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

Percentage Accurate: 57.5% → 98.5%

Time: 13.6s

Alternatives: 17

Speedup: 4.4×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 57.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.4%

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

   4. Applied rewrites 99.0%

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

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

   1. Initial program 0.0%

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

   4. Applied rewrites 0.0%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 99.0

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

   7. Applied rewrites 99.0%

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

Alternative 2: 98.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   4. Applied rewrites 99.0%

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

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

   1. Initial program 0.0%

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

   4. Applied rewrites 0.0%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 99.0

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

   7. Applied rewrites 99.0%

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

Alternative 3: 95.6% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (/
       (*
        (- 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))
      INFINITY)
   (*
    (/
     (fma (fma (* (* 4.16438922228 x) x) x y) x z)
     (fma
      (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
      x
      47.066876606))
    (- x 2.0))
   (* 4.16438922228 x)))

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.4%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 92.3

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

   5. Applied rewrites 92.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   7. Applied rewrites 96.8%

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

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

   1. Initial program 0.0%

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

   4. Applied rewrites 0.0%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 99.0

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

   7. Applied rewrites 99.0%

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

Alternative 4: 95.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{+37} \lor \neg \left(x \leq 7.5 \cdot 10^{+18}\right):\\ \;\;\;\;\left(x - 2\right) \cdot \left(\frac{z}{t\_0} + 4.16438922228\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(137.519416416, x, y\right), x, z\right)}{t\_0} \cdot \left(x - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (fma
          (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
          x
          47.066876606)))
   (if (or (<= x -5.5e+37) (not (<= x 7.5e+18)))
     (* (- x 2.0) (+ (/ z t_0) 4.16438922228))
     (* (/ (fma (fma 137.519416416 x y) x z) t_0) (- x 2.0)))))

C

double code(double x, double y, double z) {
	double t_0 = fma(fma(fma((43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606);
	double tmp;
	if ((x <= -5.5e+37) || !(x <= 7.5e+18)) {
		tmp = (x - 2.0) * ((z / t_0) + 4.16438922228);
	} else {
		tmp = (fma(fma(137.519416416, x, y), x, z) / t_0) * (x - 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(fma(fma(Float64(43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606)
	tmp = 0.0
	if ((x <= -5.5e+37) || !(x <= 7.5e+18))
		tmp = Float64(Float64(x - 2.0) * Float64(Float64(z / t_0) + 4.16438922228));
	else
		tmp = Float64(Float64(fma(fma(137.519416416, x, y), x, z) / t_0) * Float64(x - 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(43.3400022514 + x), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]}, If[Or[LessEqual[x, -5.5e+37], N[Not[LessEqual[x, 7.5e+18]], $MachinePrecision]], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(z / t$95$0), $MachinePrecision] + 4.16438922228), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(137.519416416 * x + y), $MachinePrecision] * x + z), $MachinePrecision] / t$95$0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.50000000000000016e37 or 7.5e18 < x

   1. Initial program 6.8%

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

   4. Applied rewrites 13.2%

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

   6. Applied rewrites 13.2%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 69.2%

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

       1. lift-fma.f64 N/A

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

       2. +-commutative N/A

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

       3. lift-/.f64 N/A

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

       4. lift-*.f64 N/A

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

       5. associate-/l* N/A

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

       6. distribute-lft-out N/A

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

       7. lower-*.f64 N/A

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

   11. Applied rewrites 97.3%

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

   if -5.50000000000000016e37 < x < 7.5e18

   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. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 99.0

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

   5. Applied rewrites 99.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   7. Applied rewrites 99.6%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+37} \lor \neg \left(x \leq 7.5 \cdot 10^{+18}\right):\\ \;\;\;\;\left(x - 2\right) \cdot \left(\frac{z}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} + 4.16438922228\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(137.519416416, x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \cdot \left(x - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{+37}:\\ \;\;\;\;\left(x - 2\right) \cdot \left(\frac{z}{t\_0} + 4.16438922228\right)\\ \mathbf{elif}\;x \leq 6.3 \cdot 10^{+41}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(137.519416416, x, y\right), x, z\right)}{t\_0} \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \left(\frac{\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} + 110.1139242984811}{x} - 4.16438922228\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (fma
          (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
          x
          47.066876606)))
   (if (<= x -5.5e+37)
     (* (- x 2.0) (+ (/ z t_0) 4.16438922228))
     (if (<= x 6.3e+41)
       (* (/ (fma (fma 137.519416416 x y) x z) t_0) (- x 2.0))
       (*
        (- x)
        (-
         (/
          (+
           (/ (- (/ (- 130977.50649958357 y) x) 3655.1204654076414) x)
           110.1139242984811)
          x)
         4.16438922228))))))

C

double code(double x, double y, double z) {
	double t_0 = fma(fma(fma((43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606);
	double tmp;
	if (x <= -5.5e+37) {
		tmp = (x - 2.0) * ((z / t_0) + 4.16438922228);
	} else if (x <= 6.3e+41) {
		tmp = (fma(fma(137.519416416, x, y), x, z) / t_0) * (x - 2.0);
	} else {
		tmp = -x * (((((((130977.50649958357 - y) / x) - 3655.1204654076414) / x) + 110.1139242984811) / x) - 4.16438922228);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(fma(fma(Float64(43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606)
	tmp = 0.0
	if (x <= -5.5e+37)
		tmp = Float64(Float64(x - 2.0) * Float64(Float64(z / t_0) + 4.16438922228));
	elseif (x <= 6.3e+41)
		tmp = Float64(Float64(fma(fma(137.519416416, x, y), x, z) / t_0) * Float64(x - 2.0));
	else
		tmp = Float64(Float64(-x) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(130977.50649958357 - y) / x) - 3655.1204654076414) / x) + 110.1139242984811) / x) - 4.16438922228));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(43.3400022514 + x), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]}, If[LessEqual[x, -5.5e+37], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(z / t$95$0), $MachinePrecision] + 4.16438922228), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.3e+41], N[(N[(N[(N[(137.519416416 * x + y), $MachinePrecision] * x + z), $MachinePrecision] / t$95$0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], N[((-x) * N[(N[(N[(N[(N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / x), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision] + 110.1139242984811), $MachinePrecision] / x), $MachinePrecision] - 4.16438922228), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.50000000000000016e37

   1. Initial program 9.8%

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

   4. Applied rewrites 13.6%

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

   6. Applied rewrites 11.8%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 70.2%

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

       1. lift-fma.f64 N/A

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

       2. +-commutative N/A

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

       3. lift-/.f64 N/A

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

       4. lift-*.f64 N/A

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

       5. associate-/l* N/A

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

       6. distribute-lft-out N/A

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

       7. lower-*.f64 N/A

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

   11. Applied rewrites 97.3%

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

   if -5.50000000000000016e37 < x < 6.2999999999999999e41

   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. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 98.4

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

   5. Applied rewrites 98.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   7. Applied rewrites 99.0%

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

   if 6.2999999999999999e41 < x

   1. Initial program 0.4%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 2.8

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

   5. Applied rewrites 2.8%

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

   6. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

   8. Applied rewrites 99.0%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+37}:\\ \;\;\;\;\left(x - 2\right) \cdot \left(\frac{z}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} + 4.16438922228\right)\\ \mathbf{elif}\;x \leq 6.3 \cdot 10^{+41}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(137.519416416, x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \left(\frac{\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} + 110.1139242984811}{x} - 4.16438922228\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)\\ t_1 := \left(x - 2\right) \cdot \left(\frac{z}{t\_0} + 4.16438922228\right)\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-12}:\\ \;\;\;\;\left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{t\_0}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-7}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\mathsf{fma}\left(137.519416416, x, y\right) \cdot x + z\right)}{47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (fma
          (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
          x
          47.066876606))
        (t_1 (* (- x 2.0) (+ (/ z t_0) 4.16438922228))))
   (if (<= x -3.4e+34)
     t_1
     (if (<= x -1.8e-12)
       (* (* (- x 2.0) y) (/ x t_0))
       (if (<= x 2.3e-7)
         (/ (* (- x 2.0) (+ (* (fma 137.519416416 x y) x) z)) 47.066876606)
         t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = fma(fma(fma((43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606);
	double t_1 = (x - 2.0) * ((z / t_0) + 4.16438922228);
	double tmp;
	if (x <= -3.4e+34) {
		tmp = t_1;
	} else if (x <= -1.8e-12) {
		tmp = ((x - 2.0) * y) * (x / t_0);
	} else if (x <= 2.3e-7) {
		tmp = ((x - 2.0) * ((fma(137.519416416, x, y) * x) + z)) / 47.066876606;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(fma(fma(Float64(43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606)
	t_1 = Float64(Float64(x - 2.0) * Float64(Float64(z / t_0) + 4.16438922228))
	tmp = 0.0
	if (x <= -3.4e+34)
		tmp = t_1;
	elseif (x <= -1.8e-12)
		tmp = Float64(Float64(Float64(x - 2.0) * y) * Float64(x / t_0));
	elseif (x <= 2.3e-7)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(fma(137.519416416, x, y) * x) + z)) / 47.066876606);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(43.3400022514 + x), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x - 2.0), $MachinePrecision] * N[(N[(z / t$95$0), $MachinePrecision] + 4.16438922228), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.4e+34], t$95$1, If[LessEqual[x, -1.8e-12], N[(N[(N[(x - 2.0), $MachinePrecision] * y), $MachinePrecision] * N[(x / t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e-7], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(137.519416416 * x + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / 47.066876606), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.3999999999999999e34 or 2.29999999999999995e-7 < x

   1. Initial program 10.2%

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

   4. Applied rewrites 17.0%

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

   6. Applied rewrites 17.1%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 68.1%

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

       1. lift-fma.f64 N/A

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

       2. +-commutative N/A

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

       3. lift-/.f64 N/A

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

       4. lift-*.f64 N/A

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

       5. associate-/l* N/A

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

       6. distribute-lft-out N/A

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

       7. lower-*.f64 N/A

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

   11. Applied rewrites 94.9%

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

   if -3.3999999999999999e34 < x < -1.8e-12

   1. Initial program 99.1%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. +-commutative N/A

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

      15. *-commutative N/A

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

      16. lower-fma.f64 N/A

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

      17. lower-+.f64 79.7

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

   5. Applied rewrites 79.7%

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

   if -1.8e-12 < x < 2.29999999999999995e-7

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 99.7

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

   5. Applied rewrites 99.7%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 99.2%

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

Alternative 7: 93.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{+34} \lor \neg \left(x \leq 7.5 \cdot 10^{+18}\right):\\ \;\;\;\;\left(x - 2\right) \cdot \left(\frac{z}{t\_0} + 4.16438922228\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, z\right) \cdot \frac{x - 2}{t\_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (fma
          (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
          x
          47.066876606)))
   (if (or (<= x -3.4e+34) (not (<= x 7.5e+18)))
     (* (- x 2.0) (+ (/ z t_0) 4.16438922228))
     (* (fma y x z) (/ (- x 2.0) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = fma(fma(fma((43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606);
	double tmp;
	if ((x <= -3.4e+34) || !(x <= 7.5e+18)) {
		tmp = (x - 2.0) * ((z / t_0) + 4.16438922228);
	} else {
		tmp = fma(y, x, z) * ((x - 2.0) / t_0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(fma(fma(Float64(43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606)
	tmp = 0.0
	if ((x <= -3.4e+34) || !(x <= 7.5e+18))
		tmp = Float64(Float64(x - 2.0) * Float64(Float64(z / t_0) + 4.16438922228));
	else
		tmp = Float64(fma(y, x, z) * Float64(Float64(x - 2.0) / t_0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(43.3400022514 + x), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]}, If[Or[LessEqual[x, -3.4e+34], N[Not[LessEqual[x, 7.5e+18]], $MachinePrecision]], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(z / t$95$0), $MachinePrecision] + 4.16438922228), $MachinePrecision]), $MachinePrecision], N[(N[(y * x + z), $MachinePrecision] * N[(N[(x - 2.0), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.3999999999999999e34 or 7.5e18 < x

   1. Initial program 7.7%

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

   4. Applied rewrites 14.0%

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

   6. Applied rewrites 14.0%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 69.5%

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

       1. lift-fma.f64 N/A

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

       2. +-commutative N/A

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

       3. lift-/.f64 N/A

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

       4. lift-*.f64 N/A

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

       5. associate-/l* N/A

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

       6. distribute-lft-out N/A

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

       7. lower-*.f64 N/A

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

   11. Applied rewrites 97.3%

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

   if -3.3999999999999999e34 < x < 7.5e18

   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. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 96.6

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

   5. Applied rewrites 96.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

   7. Applied rewrites 96.9%

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

   8. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 96.9

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

   10. Applied rewrites 96.9%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+34} \lor \neg \left(x \leq 7.5 \cdot 10^{+18}\right):\\ \;\;\;\;\left(x - 2\right) \cdot \left(\frac{z}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} + 4.16438922228\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, z\right) \cdot \frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 94.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-5} \lor \neg \left(x \leq 2.3 \cdot 10^{-7}\right):\\ \;\;\;\;\left(x - 2\right) \cdot \left(\frac{z}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} + 4.16438922228\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\mathsf{fma}\left(137.519416416, x, y\right) \cdot x + z\right)}{47.066876606}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.8e-5) (not (<= x 2.3e-7)))
   (*
    (- x 2.0)
    (+
     (/
      z
      (fma
       (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
       x
       47.066876606))
     4.16438922228))
   (/ (* (- x 2.0) (+ (* (fma 137.519416416 x y) x) z)) 47.066876606)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.8e-5) || !(x <= 2.3e-7)) {
		tmp = (x - 2.0) * ((z / fma(fma(fma((43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606)) + 4.16438922228);
	} else {
		tmp = ((x - 2.0) * ((fma(137.519416416, x, y) * x) + z)) / 47.066876606;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.8e-5) || !(x <= 2.3e-7))
		tmp = Float64(Float64(x - 2.0) * Float64(Float64(z / fma(fma(fma(Float64(43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606)) + 4.16438922228));
	else
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(fma(137.519416416, x, y) * x) + z)) / 47.066876606);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.8e-5], N[Not[LessEqual[x, 2.3e-7]], $MachinePrecision]], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(z / N[(N[(N[(N[(43.3400022514 + x), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision] + 4.16438922228), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(137.519416416 * x + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / 47.066876606), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.79999999999999996e-5 or 2.29999999999999995e-7 < x

   1. Initial program 16.2%

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

   4. Applied rewrites 22.5%

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

   6. Applied rewrites 22.6%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 65.5%

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

       1. lift-fma.f64 N/A

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

       2. +-commutative N/A

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

       3. lift-/.f64 N/A

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

       4. lift-*.f64 N/A

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

       5. associate-/l* N/A

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

       6. distribute-lft-out N/A

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

       7. lower-*.f64 N/A

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

   11. Applied rewrites 90.5%

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

   if -2.79999999999999996e-5 < x < 2.29999999999999995e-7

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 99.6

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

   5. Applied rewrites 99.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 97.4%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-5} \lor \neg \left(x \leq 2.3 \cdot 10^{-7}\right):\\ \;\;\;\;\left(x - 2\right) \cdot \left(\frac{z}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} + 4.16438922228\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\mathsf{fma}\left(137.519416416, x, y\right) \cdot x + z\right)}{47.066876606}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-2 \cdot y\right) \cdot \left(\mathsf{fma}\left(-0.14147091005106402, x, 0.0212463641547976\right) \cdot x\right)\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{+37}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-143}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-126}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot z}{47.066876606}\\ \mathbf{elif}\;x \leq 225000000000:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (* (* -2.0 y) (* (fma -0.14147091005106402 x 0.0212463641547976) x))))
   (if (<= x -4.2e+37)
     (* 4.16438922228 x)
     (if (<= x -3.4e-143)
       t_0
       (if (<= x 5e-126)
         (/ (* (- x 2.0) z) 47.066876606)
         (if (<= x 225000000000.0) t_0 (* 4.16438922228 x)))))))

C

double code(double x, double y, double z) {
	double t_0 = (-2.0 * y) * (fma(-0.14147091005106402, x, 0.0212463641547976) * x);
	double tmp;
	if (x <= -4.2e+37) {
		tmp = 4.16438922228 * x;
	} else if (x <= -3.4e-143) {
		tmp = t_0;
	} else if (x <= 5e-126) {
		tmp = ((x - 2.0) * z) / 47.066876606;
	} else if (x <= 225000000000.0) {
		tmp = t_0;
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-2.0 * y) * Float64(fma(-0.14147091005106402, x, 0.0212463641547976) * x))
	tmp = 0.0
	if (x <= -4.2e+37)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= -3.4e-143)
		tmp = t_0;
	elseif (x <= 5e-126)
		tmp = Float64(Float64(Float64(x - 2.0) * z) / 47.066876606);
	elseif (x <= 225000000000.0)
		tmp = t_0;
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(-2.0 * y), $MachinePrecision] * N[(N[(-0.14147091005106402 * x + 0.0212463641547976), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.2e+37], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, -3.4e-143], t$95$0, If[LessEqual[x, 5e-126], N[(N[(N[(x - 2.0), $MachinePrecision] * z), $MachinePrecision] / 47.066876606), $MachinePrecision], If[LessEqual[x, 225000000000.0], t$95$0, N[(4.16438922228 * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.2000000000000002e37 or 2.25e11 < x

   1. Initial program 6.8%

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

   4. Applied rewrites 13.2%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 94.1

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

   7. Applied rewrites 94.1%

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

   if -4.2000000000000002e37 < x < -3.39999999999999983e-143 or 5.00000000000000006e-126 < x < 2.25e11

   1. Initial program 98.0%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

   5. Applied rewrites 69.0%

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

   6. Taylor expanded in x around 0

      \[\leadsto \left(\left(x - 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right)\right) \cdot \left(x \cdot \color{blue}{\left(\frac{500000000}{23533438303} + \frac{-78349803973500000000}{553822718361107519809} \cdot x\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 56.9%

      \[\leadsto \left(\left(x - 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right)\right) \cdot \left(\mathsf{fma}\left(-0.14147091005106402, x, 0.0212463641547976\right) \cdot \color{blue}{x}\right) \]

   9. Taylor expanded in x around 0

      \[\leadsto \left(-2 \cdot y\right) \cdot \left(\color{blue}{\mathsf{fma}\left(\frac{-78349803973500000000}{553822718361107519809}, x, \frac{500000000}{23533438303}\right)} \cdot x\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 51.0%

       \[\leadsto \left(-2 \cdot y\right) \cdot \left(\color{blue}{\mathsf{fma}\left(-0.14147091005106402, x, 0.0212463641547976\right)} \cdot x\right) \]

   if -3.39999999999999983e-143 < x < 5.00000000000000006e-126

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 15.6

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

   5. Applied rewrites 15.6%

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

   6. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 15.6

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

   8. Applied rewrites 15.6%

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

   9. Taylor expanded in z around inf

      \[\leadsto \frac{\color{blue}{z \cdot \left(x - 2\right)}}{\mathsf{fma}\left(\frac{156699607947}{500000000}, x, \frac{23533438303}{500000000}\right)} \]
   10. Step-by-step derivation

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lower--.f64 86.2

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

   11. Applied rewrites 86.2%

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

   12. Taylor expanded in x around 0

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

   14. Applied rewrites 86.2%

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

Alternative 10: 90.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+37} \lor \neg \left(x \leq 225000000000\right):\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\mathsf{fma}\left(137.519416416, x, y\right) \cdot x + z\right)}{47.066876606}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.2e+37) (not (<= x 225000000000.0)))
   (* 4.16438922228 x)
   (/ (* (- x 2.0) (+ (* (fma 137.519416416 x y) x) z)) 47.066876606)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.2e+37) || !(x <= 225000000000.0)) {
		tmp = 4.16438922228 * x;
	} else {
		tmp = ((x - 2.0) * ((fma(137.519416416, x, y) * x) + z)) / 47.066876606;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.2e+37) || !(x <= 225000000000.0))
		tmp = Float64(4.16438922228 * x);
	else
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(fma(137.519416416, x, y) * x) + z)) / 47.066876606);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.2e+37], N[Not[LessEqual[x, 225000000000.0]], $MachinePrecision]], N[(4.16438922228 * x), $MachinePrecision], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(137.519416416 * x + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / 47.066876606), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.2000000000000002e37 or 2.25e11 < x

   1. Initial program 6.8%

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

   4. Applied rewrites 13.2%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 94.1

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

   7. Applied rewrites 94.1%

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

   if -4.2000000000000002e37 < x < 2.25e11

   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. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 99.0

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

   5. Applied rewrites 99.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 89.9%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+37} \lor \neg \left(x \leq 225000000000\right):\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\mathsf{fma}\left(137.519416416, x, y\right) \cdot x + z\right)}{47.066876606}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y \cdot x\right) \cdot -0.0424927283095952\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{+37}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-143}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-126}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot z}{47.066876606}\\ \mathbf{elif}\;x \leq 0.09:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* y x) -0.0424927283095952)))
   (if (<= x -4.2e+37)
     (* 4.16438922228 x)
     (if (<= x -3.4e-143)
       t_0
       (if (<= x 5e-126)
         (/ (* (- x 2.0) z) 47.066876606)
         (if (<= x 0.09)
           t_0
           (* (- 4.16438922228 (/ 110.1139242984811 x)) x)))))))

C

double code(double x, double y, double z) {
	double t_0 = (y * x) * -0.0424927283095952;
	double tmp;
	if (x <= -4.2e+37) {
		tmp = 4.16438922228 * x;
	} else if (x <= -3.4e-143) {
		tmp = t_0;
	} else if (x <= 5e-126) {
		tmp = ((x - 2.0) * z) / 47.066876606;
	} else if (x <= 0.09) {
		tmp = t_0;
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (y * x) * (-0.0424927283095952d0)
    if (x <= (-4.2d+37)) then
        tmp = 4.16438922228d0 * x
    else if (x <= (-3.4d-143)) then
        tmp = t_0
    else if (x <= 5d-126) then
        tmp = ((x - 2.0d0) * z) / 47.066876606d0
    else if (x <= 0.09d0) then
        tmp = t_0
    else
        tmp = (4.16438922228d0 - (110.1139242984811d0 / x)) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y * x) * -0.0424927283095952;
	double tmp;
	if (x <= -4.2e+37) {
		tmp = 4.16438922228 * x;
	} else if (x <= -3.4e-143) {
		tmp = t_0;
	} else if (x <= 5e-126) {
		tmp = ((x - 2.0) * z) / 47.066876606;
	} else if (x <= 0.09) {
		tmp = t_0;
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y * x) * -0.0424927283095952
	tmp = 0
	if x <= -4.2e+37:
		tmp = 4.16438922228 * x
	elif x <= -3.4e-143:
		tmp = t_0
	elif x <= 5e-126:
		tmp = ((x - 2.0) * z) / 47.066876606
	elif x <= 0.09:
		tmp = t_0
	else:
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * x) * -0.0424927283095952)
	tmp = 0.0
	if (x <= -4.2e+37)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= -3.4e-143)
		tmp = t_0;
	elseif (x <= 5e-126)
		tmp = Float64(Float64(Float64(x - 2.0) * z) / 47.066876606);
	elseif (x <= 0.09)
		tmp = t_0;
	else
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y * x) * -0.0424927283095952;
	tmp = 0.0;
	if (x <= -4.2e+37)
		tmp = 4.16438922228 * x;
	elseif (x <= -3.4e-143)
		tmp = t_0;
	elseif (x <= 5e-126)
		tmp = ((x - 2.0) * z) / 47.066876606;
	elseif (x <= 0.09)
		tmp = t_0;
	else
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * x), $MachinePrecision] * -0.0424927283095952), $MachinePrecision]}, If[LessEqual[x, -4.2e+37], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, -3.4e-143], t$95$0, If[LessEqual[x, 5e-126], N[(N[(N[(x - 2.0), $MachinePrecision] * z), $MachinePrecision] / 47.066876606), $MachinePrecision], If[LessEqual[x, 0.09], t$95$0, N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.2000000000000002e37

   1. Initial program 9.8%

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

   4. Applied rewrites 13.6%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 92.7

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

   7. Applied rewrites 92.7%

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

   if -4.2000000000000002e37 < x < -3.39999999999999983e-143 or 5.00000000000000006e-126 < x < 0.089999999999999997

   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. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

   5. Applied rewrites 69.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 53.2%

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

   if -3.39999999999999983e-143 < x < 5.00000000000000006e-126

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 15.6

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

   5. Applied rewrites 15.6%

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

   6. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 15.6

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

   8. Applied rewrites 15.6%

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

   9. Taylor expanded in z around inf

      \[\leadsto \frac{\color{blue}{z \cdot \left(x - 2\right)}}{\mathsf{fma}\left(\frac{156699607947}{500000000}, x, \frac{23533438303}{500000000}\right)} \]
   10. Step-by-step derivation

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lower--.f64 86.2

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

   11. Applied rewrites 86.2%

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

   12. Taylor expanded in x around 0

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

   14. Applied rewrites 86.2%

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

   if 0.089999999999999997 < x

   1. Initial program 8.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 89.2

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

   5. Applied rewrites 89.2%

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

Alternative 12: 72.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y \cdot x\right) \cdot -0.0424927283095952\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{+37}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-143}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-126}:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{elif}\;x \leq 0.09:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* y x) -0.0424927283095952)))
   (if (<= x -4.2e+37)
     (* 4.16438922228 x)
     (if (<= x -3.4e-143)
       t_0
       (if (<= x 5e-126)
         (* -0.0424927283095952 z)
         (if (<= x 0.09)
           t_0
           (* (- 4.16438922228 (/ 110.1139242984811 x)) x)))))))

C

double code(double x, double y, double z) {
	double t_0 = (y * x) * -0.0424927283095952;
	double tmp;
	if (x <= -4.2e+37) {
		tmp = 4.16438922228 * x;
	} else if (x <= -3.4e-143) {
		tmp = t_0;
	} else if (x <= 5e-126) {
		tmp = -0.0424927283095952 * z;
	} else if (x <= 0.09) {
		tmp = t_0;
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (y * x) * (-0.0424927283095952d0)
    if (x <= (-4.2d+37)) then
        tmp = 4.16438922228d0 * x
    else if (x <= (-3.4d-143)) then
        tmp = t_0
    else if (x <= 5d-126) then
        tmp = (-0.0424927283095952d0) * z
    else if (x <= 0.09d0) then
        tmp = t_0
    else
        tmp = (4.16438922228d0 - (110.1139242984811d0 / x)) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y * x) * -0.0424927283095952;
	double tmp;
	if (x <= -4.2e+37) {
		tmp = 4.16438922228 * x;
	} else if (x <= -3.4e-143) {
		tmp = t_0;
	} else if (x <= 5e-126) {
		tmp = -0.0424927283095952 * z;
	} else if (x <= 0.09) {
		tmp = t_0;
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y * x) * -0.0424927283095952
	tmp = 0
	if x <= -4.2e+37:
		tmp = 4.16438922228 * x
	elif x <= -3.4e-143:
		tmp = t_0
	elif x <= 5e-126:
		tmp = -0.0424927283095952 * z
	elif x <= 0.09:
		tmp = t_0
	else:
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * x) * -0.0424927283095952)
	tmp = 0.0
	if (x <= -4.2e+37)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= -3.4e-143)
		tmp = t_0;
	elseif (x <= 5e-126)
		tmp = Float64(-0.0424927283095952 * z);
	elseif (x <= 0.09)
		tmp = t_0;
	else
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y * x) * -0.0424927283095952;
	tmp = 0.0;
	if (x <= -4.2e+37)
		tmp = 4.16438922228 * x;
	elseif (x <= -3.4e-143)
		tmp = t_0;
	elseif (x <= 5e-126)
		tmp = -0.0424927283095952 * z;
	elseif (x <= 0.09)
		tmp = t_0;
	else
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * x), $MachinePrecision] * -0.0424927283095952), $MachinePrecision]}, If[LessEqual[x, -4.2e+37], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, -3.4e-143], t$95$0, If[LessEqual[x, 5e-126], N[(-0.0424927283095952 * z), $MachinePrecision], If[LessEqual[x, 0.09], t$95$0, N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.2000000000000002e37

   1. Initial program 9.8%

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

   4. Applied rewrites 13.6%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 92.7

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

   7. Applied rewrites 92.7%

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

   if -4.2000000000000002e37 < x < -3.39999999999999983e-143 or 5.00000000000000006e-126 < x < 0.089999999999999997

   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. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

   5. Applied rewrites 69.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 53.2%

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

   if -3.39999999999999983e-143 < x < 5.00000000000000006e-126

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 85.8

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

   5. Applied rewrites 85.8%

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

   if 0.089999999999999997 < x

   1. Initial program 8.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 89.2

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

   5. Applied rewrites 89.2%

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

Alternative 13: 89.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -36 \lor \neg \left(x \leq 225000000000\right):\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(y, x, z\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -36.0) (not (<= x 225000000000.0)))
   (* 4.16438922228 x)
   (/ (* (- x 2.0) (fma y x z)) (fma 313.399215894 x 47.066876606))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -36.0) || !(x <= 225000000000.0)) {
		tmp = 4.16438922228 * x;
	} else {
		tmp = ((x - 2.0) * fma(y, x, z)) / fma(313.399215894, x, 47.066876606);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -36.0) || !(x <= 225000000000.0))
		tmp = Float64(4.16438922228 * x);
	else
		tmp = Float64(Float64(Float64(x - 2.0) * fma(y, x, z)) / fma(313.399215894, x, 47.066876606));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -36.0], N[Not[LessEqual[x, 225000000000.0]], $MachinePrecision]], N[(4.16438922228 * x), $MachinePrecision], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(y * x + z), $MachinePrecision]), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -36 or 2.25e11 < x

   1. Initial program 12.6%

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

   4. Applied rewrites 18.5%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 88.6

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

   7. Applied rewrites 88.6%

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

   if -36 < x < 2.25e11

   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. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 34.6

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

   5. Applied rewrites 34.6%

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

   6. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 33.9

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

   8. Applied rewrites 33.9%

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

   9. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{\left(z + x \cdot y\right)}}{\mathsf{fma}\left(\frac{156699607947}{500000000}, x, \frac{23533438303}{500000000}\right)} \]
   10. Step-by-step derivation

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. lower-fma.f64 93.9

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

   11. Applied rewrites 93.9%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -36 \lor \neg \left(x \leq 225000000000\right):\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(y, x, z\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 71.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y \cdot x\right) \cdot -0.0424927283095952\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{+37}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-143}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-126}:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* y x) -0.0424927283095952)))
   (if (<= x -4.2e+37)
     (* 4.16438922228 x)
     (if (<= x -3.4e-143)
       t_0
       (if (<= x 5e-126)
         (* -0.0424927283095952 z)
         (if (<= x 2.0) t_0 (* 4.16438922228 x)))))))

C

double code(double x, double y, double z) {
	double t_0 = (y * x) * -0.0424927283095952;
	double tmp;
	if (x <= -4.2e+37) {
		tmp = 4.16438922228 * x;
	} else if (x <= -3.4e-143) {
		tmp = t_0;
	} else if (x <= 5e-126) {
		tmp = -0.0424927283095952 * z;
	} else if (x <= 2.0) {
		tmp = t_0;
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (y * x) * (-0.0424927283095952d0)
    if (x <= (-4.2d+37)) then
        tmp = 4.16438922228d0 * x
    else if (x <= (-3.4d-143)) then
        tmp = t_0
    else if (x <= 5d-126) then
        tmp = (-0.0424927283095952d0) * z
    else if (x <= 2.0d0) then
        tmp = t_0
    else
        tmp = 4.16438922228d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y * x) * -0.0424927283095952;
	double tmp;
	if (x <= -4.2e+37) {
		tmp = 4.16438922228 * x;
	} else if (x <= -3.4e-143) {
		tmp = t_0;
	} else if (x <= 5e-126) {
		tmp = -0.0424927283095952 * z;
	} else if (x <= 2.0) {
		tmp = t_0;
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y * x) * -0.0424927283095952
	tmp = 0
	if x <= -4.2e+37:
		tmp = 4.16438922228 * x
	elif x <= -3.4e-143:
		tmp = t_0
	elif x <= 5e-126:
		tmp = -0.0424927283095952 * z
	elif x <= 2.0:
		tmp = t_0
	else:
		tmp = 4.16438922228 * x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * x) * -0.0424927283095952)
	tmp = 0.0
	if (x <= -4.2e+37)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= -3.4e-143)
		tmp = t_0;
	elseif (x <= 5e-126)
		tmp = Float64(-0.0424927283095952 * z);
	elseif (x <= 2.0)
		tmp = t_0;
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y * x) * -0.0424927283095952;
	tmp = 0.0;
	if (x <= -4.2e+37)
		tmp = 4.16438922228 * x;
	elseif (x <= -3.4e-143)
		tmp = t_0;
	elseif (x <= 5e-126)
		tmp = -0.0424927283095952 * z;
	elseif (x <= 2.0)
		tmp = t_0;
	else
		tmp = 4.16438922228 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * x), $MachinePrecision] * -0.0424927283095952), $MachinePrecision]}, If[LessEqual[x, -4.2e+37], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, -3.4e-143], t$95$0, If[LessEqual[x, 5e-126], N[(-0.0424927283095952 * z), $MachinePrecision], If[LessEqual[x, 2.0], t$95$0, N[(4.16438922228 * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.2000000000000002e37 or 2 < x

   1. Initial program 8.5%

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

   4. Applied rewrites 15.5%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 91.6

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

   7. Applied rewrites 91.6%

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

   if -4.2000000000000002e37 < x < -3.39999999999999983e-143 or 5.00000000000000006e-126 < x < 2

   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. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

   5. Applied rewrites 68.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 52.4%

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

   if -3.39999999999999983e-143 < x < 5.00000000000000006e-126

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 85.8

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

   5. Applied rewrites 85.8%

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

Alternative 15: 88.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+37} \lor \neg \left(x \leq 13500000000\right):\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-0.0424927283095952, y, 0.3041881842569256 \cdot z\right), x, -0.0424927283095952 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.2e+37) (not (<= x 13500000000.0)))
   (* 4.16438922228 x)
   (fma
    (fma -0.0424927283095952 y (* 0.3041881842569256 z))
    x
    (* -0.0424927283095952 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.2e+37) || !(x <= 13500000000.0)) {
		tmp = 4.16438922228 * x;
	} else {
		tmp = fma(fma(-0.0424927283095952, y, (0.3041881842569256 * z)), x, (-0.0424927283095952 * z));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.2e+37) || !(x <= 13500000000.0))
		tmp = Float64(4.16438922228 * x);
	else
		tmp = fma(fma(-0.0424927283095952, y, Float64(0.3041881842569256 * z)), x, Float64(-0.0424927283095952 * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.2e+37], N[Not[LessEqual[x, 13500000000.0]], $MachinePrecision]], N[(4.16438922228 * x), $MachinePrecision], N[(N[(-0.0424927283095952 * y + N[(0.3041881842569256 * z), $MachinePrecision]), $MachinePrecision] * x + N[(-0.0424927283095952 * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.2000000000000002e37 or 1.35e10 < x

   1. Initial program 7.7%

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

   4. Applied rewrites 14.8%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 92.4

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

   7. Applied rewrites 92.4%

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

   if -4.2000000000000002e37 < x < 1.35e10

   1. Initial program 99.6%

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

   4. Applied rewrites 99.6%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. metadata-eval N/A

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

      8. lower-*.f64 88.8

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

   7. Applied rewrites 88.8%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+37} \lor \neg \left(x \leq 13500000000\right):\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-0.0424927283095952, y, 0.3041881842569256 \cdot z\right), x, -0.0424927283095952 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 76.3% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1000 \lor \neg \left(x \leq 175000000000\right):\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1000.0) (not (<= x 175000000000.0)))
   (* 4.16438922228 x)
   (* -0.0424927283095952 z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1000.0) || !(x <= 175000000000.0)) {
		tmp = 4.16438922228 * x;
	} else {
		tmp = -0.0424927283095952 * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1000.0d0)) .or. (.not. (x <= 175000000000.0d0))) then
        tmp = 4.16438922228d0 * x
    else
        tmp = (-0.0424927283095952d0) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1000.0) || !(x <= 175000000000.0)) {
		tmp = 4.16438922228 * x;
	} else {
		tmp = -0.0424927283095952 * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1000.0) or not (x <= 175000000000.0):
		tmp = 4.16438922228 * x
	else:
		tmp = -0.0424927283095952 * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1000.0) || !(x <= 175000000000.0))
		tmp = Float64(4.16438922228 * x);
	else
		tmp = Float64(-0.0424927283095952 * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1000.0) || ~((x <= 175000000000.0)))
		tmp = 4.16438922228 * x;
	else
		tmp = -0.0424927283095952 * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1000.0], N[Not[LessEqual[x, 175000000000.0]], $MachinePrecision]], N[(4.16438922228 * x), $MachinePrecision], N[(-0.0424927283095952 * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1e3 or 1.75e11 < x

   1. Initial program 13.3%

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

   4. Applied rewrites 19.2%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 87.8

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

   7. Applied rewrites 87.8%

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

   if -1e3 < x < 1.75e11

   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. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 61.9

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

   5. Applied rewrites 61.9%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1000 \lor \neg \left(x \leq 175000000000\right):\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 33.8% accurate, 13.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 60.8%

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

3. Taylor expanded in x around 0

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

   1. lower-*.f64 35.5

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

5. Applied rewrites 35.5%

   \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]
6. Add Preprocessing

Developer Target 1: 98.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024320 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C"
  :precision binary64

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

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