      7. lift-+.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\left(x \cdot x - 2 \cdot 2\right) \cdot \frac{1}{\color{blue}{x + 2}}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \color{blue}{\left(\left(x \cdot x - 2 \cdot 2\right) \cdot \frac{1}{x + 2}\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\left(\color{blue}{x \cdot x} - 2 \cdot 2\right) \cdot \frac{1}{x + 2}\right) \]

      10. sub-neg N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\color{blue}{\left(x \cdot x + \left(\mathsf{neg}\left(2 \cdot 2\right)\right)\right)} \cdot \frac{1}{x + 2}\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\left(\color{blue}{x \cdot x} + \left(\mathsf{neg}\left(2 \cdot 2\right)\right)\right) \cdot \frac{1}{x + 2}\right) \]

      12. metadata-eval N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\left(x \cdot x + \left(\mathsf{neg}\left(\color{blue}{4}\right)\right)\right) \cdot \frac{1}{x + 2}\right) \]

      13. metadata-eval N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\left(x \cdot x + \color{blue}{-4}\right) \cdot \frac{1}{x + 2}\right) \]

      14. lift-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\color{blue}{\mathsf{fma}\left(x, x, -4\right)} \cdot \frac{1}{x + 2}\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\mathsf{fma}\left(x, x, -4\right) \cdot \frac{1}{\color{blue}{x + 2}}\right) \]

      16. metadata-eval N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\mathsf{fma}\left(x, x, -4\right) \cdot \frac{1}{x + \color{blue}{\left(\mathsf{neg}\left(-2\right)\right)}}\right) \]

      17. sub-neg N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\mathsf{fma}\left(x, x, -4\right) \cdot \frac{1}{\color{blue}{x - -2}}\right) \]

      18. lower-/.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\mathsf{fma}\left(x, x, -4\right) \cdot \color{blue}{\frac{1}{x - -2}}\right) \]

      19. sub-neg N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\mathsf{fma}\left(x, x, -4\right) \cdot \frac{1}{\color{blue}{x + \left(\mathsf{neg}\left(-2\right)\right)}}\right) \]

      20. metadata-eval N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\mathsf{fma}\left(x, x, -4\right) \cdot \frac{1}{x + \color{blue}{2}}\right) \]

      21. lift-+.f64 18.6

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot 4.16438922228\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \cdot \left(\mathsf{fma}\left(x, x, -4\right) \cdot \frac{1}{\color{blue}{x + 2}}\right) \]

   9. Applied egg-rr 18.6%

      \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot 4.16438922228\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \cdot \color{blue}{\left(\mathsf{fma}\left(x, x, -4\right) \cdot \frac{1}{x + 2}\right)} \]

   10. Taylor expanded in x around -inf

       \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{-1 \cdot \frac{y - \frac{808287438222243669041480252986729310388407301}{3125000000000000000000000000000000000000}}{x} - \frac{4428647632681196606708299159837293}{625000000000000000000000000000}}{x} - \frac{23601677089235136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \color{blue}{\left(-1 \cdot x\right) \cdot \left(-1 \cdot \frac{-1 \cdot \frac{-1 \cdot \frac{y - \frac{808287438222243669041480252986729310388407301}{3125000000000000000000000000000000000000}}{x} - \frac{4428647632681196606708299159837293}{625000000000000000000000000000}}{x} - \frac{23601677089235136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right)} \]

       2. *-commutative N/A

          \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{-1 \cdot \frac{y - \frac{808287438222243669041480252986729310388407301}{3125000000000000000000000000000000000000}}{x} - \frac{4428647632681196606708299159837293}{625000000000000000000000000000}}{x} - \frac{23601677089235136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right) \cdot \left(-1 \cdot x\right)} \]

       3. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{-1 \cdot \frac{y - \frac{808287438222243669041480252986729310388407301}{3125000000000000000000000000000000000000}}{x} - \frac{4428647632681196606708299159837293}{625000000000000000000000000000}}{x} - \frac{23601677089235136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right) \cdot \left(-1 \cdot x\right)} \]

   12. Simplified 95.3%

       \[\leadsto \color{blue}{\left(-4.16438922228 - \frac{-188.81341671388108 - \frac{-7085.836212289914 - \frac{y + -258651.98023111798}{x}}{x}}{x}\right) \cdot \left(-x\right)} \]

   if -3.5000000000000001e35 < x < 1.45e13

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 98.2

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

   5. Simplified 98.2%

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

   if 1.45e13 < x

   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. Add Preprocessing

   4. Applied egg-rr 29.4%

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

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   7. Simplified 96.0%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \left(\frac{-188.81341671388108 + \frac{\frac{y + -258651.98023111798}{x} - -7085.836212289914}{x}}{x} - -4.16438922228\right)\\ \mathbf{elif}\;x \leq 14500000000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(x, \mathsf{fma}\left(x, 137.519416416, y\right), z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y + -124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 93.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \left(\frac{-188.81341671388108 + \frac{\frac{y + -258651.98023111798}{x} - -7085.836212289914}{x}}{x} - -4.16438922228\right)\\ \mathbf{elif}\;x \leq 14500000000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(x, y, z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y + -124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.5e+35)
   (*
    x
    (-
     (/
      (+
       -188.81341671388108
       (/ (- (/ (+ y -258651.98023111798) x) -7085.836212289914) x))
      x)
     -4.16438922228))
   (if (<= x 14500000000000.0)
     (/
      (* (- x 2.0) (fma x y z))
      (+
       (*
        x
        (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
       47.066876606))
     (*
      (+ x -2.0)
      (+
       4.16438922228
       (/
        (-
         (/ (+ 3451.550173699799 (/ (+ y -124074.40615218398) x)) x)
         101.7851458539211)
        x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.5e+35) {
		tmp = x * (((-188.81341671388108 + ((((y + -258651.98023111798) / x) - -7085.836212289914) / x)) / x) - -4.16438922228);
	} else if (x <= 14500000000000.0) {
		tmp = ((x - 2.0) * fma(x, y, z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y + -124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.5e+35)
		tmp = Float64(x * Float64(Float64(Float64(-188.81341671388108 + Float64(Float64(Float64(Float64(y + -258651.98023111798) / x) - -7085.836212289914) / x)) / x) - -4.16438922228));
	elseif (x <= 14500000000000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * fma(x, y, z)) / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(Float64(y + -124074.40615218398) / x)) / x) - 101.7851458539211) / x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.5e+35], N[(x * N[(N[(N[(-188.81341671388108 + N[(N[(N[(N[(y + -258651.98023111798), $MachinePrecision] / x), $MachinePrecision] - -7085.836212289914), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - -4.16438922228), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 14500000000000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(x * y + z), $MachinePrecision]), $MachinePrecision] / N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(N[(N[(N[(3451.550173699799 + N[(N[(y + -124074.40615218398), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.5000000000000001e35

   1. Initial program 7.9%

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

   4. Applied egg-rr 18.6%

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

   5. Taylor expanded in x around inf

      \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{\frac{104109730557}{25000000000} \cdot {x}^{2}}, y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(x + -2\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. unpow2 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 18.6

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

   7. Simplified 18.6%

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

      1. flip-+ N/A

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

      2. metadata-eval N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \frac{x \cdot x - \color{blue}{4}}{x - -2} \]

      3. metadata-eval N/A

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

      4. div-inv N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \color{blue}{\left(\left(x \cdot x - 2 \cdot 2\right) \cdot \frac{1}{x - -2}\right)} \]

      5. sub-neg N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\left(x \cdot x - 2 \cdot 2\right) \cdot \frac{1}{\color{blue}{x + \left(\mathsf{neg}\left(-2\right)\right)}}\right) \]

      6. metadata-eval N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\left(x \cdot x - 2 \cdot 2\right) \cdot \frac{1}{x + \color{blue}{2}}\right) \]

      7. lift-+.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\left(x \cdot x - 2 \cdot 2\right) \cdot \frac{1}{\color{blue}{x + 2}}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \color{blue}{\left(\left(x \cdot x - 2 \cdot 2\right) \cdot \frac{1}{x + 2}\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\left(\color{blue}{x \cdot x} - 2 \cdot 2\right) \cdot \frac{1}{x + 2}\right) \]

      10. sub-neg N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\color{blue}{\left(x \cdot x + \left(\mathsf{neg}\left(2 \cdot 2\right)\right)\right)} \cdot \frac{1}{x + 2}\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\left(\color{blue}{x \cdot x} + \left(\mathsf{neg}\left(2 \cdot 2\right)\right)\right) \cdot \frac{1}{x + 2}\right) \]

      12. metadata-eval N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\left(x \cdot x + \left(\mathsf{neg}\left(\color{blue}{4}\right)\right)\right) \cdot \frac{1}{x + 2}\right) \]

      13. metadata-eval N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\left(x \cdot x + \color{blue}{-4}\right) \cdot \frac{1}{x + 2}\right) \]

      14. lift-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\color{blue}{\mathsf{fma}\left(x, x, -4\right)} \cdot \frac{1}{x + 2}\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\mathsf{fma}\left(x, x, -4\right) \cdot \frac{1}{\color{blue}{x + 2}}\right) \]

      16. metadata-eval N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\mathsf{fma}\left(x, x, -4\right) \cdot \frac{1}{x + \color{blue}{\left(\mathsf{neg}\left(-2\right)\right)}}\right) \]

      17. sub-neg N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\mathsf{fma}\left(x, x, -4\right) \cdot \frac{1}{\color{blue}{x - -2}}\right) \]

      18. lower-/.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\mathsf{fma}\left(x, x, -4\right) \cdot \color{blue}{\frac{1}{x - -2}}\right) \]

      19. sub-neg N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\mathsf{fma}\left(x, x, -4\right) \cdot \frac{1}{\color{blue}{x + \left(\mathsf{neg}\left(-2\right)\right)}}\right) \]

      20. metadata-eval N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\mathsf{fma}\left(x, x, -4\right) \cdot \frac{1}{x + \color{blue}{2}}\right) \]

      21. lift-+.f64 18.6

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot 4.16438922228\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \cdot \left(\mathsf{fma}\left(x, x, -4\right) \cdot \frac{1}{\color{blue}{x + 2}}\right) \]

   9. Applied egg-rr 18.6%

      \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot 4.16438922228\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \cdot \color{blue}{\left(\mathsf{fma}\left(x, x, -4\right) \cdot \frac{1}{x + 2}\right)} \]

   10. Taylor expanded in x around -inf

       \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{-1 \cdot \frac{y - \frac{808287438222243669041480252986729310388407301}{3125000000000000000000000000000000000000}}{x} - \frac{4428647632681196606708299159837293}{625000000000000000000000000000}}{x} - \frac{23601677089235136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \color{blue}{\left(-1 \cdot x\right) \cdot \left(-1 \cdot \frac{-1 \cdot \frac{-1 \cdot \frac{y - \frac{808287438222243669041480252986729310388407301}{3125000000000000000000000000000000000000}}{x} - \frac{4428647632681196606708299159837293}{625000000000000000000000000000}}{x} - \frac{23601677089235136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right)} \]

       2. *-commutative N/A

          \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{-1 \cdot \frac{y - \frac{808287438222243669041480252986729310388407301}{3125000000000000000000000000000000000000}}{x} - \frac{4428647632681196606708299159837293}{625000000000000000000000000000}}{x} - \frac{23601677089235136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right) \cdot \left(-1 \cdot x\right)} \]

       3. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{-1 \cdot \frac{y - \frac{808287438222243669041480252986729310388407301}{3125000000000000000000000000000000000000}}{x} - \frac{4428647632681196606708299159837293}{625000000000000000000000000000}}{x} - \frac{23601677089235136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right) \cdot \left(-1 \cdot x\right)} \]

   12. Simplified 95.3%

       \[\leadsto \color{blue}{\left(-4.16438922228 - \frac{-188.81341671388108 - \frac{-7085.836212289914 - \frac{y + -258651.98023111798}{x}}{x}}{x}\right) \cdot \left(-x\right)} \]

   if -3.5000000000000001e35 < x < 1.45e13

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 96.2

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

   5. Simplified 96.2%

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

   if 1.45e13 < x

   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. Add Preprocessing

   4. Applied egg-rr 29.4%

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

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   7. Simplified 96.0%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \left(\frac{-188.81341671388108 + \frac{\frac{y + -258651.98023111798}{x} - -7085.836212289914}{x}}{x} - -4.16438922228\right)\\ \mathbf{elif}\;x \leq 14500000000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(x, y, z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y + -124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 93.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(\frac{-188.81341671388108 + \frac{\frac{y + -258651.98023111798}{x} - -7085.836212289914}{x}}{x} - -4.16438922228\right)\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{+35}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+14}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(x, y, z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          x
          (-
           (/
            (+
             -188.81341671388108
             (/ (- (/ (+ y -258651.98023111798) x) -7085.836212289914) x))
            x)
           -4.16438922228))))
   (if (<= x -3.5e+35)
     t_0
     (if (<= x 5.4e+14)
       (/
        (* (- x 2.0) (fma x y z))
        (+
         (*
          x
          (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
         47.066876606))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (((-188.81341671388108 + ((((y + -258651.98023111798) / x) - -7085.836212289914) / x)) / x) - -4.16438922228);
	double tmp;
	if (x <= -3.5e+35) {
		tmp = t_0;
	} else if (x <= 5.4e+14) {
		tmp = ((x - 2.0) * fma(x, y, z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(Float64(Float64(-188.81341671388108 + Float64(Float64(Float64(Float64(y + -258651.98023111798) / x) - -7085.836212289914) / x)) / x) - -4.16438922228))
	tmp = 0.0
	if (x <= -3.5e+35)
		tmp = t_0;
	elseif (x <= 5.4e+14)
		tmp = Float64(Float64(Float64(x - 2.0) * fma(x, y, z)) / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(N[(N[(-188.81341671388108 + N[(N[(N[(N[(y + -258651.98023111798), $MachinePrecision] / x), $MachinePrecision] - -7085.836212289914), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - -4.16438922228), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.5e+35], t$95$0, If[LessEqual[x, 5.4e+14], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(x * y + z), $MachinePrecision]), $MachinePrecision] / N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.5000000000000001e35 or 5.4e14 < x

   1. Initial program 14.0%

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

   4. Applied egg-rr 24.5%

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

   5. Taylor expanded in x around inf

      \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{\frac{104109730557}{25000000000} \cdot {x}^{2}}, y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(x + -2\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. unpow2 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 24.5

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

   7. Simplified 24.5%

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

      1. flip-+ N/A

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

      2. metadata-eval N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \frac{x \cdot x - \color{blue}{4}}{x - -2} \]

      3. metadata-eval N/A

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

      4. div-inv N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \color{blue}{\left(\left(x \cdot x - 2 \cdot 2\right) \cdot \frac{1}{x - -2}\right)} \]

      5. sub-neg N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\left(x \cdot x - 2 \cdot 2\right) \cdot \frac{1}{\color{blue}{x + \left(\mathsf{neg}\left(-2\right)\right)}}\right) \]

      6. metadata-eval N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\left(x \cdot x - 2 \cdot 2\right) \cdot \frac{1}{x + \color{blue}{2}}\right) \]

      7. lift-+.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\left(x \cdot x - 2 \cdot 2\right) \cdot \frac{1}{\color{blue}{x + 2}}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \color{blue}{\left(\left(x \cdot x - 2 \cdot 2\right) \cdot \frac{1}{x + 2}\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\left(\color{blue}{x \cdot x} - 2 \cdot 2\right) \cdot \frac{1}{x + 2}\right) \]

      10. sub-neg N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\color{blue}{\left(x \cdot x + \left(\mathsf{neg}\left(2 \cdot 2\right)\right)\right)} \cdot \frac{1}{x + 2}\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\left(\color{blue}{x \cdot x} + \left(\mathsf{neg}\left(2 \cdot 2\right)\right)\right) \cdot \frac{1}{x + 2}\right) \]

      12. metadata-eval N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\left(x \cdot x + \left(\mathsf{neg}\left(\color{blue}{4}\right)\right)\right) \cdot \frac{1}{x + 2}\right) \]

      13. metadata-eval N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\left(x \cdot x + \color{blue}{-4}\right) \cdot \frac{1}{x + 2}\right) \]

      14. lift-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\color{blue}{\mathsf{fma}\left(x, x, -4\right)} \cdot \frac{1}{x + 2}\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\mathsf{fma}\left(x, x, -4\right) \cdot \frac{1}{\color{blue}{x + 2}}\right) \]

      16. metadata-eval N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\mathsf{fma}\left(x, x, -4\right) \cdot \frac{1}{x + \color{blue}{\left(\mathsf{neg}\left(-2\right)\right)}}\right) \]

      17. sub-neg N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\mathsf{fma}\left(x, x, -4\right) \cdot \frac{1}{\color{blue}{x - -2}}\right) \]

      18. lower-/.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\mathsf{fma}\left(x, x, -4\right) \cdot \color{blue}{\frac{1}{x - -2}}\right) \]

      19. sub-neg N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\mathsf{fma}\left(x, x, -4\right) \cdot \frac{1}{\color{blue}{x + \left(\mathsf{neg}\left(-2\right)\right)}}\right) \]

      20. metadata-eval N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\mathsf{fma}\left(x, x, -4\right) \cdot \frac{1}{x + \color{blue}{2}}\right) \]

      21. lift-+.f64 24.5

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot 4.16438922228\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \cdot \left(\mathsf{fma}\left(x, x, -4\right) \cdot \frac{1}{\color{blue}{x + 2}}\right) \]

   9. Applied egg-rr 24.5%

      \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot 4.16438922228\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \cdot \color{blue}{\left(\mathsf{fma}\left(x, x, -4\right) \cdot \frac{1}{x + 2}\right)} \]

   10. Taylor expanded in x around -inf

       \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{-1 \cdot \frac{y - \frac{808287438222243669041480252986729310388407301}{3125000000000000000000000000000000000000}}{x} - \frac{4428647632681196606708299159837293}{625000000000000000000000000000}}{x} - \frac{23601677089235136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \color{blue}{\left(-1 \cdot x\right) \cdot \left(-1 \cdot \frac{-1 \cdot \frac{-1 \cdot \frac{y - \frac{808287438222243669041480252986729310388407301}{3125000000000000000000000000000000000000}}{x} - \frac{4428647632681196606708299159837293}{625000000000000000000000000000}}{x} - \frac{23601677089235136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right)} \]

       2. *-commutative N/A

          \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{-1 \cdot \frac{y - \frac{808287438222243669041480252986729310388407301}{3125000000000000000000000000000000000000}}{x} - \frac{4428647632681196606708299159837293}{625000000000000000000000000000}}{x} - \frac{23601677089235136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right) \cdot \left(-1 \cdot x\right)} \]

       3. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{-1 \cdot \frac{y - \frac{808287438222243669041480252986729310388407301}{3125000000000000000000000000000000000000}}{x} - \frac{4428647632681196606708299159837293}{625000000000000000000000000000}}{x} - \frac{23601677089235136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right) \cdot \left(-1 \cdot x\right)} \]

   12. Simplified 95.7%

       \[\leadsto \color{blue}{\left(-4.16438922228 - \frac{-188.81341671388108 - \frac{-7085.836212289914 - \frac{y + -258651.98023111798}{x}}{x}}{x}\right) \cdot \left(-x\right)} \]

   if -3.5000000000000001e35 < x < 5.4e14

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 96.2

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

   5. Simplified 96.2%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \left(\frac{-188.81341671388108 + \frac{\frac{y + -258651.98023111798}{x} - -7085.836212289914}{x}}{x} - -4.16438922228\right)\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+14}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(x, y, z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{-188.81341671388108 + \frac{\frac{y + -258651.98023111798}{x} - -7085.836212289914}{x}}{x} - -4.16438922228\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 95.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(\frac{-188.81341671388108 + \frac{\frac{y + -258651.98023111798}{x} - -7085.836212289914}{x}}{x} - -4.16438922228\right)\\ \mathbf{if}\;x \leq -36:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 230:\\ \;\;\;\;\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, 313.399215894, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          x
          (-
           (/
            (+
             -188.81341671388108
             (/ (- (/ (+ y -258651.98023111798) x) -7085.836212289914) x))
            x)
           -4.16438922228))))
   (if (<= x -36.0)
     t_0
     (if (<= x 230.0)
       (*
        (+ x -2.0)
        (/
         (fma
          x
          (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y)
          z)
         (fma x 313.399215894 47.066876606)))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (((-188.81341671388108 + ((((y + -258651.98023111798) / x) - -7085.836212289914) / x)) / x) - -4.16438922228);
	double tmp;
	if (x <= -36.0) {
		tmp = t_0;
	} else if (x <= 230.0) {
		tmp = (x + -2.0) * (fma(x, fma(x, fma(x, fma(x, 4.16438922228, 78.6994924154), 137.519416416), y), z) / fma(x, 313.399215894, 47.066876606));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(Float64(Float64(-188.81341671388108 + Float64(Float64(Float64(Float64(y + -258651.98023111798) / x) - -7085.836212289914) / x)) / x) - -4.16438922228))
	tmp = 0.0
	if (x <= -36.0)
		tmp = t_0;
	elseif (x <= 230.0)
		tmp = Float64(Float64(x + -2.0) * Float64(fma(x, fma(x, fma(x, fma(x, 4.16438922228, 78.6994924154), 137.519416416), y), z) / fma(x, 313.399215894, 47.066876606)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(N[(N[(-188.81341671388108 + N[(N[(N[(N[(y + -258651.98023111798), $MachinePrecision] / x), $MachinePrecision] - -7085.836212289914), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - -4.16438922228), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -36.0], t$95$0, If[LessEqual[x, 230.0], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(x * N[(x * N[(x * N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] + 137.519416416), $MachinePrecision] + y), $MachinePrecision] + z), $MachinePrecision] / N[(x * 313.399215894 + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -36 or 230 < x

   1. Initial program 17.4%

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

   4. Applied egg-rr 27.6%

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

   5. Taylor expanded in x around inf

      \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{\frac{104109730557}{25000000000} \cdot {x}^{2}}, y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(x + -2\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. unpow2 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 27.0

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

   7. Simplified 27.0%

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

      1. flip-+ N/A

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

      2. metadata-eval N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \frac{x \cdot x - \color{blue}{4}}{x - -2} \]

      3. metadata-eval N/A

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

      4. div-inv N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \color{blue}{\left(\left(x \cdot x - 2 \cdot 2\right) \cdot \frac{1}{x - -2}\right)} \]

      5. sub-neg N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\left(x \cdot x - 2 \cdot 2\right) \cdot \frac{1}{\color{blue}{x + \left(\mathsf{neg}\left(-2\right)\right)}}\right) \]

      6. metadata-eval N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\left(x \cdot x - 2 \cdot 2\right) \cdot \frac{1}{x + \color{blue}{2}}\right) \]

      7. lift-+.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\left(x \cdot x - 2 \cdot 2\right) \cdot \frac{1}{\color{blue}{x + 2}}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \color{blue}{\left(\left(x \cdot x - 2 \cdot 2\right) \cdot \frac{1}{x + 2}\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\left(\color{blue}{x \cdot x} - 2 \cdot 2\right) \cdot \frac{1}{x + 2}\right) \]

      10. sub-neg N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\color{blue}{\left(x \cdot x + \left(\mathsf{neg}\left(2 \cdot 2\right)\right)\right)} \cdot \frac{1}{x + 2}\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\left(\color{blue}{x \cdot x} + \left(\mathsf{neg}\left(2 \cdot 2\right)\right)\right) \cdot \frac{1}{x + 2}\right) \]

      12. metadata-eval N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\left(x \cdot x + \left(\mathsf{neg}\left(\color{blue}{4}\right)\right)\right) \cdot \frac{1}{x + 2}\right) \]

      13. metadata-eval N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\left(x \cdot x + \color{blue}{-4}\right) \cdot \frac{1}{x + 2}\right) \]

      14. lift-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\color{blue}{\mathsf{fma}\left(x, x, -4\right)} \cdot \frac{1}{x + 2}\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\mathsf{fma}\left(x, x, -4\right) \cdot \frac{1}{\color{blue}{x + 2}}\right) \]

      16. metadata-eval N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\mathsf{fma}\left(x, x, -4\right) \cdot \frac{1}{x + \color{blue}{\left(\mathsf{neg}\left(-2\right)\right)}}\right) \]

      17. sub-neg N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\mathsf{fma}\left(x, x, -4\right) \cdot \frac{1}{\color{blue}{x - -2}}\right) \]

      18. lower-/.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\mathsf{fma}\left(x, x, -4\right) \cdot \color{blue}{\frac{1}{x - -2}}\right) \]

      19. sub-neg N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\mathsf{fma}\left(x, x, -4\right) \cdot \frac{1}{\color{blue}{x + \left(\mathsf{neg}\left(-2\right)\right)}}\right) \]

      20. metadata-eval N/A

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot \frac{104109730557}{25000000000}\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + \frac{216700011257}{5000000000}, \frac{263505074721}{1000000000}\right), \frac{156699607947}{500000000}\right), \frac{23533438303}{500000000}\right)} \cdot \left(\mathsf{fma}\left(x, x, -4\right) \cdot \frac{1}{x + \color{blue}{2}}\right) \]

      21. lift-+.f64 27.0

          \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot 4.16438922228\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \cdot \left(\mathsf{fma}\left(x, x, -4\right) \cdot \frac{1}{\color{blue}{x + 2}}\right) \]

   9. Applied egg-rr 27.0%

      \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot \left(x \cdot 4.16438922228\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \cdot \color{blue}{\left(\mathsf{fma}\left(x, x, -4\right) \cdot \frac{1}{x + 2}\right)} \]

   10. Taylor expanded in x around -inf

       \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{-1 \cdot \frac{y - \frac{808287438222243669041480252986729310388407301}{3125000000000000000000000000000000000000}}{x} - \frac{4428647632681196606708299159837293}{625000000000000000000000000000}}{x} - \frac{23601677089235136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \color{blue}{\left(-1 \cdot x\right) \cdot \left(-1 \cdot \frac{-1 \cdot \frac{-1 \cdot \frac{y - \frac{808287438222243669041480252986729310388407301}{3125000000000000000000000000000000000000}}{x} - \frac{4428647632681196606708299159837293}{625000000000000000000000000000}}{x} - \frac{23601677089235136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right)} \]

       2. *-commutative N/A

          \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{-1 \cdot \frac{y - \frac{808287438222243669041480252986729310388407301}{3125000000000000000000000000000000000000}}{x} - \frac{4428647632681196606708299159837293}{625000000000000000000000000000}}{x} - \frac{23601677089235136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right) \cdot \left(-1 \cdot x\right)} \]

       3. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{-1 \cdot \frac{y - \frac{808287438222243669041480252986729310388407301}{3125000000000000000000000000000000000000}}{x} - \frac{4428647632681196606708299159837293}{625000000000000000000000000000}}{x} - \frac{23601677089235136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right) \cdot \left(-1 \cdot x\right)} \]

   12. Simplified 93.1%

       \[\leadsto \color{blue}{\left(-4.16438922228 - \frac{-188.81341671388108 - \frac{-7085.836212289914 - \frac{y + -258651.98023111798}{x}}{x}}{x}\right) \cdot \left(-x\right)} \]

   if -36 < x < 230

   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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 96.7%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -36:\\ \;\;\;\;x \cdot \left(\frac{-188.81341671388108 + \frac{\frac{y + -258651.98023111798}{x} - -7085.836212289914}{x}}{x} - -4.16438922228\right)\\ \mathbf{elif}\;x \leq 230:\\ \;\;\;\;\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, 313.399215894, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{-188.81341671388108 + \frac{\frac{y + -258651.98023111798}{x} - -7085.836212289914}{x}}{x} - -4.16438922228\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 92.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -36:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 680:\\ \;\;\;\;\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, 313.399215894, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -36.0)
   (* x 4.16438922228)
   (if (<= x 680.0)
     (*
      (+ x -2.0)
      (/
       (fma
        x
        (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y)
        z)
       (fma x 313.399215894 47.066876606)))
     (*
      (+ x -2.0)
      (-
       4.16438922228
       (/ (+ 101.7851458539211 (/ -3451.550173699799 x)) x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -36.0) {
		tmp = x * 4.16438922228;
	} else if (x <= 680.0) {
		tmp = (x + -2.0) * (fma(x, fma(x, fma(x, fma(x, 4.16438922228, 78.6994924154), 137.519416416), y), z) / fma(x, 313.399215894, 47.066876606));
	} 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 <= -36.0)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 680.0)
		tmp = Float64(Float64(x + -2.0) * Float64(fma(x, fma(x, fma(x, fma(x, 4.16438922228, 78.6994924154), 137.519416416), y), z) / fma(x, 313.399215894, 47.066876606)));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 - Float64(Float64(101.7851458539211 + Float64(-3451.550173699799 / x)) / x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -36.0], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 680.0], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(x * N[(x * N[(x * N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] + 137.519416416), $MachinePrecision] + y), $MachinePrecision] + z), $MachinePrecision] / N[(x * 313.399215894 + 47.066876606), $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 < -36

   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. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 88.5

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

   5. Simplified 88.5%

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

   if -36 < x < 680

   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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 96.7%

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

   if 680 < x

   1. Initial program 22.5%

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

   4. Applied egg-rr 32.5%

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

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} + \color{blue}{\left(\mathsf{neg}\left(\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x}\right)\right)}\right) \cdot \left(x + -2\right) \]

      2. unsub-neg N/A

         \[\leadsto \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x}\right)} \cdot \left(x + -2\right) \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x}\right)} \cdot \left(x + -2\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \color{blue}{\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x}}\right) \cdot \left(x + -2\right) \]

      5. sub-neg N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\color{blue}{\frac{12723143231740136880149}{125000000000000000000} + \left(\mathsf{neg}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}\right)\right)}}{x}\right) \cdot \left(x + -2\right) \]

      6. lower-+.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\color{blue}{\frac{12723143231740136880149}{125000000000000000000} + \left(\mathsf{neg}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}\right)\right)}}{x}\right) \cdot \left(x + -2\right) \]

      7. associate-*r/ N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\frac{12723143231740136880149}{125000000000000000000} + \left(\mathsf{neg}\left(\color{blue}{\frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot 1}{x}}\right)\right)}{x}\right) \cdot \left(x + -2\right) \]

      8. metadata-eval N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\frac{12723143231740136880149}{125000000000000000000} + \left(\mathsf{neg}\left(\frac{\color{blue}{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}}{x}\right)\right)}{x}\right) \cdot \left(x + -2\right) \]

      9. distribute-neg-frac N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\frac{12723143231740136880149}{125000000000000000000} + \color{blue}{\frac{\mathsf{neg}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}\right)}{x}}}{x}\right) \cdot \left(x + -2\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\frac{12723143231740136880149}{125000000000000000000} + \color{blue}{\frac{\mathsf{neg}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}\right)}{x}}}{x}\right) \cdot \left(x + -2\right) \]

      11. metadata-eval 81.7

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

   7. Simplified 81.7%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -36:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 680:\\ \;\;\;\;\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, 313.399215894, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 88.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+35}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 0.006:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-0.0424927283095952, y, z \cdot 0.3041881842569256\right), z \cdot -0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.2e+35)
   (* x 4.16438922228)
   (if (<= x 0.006)
     (fma
      x
      (fma -0.0424927283095952 y (* z 0.3041881842569256))
      (* z -0.0424927283095952))
     (*
      (+ x -2.0)
      (-
       4.16438922228
       (/ (+ 101.7851458539211 (/ -3451.550173699799 x)) x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.2e+35) {
		tmp = x * 4.16438922228;
	} else if (x <= 0.006) {
		tmp = fma(x, fma(-0.0424927283095952, y, (z * 0.3041881842569256)), (z * -0.0424927283095952));
	} 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 <= -3.2e+35)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 0.006)
		tmp = fma(x, fma(-0.0424927283095952, y, Float64(z * 0.3041881842569256)), Float64(z * -0.0424927283095952));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 - Float64(Float64(101.7851458539211 + Float64(-3451.550173699799 / x)) / x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.2e+35], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 0.006], N[(x * N[(-0.0424927283095952 * y + N[(z * 0.3041881842569256), $MachinePrecision]), $MachinePrecision] + N[(z * -0.0424927283095952), $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 < -3.19999999999999983e35

   1. Initial program 7.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 91.8

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

   5. Simplified 91.8%

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

   if -3.19999999999999983e35 < x < 0.0060000000000000001

   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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. sub-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

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

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

      7. metadata-eval N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 93.9

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

   7. Simplified 93.9%

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

   if 0.0060000000000000001 < x

   1. Initial program 25.8%

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

   4. Applied egg-rr 35.4%

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

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} + \color{blue}{\left(\mathsf{neg}\left(\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x}\right)\right)}\right) \cdot \left(x + -2\right) \]

      2. unsub-neg N/A

         \[\leadsto \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x}\right)} \cdot \left(x + -2\right) \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x}\right)} \cdot \left(x + -2\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \color{blue}{\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x}}\right) \cdot \left(x + -2\right) \]

      5. sub-neg N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\color{blue}{\frac{12723143231740136880149}{125000000000000000000} + \left(\mathsf{neg}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}\right)\right)}}{x}\right) \cdot \left(x + -2\right) \]

      6. lower-+.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\color{blue}{\frac{12723143231740136880149}{125000000000000000000} + \left(\mathsf{neg}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}\right)\right)}}{x}\right) \cdot \left(x + -2\right) \]

      7. associate-*r/ N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\frac{12723143231740136880149}{125000000000000000000} + \left(\mathsf{neg}\left(\color{blue}{\frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot 1}{x}}\right)\right)}{x}\right) \cdot \left(x + -2\right) \]

      8. metadata-eval N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\frac{12723143231740136880149}{125000000000000000000} + \left(\mathsf{neg}\left(\frac{\color{blue}{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}}{x}\right)\right)}{x}\right) \cdot \left(x + -2\right) \]

      9. distribute-neg-frac N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\frac{12723143231740136880149}{125000000000000000000} + \color{blue}{\frac{\mathsf{neg}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}\right)}{x}}}{x}\right) \cdot \left(x + -2\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\frac{12723143231740136880149}{125000000000000000000} + \color{blue}{\frac{\mathsf{neg}\left(\frac{2157218858562374472887084159837293}{625000000000000000000000000000}\right)}{x}}}{x}\right) \cdot \left(x + -2\right) \]

      11. metadata-eval 78.5

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

   7. Simplified 78.5%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+35}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 0.006:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-0.0424927283095952, y, z \cdot 0.3041881842569256\right), z \cdot -0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 88.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+35}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 0.006:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-0.0424927283095952, y, z \cdot 0.3041881842569256\right), z \cdot -0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.2e+35)
   (* x 4.16438922228)
   (if (<= x 0.006)
     (fma
      x
      (fma -0.0424927283095952 y (* z 0.3041881842569256))
      (* z -0.0424927283095952))
     (* x (+ 4.16438922228 (/ -110.1139242984811 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.2e+35) {
		tmp = x * 4.16438922228;
	} else if (x <= 0.006) {
		tmp = fma(x, fma(-0.0424927283095952, y, (z * 0.3041881842569256)), (z * -0.0424927283095952));
	} else {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.2e+35)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 0.006)
		tmp = fma(x, fma(-0.0424927283095952, y, Float64(z * 0.3041881842569256)), Float64(z * -0.0424927283095952));
	else
		tmp = Float64(x * Float64(4.16438922228 + Float64(-110.1139242984811 / x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.2e+35], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 0.006], N[(x * N[(-0.0424927283095952 * y + N[(z * 0.3041881842569256), $MachinePrecision]), $MachinePrecision] + N[(z * -0.0424927283095952), $MachinePrecision]), $MachinePrecision], N[(x * N[(4.16438922228 + N[(-110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.19999999999999983e35

   1. Initial program 7.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 91.8

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

   5. Simplified 91.8%

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

   if -3.19999999999999983e35 < x < 0.0060000000000000001

   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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. sub-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

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

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

      7. metadata-eval N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 93.9

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

   7. Simplified 93.9%

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

   if 0.0060000000000000001 < x

   1. Initial program 25.8%

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

   3. Taylor expanded in x around inf

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. neg-sub0 N/A

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

      4. associate-+l- N/A

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

      5. neg-sub0 N/A

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

      6. lower-*.f64 N/A

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

      7. neg-sub0 N/A

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

      8. associate-+l- N/A

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

      9. neg-sub0 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. associate-*r/ N/A

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

      13. metadata-eval N/A

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

      14. distribute-neg-frac N/A

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

      15. lower-/.f64 N/A

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

      16. metadata-eval 78.4

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

   5. Simplified 78.4%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+35}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 0.006:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-0.0424927283095952, y, z \cdot 0.3041881842569256\right), z \cdot -0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 76.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+35}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 0.006:\\ \;\;\;\;\mathsf{fma}\left(-0.0424927283095952, z, x \cdot \left(z \cdot 0.3041881842569256\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \frac{-110.1139242984811}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.2e+35)
   (* x 4.16438922228)
   (if (<= x 0.006)
     (fma -0.0424927283095952 z (* x (* z 0.3041881842569256)))
     (* x (+ 4.16438922228 (/ -110.1139242984811 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.2e+35) {
		tmp = x * 4.16438922228;
	} else if (x <= 0.006) {
		tmp = fma(-0.0424927283095952, z, (x * (z * 0.3041881842569256)));
	} else {
		tmp = x * (4.16438922228 + (-110.1139242984811 / x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.2e+35)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 0.006)
		tmp = fma(-0.0424927283095952, z, Float64(x * Float64(z * 0.3041881842569256)));
	else
		tmp = Float64(x * Float64(4.16438922228 + Float64(-110.1139242984811 / x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.2e+35], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 0.006], N[(-0.0424927283095952 * z + N[(x * N[(z * 0.3041881842569256), $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 < -3.19999999999999983e35

   1. Initial program 7.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 91.8

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

   5. Simplified 91.8%

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

   if -3.19999999999999983e35 < x < 0.0060000000000000001

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. lower-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 72.3

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

   5. Simplified 72.3%

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

   6. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 70.9

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

   8. Simplified 70.9%

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

   9. Taylor expanded in x around 0

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

       1. sub-neg N/A

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

       2. lower-fma.f64 N/A

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

       3. sub-neg N/A

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

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

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

       5. metadata-eval N/A

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

       6. metadata-eval N/A

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

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

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

       8. *-commutative N/A

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

       9. lower-*.f64 N/A

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

       10. *-commutative N/A

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

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

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

       12. lower-*.f64 N/A

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

       13. metadata-eval 70.2

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

   11. Simplified 70.2%

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

   if 0.0060000000000000001 < x

   1. Initial program 25.8%

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

   3. Taylor expanded in x around inf

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. neg-sub0 N/A

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

      4. associate-+l- N/A

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

      5. neg-sub0 N/A

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

      6. lower-*.f64 N/A

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

      7. neg-sub0 N/A

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

      8. associate-+l- N/A

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

      9. neg-sub0 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. associate-*r/ N/A

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

      13. metadata-eval N/A

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

      14. distribute-neg-frac N/A

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

      15. lower-/.f64 N/A

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

      16. metadata-eval 78.4

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

   5. Simplified 78.4%

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

Alternative 14: 76.1% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+35}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 0.006:\\ \;\;\;\;\mathsf{fma}\left(-0.0424927283095952, z, x \cdot \left(z \cdot 0.3041881842569256\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, -8.32877844456\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.2e+35)
   (* x 4.16438922228)
   (if (<= x 0.006)
     (fma -0.0424927283095952 z (* x (* z 0.3041881842569256)))
     (fma x 4.16438922228 -8.32877844456))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.2e+35) {
		tmp = x * 4.16438922228;
	} else if (x <= 0.006) {
		tmp = fma(-0.0424927283095952, z, (x * (z * 0.3041881842569256)));
	} else {
		tmp = fma(x, 4.16438922228, -8.32877844456);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.2e+35)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 0.006)
		tmp = fma(-0.0424927283095952, z, Float64(x * Float64(z * 0.3041881842569256)));
	else
		tmp = fma(x, 4.16438922228, -8.32877844456);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.2e+35], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 0.006], N[(-0.0424927283095952 * z + N[(x * N[(z * 0.3041881842569256), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * 4.16438922228 + -8.32877844456), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.19999999999999983e35

   1. Initial program 7.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 91.8

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

   5. Simplified 91.8%

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

   if -3.19999999999999983e35 < x < 0.0060000000000000001

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. lower-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 72.3

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

   5. Simplified 72.3%

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

   6. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 70.9

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

   8. Simplified 70.9%

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

   9. Taylor expanded in x around 0

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

       1. sub-neg N/A

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

       2. lower-fma.f64 N/A

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

       3. sub-neg N/A

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

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

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

       5. metadata-eval N/A

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

       6. metadata-eval N/A

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

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

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

       8. *-commutative N/A

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

       9. lower-*.f64 N/A

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

       10. *-commutative N/A

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

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

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

       12. lower-*.f64 N/A

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

       13. metadata-eval 70.2

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

   11. Simplified 70.2%

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

   if 0.0060000000000000001 < x

   1. Initial program 25.8%

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

   4. Applied egg-rr 35.4%

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

   5. Taylor expanded in x around inf

      \[\leadsto \frac{\mathsf{fma}\left(x, x, -4\right) \cdot \color{blue}{\frac{104109730557}{25000000000}}}{x + 2} \]
   6. Step-by-step derivation

   7. Simplified 35.1%

      \[\leadsto \frac{\mathsf{fma}\left(x, x, -4\right) \cdot \color{blue}{4.16438922228}}{x + 2} \]

   8. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x - \frac{104109730557}{12500000000}} \]
   9. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x + \left(\mathsf{neg}\left(\frac{104109730557}{12500000000}\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{x \cdot \frac{104109730557}{25000000000}} + \left(\mathsf{neg}\left(\frac{104109730557}{12500000000}\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \mathsf{neg}\left(\frac{104109730557}{12500000000}\right)\right)} \]

      4. metadata-eval 78.3

         \[\leadsto \mathsf{fma}\left(x, 4.16438922228, \color{blue}{-8.32877844456}\right) \]

   10. Simplified 78.3%

       \[\leadsto \color{blue}{\mathsf{fma}\left(x, 4.16438922228, -8.32877844456\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 76.0% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+35}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 245:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, -8.32877844456\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.2e+35)
   (* x 4.16438922228)
   (if (<= x 245.0)
     (* (+ x -2.0) (* z 0.0212463641547976))
     (fma x 4.16438922228 -8.32877844456))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.2e+35) {
		tmp = x * 4.16438922228;
	} else if (x <= 245.0) {
		tmp = (x + -2.0) * (z * 0.0212463641547976);
	} else {
		tmp = fma(x, 4.16438922228, -8.32877844456);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.2e+35)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 245.0)
		tmp = Float64(Float64(x + -2.0) * Float64(z * 0.0212463641547976));
	else
		tmp = fma(x, 4.16438922228, -8.32877844456);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.2e+35], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 245.0], N[(N[(x + -2.0), $MachinePrecision] * N[(z * 0.0212463641547976), $MachinePrecision]), $MachinePrecision], N[(x * 4.16438922228 + -8.32877844456), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.19999999999999983e35

   1. Initial program 7.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 91.8

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

   5. Simplified 91.8%

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

   if -3.19999999999999983e35 < x < 245

   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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 68.3

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

   7. Simplified 68.3%

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

   if 245 < x

   1. Initial program 22.5%

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

   4. Applied egg-rr 32.5%

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

   5. Taylor expanded in x around inf

      \[\leadsto \frac{\mathsf{fma}\left(x, x, -4\right) \cdot \color{blue}{\frac{104109730557}{25000000000}}}{x + 2} \]
   6. Step-by-step derivation

   7. Simplified 36.4%

      \[\leadsto \frac{\mathsf{fma}\left(x, x, -4\right) \cdot \color{blue}{4.16438922228}}{x + 2} \]

   8. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x - \frac{104109730557}{12500000000}} \]
   9. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x + \left(\mathsf{neg}\left(\frac{104109730557}{12500000000}\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{x \cdot \frac{104109730557}{25000000000}} + \left(\mathsf{neg}\left(\frac{104109730557}{12500000000}\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \mathsf{neg}\left(\frac{104109730557}{12500000000}\right)\right)} \]

      4. metadata-eval 81.5

         \[\leadsto \mathsf{fma}\left(x, 4.16438922228, \color{blue}{-8.32877844456}\right) \]

   10. Simplified 81.5%

       \[\leadsto \color{blue}{\mathsf{fma}\left(x, 4.16438922228, -8.32877844456\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+35}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 245:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, -8.32877844456\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 76.0% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+35}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 1.96:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, -8.32877844456\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.2e+35)
   (* x 4.16438922228)
   (if (<= x 1.96)
     (* z -0.0424927283095952)
     (fma x 4.16438922228 -8.32877844456))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.2e+35) {
		tmp = x * 4.16438922228;
	} else if (x <= 1.96) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = fma(x, 4.16438922228, -8.32877844456);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.2e+35)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 1.96)
		tmp = Float64(z * -0.0424927283095952);
	else
		tmp = fma(x, 4.16438922228, -8.32877844456);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.2e+35], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 1.96], N[(z * -0.0424927283095952), $MachinePrecision], N[(x * 4.16438922228 + -8.32877844456), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.19999999999999983e35

   1. Initial program 7.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 91.8

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

   5. Simplified 91.8%

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

   if -3.19999999999999983e35 < x < 1.96

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 68.7

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

   5. Simplified 68.7%

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

   if 1.96 < x

   1. Initial program 23.7%

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

   4. Applied egg-rr 33.5%

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

   5. Taylor expanded in x around inf

      \[\leadsto \frac{\mathsf{fma}\left(x, x, -4\right) \cdot \color{blue}{\frac{104109730557}{25000000000}}}{x + 2} \]
   6. Step-by-step derivation

   7. Simplified 35.9%

      \[\leadsto \frac{\mathsf{fma}\left(x, x, -4\right) \cdot \color{blue}{4.16438922228}}{x + 2} \]

   8. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x - \frac{104109730557}{12500000000}} \]
   9. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x + \left(\mathsf{neg}\left(\frac{104109730557}{12500000000}\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{x \cdot \frac{104109730557}{25000000000}} + \left(\mathsf{neg}\left(\frac{104109730557}{12500000000}\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \mathsf{neg}\left(\frac{104109730557}{12500000000}\right)\right)} \]

      4. metadata-eval 80.4

         \[\leadsto \mathsf{fma}\left(x, 4.16438922228, \color{blue}{-8.32877844456}\right) \]

   10. Simplified 80.4%

       \[\leadsto \color{blue}{\mathsf{fma}\left(x, 4.16438922228, -8.32877844456\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 17: 76.0% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+35}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.2e+35)
   (* x 4.16438922228)
   (if (<= x 2.0) (* z -0.0424927283095952) (* x 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.2e+35) {
		tmp = x * 4.16438922228;
	} else if (x <= 2.0) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-3.2d+35)) then
        tmp = x * 4.16438922228d0
    else if (x <= 2.0d0) then
        tmp = z * (-0.0424927283095952d0)
    else
        tmp = x * 4.16438922228d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.2e+35) {
		tmp = x * 4.16438922228;
	} else if (x <= 2.0) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.2e+35:
		tmp = x * 4.16438922228
	elif x <= 2.0:
		tmp = z * -0.0424927283095952
	else:
		tmp = x * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.2e+35)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 2.0)
		tmp = Float64(z * -0.0424927283095952);
	else
		tmp = Float64(x * 4.16438922228);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.2e+35)
		tmp = x * 4.16438922228;
	elseif (x <= 2.0)
		tmp = z * -0.0424927283095952;
	else
		tmp = x * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.2e+35], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 2.0], N[(z * -0.0424927283095952), $MachinePrecision], N[(x * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.19999999999999983e35 or 2 < x

   1. Initial program 16.8%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 85.4

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

   5. Simplified 85.4%

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

   if -3.19999999999999983e35 < x < 2

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 68.7

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

   5. Simplified 68.7%

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

Alternative 18: 44.7% accurate, 13.2× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * 4.16438922228d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 60.5%

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

3. Taylor expanded in x around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 42.2

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

5. Simplified 42.2%

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

Alternative 19: 3.4% accurate, 79.0× speedup

Math

\[\begin{array}{l} \\ -8.32877844456 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 -8.32877844456)

C

double code(double x, double y, double z) {
	return -8.32877844456;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = -8.32877844456d0
end function

Java

public static double code(double x, double y, double z) {
	return -8.32877844456;
}

Python

def code(x, y, z):
	return -8.32877844456

Julia

function code(x, y, z)
	return -8.32877844456
end

MATLAB

function tmp = code(x, y, z)
	tmp = -8.32877844456;
end

Wolfram

code[x_, y_, z_] := -8.32877844456

Derivation

1. Initial program 60.5%

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

4. Applied egg-rr 65.3%

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

5. Taylor expanded in x around inf

   \[\leadsto \frac{\mathsf{fma}\left(x, x, -4\right) \cdot \color{blue}{\frac{104109730557}{25000000000}}}{x + 2} \]
6. Step-by-step derivation

7. Simplified 20.1%

   \[\leadsto \frac{\mathsf{fma}\left(x, x, -4\right) \cdot \color{blue}{4.16438922228}}{x + 2} \]

8. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{-104109730557}{12500000000}} \]
9. Step-by-step derivation

10. Simplified 3.2%

    \[\leadsto \color{blue}{-8.32877844456} \]
11. Add Preprocessing

Developer Target 1: 98.9% 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 2024212 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -332612872587000500000000000000000000000000000000000000000000000) (- (+ (/ y (* x x)) (* 104109730557/25000000000 x)) 1101139242984811/10000000000000) (if (< x 94299917145546730000000000000000000000000000000000000000) (* (/ (- x 2) 1) (/ (+ (* (+ (* (+ (* (+ (* x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z) (+ (* (+ (+ (* 263505074721/1000000000 x) (+ (* 216700011257/5000000000 (* x x)) (* x (* x x)))) 156699607947/500000000) x) 23533438303/500000000))) (- (+ (/ y (* x x)) (* 104109730557/25000000000 x)) 1101139242984811/10000000000000))))

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