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

Percentage Accurate: 58.7% → 98.3%

Time: 19.4s

Alternatives: 22

Speedup: 5.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 58.7% 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: 98.3% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right)\right)} \leq \infty:\\ \;\;\;\;\frac{x + -2}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y - 130977.50649958357}{{x}^{2}} + \left(x \cdot 4.16438922228 + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) - 110.1139242984811\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (/
       (*
        (- x 2.0)
        (+
         (*
          x
          (+
           (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
           y))
         z))
       (+
        47.066876606
        (*
         x
         (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721))))))
      INFINITY)
   (/
    (+ x -2.0)
    (/
     (fma
      (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
      x
      47.066876606)
     (fma
      (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
      x
      z)))
   (-
    (+
     (/ (- y 130977.50649958357) (pow x 2.0))
     (+ (* x 4.16438922228) (* 3655.1204654076414 (/ 1.0 x))))
    110.1139242984811)))

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)) / (47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721)))))) <= ((double) INFINITY)) {
		tmp = (x + -2.0) / (fma(fma(fma((x + 43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606) / fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z));
	} else {
		tmp = (((y - 130977.50649958357) / pow(x, 2.0)) + ((x * 4.16438922228) + (3655.1204654076414 * (1.0 / x)))) - 110.1139242984811;
	}
	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(47.066876606 + Float64(x * Float64(313.399215894 + Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)))))) <= Inf)
		tmp = Float64(Float64(x + -2.0) / Float64(fma(fma(fma(Float64(x + 43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606) / fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z)));
	else
		tmp = Float64(Float64(Float64(Float64(y - 130977.50649958357) / (x ^ 2.0)) + Float64(Float64(x * 4.16438922228) + Float64(3655.1204654076414 * Float64(1.0 / x)))) - 110.1139242984811);
	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[(47.066876606 + N[(x * N[(313.399215894 + N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(x + -2.0), $MachinePrecision] / N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision] / N[(N[(N[(N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y - 130977.50649958357), $MachinePrecision] / N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision] + N[(N[(x * 4.16438922228), $MachinePrecision] + N[(3655.1204654076414 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 110.1139242984811), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.5%

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

      1. associate-/l* 97.7%

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

      2. sub-neg 97.7%

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

      3. metadata-eval 97.7%

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

      4. fma-def 97.7%

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

      5. fma-def 97.7%

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

      6. fma-def 97.7%

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

      7. fma-def 97.7%

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

      8. fma-def 97.7%

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

      9. fma-def 97.7%

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

      10. fma-def 97.7%

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

   3. Simplified 97.7%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in x around -inf 99.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} + \left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) - 110.1139242984811} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right)\right)} \leq \infty:\\ \;\;\;\;\frac{x + -2}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y - 130977.50649958357}{{x}^{2}} + \left(x \cdot 4.16438922228 + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) - 110.1139242984811\\ \end{array} \]

Alternative 2: 98.3% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right)\right)} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right) \cdot \frac{x + -2}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y - 130977.50649958357}{{x}^{2}} + \left(x \cdot 4.16438922228 + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) - 110.1139242984811\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (/
       (*
        (- x 2.0)
        (+
         (*
          x
          (+
           (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
           y))
         z))
       (+
        47.066876606
        (*
         x
         (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721))))))
      INFINITY)
   (*
    (fma
     x
     (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y)
     z)
    (/
     (+ x -2.0)
     (fma
      x
      (fma x (fma x (+ x 43.3400022514) 263.505074721) 313.399215894)
      47.066876606)))
   (-
    (+
     (/ (- y 130977.50649958357) (pow x 2.0))
     (+ (* x 4.16438922228) (* 3655.1204654076414 (/ 1.0 x))))
    110.1139242984811)))

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)) / (47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721)))))) <= ((double) INFINITY)) {
		tmp = fma(x, fma(x, fma(x, fma(x, 4.16438922228, 78.6994924154), 137.519416416), y), z) * ((x + -2.0) / fma(x, fma(x, fma(x, (x + 43.3400022514), 263.505074721), 313.399215894), 47.066876606));
	} else {
		tmp = (((y - 130977.50649958357) / pow(x, 2.0)) + ((x * 4.16438922228) + (3655.1204654076414 * (1.0 / x)))) - 110.1139242984811;
	}
	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(47.066876606 + Float64(x * Float64(313.399215894 + Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)))))) <= Inf)
		tmp = Float64(fma(x, fma(x, fma(x, fma(x, 4.16438922228, 78.6994924154), 137.519416416), y), z) * Float64(Float64(x + -2.0) / fma(x, fma(x, fma(x, Float64(x + 43.3400022514), 263.505074721), 313.399215894), 47.066876606)));
	else
		tmp = Float64(Float64(Float64(Float64(y - 130977.50649958357) / (x ^ 2.0)) + Float64(Float64(x * 4.16438922228) + Float64(3655.1204654076414 * Float64(1.0 / x)))) - 110.1139242984811);
	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[(47.066876606 + N[(x * N[(313.399215894 + N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(x * N[(x * N[(x * N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] + 137.519416416), $MachinePrecision] + y), $MachinePrecision] + z), $MachinePrecision] * N[(N[(x + -2.0), $MachinePrecision] / N[(x * N[(x * N[(x * N[(x + 43.3400022514), $MachinePrecision] + 263.505074721), $MachinePrecision] + 313.399215894), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y - 130977.50649958357), $MachinePrecision] / N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision] + N[(N[(x * 4.16438922228), $MachinePrecision] + N[(3655.1204654076414 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 110.1139242984811), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.5%

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

   3. Simplified 97.6%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in x around -inf 99.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} + \left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) - 110.1139242984811} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right)\right)} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right) \cdot \frac{x + -2}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y - 130977.50649958357}{{x}^{2}} + \left(x \cdot 4.16438922228 + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) - 110.1139242984811\\ \end{array} \]

Alternative 3: 96.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right)\right)}\\ \mathbf{if}\;t_0 \leq 5 \cdot 10^{+296}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y - 130977.50649958357}{{x}^{2}} + \left(x \cdot 4.16438922228 + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) - 110.1139242984811\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (/
          (*
           (- x 2.0)
           (+
            (*
             x
             (+
              (*
               x
               (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
              y))
            z))
          (+
           47.066876606
           (*
            x
            (+
             313.399215894
             (* x (+ (* x (+ x 43.3400022514)) 263.505074721))))))))
   (if (<= t_0 5e+296)
     t_0
     (-
      (+
       (/ (- y 130977.50649958357) (pow x 2.0))
       (+ (* x 4.16438922228) (* 3655.1204654076414 (/ 1.0 x))))
      110.1139242984811))))

C

double code(double x, double y, double z) {
	double t_0 = ((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / (47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721)))));
	double tmp;
	if (t_0 <= 5e+296) {
		tmp = t_0;
	} else {
		tmp = (((y - 130977.50649958357) / pow(x, 2.0)) + ((x * 4.16438922228) + (3655.1204654076414 * (1.0 / x)))) - 110.1139242984811;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((x - 2.0d0) * ((x * ((x * ((x * ((x * 4.16438922228d0) + 78.6994924154d0)) + 137.519416416d0)) + y)) + z)) / (47.066876606d0 + (x * (313.399215894d0 + (x * ((x * (x + 43.3400022514d0)) + 263.505074721d0)))))
    if (t_0 <= 5d+296) then
        tmp = t_0
    else
        tmp = (((y - 130977.50649958357d0) / (x ** 2.0d0)) + ((x * 4.16438922228d0) + (3655.1204654076414d0 * (1.0d0 / x)))) - 110.1139242984811d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / (47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721)))));
	double tmp;
	if (t_0 <= 5e+296) {
		tmp = t_0;
	} else {
		tmp = (((y - 130977.50649958357) / Math.pow(x, 2.0)) + ((x * 4.16438922228) + (3655.1204654076414 * (1.0 / x)))) - 110.1139242984811;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / (47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721)))))
	tmp = 0
	if t_0 <= 5e+296:
		tmp = t_0
	else:
		tmp = (((y - 130977.50649958357) / math.pow(x, 2.0)) + ((x * 4.16438922228) + (3655.1204654076414 * (1.0 / x)))) - 110.1139242984811
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(x - 2.0) * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721))))))
	tmp = 0.0
	if (t_0 <= 5e+296)
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(Float64(y - 130977.50649958357) / (x ^ 2.0)) + Float64(Float64(x * 4.16438922228) + Float64(3655.1204654076414 * Float64(1.0 / x)))) - 110.1139242984811);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / (47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721)))));
	tmp = 0.0;
	if (t_0 <= 5e+296)
		tmp = t_0;
	else
		tmp = (((y - 130977.50649958357) / (x ^ 2.0)) + ((x * 4.16438922228) + (3655.1204654076414 * (1.0 / x)))) - 110.1139242984811;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(x * N[(N[(x * N[(N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision] + 137.519416416), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(47.066876606 + N[(x * N[(313.399215894 + N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 5e+296], t$95$0, N[(N[(N[(N[(y - 130977.50649958357), $MachinePrecision] / N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision] + N[(N[(x * 4.16438922228), $MachinePrecision] + N[(3655.1204654076414 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 110.1139242984811), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x 2) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000)) < 5.0000000000000001e296

   1. Initial program 97.2%

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

   if 5.0000000000000001e296 < (/.f64 (*.f64 (-.f64 x 2) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000))

   1. Initial program 0.1%

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

   3. Simplified 2.2%

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

   4. Taylor expanded in x around -inf 98.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} + \left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) - 110.1139242984811} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right)\right)} \leq 5 \cdot 10^{+296}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y - 130977.50649958357}{{x}^{2}} + \left(x \cdot 4.16438922228 + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) - 110.1139242984811\\ \end{array} \]

Alternative 4: 96.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right)\right)}\\ \mathbf{if}\;t_0 \leq 5 \cdot 10^{+296}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (/
          (*
           (- x 2.0)
           (+
            (*
             x
             (+
              (*
               x
               (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
              y))
            z))
          (+
           47.066876606
           (*
            x
            (+
             313.399215894
             (* x (+ (* x (+ x 43.3400022514)) 263.505074721))))))))
   (if (<= t_0 5e+296) t_0 (/ (+ x -2.0) 0.24013125253755718))))

C

double code(double x, double y, double z) {
	double t_0 = ((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / (47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721)))));
	double tmp;
	if (t_0 <= 5e+296) {
		tmp = t_0;
	} else {
		tmp = (x + -2.0) / 0.24013125253755718;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((x - 2.0d0) * ((x * ((x * ((x * ((x * 4.16438922228d0) + 78.6994924154d0)) + 137.519416416d0)) + y)) + z)) / (47.066876606d0 + (x * (313.399215894d0 + (x * ((x * (x + 43.3400022514d0)) + 263.505074721d0)))))
    if (t_0 <= 5d+296) then
        tmp = t_0
    else
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / (47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721)))));
	double tmp;
	if (t_0 <= 5e+296) {
		tmp = t_0;
	} else {
		tmp = (x + -2.0) / 0.24013125253755718;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / (47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721)))))
	tmp = 0
	if t_0 <= 5e+296:
		tmp = t_0
	else:
		tmp = (x + -2.0) / 0.24013125253755718
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(x - 2.0) * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721))))))
	tmp = 0.0
	if (t_0 <= 5e+296)
		tmp = t_0;
	else
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / (47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721)))));
	tmp = 0.0;
	if (t_0 <= 5e+296)
		tmp = t_0;
	else
		tmp = (x + -2.0) / 0.24013125253755718;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(x * N[(N[(x * N[(N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision] + 137.519416416), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(47.066876606 + N[(x * N[(313.399215894 + N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 5e+296], t$95$0, N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x 2) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000)) < 5.0000000000000001e296

   1. Initial program 97.2%

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

   if 5.0000000000000001e296 < (/.f64 (*.f64 (-.f64 x 2) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000))

   1. Initial program 0.1%

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

      1. associate-/l* 2.2%

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

      2. sub-neg 2.2%

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

      3. metadata-eval 2.2%

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

      4. fma-def 2.2%

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

      5. fma-def 2.2%

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

      6. fma-def 2.2%

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

      7. fma-def 2.2%

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

      8. fma-def 2.2%

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

      9. fma-def 2.2%

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

      10. fma-def 2.2%

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

   3. Simplified 2.2%

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

   4. Taylor expanded in x around inf 96.5%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right)\right)} \leq 5 \cdot 10^{+296}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]

Alternative 5: 88.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + -2}{0.24013125253755718}\\ t_1 := x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right)\\ t_2 := \frac{x + -2}{\frac{313.399215894 + \left(47.066876606 \cdot \frac{1}{x} + t_1\right)}{y}}\\ \mathbf{if}\;x \leq -5.2 \cdot 10^{+45}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -0.000102:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-60}:\\ \;\;\;\;z \cdot -0.0424927283095952 + x \cdot \left(0.0212463641547976 \cdot \left(z + y \cdot -2\right) - z \cdot -0.28294182010212804\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-6}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}{x \cdot \left(y + x \cdot 137.519416416\right)}}\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot \left(313.399215894 + t_1\right)}{z}}\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x -2.0) 0.24013125253755718))
        (t_1 (* x (+ (* x (+ x 43.3400022514)) 263.505074721)))
        (t_2
         (/
          (+ x -2.0)
          (/ (+ 313.399215894 (+ (* 47.066876606 (/ 1.0 x)) t_1)) y))))
   (if (<= x -5.2e+45)
     t_0
     (if (<= x -0.000102)
       t_2
       (if (<= x 2.3e-60)
         (+
          (* z -0.0424927283095952)
          (*
           x
           (-
            (* 0.0212463641547976 (+ z (* y -2.0)))
            (* z -0.28294182010212804))))
         (if (<= x 7.4e-6)
           (/
            (+ x -2.0)
            (/
             (+ 47.066876606 (* x (+ 313.399215894 (* x 263.505074721))))
             (* x (+ y (* x 137.519416416)))))
           (if (<= x 3.5e+32)
             (/ (+ x -2.0) (/ (+ 47.066876606 (* x (+ 313.399215894 t_1))) z))
             (if (<= x 5e+42) t_2 t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + -2.0) / 0.24013125253755718;
	double t_1 = x * ((x * (x + 43.3400022514)) + 263.505074721);
	double t_2 = (x + -2.0) / ((313.399215894 + ((47.066876606 * (1.0 / x)) + t_1)) / y);
	double tmp;
	if (x <= -5.2e+45) {
		tmp = t_0;
	} else if (x <= -0.000102) {
		tmp = t_2;
	} else if (x <= 2.3e-60) {
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)));
	} else if (x <= 7.4e-6) {
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + (x * 263.505074721)))) / (x * (y + (x * 137.519416416))));
	} else if (x <= 3.5e+32) {
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + t_1))) / z);
	} else if (x <= 5e+42) {
		tmp = t_2;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (x + (-2.0d0)) / 0.24013125253755718d0
    t_1 = x * ((x * (x + 43.3400022514d0)) + 263.505074721d0)
    t_2 = (x + (-2.0d0)) / ((313.399215894d0 + ((47.066876606d0 * (1.0d0 / x)) + t_1)) / y)
    if (x <= (-5.2d+45)) then
        tmp = t_0
    else if (x <= (-0.000102d0)) then
        tmp = t_2
    else if (x <= 2.3d-60) then
        tmp = (z * (-0.0424927283095952d0)) + (x * ((0.0212463641547976d0 * (z + (y * (-2.0d0)))) - (z * (-0.28294182010212804d0))))
    else if (x <= 7.4d-6) then
        tmp = (x + (-2.0d0)) / ((47.066876606d0 + (x * (313.399215894d0 + (x * 263.505074721d0)))) / (x * (y + (x * 137.519416416d0))))
    else if (x <= 3.5d+32) then
        tmp = (x + (-2.0d0)) / ((47.066876606d0 + (x * (313.399215894d0 + t_1))) / z)
    else if (x <= 5d+42) then
        tmp = t_2
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + -2.0) / 0.24013125253755718;
	double t_1 = x * ((x * (x + 43.3400022514)) + 263.505074721);
	double t_2 = (x + -2.0) / ((313.399215894 + ((47.066876606 * (1.0 / x)) + t_1)) / y);
	double tmp;
	if (x <= -5.2e+45) {
		tmp = t_0;
	} else if (x <= -0.000102) {
		tmp = t_2;
	} else if (x <= 2.3e-60) {
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)));
	} else if (x <= 7.4e-6) {
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + (x * 263.505074721)))) / (x * (y + (x * 137.519416416))));
	} else if (x <= 3.5e+32) {
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + t_1))) / z);
	} else if (x <= 5e+42) {
		tmp = t_2;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + -2.0) / 0.24013125253755718
	t_1 = x * ((x * (x + 43.3400022514)) + 263.505074721)
	t_2 = (x + -2.0) / ((313.399215894 + ((47.066876606 * (1.0 / x)) + t_1)) / y)
	tmp = 0
	if x <= -5.2e+45:
		tmp = t_0
	elif x <= -0.000102:
		tmp = t_2
	elif x <= 2.3e-60:
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)))
	elif x <= 7.4e-6:
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + (x * 263.505074721)))) / (x * (y + (x * 137.519416416))))
	elif x <= 3.5e+32:
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + t_1))) / z)
	elif x <= 5e+42:
		tmp = t_2
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + -2.0) / 0.24013125253755718)
	t_1 = Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721))
	t_2 = Float64(Float64(x + -2.0) / Float64(Float64(313.399215894 + Float64(Float64(47.066876606 * Float64(1.0 / x)) + t_1)) / y))
	tmp = 0.0
	if (x <= -5.2e+45)
		tmp = t_0;
	elseif (x <= -0.000102)
		tmp = t_2;
	elseif (x <= 2.3e-60)
		tmp = Float64(Float64(z * -0.0424927283095952) + Float64(x * Float64(Float64(0.0212463641547976 * Float64(z + Float64(y * -2.0))) - Float64(z * -0.28294182010212804))));
	elseif (x <= 7.4e-6)
		tmp = Float64(Float64(x + -2.0) / Float64(Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(x * 263.505074721)))) / Float64(x * Float64(y + Float64(x * 137.519416416)))));
	elseif (x <= 3.5e+32)
		tmp = Float64(Float64(x + -2.0) / Float64(Float64(47.066876606 + Float64(x * Float64(313.399215894 + t_1))) / z));
	elseif (x <= 5e+42)
		tmp = t_2;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + -2.0) / 0.24013125253755718;
	t_1 = x * ((x * (x + 43.3400022514)) + 263.505074721);
	t_2 = (x + -2.0) / ((313.399215894 + ((47.066876606 * (1.0 / x)) + t_1)) / y);
	tmp = 0.0;
	if (x <= -5.2e+45)
		tmp = t_0;
	elseif (x <= -0.000102)
		tmp = t_2;
	elseif (x <= 2.3e-60)
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)));
	elseif (x <= 7.4e-6)
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + (x * 263.505074721)))) / (x * (y + (x * 137.519416416))));
	elseif (x <= 3.5e+32)
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + t_1))) / z);
	elseif (x <= 5e+42)
		tmp = t_2;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + -2.0), $MachinePrecision] / N[(N[(313.399215894 + N[(N[(47.066876606 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.2e+45], t$95$0, If[LessEqual[x, -0.000102], t$95$2, If[LessEqual[x, 2.3e-60], N[(N[(z * -0.0424927283095952), $MachinePrecision] + N[(x * N[(N[(0.0212463641547976 * N[(z + N[(y * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * -0.28294182010212804), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.4e-6], N[(N[(x + -2.0), $MachinePrecision] / N[(N[(47.066876606 + N[(x * N[(313.399215894 + N[(x * 263.505074721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x * N[(y + N[(x * 137.519416416), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.5e+32], N[(N[(x + -2.0), $MachinePrecision] / N[(N[(47.066876606 + N[(x * N[(313.399215894 + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e+42], t$95$2, t$95$0]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -5.20000000000000014e45 or 5.00000000000000007e42 < x

   1. Initial program 5.1%

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

      1. associate-/l* 9.0%

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

      2. sub-neg 9.0%

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

      3. metadata-eval 9.0%

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

      4. fma-def 9.0%

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

      5. fma-def 9.0%

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

      6. fma-def 9.0%

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

      7. fma-def 9.0%

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

      8. fma-def 9.0%

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

      9. fma-def 9.0%

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

      10. fma-def 9.0%

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

   3. Simplified 9.0%

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

   4. Taylor expanded in x around inf 96.7%

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

   if -5.20000000000000014e45 < x < -1.01999999999999999e-4 or 3.5000000000000001e32 < x < 5.00000000000000007e42

   1. Initial program 86.5%

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

      1. associate-/l* 86.8%

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

      2. sub-neg 86.8%

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

      3. metadata-eval 86.8%

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

      4. fma-def 86.8%

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

      5. fma-def 86.8%

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

      6. fma-def 86.7%

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

      7. fma-def 86.7%

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

      8. fma-def 86.7%

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

      9. fma-def 86.7%

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

      10. fma-def 86.7%

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

   3. Simplified 86.7%

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

   4. Taylor expanded in y around inf 53.2%

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

   5. Taylor expanded in y around inf 80.0%

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

   if -1.01999999999999999e-4 < x < 2.3000000000000001e-60

   1. Initial program 99.7%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around 0 93.2%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z + x \cdot \left(0.0212463641547976 \cdot \left(z + -2 \cdot y\right) - -0.28294182010212804 \cdot z\right)} \]

   if 2.3000000000000001e-60 < x < 7.4000000000000003e-6

   1. Initial program 99.4%

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

      1. associate-/l* 99.1%

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

      2. sub-neg 99.1%

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

      3. metadata-eval 99.1%

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

      4. fma-def 99.1%

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

      5. fma-def 99.1%

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

      6. fma-def 99.1%

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

      7. fma-def 99.1%

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

      8. fma-def 99.1%

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

      9. fma-def 99.1%

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

      10. fma-def 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in z around 0 91.1%

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

   5. Taylor expanded in x around 0 88.0%

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

      1. *-commutative 88.0%

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

   7. Simplified 88.0%

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

   8. Taylor expanded in x around 0 88.0%

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

      1. *-commutative 88.0%

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

   10. Simplified 88.0%

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

   if 7.4000000000000003e-6 < x < 3.5000000000000001e32

   1. Initial program 99.0%

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

      1. associate-/l* 99.3%

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

      2. sub-neg 99.3%

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

      3. metadata-eval 99.3%

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

      4. fma-def 99.3%

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

      5. fma-def 99.3%

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

      6. fma-def 99.3%

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

      7. fma-def 99.3%

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

      8. fma-def 99.3%

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

      9. fma-def 99.3%

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

      10. fma-def 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in z around inf 63.0%

      \[\leadsto \frac{x + -2}{\color{blue}{\frac{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right)\right)}{z}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+45}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -0.000102:\\ \;\;\;\;\frac{x + -2}{\frac{313.399215894 + \left(47.066876606 \cdot \frac{1}{x} + x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right)\right)}{y}}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-60}:\\ \;\;\;\;z \cdot -0.0424927283095952 + x \cdot \left(0.0212463641547976 \cdot \left(z + y \cdot -2\right) - z \cdot -0.28294182010212804\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-6}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}{x \cdot \left(y + x \cdot 137.519416416\right)}}\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right)\right)}{z}}\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+42}:\\ \;\;\;\;\frac{x + -2}{\frac{313.399215894 + \left(47.066876606 \cdot \frac{1}{x} + x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right)\right)}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]

Alternative 6: 88.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + -2}{0.24013125253755718}\\ t_1 := x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right)\\ \mathbf{if}\;x \leq -5.2 \cdot 10^{+45}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-5}:\\ \;\;\;\;\frac{x + -2}{\frac{313.399215894 + \left(47.066876606 \cdot \frac{1}{x} + t_1\right)}{y}}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-60}:\\ \;\;\;\;z \cdot -0.0424927283095952 + x \cdot \left(0.0212463641547976 \cdot \left(z + y \cdot -2\right) - z \cdot -0.28294182010212804\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+39}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot \left(313.399215894 + t_1\right)}{x \cdot \left(y + x \cdot 137.519416416\right)}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x -2.0) 0.24013125253755718))
        (t_1 (* x (+ (* x (+ x 43.3400022514)) 263.505074721))))
   (if (<= x -5.2e+45)
     t_0
     (if (<= x -4.8e-5)
       (/
        (+ x -2.0)
        (/ (+ 313.399215894 (+ (* 47.066876606 (/ 1.0 x)) t_1)) y))
       (if (<= x 2.3e-60)
         (+
          (* z -0.0424927283095952)
          (*
           x
           (-
            (* 0.0212463641547976 (+ z (* y -2.0)))
            (* z -0.28294182010212804))))
         (if (<= x 6.5e+39)
           (/
            (+ x -2.0)
            (/
             (+ 47.066876606 (* x (+ 313.399215894 t_1)))
             (* x (+ y (* x 137.519416416)))))
           t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + -2.0) / 0.24013125253755718;
	double t_1 = x * ((x * (x + 43.3400022514)) + 263.505074721);
	double tmp;
	if (x <= -5.2e+45) {
		tmp = t_0;
	} else if (x <= -4.8e-5) {
		tmp = (x + -2.0) / ((313.399215894 + ((47.066876606 * (1.0 / x)) + t_1)) / y);
	} else if (x <= 2.3e-60) {
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)));
	} else if (x <= 6.5e+39) {
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + t_1))) / (x * (y + (x * 137.519416416))));
	} 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) :: t_1
    real(8) :: tmp
    t_0 = (x + (-2.0d0)) / 0.24013125253755718d0
    t_1 = x * ((x * (x + 43.3400022514d0)) + 263.505074721d0)
    if (x <= (-5.2d+45)) then
        tmp = t_0
    else if (x <= (-4.8d-5)) then
        tmp = (x + (-2.0d0)) / ((313.399215894d0 + ((47.066876606d0 * (1.0d0 / x)) + t_1)) / y)
    else if (x <= 2.3d-60) then
        tmp = (z * (-0.0424927283095952d0)) + (x * ((0.0212463641547976d0 * (z + (y * (-2.0d0)))) - (z * (-0.28294182010212804d0))))
    else if (x <= 6.5d+39) then
        tmp = (x + (-2.0d0)) / ((47.066876606d0 + (x * (313.399215894d0 + t_1))) / (x * (y + (x * 137.519416416d0))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + -2.0) / 0.24013125253755718;
	double t_1 = x * ((x * (x + 43.3400022514)) + 263.505074721);
	double tmp;
	if (x <= -5.2e+45) {
		tmp = t_0;
	} else if (x <= -4.8e-5) {
		tmp = (x + -2.0) / ((313.399215894 + ((47.066876606 * (1.0 / x)) + t_1)) / y);
	} else if (x <= 2.3e-60) {
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)));
	} else if (x <= 6.5e+39) {
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + t_1))) / (x * (y + (x * 137.519416416))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + -2.0) / 0.24013125253755718
	t_1 = x * ((x * (x + 43.3400022514)) + 263.505074721)
	tmp = 0
	if x <= -5.2e+45:
		tmp = t_0
	elif x <= -4.8e-5:
		tmp = (x + -2.0) / ((313.399215894 + ((47.066876606 * (1.0 / x)) + t_1)) / y)
	elif x <= 2.3e-60:
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)))
	elif x <= 6.5e+39:
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + t_1))) / (x * (y + (x * 137.519416416))))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + -2.0) / 0.24013125253755718)
	t_1 = Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721))
	tmp = 0.0
	if (x <= -5.2e+45)
		tmp = t_0;
	elseif (x <= -4.8e-5)
		tmp = Float64(Float64(x + -2.0) / Float64(Float64(313.399215894 + Float64(Float64(47.066876606 * Float64(1.0 / x)) + t_1)) / y));
	elseif (x <= 2.3e-60)
		tmp = Float64(Float64(z * -0.0424927283095952) + Float64(x * Float64(Float64(0.0212463641547976 * Float64(z + Float64(y * -2.0))) - Float64(z * -0.28294182010212804))));
	elseif (x <= 6.5e+39)
		tmp = Float64(Float64(x + -2.0) / Float64(Float64(47.066876606 + Float64(x * Float64(313.399215894 + t_1))) / Float64(x * Float64(y + Float64(x * 137.519416416)))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + -2.0) / 0.24013125253755718;
	t_1 = x * ((x * (x + 43.3400022514)) + 263.505074721);
	tmp = 0.0;
	if (x <= -5.2e+45)
		tmp = t_0;
	elseif (x <= -4.8e-5)
		tmp = (x + -2.0) / ((313.399215894 + ((47.066876606 * (1.0 / x)) + t_1)) / y);
	elseif (x <= 2.3e-60)
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)));
	elseif (x <= 6.5e+39)
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + t_1))) / (x * (y + (x * 137.519416416))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.2e+45], t$95$0, If[LessEqual[x, -4.8e-5], N[(N[(x + -2.0), $MachinePrecision] / N[(N[(313.399215894 + N[(N[(47.066876606 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e-60], N[(N[(z * -0.0424927283095952), $MachinePrecision] + N[(x * N[(N[(0.0212463641547976 * N[(z + N[(y * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * -0.28294182010212804), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.5e+39], N[(N[(x + -2.0), $MachinePrecision] / N[(N[(47.066876606 + N[(x * N[(313.399215894 + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x * N[(y + N[(x * 137.519416416), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.20000000000000014e45 or 6.5000000000000001e39 < x

   1. Initial program 5.1%

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

      1. associate-/l* 9.0%

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

      2. sub-neg 9.0%

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

      3. metadata-eval 9.0%

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

      4. fma-def 9.0%

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

      5. fma-def 9.0%

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

      6. fma-def 9.0%

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

      7. fma-def 9.0%

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

      8. fma-def 9.0%

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

      9. fma-def 9.0%

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

      10. fma-def 9.0%

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

   3. Simplified 9.0%

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

   4. Taylor expanded in x around inf 96.7%

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

   if -5.20000000000000014e45 < x < -4.8000000000000001e-5

   1. Initial program 80.3%

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

      1. associate-/l* 80.6%

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

      2. sub-neg 80.6%

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

      3. metadata-eval 80.6%

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

      4. fma-def 80.6%

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

      5. fma-def 80.6%

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

      6. fma-def 80.4%

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

      7. fma-def 80.4%

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

      8. fma-def 80.4%

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

      9. fma-def 80.4%

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

      10. fma-def 80.4%

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

   3. Simplified 80.4%

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

   4. Taylor expanded in y around inf 40.1%

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

   5. Taylor expanded in y around inf 70.3%

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

   if -4.8000000000000001e-5 < x < 2.3000000000000001e-60

   1. Initial program 99.7%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around 0 93.2%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z + x \cdot \left(0.0212463641547976 \cdot \left(z + -2 \cdot y\right) - -0.28294182010212804 \cdot z\right)} \]

   if 2.3000000000000001e-60 < x < 6.5000000000000001e39

   1. Initial program 99.2%

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

      1. associate-/l* 99.2%

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

      2. sub-neg 99.2%

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

      3. metadata-eval 99.2%

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

      4. fma-def 99.2%

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

      5. fma-def 99.2%

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

      6. fma-def 99.2%

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

      7. fma-def 99.2%

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

      8. fma-def 99.2%

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

      9. fma-def 99.2%

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

      10. fma-def 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in z around 0 75.2%

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

   5. Taylor expanded in x around 0 66.2%

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

      1. *-commutative 66.2%

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

   7. Simplified 66.2%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+45}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-5}:\\ \;\;\;\;\frac{x + -2}{\frac{313.399215894 + \left(47.066876606 \cdot \frac{1}{x} + x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right)\right)}{y}}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-60}:\\ \;\;\;\;z \cdot -0.0424927283095952 + x \cdot \left(0.0212463641547976 \cdot \left(z + y \cdot -2\right) - z \cdot -0.28294182010212804\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+39}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right)\right)}{x \cdot \left(y + x \cdot 137.519416416\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]

Alternative 7: 88.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right)\right)\\ t_1 := \frac{x + -2}{0.24013125253755718}\\ \mathbf{if}\;x \leq -7 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-60}:\\ \;\;\;\;z \cdot -0.0424927283095952 + x \cdot \left(0.0212463641547976 \cdot \left(z + y \cdot -2\right) - z \cdot -0.28294182010212804\right)\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-7}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}{x \cdot \left(y + x \cdot 137.519416416\right)}}\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+33}:\\ \;\;\;\;\frac{x + -2}{\frac{t_0}{z}}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+39}:\\ \;\;\;\;\frac{x \cdot \left(\left(x - 2\right) \cdot y\right)}{t_0}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          47.066876606
          (*
           x
           (+
            313.399215894
            (* x (+ (* x (+ x 43.3400022514)) 263.505074721))))))
        (t_1 (/ (+ x -2.0) 0.24013125253755718)))
   (if (<= x -7e+14)
     t_1
     (if (<= x 2.3e-60)
       (+
        (* z -0.0424927283095952)
        (*
         x
         (-
          (* 0.0212463641547976 (+ z (* y -2.0)))
          (* z -0.28294182010212804))))
       (if (<= x 7.6e-7)
         (/
          (+ x -2.0)
          (/
           (+ 47.066876606 (* x (+ 313.399215894 (* x 263.505074721))))
           (* x (+ y (* x 137.519416416)))))
         (if (<= x 1.15e+33)
           (/ (+ x -2.0) (/ t_0 z))
           (if (<= x 2.5e+39) (/ (* x (* (- x 2.0) y)) t_0) t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = 47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721))));
	double t_1 = (x + -2.0) / 0.24013125253755718;
	double tmp;
	if (x <= -7e+14) {
		tmp = t_1;
	} else if (x <= 2.3e-60) {
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)));
	} else if (x <= 7.6e-7) {
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + (x * 263.505074721)))) / (x * (y + (x * 137.519416416))));
	} else if (x <= 1.15e+33) {
		tmp = (x + -2.0) / (t_0 / z);
	} else if (x <= 2.5e+39) {
		tmp = (x * ((x - 2.0) * y)) / t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 47.066876606d0 + (x * (313.399215894d0 + (x * ((x * (x + 43.3400022514d0)) + 263.505074721d0))))
    t_1 = (x + (-2.0d0)) / 0.24013125253755718d0
    if (x <= (-7d+14)) then
        tmp = t_1
    else if (x <= 2.3d-60) then
        tmp = (z * (-0.0424927283095952d0)) + (x * ((0.0212463641547976d0 * (z + (y * (-2.0d0)))) - (z * (-0.28294182010212804d0))))
    else if (x <= 7.6d-7) then
        tmp = (x + (-2.0d0)) / ((47.066876606d0 + (x * (313.399215894d0 + (x * 263.505074721d0)))) / (x * (y + (x * 137.519416416d0))))
    else if (x <= 1.15d+33) then
        tmp = (x + (-2.0d0)) / (t_0 / z)
    else if (x <= 2.5d+39) then
        tmp = (x * ((x - 2.0d0) * y)) / t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721))));
	double t_1 = (x + -2.0) / 0.24013125253755718;
	double tmp;
	if (x <= -7e+14) {
		tmp = t_1;
	} else if (x <= 2.3e-60) {
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)));
	} else if (x <= 7.6e-7) {
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + (x * 263.505074721)))) / (x * (y + (x * 137.519416416))));
	} else if (x <= 1.15e+33) {
		tmp = (x + -2.0) / (t_0 / z);
	} else if (x <= 2.5e+39) {
		tmp = (x * ((x - 2.0) * y)) / t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721))))
	t_1 = (x + -2.0) / 0.24013125253755718
	tmp = 0
	if x <= -7e+14:
		tmp = t_1
	elif x <= 2.3e-60:
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)))
	elif x <= 7.6e-7:
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + (x * 263.505074721)))) / (x * (y + (x * 137.519416416))))
	elif x <= 1.15e+33:
		tmp = (x + -2.0) / (t_0 / z)
	elif x <= 2.5e+39:
		tmp = (x * ((x - 2.0) * y)) / t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)))))
	t_1 = Float64(Float64(x + -2.0) / 0.24013125253755718)
	tmp = 0.0
	if (x <= -7e+14)
		tmp = t_1;
	elseif (x <= 2.3e-60)
		tmp = Float64(Float64(z * -0.0424927283095952) + Float64(x * Float64(Float64(0.0212463641547976 * Float64(z + Float64(y * -2.0))) - Float64(z * -0.28294182010212804))));
	elseif (x <= 7.6e-7)
		tmp = Float64(Float64(x + -2.0) / Float64(Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(x * 263.505074721)))) / Float64(x * Float64(y + Float64(x * 137.519416416)))));
	elseif (x <= 1.15e+33)
		tmp = Float64(Float64(x + -2.0) / Float64(t_0 / z));
	elseif (x <= 2.5e+39)
		tmp = Float64(Float64(x * Float64(Float64(x - 2.0) * y)) / t_0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721))));
	t_1 = (x + -2.0) / 0.24013125253755718;
	tmp = 0.0;
	if (x <= -7e+14)
		tmp = t_1;
	elseif (x <= 2.3e-60)
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)));
	elseif (x <= 7.6e-7)
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + (x * 263.505074721)))) / (x * (y + (x * 137.519416416))));
	elseif (x <= 1.15e+33)
		tmp = (x + -2.0) / (t_0 / z);
	elseif (x <= 2.5e+39)
		tmp = (x * ((x - 2.0) * y)) / t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(47.066876606 + N[(x * N[(313.399215894 + N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]}, If[LessEqual[x, -7e+14], t$95$1, If[LessEqual[x, 2.3e-60], N[(N[(z * -0.0424927283095952), $MachinePrecision] + N[(x * N[(N[(0.0212463641547976 * N[(z + N[(y * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * -0.28294182010212804), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.6e-7], N[(N[(x + -2.0), $MachinePrecision] / N[(N[(47.066876606 + N[(x * N[(313.399215894 + N[(x * 263.505074721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x * N[(y + N[(x * 137.519416416), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e+33], N[(N[(x + -2.0), $MachinePrecision] / N[(t$95$0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e+39], N[(N[(x * N[(N[(x - 2.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -7e14 or 2.50000000000000008e39 < x

   1. Initial program 7.8%

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

      1. associate-/l* 11.5%

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

      2. sub-neg 11.5%

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

      3. metadata-eval 11.5%

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

      4. fma-def 11.5%

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

      5. fma-def 11.5%

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

      6. fma-def 11.5%

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

      7. fma-def 11.5%

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

      8. fma-def 11.5%

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

      9. fma-def 11.5%

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

      10. fma-def 11.5%

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

   3. Simplified 11.5%

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

   4. Taylor expanded in x around inf 93.9%

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

   if -7e14 < x < 2.3000000000000001e-60

   1. Initial program 99.7%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 90.0%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z + x \cdot \left(0.0212463641547976 \cdot \left(z + -2 \cdot y\right) - -0.28294182010212804 \cdot z\right)} \]

   if 2.3000000000000001e-60 < x < 7.60000000000000029e-7

   1. Initial program 99.4%

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

      1. associate-/l* 99.1%

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

      2. sub-neg 99.1%

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

      3. metadata-eval 99.1%

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

      4. fma-def 99.1%

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

      5. fma-def 99.1%

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

      6. fma-def 99.1%

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

      7. fma-def 99.1%

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

      8. fma-def 99.1%

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

      9. fma-def 99.1%

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

      10. fma-def 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in z around 0 91.1%

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

   5. Taylor expanded in x around 0 88.0%

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

      1. *-commutative 88.0%

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

   7. Simplified 88.0%

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

   8. Taylor expanded in x around 0 88.0%

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

      1. *-commutative 88.0%

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

   10. Simplified 88.0%

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

   if 7.60000000000000029e-7 < x < 1.15000000000000005e33

   1. Initial program 99.0%

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

      1. associate-/l* 99.3%

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

      2. sub-neg 99.3%

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

      3. metadata-eval 99.3%

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

      4. fma-def 99.3%

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

      5. fma-def 99.3%

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

      6. fma-def 99.3%

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

      7. fma-def 99.3%

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

      8. fma-def 99.3%

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

      9. fma-def 99.3%

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

      10. fma-def 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in z around inf 63.0%

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

   if 1.15000000000000005e33 < x < 2.50000000000000008e39

   1. Initial program 98.8%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in y around inf 98.8%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y \cdot \left(x - 2\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right)\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+14}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-60}:\\ \;\;\;\;z \cdot -0.0424927283095952 + x \cdot \left(0.0212463641547976 \cdot \left(z + y \cdot -2\right) - z \cdot -0.28294182010212804\right)\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-7}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}{x \cdot \left(y + x \cdot 137.519416416\right)}}\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+33}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right)\right)}{z}}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+39}:\\ \;\;\;\;\frac{x \cdot \left(\left(x - 2\right) \cdot y\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]

Alternative 8: 88.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right)\right)\\ t_1 := \frac{x + -2}{0.24013125253755718}\\ \mathbf{if}\;x \leq -7 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-60}:\\ \;\;\;\;z \cdot -0.0424927283095952 + x \cdot \left(0.0212463641547976 \cdot \left(z + y \cdot -2\right) - z \cdot -0.28294182010212804\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-6}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}{x \cdot \left(y + x \cdot 137.519416416\right)}}\\ \mathbf{elif}\;x \leq 10^{+33}:\\ \;\;\;\;\frac{x + -2}{\frac{t_0}{z}}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+39}:\\ \;\;\;\;\frac{x + -2}{\frac{t_0}{x \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          47.066876606
          (*
           x
           (+
            313.399215894
            (* x (+ (* x (+ x 43.3400022514)) 263.505074721))))))
        (t_1 (/ (+ x -2.0) 0.24013125253755718)))
   (if (<= x -7e+14)
     t_1
     (if (<= x 2.3e-60)
       (+
        (* z -0.0424927283095952)
        (*
         x
         (-
          (* 0.0212463641547976 (+ z (* y -2.0)))
          (* z -0.28294182010212804))))
       (if (<= x 3.7e-6)
         (/
          (+ x -2.0)
          (/
           (+ 47.066876606 (* x (+ 313.399215894 (* x 263.505074721))))
           (* x (+ y (* x 137.519416416)))))
         (if (<= x 1e+33)
           (/ (+ x -2.0) (/ t_0 z))
           (if (<= x 2.5e+39) (/ (+ x -2.0) (/ t_0 (* x y))) t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = 47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721))));
	double t_1 = (x + -2.0) / 0.24013125253755718;
	double tmp;
	if (x <= -7e+14) {
		tmp = t_1;
	} else if (x <= 2.3e-60) {
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)));
	} else if (x <= 3.7e-6) {
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + (x * 263.505074721)))) / (x * (y + (x * 137.519416416))));
	} else if (x <= 1e+33) {
		tmp = (x + -2.0) / (t_0 / z);
	} else if (x <= 2.5e+39) {
		tmp = (x + -2.0) / (t_0 / (x * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 47.066876606d0 + (x * (313.399215894d0 + (x * ((x * (x + 43.3400022514d0)) + 263.505074721d0))))
    t_1 = (x + (-2.0d0)) / 0.24013125253755718d0
    if (x <= (-7d+14)) then
        tmp = t_1
    else if (x <= 2.3d-60) then
        tmp = (z * (-0.0424927283095952d0)) + (x * ((0.0212463641547976d0 * (z + (y * (-2.0d0)))) - (z * (-0.28294182010212804d0))))
    else if (x <= 3.7d-6) then
        tmp = (x + (-2.0d0)) / ((47.066876606d0 + (x * (313.399215894d0 + (x * 263.505074721d0)))) / (x * (y + (x * 137.519416416d0))))
    else if (x <= 1d+33) then
        tmp = (x + (-2.0d0)) / (t_0 / z)
    else if (x <= 2.5d+39) then
        tmp = (x + (-2.0d0)) / (t_0 / (x * y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721))));
	double t_1 = (x + -2.0) / 0.24013125253755718;
	double tmp;
	if (x <= -7e+14) {
		tmp = t_1;
	} else if (x <= 2.3e-60) {
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)));
	} else if (x <= 3.7e-6) {
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + (x * 263.505074721)))) / (x * (y + (x * 137.519416416))));
	} else if (x <= 1e+33) {
		tmp = (x + -2.0) / (t_0 / z);
	} else if (x <= 2.5e+39) {
		tmp = (x + -2.0) / (t_0 / (x * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721))))
	t_1 = (x + -2.0) / 0.24013125253755718
	tmp = 0
	if x <= -7e+14:
		tmp = t_1
	elif x <= 2.3e-60:
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)))
	elif x <= 3.7e-6:
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + (x * 263.505074721)))) / (x * (y + (x * 137.519416416))))
	elif x <= 1e+33:
		tmp = (x + -2.0) / (t_0 / z)
	elif x <= 2.5e+39:
		tmp = (x + -2.0) / (t_0 / (x * y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)))))
	t_1 = Float64(Float64(x + -2.0) / 0.24013125253755718)
	tmp = 0.0
	if (x <= -7e+14)
		tmp = t_1;
	elseif (x <= 2.3e-60)
		tmp = Float64(Float64(z * -0.0424927283095952) + Float64(x * Float64(Float64(0.0212463641547976 * Float64(z + Float64(y * -2.0))) - Float64(z * -0.28294182010212804))));
	elseif (x <= 3.7e-6)
		tmp = Float64(Float64(x + -2.0) / Float64(Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(x * 263.505074721)))) / Float64(x * Float64(y + Float64(x * 137.519416416)))));
	elseif (x <= 1e+33)
		tmp = Float64(Float64(x + -2.0) / Float64(t_0 / z));
	elseif (x <= 2.5e+39)
		tmp = Float64(Float64(x + -2.0) / Float64(t_0 / Float64(x * y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721))));
	t_1 = (x + -2.0) / 0.24013125253755718;
	tmp = 0.0;
	if (x <= -7e+14)
		tmp = t_1;
	elseif (x <= 2.3e-60)
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)));
	elseif (x <= 3.7e-6)
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + (x * 263.505074721)))) / (x * (y + (x * 137.519416416))));
	elseif (x <= 1e+33)
		tmp = (x + -2.0) / (t_0 / z);
	elseif (x <= 2.5e+39)
		tmp = (x + -2.0) / (t_0 / (x * y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(47.066876606 + N[(x * N[(313.399215894 + N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]}, If[LessEqual[x, -7e+14], t$95$1, If[LessEqual[x, 2.3e-60], N[(N[(z * -0.0424927283095952), $MachinePrecision] + N[(x * N[(N[(0.0212463641547976 * N[(z + N[(y * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * -0.28294182010212804), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.7e-6], N[(N[(x + -2.0), $MachinePrecision] / N[(N[(47.066876606 + N[(x * N[(313.399215894 + N[(x * 263.505074721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x * N[(y + N[(x * 137.519416416), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1e+33], N[(N[(x + -2.0), $MachinePrecision] / N[(t$95$0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e+39], N[(N[(x + -2.0), $MachinePrecision] / N[(t$95$0 / N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -7e14 or 2.50000000000000008e39 < x

   1. Initial program 7.8%

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

      1. associate-/l* 11.5%

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

      2. sub-neg 11.5%

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

      3. metadata-eval 11.5%

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

      4. fma-def 11.5%

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

      5. fma-def 11.5%

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

      6. fma-def 11.5%

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

      7. fma-def 11.5%

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

      8. fma-def 11.5%

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

      9. fma-def 11.5%

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

      10. fma-def 11.5%

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

   3. Simplified 11.5%

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

   4. Taylor expanded in x around inf 93.9%

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

   if -7e14 < x < 2.3000000000000001e-60

   1. Initial program 99.7%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 90.0%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z + x \cdot \left(0.0212463641547976 \cdot \left(z + -2 \cdot y\right) - -0.28294182010212804 \cdot z\right)} \]

   if 2.3000000000000001e-60 < x < 3.7000000000000002e-6

   1. Initial program 99.4%

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

      1. associate-/l* 99.1%

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

      2. sub-neg 99.1%

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

      3. metadata-eval 99.1%

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

      4. fma-def 99.1%

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

      5. fma-def 99.1%

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

      6. fma-def 99.1%

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

      7. fma-def 99.1%

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

      8. fma-def 99.1%

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

      9. fma-def 99.1%

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

      10. fma-def 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in z around 0 91.1%

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

   5. Taylor expanded in x around 0 88.0%

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

      1. *-commutative 88.0%

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

   7. Simplified 88.0%

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

   8. Taylor expanded in x around 0 88.0%

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

      1. *-commutative 88.0%

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

   10. Simplified 88.0%

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

   if 3.7000000000000002e-6 < x < 9.9999999999999995e32

   1. Initial program 99.0%

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

      1. associate-/l* 99.3%

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

      2. sub-neg 99.3%

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

      3. metadata-eval 99.3%

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

      4. fma-def 99.3%

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

      5. fma-def 99.3%

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

      6. fma-def 99.3%

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

      7. fma-def 99.3%

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

      8. fma-def 99.3%

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

      9. fma-def 99.3%

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

      10. fma-def 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in z around inf 63.0%

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

   if 9.9999999999999995e32 < x < 2.50000000000000008e39

   1. Initial program 98.8%

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

      1. associate-/l* 99.2%

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

      2. sub-neg 99.2%

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

      3. metadata-eval 99.2%

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

      4. fma-def 99.2%

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

      5. fma-def 99.2%

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

      6. fma-def 99.2%

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

      7. fma-def 99.2%

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

      8. fma-def 99.2%

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

      9. fma-def 99.2%

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

      10. fma-def 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in y around inf 99.2%

      \[\leadsto \frac{x + -2}{\color{blue}{\frac{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right)\right)}{x \cdot y}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+14}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-60}:\\ \;\;\;\;z \cdot -0.0424927283095952 + x \cdot \left(0.0212463641547976 \cdot \left(z + y \cdot -2\right) - z \cdot -0.28294182010212804\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-6}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}{x \cdot \left(y + x \cdot 137.519416416\right)}}\\ \mathbf{elif}\;x \leq 10^{+33}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right)\right)}{z}}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+39}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right)\right)}{x \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]

Alternative 9: 94.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+25} \lor \neg \left(x \leq 2.5 \cdot 10^{+39}\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.2e+25) (not (<= x 2.5e+39)))
   (/ (+ x -2.0) 0.24013125253755718)
   (/
    (* (- x 2.0) (+ z (* x (+ y (* x 137.519416416)))))
    (+
     47.066876606
     (*
      x
      (+ 313.399215894 (* x (+ (* x (+ x 43.3400022514)) 263.505074721))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.2e+25) || !(x <= 2.5e+39)) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-6.2d+25)) .or. (.not. (x <= 2.5d+39))) then
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    else
        tmp = ((x - 2.0d0) * (z + (x * (y + (x * 137.519416416d0))))) / (47.066876606d0 + (x * (313.399215894d0 + (x * ((x * (x + 43.3400022514d0)) + 263.505074721d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.2e+25) || !(x <= 2.5e+39)) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721)))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.2e+25) or not (x <= 2.5e+39):
		tmp = (x + -2.0) / 0.24013125253755718
	else:
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721)))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.2e+25) || !(x <= 2.5e+39))
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	else
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(z + Float64(x * Float64(y + Float64(x * 137.519416416))))) / Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6.2e+25) || ~((x <= 2.5e+39)))
		tmp = (x + -2.0) / 0.24013125253755718;
	else
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.2e+25], N[Not[LessEqual[x, 2.5e+39]], $MachinePrecision]], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(z + N[(x * N[(y + N[(x * 137.519416416), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(47.066876606 + N[(x * N[(313.399215894 + N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.1999999999999996e25 or 2.50000000000000008e39 < x

   1. Initial program 7.8%

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

      1. associate-/l* 11.5%

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

      2. sub-neg 11.5%

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

      3. metadata-eval 11.5%

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

      4. fma-def 11.5%

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

      5. fma-def 11.5%

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

      6. fma-def 11.5%

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

      7. fma-def 11.5%

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

      8. fma-def 11.5%

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

      9. fma-def 11.5%

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

      10. fma-def 11.5%

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

   3. Simplified 11.5%

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

   4. Taylor expanded in x around inf 93.9%

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

   if -6.1999999999999996e25 < x < 2.50000000000000008e39

   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. Taylor expanded in x around 0 98.0%

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

      1. *-commutative 98.0%

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

   4. Simplified 98.0%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+25} \lor \neg \left(x \leq 2.5 \cdot 10^{+39}\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right)\right)}\\ \end{array} \]

Alternative 10: 88.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + -2}{0.24013125253755718}\\ \mathbf{if}\;x \leq -7 \cdot 10^{+14}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-60}:\\ \;\;\;\;z \cdot -0.0424927283095952 + x \cdot \left(0.0212463641547976 \cdot \left(z + y \cdot -2\right) - z \cdot -0.28294182010212804\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-8}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot 313.399215894}{x \cdot \left(y + x \cdot 137.519416416\right)}}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+39}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot z}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x -2.0) 0.24013125253755718)))
   (if (<= x -7e+14)
     t_0
     (if (<= x 2e-60)
       (+
        (* z -0.0424927283095952)
        (*
         x
         (-
          (* 0.0212463641547976 (+ z (* y -2.0)))
          (* z -0.28294182010212804))))
       (if (<= x 6e-8)
         (/
          (+ x -2.0)
          (/
           (+ 47.066876606 (* x 313.399215894))
           (* x (+ y (* x 137.519416416)))))
         (if (<= x 2.5e+39)
           (/
            (* (- x 2.0) z)
            (+
             47.066876606
             (*
              x
              (+
               313.399215894
               (* x (+ (* x (+ x 43.3400022514)) 263.505074721))))))
           t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + -2.0) / 0.24013125253755718;
	double tmp;
	if (x <= -7e+14) {
		tmp = t_0;
	} else if (x <= 2e-60) {
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)));
	} else if (x <= 6e-8) {
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / (x * (y + (x * 137.519416416))));
	} else if (x <= 2.5e+39) {
		tmp = ((x - 2.0) * z) / (47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721)))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + (-2.0d0)) / 0.24013125253755718d0
    if (x <= (-7d+14)) then
        tmp = t_0
    else if (x <= 2d-60) then
        tmp = (z * (-0.0424927283095952d0)) + (x * ((0.0212463641547976d0 * (z + (y * (-2.0d0)))) - (z * (-0.28294182010212804d0))))
    else if (x <= 6d-8) then
        tmp = (x + (-2.0d0)) / ((47.066876606d0 + (x * 313.399215894d0)) / (x * (y + (x * 137.519416416d0))))
    else if (x <= 2.5d+39) then
        tmp = ((x - 2.0d0) * z) / (47.066876606d0 + (x * (313.399215894d0 + (x * ((x * (x + 43.3400022514d0)) + 263.505074721d0)))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + -2.0) / 0.24013125253755718;
	double tmp;
	if (x <= -7e+14) {
		tmp = t_0;
	} else if (x <= 2e-60) {
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)));
	} else if (x <= 6e-8) {
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / (x * (y + (x * 137.519416416))));
	} else if (x <= 2.5e+39) {
		tmp = ((x - 2.0) * z) / (47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721)))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + -2.0) / 0.24013125253755718
	tmp = 0
	if x <= -7e+14:
		tmp = t_0
	elif x <= 2e-60:
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)))
	elif x <= 6e-8:
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / (x * (y + (x * 137.519416416))))
	elif x <= 2.5e+39:
		tmp = ((x - 2.0) * z) / (47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721)))))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + -2.0) / 0.24013125253755718)
	tmp = 0.0
	if (x <= -7e+14)
		tmp = t_0;
	elseif (x <= 2e-60)
		tmp = Float64(Float64(z * -0.0424927283095952) + Float64(x * Float64(Float64(0.0212463641547976 * Float64(z + Float64(y * -2.0))) - Float64(z * -0.28294182010212804))));
	elseif (x <= 6e-8)
		tmp = Float64(Float64(x + -2.0) / Float64(Float64(47.066876606 + Float64(x * 313.399215894)) / Float64(x * Float64(y + Float64(x * 137.519416416)))));
	elseif (x <= 2.5e+39)
		tmp = Float64(Float64(Float64(x - 2.0) * z) / Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721))))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + -2.0) / 0.24013125253755718;
	tmp = 0.0;
	if (x <= -7e+14)
		tmp = t_0;
	elseif (x <= 2e-60)
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)));
	elseif (x <= 6e-8)
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / (x * (y + (x * 137.519416416))));
	elseif (x <= 2.5e+39)
		tmp = ((x - 2.0) * z) / (47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721)))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]}, If[LessEqual[x, -7e+14], t$95$0, If[LessEqual[x, 2e-60], N[(N[(z * -0.0424927283095952), $MachinePrecision] + N[(x * N[(N[(0.0212463641547976 * N[(z + N[(y * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * -0.28294182010212804), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6e-8], N[(N[(x + -2.0), $MachinePrecision] / N[(N[(47.066876606 + N[(x * 313.399215894), $MachinePrecision]), $MachinePrecision] / N[(x * N[(y + N[(x * 137.519416416), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e+39], N[(N[(N[(x - 2.0), $MachinePrecision] * z), $MachinePrecision] / N[(47.066876606 + N[(x * N[(313.399215894 + N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7e14 or 2.50000000000000008e39 < x

   1. Initial program 7.8%

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

      1. associate-/l* 11.5%

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

      2. sub-neg 11.5%

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

      3. metadata-eval 11.5%

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

      4. fma-def 11.5%

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

      5. fma-def 11.5%

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

      6. fma-def 11.5%

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

      7. fma-def 11.5%

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

      8. fma-def 11.5%

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

      9. fma-def 11.5%

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

      10. fma-def 11.5%

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

   3. Simplified 11.5%

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

   4. Taylor expanded in x around inf 93.9%

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

   if -7e14 < x < 1.9999999999999999e-60

   1. Initial program 99.7%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 90.0%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z + x \cdot \left(0.0212463641547976 \cdot \left(z + -2 \cdot y\right) - -0.28294182010212804 \cdot z\right)} \]

   if 1.9999999999999999e-60 < x < 5.99999999999999946e-8

   1. Initial program 99.5%

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

      1. associate-/l* 99.3%

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

      2. sub-neg 99.3%

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

      3. metadata-eval 99.3%

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

      4. fma-def 99.3%

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

      5. fma-def 99.3%

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

      6. fma-def 99.3%

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

      7. fma-def 99.3%

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

      8. fma-def 99.3%

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

      9. fma-def 99.3%

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

      10. fma-def 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in z around 0 99.3%

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

   5. Taylor expanded in x around 0 95.6%

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

      1. *-commutative 95.6%

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

   7. Simplified 95.6%

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

   8. Taylor expanded in x around 0 95.6%

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

      1. *-commutative 95.6%

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

   10. Simplified 95.6%

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

   if 5.99999999999999946e-8 < x < 2.50000000000000008e39

   1. Initial program 99.0%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in z around inf 41.1%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+14}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-60}:\\ \;\;\;\;z \cdot -0.0424927283095952 + x \cdot \left(0.0212463641547976 \cdot \left(z + y \cdot -2\right) - z \cdot -0.28294182010212804\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-8}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot 313.399215894}{x \cdot \left(y + x \cdot 137.519416416\right)}}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+39}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot z}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]

Alternative 11: 88.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + -2}{0.24013125253755718}\\ \mathbf{if}\;x \leq -7 \cdot 10^{+14}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-60}:\\ \;\;\;\;z \cdot -0.0424927283095952 + x \cdot \left(0.0212463641547976 \cdot \left(z + y \cdot -2\right) - z \cdot -0.28294182010212804\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-6}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}{x \cdot \left(y + x \cdot 137.519416416\right)}}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+39}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot z}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x -2.0) 0.24013125253755718)))
   (if (<= x -7e+14)
     t_0
     (if (<= x 2.15e-60)
       (+
        (* z -0.0424927283095952)
        (*
         x
         (-
          (* 0.0212463641547976 (+ z (* y -2.0)))
          (* z -0.28294182010212804))))
       (if (<= x 7.4e-6)
         (/
          (+ x -2.0)
          (/
           (+ 47.066876606 (* x (+ 313.399215894 (* x 263.505074721))))
           (* x (+ y (* x 137.519416416)))))
         (if (<= x 2.5e+39)
           (/
            (* (- x 2.0) z)
            (+
             47.066876606
             (*
              x
              (+
               313.399215894
               (* x (+ (* x (+ x 43.3400022514)) 263.505074721))))))
           t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + -2.0) / 0.24013125253755718;
	double tmp;
	if (x <= -7e+14) {
		tmp = t_0;
	} else if (x <= 2.15e-60) {
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)));
	} else if (x <= 7.4e-6) {
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + (x * 263.505074721)))) / (x * (y + (x * 137.519416416))));
	} else if (x <= 2.5e+39) {
		tmp = ((x - 2.0) * z) / (47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721)))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + (-2.0d0)) / 0.24013125253755718d0
    if (x <= (-7d+14)) then
        tmp = t_0
    else if (x <= 2.15d-60) then
        tmp = (z * (-0.0424927283095952d0)) + (x * ((0.0212463641547976d0 * (z + (y * (-2.0d0)))) - (z * (-0.28294182010212804d0))))
    else if (x <= 7.4d-6) then
        tmp = (x + (-2.0d0)) / ((47.066876606d0 + (x * (313.399215894d0 + (x * 263.505074721d0)))) / (x * (y + (x * 137.519416416d0))))
    else if (x <= 2.5d+39) then
        tmp = ((x - 2.0d0) * z) / (47.066876606d0 + (x * (313.399215894d0 + (x * ((x * (x + 43.3400022514d0)) + 263.505074721d0)))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + -2.0) / 0.24013125253755718;
	double tmp;
	if (x <= -7e+14) {
		tmp = t_0;
	} else if (x <= 2.15e-60) {
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)));
	} else if (x <= 7.4e-6) {
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + (x * 263.505074721)))) / (x * (y + (x * 137.519416416))));
	} else if (x <= 2.5e+39) {
		tmp = ((x - 2.0) * z) / (47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721)))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + -2.0) / 0.24013125253755718
	tmp = 0
	if x <= -7e+14:
		tmp = t_0
	elif x <= 2.15e-60:
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)))
	elif x <= 7.4e-6:
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + (x * 263.505074721)))) / (x * (y + (x * 137.519416416))))
	elif x <= 2.5e+39:
		tmp = ((x - 2.0) * z) / (47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721)))))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + -2.0) / 0.24013125253755718)
	tmp = 0.0
	if (x <= -7e+14)
		tmp = t_0;
	elseif (x <= 2.15e-60)
		tmp = Float64(Float64(z * -0.0424927283095952) + Float64(x * Float64(Float64(0.0212463641547976 * Float64(z + Float64(y * -2.0))) - Float64(z * -0.28294182010212804))));
	elseif (x <= 7.4e-6)
		tmp = Float64(Float64(x + -2.0) / Float64(Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(x * 263.505074721)))) / Float64(x * Float64(y + Float64(x * 137.519416416)))));
	elseif (x <= 2.5e+39)
		tmp = Float64(Float64(Float64(x - 2.0) * z) / Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721))))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + -2.0) / 0.24013125253755718;
	tmp = 0.0;
	if (x <= -7e+14)
		tmp = t_0;
	elseif (x <= 2.15e-60)
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)));
	elseif (x <= 7.4e-6)
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + (x * 263.505074721)))) / (x * (y + (x * 137.519416416))));
	elseif (x <= 2.5e+39)
		tmp = ((x - 2.0) * z) / (47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721)))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]}, If[LessEqual[x, -7e+14], t$95$0, If[LessEqual[x, 2.15e-60], N[(N[(z * -0.0424927283095952), $MachinePrecision] + N[(x * N[(N[(0.0212463641547976 * N[(z + N[(y * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * -0.28294182010212804), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.4e-6], N[(N[(x + -2.0), $MachinePrecision] / N[(N[(47.066876606 + N[(x * N[(313.399215894 + N[(x * 263.505074721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x * N[(y + N[(x * 137.519416416), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e+39], N[(N[(N[(x - 2.0), $MachinePrecision] * z), $MachinePrecision] / N[(47.066876606 + N[(x * N[(313.399215894 + N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7e14 or 2.50000000000000008e39 < x

   1. Initial program 7.8%

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

      1. associate-/l* 11.5%

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

      2. sub-neg 11.5%

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

      3. metadata-eval 11.5%

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

      4. fma-def 11.5%

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

      5. fma-def 11.5%

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

      6. fma-def 11.5%

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

      7. fma-def 11.5%

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

      8. fma-def 11.5%

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

      9. fma-def 11.5%

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

      10. fma-def 11.5%

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

   3. Simplified 11.5%

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

   4. Taylor expanded in x around inf 93.9%

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

   if -7e14 < x < 2.15e-60

   1. Initial program 99.7%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 90.0%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z + x \cdot \left(0.0212463641547976 \cdot \left(z + -2 \cdot y\right) - -0.28294182010212804 \cdot z\right)} \]

   if 2.15e-60 < x < 7.4000000000000003e-6

   1. Initial program 99.4%

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

      1. associate-/l* 99.1%

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

      2. sub-neg 99.1%

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

      3. metadata-eval 99.1%

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

      4. fma-def 99.1%

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

      5. fma-def 99.1%

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

      6. fma-def 99.1%

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

      7. fma-def 99.1%

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

      8. fma-def 99.1%

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

      9. fma-def 99.1%

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

      10. fma-def 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in z around 0 91.1%

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

   5. Taylor expanded in x around 0 88.0%

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

      1. *-commutative 88.0%

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

   7. Simplified 88.0%

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

   8. Taylor expanded in x around 0 88.0%

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

      1. *-commutative 88.0%

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

   10. Simplified 88.0%

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

   if 7.4000000000000003e-6 < x < 2.50000000000000008e39

   1. Initial program 98.9%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in z around inf 39.7%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+14}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-60}:\\ \;\;\;\;z \cdot -0.0424927283095952 + x \cdot \left(0.0212463641547976 \cdot \left(z + y \cdot -2\right) - z \cdot -0.28294182010212804\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-6}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}{x \cdot \left(y + x \cdot 137.519416416\right)}}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+39}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot z}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]

Alternative 12: 88.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + -2}{0.24013125253755718}\\ \mathbf{if}\;x \leq -7 \cdot 10^{+14}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-60}:\\ \;\;\;\;z \cdot -0.0424927283095952 + x \cdot \left(0.0212463641547976 \cdot \left(z + y \cdot -2\right) - z \cdot -0.28294182010212804\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-6}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}{x \cdot \left(y + x \cdot 137.519416416\right)}}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+39}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right)\right)}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x -2.0) 0.24013125253755718)))
   (if (<= x -7e+14)
     t_0
     (if (<= x 2.3e-60)
       (+
        (* z -0.0424927283095952)
        (*
         x
         (-
          (* 0.0212463641547976 (+ z (* y -2.0)))
          (* z -0.28294182010212804))))
       (if (<= x 2.5e-6)
         (/
          (+ x -2.0)
          (/
           (+ 47.066876606 (* x (+ 313.399215894 (* x 263.505074721))))
           (* x (+ y (* x 137.519416416)))))
         (if (<= x 2.5e+39)
           (/
            (+ x -2.0)
            (/
             (+
              47.066876606
              (*
               x
               (+
                313.399215894
                (* x (+ (* x (+ x 43.3400022514)) 263.505074721)))))
             z))
           t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + -2.0) / 0.24013125253755718;
	double tmp;
	if (x <= -7e+14) {
		tmp = t_0;
	} else if (x <= 2.3e-60) {
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)));
	} else if (x <= 2.5e-6) {
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + (x * 263.505074721)))) / (x * (y + (x * 137.519416416))));
	} else if (x <= 2.5e+39) {
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721))))) / z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + (-2.0d0)) / 0.24013125253755718d0
    if (x <= (-7d+14)) then
        tmp = t_0
    else if (x <= 2.3d-60) then
        tmp = (z * (-0.0424927283095952d0)) + (x * ((0.0212463641547976d0 * (z + (y * (-2.0d0)))) - (z * (-0.28294182010212804d0))))
    else if (x <= 2.5d-6) then
        tmp = (x + (-2.0d0)) / ((47.066876606d0 + (x * (313.399215894d0 + (x * 263.505074721d0)))) / (x * (y + (x * 137.519416416d0))))
    else if (x <= 2.5d+39) then
        tmp = (x + (-2.0d0)) / ((47.066876606d0 + (x * (313.399215894d0 + (x * ((x * (x + 43.3400022514d0)) + 263.505074721d0))))) / z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + -2.0) / 0.24013125253755718;
	double tmp;
	if (x <= -7e+14) {
		tmp = t_0;
	} else if (x <= 2.3e-60) {
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)));
	} else if (x <= 2.5e-6) {
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + (x * 263.505074721)))) / (x * (y + (x * 137.519416416))));
	} else if (x <= 2.5e+39) {
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721))))) / z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + -2.0) / 0.24013125253755718
	tmp = 0
	if x <= -7e+14:
		tmp = t_0
	elif x <= 2.3e-60:
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)))
	elif x <= 2.5e-6:
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + (x * 263.505074721)))) / (x * (y + (x * 137.519416416))))
	elif x <= 2.5e+39:
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721))))) / z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + -2.0) / 0.24013125253755718)
	tmp = 0.0
	if (x <= -7e+14)
		tmp = t_0;
	elseif (x <= 2.3e-60)
		tmp = Float64(Float64(z * -0.0424927283095952) + Float64(x * Float64(Float64(0.0212463641547976 * Float64(z + Float64(y * -2.0))) - Float64(z * -0.28294182010212804))));
	elseif (x <= 2.5e-6)
		tmp = Float64(Float64(x + -2.0) / Float64(Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(x * 263.505074721)))) / Float64(x * Float64(y + Float64(x * 137.519416416)))));
	elseif (x <= 2.5e+39)
		tmp = Float64(Float64(x + -2.0) / Float64(Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721))))) / z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + -2.0) / 0.24013125253755718;
	tmp = 0.0;
	if (x <= -7e+14)
		tmp = t_0;
	elseif (x <= 2.3e-60)
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)));
	elseif (x <= 2.5e-6)
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + (x * 263.505074721)))) / (x * (y + (x * 137.519416416))));
	elseif (x <= 2.5e+39)
		tmp = (x + -2.0) / ((47.066876606 + (x * (313.399215894 + (x * ((x * (x + 43.3400022514)) + 263.505074721))))) / z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]}, If[LessEqual[x, -7e+14], t$95$0, If[LessEqual[x, 2.3e-60], N[(N[(z * -0.0424927283095952), $MachinePrecision] + N[(x * N[(N[(0.0212463641547976 * N[(z + N[(y * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * -0.28294182010212804), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e-6], N[(N[(x + -2.0), $MachinePrecision] / N[(N[(47.066876606 + N[(x * N[(313.399215894 + N[(x * 263.505074721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x * N[(y + N[(x * 137.519416416), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e+39], N[(N[(x + -2.0), $MachinePrecision] / N[(N[(47.066876606 + N[(x * N[(313.399215894 + N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7e14 or 2.50000000000000008e39 < x

   1. Initial program 7.8%

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

      1. associate-/l* 11.5%

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

      2. sub-neg 11.5%

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

      3. metadata-eval 11.5%

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

      4. fma-def 11.5%

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

      5. fma-def 11.5%

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

      6. fma-def 11.5%

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

      7. fma-def 11.5%

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

      8. fma-def 11.5%

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

      9. fma-def 11.5%

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

      10. fma-def 11.5%

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

   3. Simplified 11.5%

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

   4. Taylor expanded in x around inf 93.9%

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

   if -7e14 < x < 2.3000000000000001e-60

   1. Initial program 99.7%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 90.0%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z + x \cdot \left(0.0212463641547976 \cdot \left(z + -2 \cdot y\right) - -0.28294182010212804 \cdot z\right)} \]

   if 2.3000000000000001e-60 < x < 2.5000000000000002e-6

   1. Initial program 99.4%

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

      1. associate-/l* 99.1%

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

      2. sub-neg 99.1%

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

      3. metadata-eval 99.1%

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

      4. fma-def 99.1%

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

      5. fma-def 99.1%

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

      6. fma-def 99.1%

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

      7. fma-def 99.1%

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

      8. fma-def 99.1%

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

      9. fma-def 99.1%

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

      10. fma-def 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in z around 0 91.1%

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

   5. Taylor expanded in x around 0 88.0%

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

      1. *-commutative 88.0%

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

   7. Simplified 88.0%

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

   8. Taylor expanded in x around 0 88.0%

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

      1. *-commutative 88.0%

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

   10. Simplified 88.0%

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

   if 2.5000000000000002e-6 < x < 2.50000000000000008e39

   1. Initial program 98.9%

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

      1. associate-/l* 99.3%

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

      2. sub-neg 99.3%

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

      3. metadata-eval 99.3%

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

      4. fma-def 99.3%

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

      5. fma-def 99.3%

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

      6. fma-def 99.3%

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

      7. fma-def 99.3%

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

      8. fma-def 99.3%

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

      9. fma-def 99.3%

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

      10. fma-def 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in z around inf 39.9%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+14}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-60}:\\ \;\;\;\;z \cdot -0.0424927283095952 + x \cdot \left(0.0212463641547976 \cdot \left(z + y \cdot -2\right) - z \cdot -0.28294182010212804\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-6}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}{x \cdot \left(y + x \cdot 137.519416416\right)}}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+39}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right)\right)}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]

Alternative 13: 88.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + -2}{0.24013125253755718}\\ t_1 := z \cdot -0.0424927283095952 + x \cdot \left(0.0212463641547976 \cdot \left(z + y \cdot -2\right) - z \cdot -0.28294182010212804\right)\\ \mathbf{if}\;x \leq -7 \cdot 10^{+14}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-8}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot 313.399215894}{x \cdot \left(y + x \cdot 137.519416416\right)}}\\ \mathbf{elif}\;x \leq 620000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x -2.0) 0.24013125253755718))
        (t_1
         (+
          (* z -0.0424927283095952)
          (*
           x
           (-
            (* 0.0212463641547976 (+ z (* y -2.0)))
            (* z -0.28294182010212804))))))
   (if (<= x -7e+14)
     t_0
     (if (<= x 2.3e-60)
       t_1
       (if (<= x 3.8e-8)
         (/
          (+ x -2.0)
          (/
           (+ 47.066876606 (* x 313.399215894))
           (* x (+ y (* x 137.519416416)))))
         (if (<= x 620000000.0) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + -2.0) / 0.24013125253755718;
	double t_1 = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)));
	double tmp;
	if (x <= -7e+14) {
		tmp = t_0;
	} else if (x <= 2.3e-60) {
		tmp = t_1;
	} else if (x <= 3.8e-8) {
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / (x * (y + (x * 137.519416416))));
	} else if (x <= 620000000.0) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = (x + (-2.0d0)) / 0.24013125253755718d0
    t_1 = (z * (-0.0424927283095952d0)) + (x * ((0.0212463641547976d0 * (z + (y * (-2.0d0)))) - (z * (-0.28294182010212804d0))))
    if (x <= (-7d+14)) then
        tmp = t_0
    else if (x <= 2.3d-60) then
        tmp = t_1
    else if (x <= 3.8d-8) then
        tmp = (x + (-2.0d0)) / ((47.066876606d0 + (x * 313.399215894d0)) / (x * (y + (x * 137.519416416d0))))
    else if (x <= 620000000.0d0) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + -2.0) / 0.24013125253755718;
	double t_1 = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)));
	double tmp;
	if (x <= -7e+14) {
		tmp = t_0;
	} else if (x <= 2.3e-60) {
		tmp = t_1;
	} else if (x <= 3.8e-8) {
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / (x * (y + (x * 137.519416416))));
	} else if (x <= 620000000.0) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + -2.0) / 0.24013125253755718
	t_1 = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)))
	tmp = 0
	if x <= -7e+14:
		tmp = t_0
	elif x <= 2.3e-60:
		tmp = t_1
	elif x <= 3.8e-8:
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / (x * (y + (x * 137.519416416))))
	elif x <= 620000000.0:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + -2.0) / 0.24013125253755718)
	t_1 = Float64(Float64(z * -0.0424927283095952) + Float64(x * Float64(Float64(0.0212463641547976 * Float64(z + Float64(y * -2.0))) - Float64(z * -0.28294182010212804))))
	tmp = 0.0
	if (x <= -7e+14)
		tmp = t_0;
	elseif (x <= 2.3e-60)
		tmp = t_1;
	elseif (x <= 3.8e-8)
		tmp = Float64(Float64(x + -2.0) / Float64(Float64(47.066876606 + Float64(x * 313.399215894)) / Float64(x * Float64(y + Float64(x * 137.519416416)))));
	elseif (x <= 620000000.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + -2.0) / 0.24013125253755718;
	t_1 = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)));
	tmp = 0.0;
	if (x <= -7e+14)
		tmp = t_0;
	elseif (x <= 2.3e-60)
		tmp = t_1;
	elseif (x <= 3.8e-8)
		tmp = (x + -2.0) / ((47.066876606 + (x * 313.399215894)) / (x * (y + (x * 137.519416416))));
	elseif (x <= 620000000.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]}, Block[{t$95$1 = N[(N[(z * -0.0424927283095952), $MachinePrecision] + N[(x * N[(N[(0.0212463641547976 * N[(z + N[(y * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * -0.28294182010212804), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7e+14], t$95$0, If[LessEqual[x, 2.3e-60], t$95$1, If[LessEqual[x, 3.8e-8], N[(N[(x + -2.0), $MachinePrecision] / N[(N[(47.066876606 + N[(x * 313.399215894), $MachinePrecision]), $MachinePrecision] / N[(x * N[(y + N[(x * 137.519416416), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 620000000.0], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7e14 or 6.2e8 < x

   1. Initial program 16.5%

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

      1. associate-/l* 19.9%

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

      2. sub-neg 19.9%

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

      3. metadata-eval 19.9%

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

      4. fma-def 19.9%

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

      5. fma-def 19.9%

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

      6. fma-def 19.9%

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

      7. fma-def 19.9%

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

      8. fma-def 19.9%

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

      9. fma-def 19.9%

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

      10. fma-def 19.9%

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

   3. Simplified 19.9%

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

   4. Taylor expanded in x around inf 86.7%

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

   if -7e14 < x < 2.3000000000000001e-60 or 3.80000000000000028e-8 < x < 6.2e8

   1. Initial program 99.7%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 88.8%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z + x \cdot \left(0.0212463641547976 \cdot \left(z + -2 \cdot y\right) - -0.28294182010212804 \cdot z\right)} \]

   if 2.3000000000000001e-60 < x < 3.80000000000000028e-8

   1. Initial program 99.5%

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

      1. associate-/l* 99.3%

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

      2. sub-neg 99.3%

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

      3. metadata-eval 99.3%

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

      4. fma-def 99.3%

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

      5. fma-def 99.3%

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

      6. fma-def 99.3%

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

      7. fma-def 99.3%

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

      8. fma-def 99.3%

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

      9. fma-def 99.3%

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

      10. fma-def 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in z around 0 99.3%

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

   5. Taylor expanded in x around 0 95.6%

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

      1. *-commutative 95.6%

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

   7. Simplified 95.6%

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

   8. Taylor expanded in x around 0 95.6%

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

      1. *-commutative 95.6%

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

   10. Simplified 95.6%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+14}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-60}:\\ \;\;\;\;z \cdot -0.0424927283095952 + x \cdot \left(0.0212463641547976 \cdot \left(z + y \cdot -2\right) - z \cdot -0.28294182010212804\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-8}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot 313.399215894}{x \cdot \left(y + x \cdot 137.519416416\right)}}\\ \mathbf{elif}\;x \leq 620000000:\\ \;\;\;\;z \cdot -0.0424927283095952 + x \cdot \left(0.0212463641547976 \cdot \left(z + y \cdot -2\right) - z \cdot -0.28294182010212804\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]

Alternative 14: 89.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+14} \lor \neg \left(x \leq 620000000\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952 + x \cdot \left(0.0212463641547976 \cdot \left(z + y \cdot -2\right) - z \cdot -0.28294182010212804\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7e+14) (not (<= x 620000000.0)))
   (/ (+ x -2.0) 0.24013125253755718)
   (+
    (* z -0.0424927283095952)
    (*
     x
     (- (* 0.0212463641547976 (+ z (* y -2.0))) (* z -0.28294182010212804))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7e+14) || !(x <= 620000000.0)) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else {
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)));
	}
	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 <= (-7d+14)) .or. (.not. (x <= 620000000.0d0))) then
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    else
        tmp = (z * (-0.0424927283095952d0)) + (x * ((0.0212463641547976d0 * (z + (y * (-2.0d0)))) - (z * (-0.28294182010212804d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7e+14) || !(x <= 620000000.0)) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else {
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7e+14) or not (x <= 620000000.0):
		tmp = (x + -2.0) / 0.24013125253755718
	else:
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7e+14) || !(x <= 620000000.0))
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	else
		tmp = Float64(Float64(z * -0.0424927283095952) + Float64(x * Float64(Float64(0.0212463641547976 * Float64(z + Float64(y * -2.0))) - Float64(z * -0.28294182010212804))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -7e+14) || ~((x <= 620000000.0)))
		tmp = (x + -2.0) / 0.24013125253755718;
	else
		tmp = (z * -0.0424927283095952) + (x * ((0.0212463641547976 * (z + (y * -2.0))) - (z * -0.28294182010212804)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7e+14], N[Not[LessEqual[x, 620000000.0]], $MachinePrecision]], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision], N[(N[(z * -0.0424927283095952), $MachinePrecision] + N[(x * N[(N[(0.0212463641547976 * N[(z + N[(y * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * -0.28294182010212804), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7e14 or 6.2e8 < x

   1. Initial program 16.5%

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

      1. associate-/l* 19.9%

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

      2. sub-neg 19.9%

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

      3. metadata-eval 19.9%

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

      4. fma-def 19.9%

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

      5. fma-def 19.9%

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

      6. fma-def 19.9%

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

      7. fma-def 19.9%

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

      8. fma-def 19.9%

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

      9. fma-def 19.9%

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

      10. fma-def 19.9%

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

   3. Simplified 19.9%

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

   4. Taylor expanded in x around inf 86.7%

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

   if -7e14 < x < 6.2e8

   1. Initial program 99.7%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 85.9%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+14} \lor \neg \left(x \leq 620000000\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952 + x \cdot \left(0.0212463641547976 \cdot \left(z + y \cdot -2\right) - z \cdot -0.28294182010212804\right)\\ \end{array} \]

Alternative 15: 89.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+14} \lor \neg \left(x \leq 620000000\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952 + x \cdot \left(y \cdot -0.0424927283095952 - z \cdot -0.28294182010212804\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7e+14) (not (<= x 620000000.0)))
   (/ (+ x -2.0) 0.24013125253755718)
   (+
    (* z -0.0424927283095952)
    (* x (- (* y -0.0424927283095952) (* z -0.28294182010212804))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7e+14) || !(x <= 620000000.0)) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else {
		tmp = (z * -0.0424927283095952) + (x * ((y * -0.0424927283095952) - (z * -0.28294182010212804)));
	}
	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 <= (-7d+14)) .or. (.not. (x <= 620000000.0d0))) then
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    else
        tmp = (z * (-0.0424927283095952d0)) + (x * ((y * (-0.0424927283095952d0)) - (z * (-0.28294182010212804d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7e+14) || !(x <= 620000000.0)) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else {
		tmp = (z * -0.0424927283095952) + (x * ((y * -0.0424927283095952) - (z * -0.28294182010212804)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7e+14) or not (x <= 620000000.0):
		tmp = (x + -2.0) / 0.24013125253755718
	else:
		tmp = (z * -0.0424927283095952) + (x * ((y * -0.0424927283095952) - (z * -0.28294182010212804)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7e+14) || !(x <= 620000000.0))
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	else
		tmp = Float64(Float64(z * -0.0424927283095952) + Float64(x * Float64(Float64(y * -0.0424927283095952) - Float64(z * -0.28294182010212804))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -7e+14) || ~((x <= 620000000.0)))
		tmp = (x + -2.0) / 0.24013125253755718;
	else
		tmp = (z * -0.0424927283095952) + (x * ((y * -0.0424927283095952) - (z * -0.28294182010212804)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7e+14], N[Not[LessEqual[x, 620000000.0]], $MachinePrecision]], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision], N[(N[(z * -0.0424927283095952), $MachinePrecision] + N[(x * N[(N[(y * -0.0424927283095952), $MachinePrecision] - N[(z * -0.28294182010212804), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7e14 or 6.2e8 < x

   1. Initial program 16.5%

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

      1. associate-/l* 19.9%

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

      2. sub-neg 19.9%

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

      3. metadata-eval 19.9%

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

      4. fma-def 19.9%

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

      5. fma-def 19.9%

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

      6. fma-def 19.9%

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

      7. fma-def 19.9%

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

      8. fma-def 19.9%

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

      9. fma-def 19.9%

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

      10. fma-def 19.9%

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

   3. Simplified 19.9%

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

   4. Taylor expanded in x around inf 86.7%

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

   if -7e14 < x < 6.2e8

   1. Initial program 99.7%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 85.9%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z + x \cdot \left(0.0212463641547976 \cdot \left(z + -2 \cdot y\right) - -0.28294182010212804 \cdot z\right)} \]

   5. Taylor expanded in z around 0 85.3%

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

      1. *-commutative 85.3%

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

   7. Simplified 85.3%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+14} \lor \neg \left(x \leq 620000000\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952 + x \cdot \left(y \cdot -0.0424927283095952 - z \cdot -0.28294182010212804\right)\\ \end{array} \]

Alternative 16: 76.7% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \lor \neg \left(x \leq 620000000\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952 + x \cdot \left(z \cdot 0.3041881842569256\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.5) (not (<= x 620000000.0)))
   (/ (+ x -2.0) 0.24013125253755718)
   (+ (* z -0.0424927283095952) (* x (* z 0.3041881842569256)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5) || !(x <= 620000000.0)) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else {
		tmp = (z * -0.0424927283095952) + (x * (z * 0.3041881842569256));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-5.5d0)) .or. (.not. (x <= 620000000.0d0))) then
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    else
        tmp = (z * (-0.0424927283095952d0)) + (x * (z * 0.3041881842569256d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5) || !(x <= 620000000.0)) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else {
		tmp = (z * -0.0424927283095952) + (x * (z * 0.3041881842569256));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.5) or not (x <= 620000000.0):
		tmp = (x + -2.0) / 0.24013125253755718
	else:
		tmp = (z * -0.0424927283095952) + (x * (z * 0.3041881842569256))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.5) || !(x <= 620000000.0))
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	else
		tmp = Float64(Float64(z * -0.0424927283095952) + Float64(x * Float64(z * 0.3041881842569256)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.5) || ~((x <= 620000000.0)))
		tmp = (x + -2.0) / 0.24013125253755718;
	else
		tmp = (z * -0.0424927283095952) + (x * (z * 0.3041881842569256));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.5], N[Not[LessEqual[x, 620000000.0]], $MachinePrecision]], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision], N[(N[(z * -0.0424927283095952), $MachinePrecision] + N[(x * N[(z * 0.3041881842569256), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5 or 6.2e8 < x

   1. Initial program 19.3%

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

      1. associate-/l* 22.6%

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

      2. sub-neg 22.6%

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

      3. metadata-eval 22.6%

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

      4. fma-def 22.6%

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

      5. fma-def 22.6%

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

      6. fma-def 22.6%

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

      7. fma-def 22.6%

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

      8. fma-def 22.6%

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

      9. fma-def 22.6%

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

      10. fma-def 22.6%

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

   3. Simplified 22.6%

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

   4. Taylor expanded in x around inf 84.0%

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

   if -5.5 < x < 6.2e8

   1. Initial program 99.7%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 88.1%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z + x \cdot \left(0.0212463641547976 \cdot \left(z + -2 \cdot y\right) - -0.28294182010212804 \cdot z\right)} \]

   5. Taylor expanded in y around 0 66.2%

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

      1. distribute-rgt-out-- 66.2%

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

      2. metadata-eval 66.2%

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

   7. Simplified 66.2%

      \[\leadsto -0.0424927283095952 \cdot z + \color{blue}{x \cdot \left(z \cdot 0.3041881842569256\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \lor \neg \left(x \leq 620000000\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952 + x \cdot \left(z \cdot 0.3041881842569256\right)\\ \end{array} \]

Alternative 17: 89.5% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+14} \lor \neg \left(x \leq 2\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952 + -0.0424927283095952 \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7e+14) (not (<= x 2.0)))
   (/ (+ x -2.0) 0.24013125253755718)
   (+ (* z -0.0424927283095952) (* -0.0424927283095952 (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7e+14) || !(x <= 2.0)) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else {
		tmp = (z * -0.0424927283095952) + (-0.0424927283095952 * (x * y));
	}
	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 <= (-7d+14)) .or. (.not. (x <= 2.0d0))) then
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    else
        tmp = (z * (-0.0424927283095952d0)) + ((-0.0424927283095952d0) * (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7e+14) || !(x <= 2.0)) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else {
		tmp = (z * -0.0424927283095952) + (-0.0424927283095952 * (x * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7e+14) or not (x <= 2.0):
		tmp = (x + -2.0) / 0.24013125253755718
	else:
		tmp = (z * -0.0424927283095952) + (-0.0424927283095952 * (x * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7e+14) || !(x <= 2.0))
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	else
		tmp = Float64(Float64(z * -0.0424927283095952) + Float64(-0.0424927283095952 * Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -7e+14) || ~((x <= 2.0)))
		tmp = (x + -2.0) / 0.24013125253755718;
	else
		tmp = (z * -0.0424927283095952) + (-0.0424927283095952 * (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7e+14], N[Not[LessEqual[x, 2.0]], $MachinePrecision]], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision], N[(N[(z * -0.0424927283095952), $MachinePrecision] + N[(-0.0424927283095952 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7e14 or 2 < x

   1. Initial program 17.2%

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

      1. associate-/l* 20.6%

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

      2. sub-neg 20.6%

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

      3. metadata-eval 20.6%

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

      4. fma-def 20.6%

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

      5. fma-def 20.6%

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

      6. fma-def 20.6%

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

      7. fma-def 20.6%

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

      8. fma-def 20.6%

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

      9. fma-def 20.6%

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

      10. fma-def 20.6%

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

   3. Simplified 20.6%

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

   4. Taylor expanded in x around inf 86.0%

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

   if -7e14 < x < 2

   1. Initial program 99.7%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 86.5%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z + x \cdot \left(0.0212463641547976 \cdot \left(z + -2 \cdot y\right) - -0.28294182010212804 \cdot z\right)} \]

   5. Taylor expanded in z around 0 85.7%

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

      1. *-commutative 85.7%

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

   7. Simplified 85.7%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+14} \lor \neg \left(x \leq 2\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952 + -0.0424927283095952 \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 18: 76.4% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \lor \neg \left(x \leq 85000000000000\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.5) (not (<= x 85000000000000.0)))
   (/ (+ x -2.0) 0.24013125253755718)
   (* z -0.0424927283095952)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5) || !(x <= 85000000000000.0)) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else {
		tmp = z * -0.0424927283095952;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-5.5d0)) .or. (.not. (x <= 85000000000000.0d0))) then
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    else
        tmp = z * (-0.0424927283095952d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5) || !(x <= 85000000000000.0)) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else {
		tmp = z * -0.0424927283095952;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.5) or not (x <= 85000000000000.0):
		tmp = (x + -2.0) / 0.24013125253755718
	else:
		tmp = z * -0.0424927283095952
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.5) || !(x <= 85000000000000.0))
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	else
		tmp = Float64(z * -0.0424927283095952);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.5) || ~((x <= 85000000000000.0)))
		tmp = (x + -2.0) / 0.24013125253755718;
	else
		tmp = z * -0.0424927283095952;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.5], N[Not[LessEqual[x, 85000000000000.0]], $MachinePrecision]], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision], N[(z * -0.0424927283095952), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5 or 8.5e13 < x

   1. Initial program 18.6%

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

      1. associate-/l* 21.9%

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

      2. sub-neg 21.9%

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

      3. metadata-eval 21.9%

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

      4. fma-def 21.9%

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

      5. fma-def 21.9%

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

      6. fma-def 21.9%

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

      7. fma-def 21.9%

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

      8. fma-def 21.9%

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

      9. fma-def 21.9%

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

      10. fma-def 21.9%

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

   3. Simplified 21.9%

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

   4. Taylor expanded in x around inf 84.7%

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

   if -5.5 < x < 8.5e13

   1. Initial program 99.7%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 64.9%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \lor \neg \left(x \leq 85000000000000\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \end{array} \]

Alternative 19: 76.1% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \lor \neg \left(x \leq 85000000000000\right):\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.5) (not (<= x 85000000000000.0)))
   (* x 4.16438922228)
   (* z -0.0424927283095952)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5) || !(x <= 85000000000000.0)) {
		tmp = x * 4.16438922228;
	} else {
		tmp = z * -0.0424927283095952;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-5.5d0)) .or. (.not. (x <= 85000000000000.0d0))) then
        tmp = x * 4.16438922228d0
    else
        tmp = z * (-0.0424927283095952d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5) || !(x <= 85000000000000.0)) {
		tmp = x * 4.16438922228;
	} else {
		tmp = z * -0.0424927283095952;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.5) or not (x <= 85000000000000.0):
		tmp = x * 4.16438922228
	else:
		tmp = z * -0.0424927283095952
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.5) || !(x <= 85000000000000.0))
		tmp = Float64(x * 4.16438922228);
	else
		tmp = Float64(z * -0.0424927283095952);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.5) || ~((x <= 85000000000000.0)))
		tmp = x * 4.16438922228;
	else
		tmp = z * -0.0424927283095952;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.5], N[Not[LessEqual[x, 85000000000000.0]], $MachinePrecision]], N[(x * 4.16438922228), $MachinePrecision], N[(z * -0.0424927283095952), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5 or 8.5e13 < x

   1. Initial program 18.6%

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

   3. Simplified 21.9%

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

   4. Taylor expanded in x around inf 84.2%

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

      1. *-commutative 84.2%

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

   6. Simplified 84.2%

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

   if -5.5 < x < 8.5e13

   1. Initial program 99.7%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 64.9%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \lor \neg \left(x \leq 85000000000000\right):\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \end{array} \]

Alternative 20: 76.2% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;x \cdot 4.16438922228 - 110.1139242984811\\ \mathbf{elif}\;x \leq 85000000000000:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5)
   (- (* x 4.16438922228) 110.1139242984811)
   (if (<= x 85000000000000.0) (* z -0.0424927283095952) (* x 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = (x * 4.16438922228) - 110.1139242984811;
	} else if (x <= 85000000000000.0) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-5.5d0)) then
        tmp = (x * 4.16438922228d0) - 110.1139242984811d0
    else if (x <= 85000000000000.0d0) then
        tmp = z * (-0.0424927283095952d0)
    else
        tmp = x * 4.16438922228d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = (x * 4.16438922228) - 110.1139242984811;
	} else if (x <= 85000000000000.0) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.5:
		tmp = (x * 4.16438922228) - 110.1139242984811
	elif x <= 85000000000000.0:
		tmp = z * -0.0424927283095952
	else:
		tmp = x * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5)
		tmp = Float64(Float64(x * 4.16438922228) - 110.1139242984811);
	elseif (x <= 85000000000000.0)
		tmp = Float64(z * -0.0424927283095952);
	else
		tmp = Float64(x * 4.16438922228);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.5)
		tmp = (x * 4.16438922228) - 110.1139242984811;
	elseif (x <= 85000000000000.0)
		tmp = z * -0.0424927283095952;
	else
		tmp = x * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5], N[(N[(x * 4.16438922228), $MachinePrecision] - 110.1139242984811), $MachinePrecision], If[LessEqual[x, 85000000000000.0], N[(z * -0.0424927283095952), $MachinePrecision], N[(x * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5

   1. Initial program 19.9%

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

   3. Simplified 25.6%

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

   4. Taylor expanded in x around inf 82.0%

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

   if -5.5 < x < 8.5e13

   1. Initial program 99.7%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 64.9%

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

   if 8.5e13 < x

   1. Initial program 17.7%

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

   3. Simplified 19.1%

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

   4. Taylor expanded in x around inf 85.9%

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

      1. *-commutative 85.9%

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

   6. Simplified 85.9%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;x \cdot 4.16438922228 - 110.1139242984811\\ \mathbf{elif}\;x \leq 85000000000000:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

Alternative 21: 34.9% accurate, 12.3× speedup

Math

\[\begin{array}{l} \\ z \cdot -0.0424927283095952 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* z -0.0424927283095952))

C

double code(double x, double y, double z) {
	return z * -0.0424927283095952;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = z * (-0.0424927283095952d0)
end function

Java

public static double code(double x, double y, double z) {
	return z * -0.0424927283095952;
}

Python

def code(x, y, z):
	return z * -0.0424927283095952

Julia

function code(x, y, z)
	return Float64(z * -0.0424927283095952)
end

MATLAB

function tmp = code(x, y, z)
	tmp = z * -0.0424927283095952;
end

Wolfram

code[x_, y_, z_] := N[(z * -0.0424927283095952), $MachinePrecision]

Derivation

1. Initial program 62.3%

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

3. Simplified 63.7%

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

4. Taylor expanded in x around 0 36.4%

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

5. Final simplification 36.4%

   \[\leadsto z \cdot -0.0424927283095952 \]

Alternative 22: 3.3% accurate, 37.0× speedup

Math

\[\begin{array}{l} \\ 78.6994924154 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 78.6994924154)

C

double code(double x, double y, double z) {
	return 78.6994924154;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 78.6994924154d0
end function

Java

public static double code(double x, double y, double z) {
	return 78.6994924154;
}

Python

def code(x, y, z):
	return 78.6994924154

Julia

function code(x, y, z)
	return 78.6994924154
end

MATLAB

function tmp = code(x, y, z)
	tmp = 78.6994924154;
end

Wolfram

code[x_, y_, z_] := 78.6994924154

Derivation

1. Initial program 62.3%

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

   1. add-cube-cbrt 62.3%

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(\color{blue}{\left(\sqrt[3]{x \cdot 4.16438922228} \cdot \sqrt[3]{x \cdot 4.16438922228}\right) \cdot \sqrt[3]{x \cdot 4.16438922228}} + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   2. pow3 62.3%

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(\color{blue}{{\left(\sqrt[3]{x \cdot 4.16438922228}\right)}^{3}} + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

3. Applied egg-rr 62.3%

   \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(\color{blue}{{\left(\sqrt[3]{x \cdot 4.16438922228}\right)}^{3}} + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

4. Taylor expanded in x around -inf 2.9%

   \[\leadsto \color{blue}{78.6994924154} \]

5. Final simplification 2.9%

   \[\leadsto 78.6994924154 \]

Developer target: 98.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023334 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C"
  :precision binary64

  :herbie-target
  (if (< x -3.326128725870005e+62) (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811) (if (< x 9.429991714554673e+55) (* (/ (- x 2.0) 1.0) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (+ (* 263.505074721 x) (+ (* 43.3400022514 (* x x)) (* x (* x x)))) 313.399215894) x) 47.066876606))) (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811)))

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