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

Percentage Accurate: 57.8% → 96.2%

Time: 12.5s

Alternatives: 19

Speedup: 4.4×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 57.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2200000:\\ \;\;\;\;\left(-x\right) \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{y - 130977.50649958357}{x}, -1, -3655.1204654076414\right)}{x}, -1, -110.1139242984811\right)}{x}, -1, -4.16438922228\right)\\ \mathbf{elif}\;x \leq 27000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(137.519416416, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right) \cdot \left(x - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2200000.0)
   (*
    (- x)
    (fma
     (/
      (fma
       (/ (fma (/ (- y 130977.50649958357) x) -1.0 -3655.1204654076414) x)
       -1.0
       -110.1139242984811)
      x)
     -1.0
     -4.16438922228))
   (if (<= x 27000.0)
     (/
      (* (- x 2.0) (fma (fma 137.519416416 x y) x z))
      (+
       (*
        (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894)
        x)
       47.066876606))
     (*
      (-
       4.16438922228
       (/
        (-
         101.7851458539211
         (/ (- 3451.550173699799 (/ (- 124074.40615218398 y) x)) x))
        x))
      (- x 2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2200000.0) {
		tmp = -x * fma((fma((fma(((y - 130977.50649958357) / x), -1.0, -3655.1204654076414) / x), -1.0, -110.1139242984811) / x), -1.0, -4.16438922228);
	} else if (x <= 27000.0) {
		tmp = ((x - 2.0) * fma(fma(137.519416416, x, y), x, z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
	} else {
		tmp = (4.16438922228 - ((101.7851458539211 - ((3451.550173699799 - ((124074.40615218398 - y) / x)) / x)) / x)) * (x - 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2200000.0)
		tmp = Float64(Float64(-x) * fma(Float64(fma(Float64(fma(Float64(Float64(y - 130977.50649958357) / x), -1.0, -3655.1204654076414) / x), -1.0, -110.1139242984811) / x), -1.0, -4.16438922228));
	elseif (x <= 27000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * fma(fma(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));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(Float64(101.7851458539211 - Float64(Float64(3451.550173699799 - Float64(Float64(124074.40615218398 - y) / x)) / x)) / x)) * Float64(x - 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2200000.0], N[((-x) * N[(N[(N[(N[(N[(N[(N[(y - 130977.50649958357), $MachinePrecision] / x), $MachinePrecision] * -1.0 + -3655.1204654076414), $MachinePrecision] / x), $MachinePrecision] * -1.0 + -110.1139242984811), $MachinePrecision] / x), $MachinePrecision] * -1.0 + -4.16438922228), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 27000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(137.519416416 * x + y), $MachinePrecision] * x + 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], N[(N[(4.16438922228 - N[(N[(101.7851458539211 - N[(N[(3451.550173699799 - N[(N[(124074.40615218398 - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2e6

   1. Initial program 11.1%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 15.7%

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

   6. Taylor expanded in x around -inf

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

   8. Applied rewrites 99.1%

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

   if -2.2e6 < x < 27000

   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

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 99.2

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

   5. Applied rewrites 99.2%

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

   if 27000 < x

   1. Initial program 20.3%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. 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 20.3%

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

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   7. Applied rewrites 98.6%

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

Alternative 2: 97.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \leq 5 \cdot 10^{+291}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(17.342137594641823, x \cdot x, -6193.6101064416025\right)}{\mathsf{fma}\left(x, 4.16438922228, -78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

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))
      5e+291)
   (*
    (/
     (fma
      (fma
       (fma
        (/
         (fma 17.342137594641823 (* x x) -6193.6101064416025)
         (fma x 4.16438922228 -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)) <= 5e+291) {
		tmp = (fma(fma(fma((fma(17.342137594641823, (x * x), -6193.6101064416025) / fma(x, 4.16438922228, -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)) <= 5e+291)
		tmp = Float64(Float64(fma(fma(fma(Float64(fma(17.342137594641823, Float64(x * x), -6193.6101064416025) / fma(x, 4.16438922228, -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], 5e+291], N[(N[(N[(N[(N[(N[(N[(17.342137594641823 * N[(x * x), $MachinePrecision] + -6193.6101064416025), $MachinePrecision] / N[(x * 4.16438922228 + -78.6994924154), $MachinePrecision]), $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))) < 5.0000000000000001e291

   1. Initial program 96.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing
   3. 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 98.4%

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

      1. lift-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. flip-+ N/A

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

      4. lower-/.f64 N/A

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

      5. sub-neg N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. swap-sqr N/A

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

      9. lower-fma.f64 N/A

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

      10. metadata-eval N/A

          \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(\color{blue}{\frac{10838835996651139530249}{625000000000000000000}}, x \cdot x, \mathsf{neg}\left(\frac{393497462077}{5000000000} \cdot \frac{393497462077}{5000000000}\right)\right)}{x \cdot \frac{104109730557}{25000000000} - \frac{393497462077}{5000000000}}, x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{216700011257}{5000000000} + x, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \cdot \left(x - 2\right) \]

      11. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{10838835996651139530249}{625000000000000000000}, \color{blue}{x \cdot x}, \mathsf{neg}\left(\frac{393497462077}{5000000000} \cdot \frac{393497462077}{5000000000}\right)\right)}{x \cdot \frac{104109730557}{25000000000} - \frac{393497462077}{5000000000}}, x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{216700011257}{5000000000} + x, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \cdot \left(x - 2\right) \]

      12. metadata-eval N/A

          \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{10838835996651139530249}{625000000000000000000}, x \cdot x, \mathsf{neg}\left(\color{blue}{\frac{154840252661040053153929}{25000000000000000000}}\right)\right)}{x \cdot \frac{104109730557}{25000000000} - \frac{393497462077}{5000000000}}, x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{216700011257}{5000000000} + x, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \cdot \left(x - 2\right) \]

      13. metadata-eval N/A

          \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{10838835996651139530249}{625000000000000000000}, x \cdot x, \color{blue}{\frac{-154840252661040053153929}{25000000000000000000}}\right)}{x \cdot \frac{104109730557}{25000000000} - \frac{393497462077}{5000000000}}, x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{216700011257}{5000000000} + x, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \cdot \left(x - 2\right) \]

      14. sub-neg N/A

          \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{10838835996651139530249}{625000000000000000000}, x \cdot x, \frac{-154840252661040053153929}{25000000000000000000}\right)}{\color{blue}{x \cdot \frac{104109730557}{25000000000} + \left(\mathsf{neg}\left(\frac{393497462077}{5000000000}\right)\right)}}, x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{216700011257}{5000000000} + x, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \cdot \left(x - 2\right) \]

      15. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{10838835996651139530249}{625000000000000000000}, x \cdot x, \frac{-154840252661040053153929}{25000000000000000000}\right)}{\color{blue}{\mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \mathsf{neg}\left(\frac{393497462077}{5000000000}\right)\right)}}, x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{216700011257}{5000000000} + x, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \cdot \left(x - 2\right) \]

      16. metadata-eval 98.4

          \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(17.342137594641823, x \cdot x, -6193.6101064416025\right)}{\mathsf{fma}\left(x, 4.16438922228, \color{blue}{-78.6994924154}\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \cdot \left(x - 2\right) \]

   6. Applied rewrites 98.4%

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\frac{\mathsf{fma}\left(17.342137594641823, x \cdot x, -6193.6101064416025\right)}{\mathsf{fma}\left(x, 4.16438922228, -78.6994924154\right)}}, x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \cdot \left(x - 2\right) \]

   if 5.0000000000000001e291 < (/.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
   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 0.0%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 99.1

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

   7. Applied rewrites 99.1%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \leq 5 \cdot 10^{+291}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(17.342137594641823, x \cdot x, -6193.6101064416025\right)}{\mathsf{fma}\left(x, 4.16438922228, -78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \leq 5 \cdot 10^{+291}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

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))
      5e+291)
   (*
    (/
     (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)) <= 5e+291) {
		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)) <= 5e+291)
		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], 5e+291], 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))) < 5.0000000000000001e291

   1. Initial program 96.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing
   3. 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 98.4%

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

   if 5.0000000000000001e291 < (/.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
   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 0.0%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 99.1

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

   7. Applied rewrites 99.1%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \leq 5 \cdot 10^{+291}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2200000 \lor \neg \left(x \leq 27000\right):\\ \;\;\;\;\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right) \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(137.519416416, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2200000.0) (not (<= x 27000.0)))
   (*
    (-
     4.16438922228
     (/
      (-
       101.7851458539211
       (/ (- 3451.550173699799 (/ (- 124074.40615218398 y) x)) x))
      x))
    (- x 2.0))
   (/
    (* (- x 2.0) (fma (fma 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) {
	double tmp;
	if ((x <= -2200000.0) || !(x <= 27000.0)) {
		tmp = (4.16438922228 - ((101.7851458539211 - ((3451.550173699799 - ((124074.40615218398 - y) / x)) / x)) / x)) * (x - 2.0);
	} else {
		tmp = ((x - 2.0) * fma(fma(137.519416416, x, y), x, z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2200000.0) || !(x <= 27000.0))
		tmp = Float64(Float64(4.16438922228 - Float64(Float64(101.7851458539211 - Float64(Float64(3451.550173699799 - Float64(Float64(124074.40615218398 - y) / x)) / x)) / x)) * Float64(x - 2.0));
	else
		tmp = Float64(Float64(Float64(x - 2.0) * fma(fma(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
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2200000.0], N[Not[LessEqual[x, 27000.0]], $MachinePrecision]], N[(N[(4.16438922228 - N[(N[(101.7851458539211 - N[(N[(3451.550173699799 - N[(N[(124074.40615218398 - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(137.519416416 * x + y), $MachinePrecision] * x + 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]]

Derivation

1. Split input into 2 regimes

2. if x < -2.2e6 or 27000 < x

   1. Initial program 15.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing
   3. 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 17.7%

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

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   7. Applied rewrites 98.9%

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

   if -2.2e6 < x < 27000

   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

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 99.2

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

   5. Applied rewrites 99.2%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2200000 \lor \neg \left(x \leq 27000\right):\\ \;\;\;\;\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right) \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(137.519416416, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -36 \lor \neg \left(x \leq 14500\right):\\ \;\;\;\;\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right) \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)} \cdot \left(x - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -36.0) (not (<= x 14500.0)))
   (*
    (-
     4.16438922228
     (/
      (-
       101.7851458539211
       (/ (- 3451.550173699799 (/ (- 124074.40615218398 y) x)) x))
      x))
    (- x 2.0))
   (*
    (/
     (fma
      (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
      x
      z)
     (fma 313.399215894 x 47.066876606))
    (- x 2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -36.0) || !(x <= 14500.0)) {
		tmp = (4.16438922228 - ((101.7851458539211 - ((3451.550173699799 - ((124074.40615218398 - y) / x)) / x)) / x)) * (x - 2.0);
	} else {
		tmp = (fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(313.399215894, x, 47.066876606)) * (x - 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -36.0) || !(x <= 14500.0))
		tmp = Float64(Float64(4.16438922228 - Float64(Float64(101.7851458539211 - Float64(Float64(3451.550173699799 - Float64(Float64(124074.40615218398 - y) / x)) / x)) / x)) * Float64(x - 2.0));
	else
		tmp = Float64(Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(313.399215894, x, 47.066876606)) * Float64(x - 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -36.0], N[Not[LessEqual[x, 14500.0]], $MachinePrecision]], N[(N[(4.16438922228 - N[(N[(101.7851458539211 - N[(N[(3451.550173699799 - N[(N[(124074.40615218398 - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -36 or 14500 < x

   1. Initial program 15.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing
   3. 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 17.7%

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

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   7. Applied rewrites 98.9%

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

   if -36 < x < 14500

   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. 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 99.7%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 97.2%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -36 \lor \neg \left(x \leq 14500\right):\\ \;\;\;\;\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x}}{x}\right) \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)} \cdot \left(x - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 92.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -36:\\ \;\;\;\;\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799}{x}}{x}\right) \cdot \left(x - 2\right)\\ \mathbf{elif}\;x \leq 14500:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)} \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\frac{3451.550173699799}{x \cdot x} + 4.16438922228\right) - \frac{101.7851458539211}{x}\right) \cdot \left(x - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -36.0)
   (*
    (- 4.16438922228 (/ (- 101.7851458539211 (/ 3451.550173699799 x)) x))
    (- x 2.0))
   (if (<= x 14500.0)
     (*
      (/
       (fma
        (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
        x
        z)
       (fma 313.399215894 x 47.066876606))
      (- x 2.0))
     (*
      (-
       (+ (/ 3451.550173699799 (* x x)) 4.16438922228)
       (/ 101.7851458539211 x))
      (- x 2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -36.0) {
		tmp = (4.16438922228 - ((101.7851458539211 - (3451.550173699799 / x)) / x)) * (x - 2.0);
	} else if (x <= 14500.0) {
		tmp = (fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(313.399215894, x, 47.066876606)) * (x - 2.0);
	} else {
		tmp = (((3451.550173699799 / (x * x)) + 4.16438922228) - (101.7851458539211 / x)) * (x - 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -36.0)
		tmp = Float64(Float64(4.16438922228 - Float64(Float64(101.7851458539211 - Float64(3451.550173699799 / x)) / x)) * Float64(x - 2.0));
	elseif (x <= 14500.0)
		tmp = Float64(Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(313.399215894, x, 47.066876606)) * Float64(x - 2.0));
	else
		tmp = Float64(Float64(Float64(Float64(3451.550173699799 / Float64(x * x)) + 4.16438922228) - Float64(101.7851458539211 / x)) * Float64(x - 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -36.0], N[(N[(4.16438922228 - N[(N[(101.7851458539211 - N[(3451.550173699799 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 14500.0], N[(N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(3451.550173699799 / N[(x * x), $MachinePrecision]), $MachinePrecision] + 4.16438922228), $MachinePrecision] - N[(101.7851458539211 / x), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -36

   1. Initial program 11.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing
   3. 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 15.6%

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

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. lower-/.f64 97.6

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

   7. Applied rewrites 97.6%

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

   if -36 < x < 14500

   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. 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 99.7%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 97.2%

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

   if 14500 < x

   1. Initial program 20.3%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. 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 20.3%

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

   5. Taylor expanded in x around inf

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r/ N/A

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

      8. metadata-eval N/A

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

      9. lower-/.f64 94.1

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

   7. Applied rewrites 94.1%

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

Alternative 7: 91.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.175:\\ \;\;\;\;\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799}{x}}{x}\right) \cdot \left(x - 2\right)\\ \mathbf{elif}\;x \leq 27:\\ \;\;\;\;\mathsf{fma}\left(z, -0.0424927283095952, \mathsf{fma}\left(\mathsf{fma}\left(0.3041881842569256, y, -5.843575199059173\right), x, -0.0424927283095952 \cdot y\right) \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\frac{3451.550173699799}{x \cdot x} + 4.16438922228\right) - \frac{101.7851458539211}{x}\right) \cdot \left(x - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.175)
   (*
    (- 4.16438922228 (/ (- 101.7851458539211 (/ 3451.550173699799 x)) x))
    (- x 2.0))
   (if (<= x 27.0)
     (fma
      z
      -0.0424927283095952
      (*
       (fma
        (fma 0.3041881842569256 y -5.843575199059173)
        x
        (* -0.0424927283095952 y))
       x))
     (*
      (-
       (+ (/ 3451.550173699799 (* x x)) 4.16438922228)
       (/ 101.7851458539211 x))
      (- x 2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.175) {
		tmp = (4.16438922228 - ((101.7851458539211 - (3451.550173699799 / x)) / x)) * (x - 2.0);
	} else if (x <= 27.0) {
		tmp = fma(z, -0.0424927283095952, (fma(fma(0.3041881842569256, y, -5.843575199059173), x, (-0.0424927283095952 * y)) * x));
	} else {
		tmp = (((3451.550173699799 / (x * x)) + 4.16438922228) - (101.7851458539211 / x)) * (x - 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.175)
		tmp = Float64(Float64(4.16438922228 - Float64(Float64(101.7851458539211 - Float64(3451.550173699799 / x)) / x)) * Float64(x - 2.0));
	elseif (x <= 27.0)
		tmp = fma(z, -0.0424927283095952, Float64(fma(fma(0.3041881842569256, y, -5.843575199059173), x, Float64(-0.0424927283095952 * y)) * x));
	else
		tmp = Float64(Float64(Float64(Float64(3451.550173699799 / Float64(x * x)) + 4.16438922228) - Float64(101.7851458539211 / x)) * Float64(x - 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.175], N[(N[(4.16438922228 - N[(N[(101.7851458539211 - N[(3451.550173699799 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 27.0], N[(z * -0.0424927283095952 + N[(N[(N[(0.3041881842569256 * y + -5.843575199059173), $MachinePrecision] * x + N[(-0.0424927283095952 * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(3451.550173699799 / N[(x * x), $MachinePrecision]), $MachinePrecision] + 4.16438922228), $MachinePrecision] - N[(101.7851458539211 / x), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.17499999999999999

   1. Initial program 13.9%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing
   3. 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 18.2%

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

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. lower-/.f64 94.7

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

   7. Applied rewrites 94.7%

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

   if -0.17499999999999999 < x < 27

   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

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z + x \cdot \left(\left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \left(\frac{-131752537360500000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)\right)\right)\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)} \]

   5. Applied rewrites 98.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(0.28294182010212804, z, \mathsf{fma}\left(\mathsf{fma}\left(0.23789659216289816, z, \mathsf{fma}\left(-6.658593866711955, \mathsf{fma}\left(0.28294182010212804, z, \mathsf{fma}\left(-2, y, z\right) \cdot 0.0212463641547976\right), \mathsf{fma}\left(0.0212463641547976, y, -5.843575199059173\right)\right)\right), x, \mathsf{fma}\left(-2, y, z\right) \cdot 0.0212463641547976\right)\right), x, -0.0424927283095952 \cdot z\right)} \]

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\frac{-1000000000}{23533438303} \cdot y + x \cdot \left(\left(\frac{500000000}{23533438303} \cdot y + \frac{156699607947000000000}{553822718361107519809} \cdot y\right) - \frac{137519416416}{23533438303}\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 98.1%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.3041881842569256, y, -5.843575199059173\right), x, -0.0424927283095952 \cdot y\right), x, -0.0424927283095952 \cdot z\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 98.2%

       \[\leadsto \mathsf{fma}\left(z, \color{blue}{-0.0424927283095952}, \mathsf{fma}\left(\mathsf{fma}\left(0.3041881842569256, y, -5.843575199059173\right), x, -0.0424927283095952 \cdot y\right) \cdot x\right) \]

   if 27 < x

   1. Initial program 21.9%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing
   3. 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 21.9%

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

   5. Taylor expanded in x around inf

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r/ N/A

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

      8. metadata-eval N/A

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

      9. lower-/.f64 92.2

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

   7. Applied rewrites 92.2%

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

Alternative 8: 91.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.175 \lor \neg \left(x \leq 27\right):\\ \;\;\;\;\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799}{x}}{x}\right) \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, -0.0424927283095952, \mathsf{fma}\left(\mathsf{fma}\left(0.3041881842569256, y, -5.843575199059173\right), x, -0.0424927283095952 \cdot y\right) \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.175) (not (<= x 27.0)))
   (*
    (- 4.16438922228 (/ (- 101.7851458539211 (/ 3451.550173699799 x)) x))
    (- x 2.0))
   (fma
    z
    -0.0424927283095952
    (*
     (fma
      (fma 0.3041881842569256 y -5.843575199059173)
      x
      (* -0.0424927283095952 y))
     x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.175) || !(x <= 27.0)) {
		tmp = (4.16438922228 - ((101.7851458539211 - (3451.550173699799 / x)) / x)) * (x - 2.0);
	} else {
		tmp = fma(z, -0.0424927283095952, (fma(fma(0.3041881842569256, y, -5.843575199059173), x, (-0.0424927283095952 * y)) * x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.175) || !(x <= 27.0))
		tmp = Float64(Float64(4.16438922228 - Float64(Float64(101.7851458539211 - Float64(3451.550173699799 / x)) / x)) * Float64(x - 2.0));
	else
		tmp = fma(z, -0.0424927283095952, Float64(fma(fma(0.3041881842569256, y, -5.843575199059173), x, Float64(-0.0424927283095952 * y)) * x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.175], N[Not[LessEqual[x, 27.0]], $MachinePrecision]], N[(N[(4.16438922228 - N[(N[(101.7851458539211 - N[(3451.550173699799 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], N[(z * -0.0424927283095952 + N[(N[(N[(0.3041881842569256 * y + -5.843575199059173), $MachinePrecision] * x + N[(-0.0424927283095952 * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.17499999999999999 or 27 < x

   1. Initial program 17.4%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing
   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 19.8%

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

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. lower-/.f64 93.6

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

   7. Applied rewrites 93.6%

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

   if -0.17499999999999999 < x < 27

   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

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z + x \cdot \left(\left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \left(\frac{-131752537360500000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)\right)\right)\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)} \]

   5. Applied rewrites 98.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(0.28294182010212804, z, \mathsf{fma}\left(\mathsf{fma}\left(0.23789659216289816, z, \mathsf{fma}\left(-6.658593866711955, \mathsf{fma}\left(0.28294182010212804, z, \mathsf{fma}\left(-2, y, z\right) \cdot 0.0212463641547976\right), \mathsf{fma}\left(0.0212463641547976, y, -5.843575199059173\right)\right)\right), x, \mathsf{fma}\left(-2, y, z\right) \cdot 0.0212463641547976\right)\right), x, -0.0424927283095952 \cdot z\right)} \]

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\frac{-1000000000}{23533438303} \cdot y + x \cdot \left(\left(\frac{500000000}{23533438303} \cdot y + \frac{156699607947000000000}{553822718361107519809} \cdot y\right) - \frac{137519416416}{23533438303}\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 98.1%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.3041881842569256, y, -5.843575199059173\right), x, -0.0424927283095952 \cdot y\right), x, -0.0424927283095952 \cdot z\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 98.2%

       \[\leadsto \mathsf{fma}\left(z, \color{blue}{-0.0424927283095952}, \mathsf{fma}\left(\mathsf{fma}\left(0.3041881842569256, y, -5.843575199059173\right), x, -0.0424927283095952 \cdot y\right) \cdot x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.175 \lor \neg \left(x \leq 27\right):\\ \;\;\;\;\left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799}{x}}{x}\right) \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, -0.0424927283095952, \mathsf{fma}\left(\mathsf{fma}\left(0.3041881842569256, y, -5.843575199059173\right), x, -0.0424927283095952 \cdot y\right) \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 91.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.175 \lor \neg \left(x \leq 27\right):\\ \;\;\;\;\left(\frac{\frac{3655.1204654076414}{x} - 110.1139242984811}{x} + 4.16438922228\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, -0.0424927283095952, \mathsf{fma}\left(\mathsf{fma}\left(0.3041881842569256, y, -5.843575199059173\right), x, -0.0424927283095952 \cdot y\right) \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.175) (not (<= x 27.0)))
   (* (+ (/ (- (/ 3655.1204654076414 x) 110.1139242984811) x) 4.16438922228) x)
   (fma
    z
    -0.0424927283095952
    (*
     (fma
      (fma 0.3041881842569256 y -5.843575199059173)
      x
      (* -0.0424927283095952 y))
     x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.175) || !(x <= 27.0)) {
		tmp = ((((3655.1204654076414 / x) - 110.1139242984811) / x) + 4.16438922228) * x;
	} else {
		tmp = fma(z, -0.0424927283095952, (fma(fma(0.3041881842569256, y, -5.843575199059173), x, (-0.0424927283095952 * y)) * x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.175) || !(x <= 27.0))
		tmp = Float64(Float64(Float64(Float64(Float64(3655.1204654076414 / x) - 110.1139242984811) / x) + 4.16438922228) * x);
	else
		tmp = fma(z, -0.0424927283095952, Float64(fma(fma(0.3041881842569256, y, -5.843575199059173), x, Float64(-0.0424927283095952 * y)) * x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.175], N[Not[LessEqual[x, 27.0]], $MachinePrecision]], N[(N[(N[(N[(N[(3655.1204654076414 / x), $MachinePrecision] - 110.1139242984811), $MachinePrecision] / x), $MachinePrecision] + 4.16438922228), $MachinePrecision] * x), $MachinePrecision], N[(z * -0.0424927283095952 + N[(N[(N[(0.3041881842569256 * y + -5.843575199059173), $MachinePrecision] * x + N[(-0.0424927283095952 * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.17499999999999999 or 27 < x

   1. Initial program 17.4%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(\frac{104109730557}{25000000000} + \frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{{x}^{2}}\right) - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\frac{104109730557}{25000000000} + \frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{{x}^{2}}\right) - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\frac{104109730557}{25000000000} + \frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{{x}^{2}}\right) - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right) \cdot x} \]

      3. associate--l+ N/A

         \[\leadsto \color{blue}{\left(\frac{104109730557}{25000000000} + \left(\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{{x}^{2}} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)\right)} \cdot x \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{{x}^{2}} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right) + \frac{104109730557}{25000000000}\right)} \cdot x \]

      5. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{{x}^{2}} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right) + \frac{104109730557}{25000000000}\right)} \cdot x \]

      6. unpow2 N/A

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

      7. associate-/r* N/A

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

      8. metadata-eval N/A

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

      9. associate-*r/ N/A

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

      10. associate-*r/ N/A

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

      11. metadata-eval N/A

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

      12. div-sub N/A

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

      13. lower-/.f64 N/A

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

      14. lower--.f64 N/A

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

      15. associate-*r/ N/A

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

      16. metadata-eval N/A

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

      17. lower-/.f64 93.6

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

   5. Applied rewrites 93.6%

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

   if -0.17499999999999999 < x < 27

   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

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z + x \cdot \left(\left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \left(\frac{-131752537360500000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)\right)\right)\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)} \]

   5. Applied rewrites 98.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(0.28294182010212804, z, \mathsf{fma}\left(\mathsf{fma}\left(0.23789659216289816, z, \mathsf{fma}\left(-6.658593866711955, \mathsf{fma}\left(0.28294182010212804, z, \mathsf{fma}\left(-2, y, z\right) \cdot 0.0212463641547976\right), \mathsf{fma}\left(0.0212463641547976, y, -5.843575199059173\right)\right)\right), x, \mathsf{fma}\left(-2, y, z\right) \cdot 0.0212463641547976\right)\right), x, -0.0424927283095952 \cdot z\right)} \]

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\frac{-1000000000}{23533438303} \cdot y + x \cdot \left(\left(\frac{500000000}{23533438303} \cdot y + \frac{156699607947000000000}{553822718361107519809} \cdot y\right) - \frac{137519416416}{23533438303}\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 98.1%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.3041881842569256, y, -5.843575199059173\right), x, -0.0424927283095952 \cdot y\right), x, -0.0424927283095952 \cdot z\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 98.2%

       \[\leadsto \mathsf{fma}\left(z, \color{blue}{-0.0424927283095952}, \mathsf{fma}\left(\mathsf{fma}\left(0.3041881842569256, y, -5.843575199059173\right), x, -0.0424927283095952 \cdot y\right) \cdot x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.175 \lor \neg \left(x \leq 27\right):\\ \;\;\;\;\left(\frac{\frac{3655.1204654076414}{x} - 110.1139242984811}{x} + 4.16438922228\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, -0.0424927283095952, \mathsf{fma}\left(\mathsf{fma}\left(0.3041881842569256, y, -5.843575199059173\right), x, -0.0424927283095952 \cdot y\right) \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 91.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.175 \lor \neg \left(x \leq 27\right):\\ \;\;\;\;\left(4.16438922228 - \frac{101.7851458539211}{x}\right) \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, -0.0424927283095952, \mathsf{fma}\left(\mathsf{fma}\left(0.3041881842569256, y, -5.843575199059173\right), x, -0.0424927283095952 \cdot y\right) \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.175) (not (<= x 27.0)))
   (* (- 4.16438922228 (/ 101.7851458539211 x)) (- x 2.0))
   (fma
    z
    -0.0424927283095952
    (*
     (fma
      (fma 0.3041881842569256 y -5.843575199059173)
      x
      (* -0.0424927283095952 y))
     x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.175) || !(x <= 27.0)) {
		tmp = (4.16438922228 - (101.7851458539211 / x)) * (x - 2.0);
	} else {
		tmp = fma(z, -0.0424927283095952, (fma(fma(0.3041881842569256, y, -5.843575199059173), x, (-0.0424927283095952 * y)) * x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.175) || !(x <= 27.0))
		tmp = Float64(Float64(4.16438922228 - Float64(101.7851458539211 / x)) * Float64(x - 2.0));
	else
		tmp = fma(z, -0.0424927283095952, Float64(fma(fma(0.3041881842569256, y, -5.843575199059173), x, Float64(-0.0424927283095952 * y)) * x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.175], N[Not[LessEqual[x, 27.0]], $MachinePrecision]], N[(N[(4.16438922228 - N[(101.7851458539211 / x), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], N[(z * -0.0424927283095952 + N[(N[(N[(0.3041881842569256 * y + -5.843575199059173), $MachinePrecision] * x + N[(-0.0424927283095952 * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.17499999999999999 or 27 < x

   1. Initial program 17.4%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing
   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 19.8%

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

   5. Taylor expanded in x around inf

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

      1. lower--.f64 N/A

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

      2. associate-*r/ N/A

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

      3. metadata-eval N/A

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

      4. lower-/.f64 92.9

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

   7. Applied rewrites 92.9%

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

   if -0.17499999999999999 < x < 27

   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

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z + x \cdot \left(\left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \left(\frac{-131752537360500000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)\right)\right)\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)} \]

   5. Applied rewrites 98.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(0.28294182010212804, z, \mathsf{fma}\left(\mathsf{fma}\left(0.23789659216289816, z, \mathsf{fma}\left(-6.658593866711955, \mathsf{fma}\left(0.28294182010212804, z, \mathsf{fma}\left(-2, y, z\right) \cdot 0.0212463641547976\right), \mathsf{fma}\left(0.0212463641547976, y, -5.843575199059173\right)\right)\right), x, \mathsf{fma}\left(-2, y, z\right) \cdot 0.0212463641547976\right)\right), x, -0.0424927283095952 \cdot z\right)} \]

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\frac{-1000000000}{23533438303} \cdot y + x \cdot \left(\left(\frac{500000000}{23533438303} \cdot y + \frac{156699607947000000000}{553822718361107519809} \cdot y\right) - \frac{137519416416}{23533438303}\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 98.1%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.3041881842569256, y, -5.843575199059173\right), x, -0.0424927283095952 \cdot y\right), x, -0.0424927283095952 \cdot z\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 98.2%

       \[\leadsto \mathsf{fma}\left(z, \color{blue}{-0.0424927283095952}, \mathsf{fma}\left(\mathsf{fma}\left(0.3041881842569256, y, -5.843575199059173\right), x, -0.0424927283095952 \cdot y\right) \cdot x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.175 \lor \neg \left(x \leq 27\right):\\ \;\;\;\;\left(4.16438922228 - \frac{101.7851458539211}{x}\right) \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, -0.0424927283095952, \mathsf{fma}\left(\mathsf{fma}\left(0.3041881842569256, y, -5.843575199059173\right), x, -0.0424927283095952 \cdot y\right) \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 89.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.03 \lor \neg \left(x \leq 14500\right):\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(0.3041881842569256, z, -0.0424927283095952 \cdot y\right), x, -0.0424927283095952 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.03) (not (<= x 14500.0)))
   (* (- 4.16438922228 (/ 110.1139242984811 x)) x)
   (fma
    (fma 0.3041881842569256 z (* -0.0424927283095952 y))
    x
    (* -0.0424927283095952 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.03) || !(x <= 14500.0)) {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	} else {
		tmp = fma(fma(0.3041881842569256, z, (-0.0424927283095952 * y)), x, (-0.0424927283095952 * z));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.03) || !(x <= 14500.0))
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	else
		tmp = fma(fma(0.3041881842569256, z, Float64(-0.0424927283095952 * y)), x, Float64(-0.0424927283095952 * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.03], N[Not[LessEqual[x, 14500.0]], $MachinePrecision]], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[(0.3041881842569256 * z + N[(-0.0424927283095952 * y), $MachinePrecision]), $MachinePrecision] * x + N[(-0.0424927283095952 * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.029999999999999999 or 14500 < x

   1. Initial program 17.4%

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

   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. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

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

      5. associate-+l- N/A

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

      6. neg-sub0 N/A

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

      7. lower-*.f64 N/A

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

      8. neg-sub0 N/A

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

      9. associate-+l- N/A

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

      10. neg-sub0 N/A

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

      11. +-commutative N/A

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

      12. sub-neg N/A

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

      13. lower--.f64 N/A

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

      14. associate-*r/ N/A

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

      15. metadata-eval N/A

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

      16. lower-/.f64 93.0

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

   5. Applied rewrites 93.0%

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

   if -0.029999999999999999 < x < 14500

   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

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z + x \cdot \left(\left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \left(\frac{-131752537360500000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)\right)\right)\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)} \]

   5. Applied rewrites 98.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(0.28294182010212804, z, \mathsf{fma}\left(\mathsf{fma}\left(0.23789659216289816, z, \mathsf{fma}\left(-6.658593866711955, \mathsf{fma}\left(0.28294182010212804, z, \mathsf{fma}\left(-2, y, z\right) \cdot 0.0212463641547976\right), \mathsf{fma}\left(0.0212463641547976, y, -5.843575199059173\right)\right)\right), x, \mathsf{fma}\left(-2, y, z\right) \cdot 0.0212463641547976\right)\right), x, -0.0424927283095952 \cdot z\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) + \frac{156699607947000000000}{553822718361107519809} \cdot z, x, \frac{-1000000000}{23533438303} \cdot z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 93.3%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.03 \lor \neg \left(x \leq 14500\right):\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(0.3041881842569256, z, -0.0424927283095952 \cdot y\right), x, -0.0424927283095952 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 89.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.03:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \mathbf{elif}\;x \leq 14500:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(0.3041881842569256, z, -0.0424927283095952 \cdot y\right), x, -0.0424927283095952 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{101.7851458539211}{x}\right) \cdot \left(x - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.03)
   (* (- 4.16438922228 (/ 110.1139242984811 x)) x)
   (if (<= x 14500.0)
     (fma
      (fma 0.3041881842569256 z (* -0.0424927283095952 y))
      x
      (* -0.0424927283095952 z))
     (* (- 4.16438922228 (/ 101.7851458539211 x)) (- x 2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.03) {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	} else if (x <= 14500.0) {
		tmp = fma(fma(0.3041881842569256, z, (-0.0424927283095952 * y)), x, (-0.0424927283095952 * z));
	} else {
		tmp = (4.16438922228 - (101.7851458539211 / x)) * (x - 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.03)
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	elseif (x <= 14500.0)
		tmp = fma(fma(0.3041881842569256, z, Float64(-0.0424927283095952 * y)), x, Float64(-0.0424927283095952 * z));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(101.7851458539211 / x)) * Float64(x - 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.03], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 14500.0], N[(N[(0.3041881842569256 * z + N[(-0.0424927283095952 * y), $MachinePrecision]), $MachinePrecision] * x + N[(-0.0424927283095952 * z), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(101.7851458539211 / x), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.029999999999999999

   1. Initial program 15.2%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   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. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

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

      5. associate-+l- N/A

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

      6. neg-sub0 N/A

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

      7. lower-*.f64 N/A

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

      8. neg-sub0 N/A

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

      9. associate-+l- N/A

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

      10. neg-sub0 N/A

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

      11. +-commutative N/A

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

      12. sub-neg N/A

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

      13. lower--.f64 N/A

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

      14. associate-*r/ N/A

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

      15. metadata-eval N/A

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

      16. lower-/.f64 92.8

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

   5. Applied rewrites 92.8%

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

   if -0.029999999999999999 < x < 14500

   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

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z + x \cdot \left(\left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \left(\frac{-131752537360500000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)\right)\right)\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)} \]

   5. Applied rewrites 98.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(0.28294182010212804, z, \mathsf{fma}\left(\mathsf{fma}\left(0.23789659216289816, z, \mathsf{fma}\left(-6.658593866711955, \mathsf{fma}\left(0.28294182010212804, z, \mathsf{fma}\left(-2, y, z\right) \cdot 0.0212463641547976\right), \mathsf{fma}\left(0.0212463641547976, y, -5.843575199059173\right)\right)\right), x, \mathsf{fma}\left(-2, y, z\right) \cdot 0.0212463641547976\right)\right), x, -0.0424927283095952 \cdot z\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) + \frac{156699607947000000000}{553822718361107519809} \cdot z, x, \frac{-1000000000}{23533438303} \cdot z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 93.3%

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

   if 14500 < x

   1. Initial program 20.3%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. 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 20.3%

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

   5. Taylor expanded in x around inf

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

      1. lower--.f64 N/A

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

      2. associate-*r/ N/A

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

      3. metadata-eval N/A

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

      4. lower-/.f64 93.3

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

   7. Applied rewrites 93.3%

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

Alternative 13: 89.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.03 \lor \neg \left(x \leq 2\right):\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.0424927283095952 \cdot y, x, -0.0424927283095952 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.03) (not (<= x 2.0)))
   (* (- 4.16438922228 (/ 110.1139242984811 x)) x)
   (fma (* -0.0424927283095952 y) x (* -0.0424927283095952 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.03) || !(x <= 2.0)) {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	} else {
		tmp = fma((-0.0424927283095952 * y), x, (-0.0424927283095952 * z));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.03) || !(x <= 2.0))
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	else
		tmp = fma(Float64(-0.0424927283095952 * y), x, Float64(-0.0424927283095952 * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.03], N[Not[LessEqual[x, 2.0]], $MachinePrecision]], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[(-0.0424927283095952 * y), $MachinePrecision] * x + N[(-0.0424927283095952 * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.029999999999999999 or 2 < x

   1. Initial program 18.1%

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

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

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

      5. associate-+l- N/A

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

      6. neg-sub0 N/A

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

      7. lower-*.f64 N/A

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

      8. neg-sub0 N/A

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

      9. associate-+l- N/A

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

      10. neg-sub0 N/A

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

      11. +-commutative N/A

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

      12. sub-neg N/A

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

      13. lower--.f64 N/A

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

      14. associate-*r/ N/A

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

      15. metadata-eval N/A

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

      16. lower-/.f64 92.2

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

   5. Applied rewrites 92.2%

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

   if -0.029999999999999999 < x < 2

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z + x \cdot \left(\left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \left(\frac{-131752537360500000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)\right)\right)\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)} \]

   5. Applied rewrites 99.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(0.28294182010212804, z, \mathsf{fma}\left(\mathsf{fma}\left(0.23789659216289816, z, \mathsf{fma}\left(-6.658593866711955, \mathsf{fma}\left(0.28294182010212804, z, \mathsf{fma}\left(-2, y, z\right) \cdot 0.0212463641547976\right), \mathsf{fma}\left(0.0212463641547976, y, -5.843575199059173\right)\right)\right), x, \mathsf{fma}\left(-2, y, z\right) \cdot 0.0212463641547976\right)\right), x, -0.0424927283095952 \cdot z\right)} \]

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\frac{-1000000000}{23533438303} \cdot y + x \cdot \left(\left(\frac{500000000}{23533438303} \cdot y + \frac{156699607947000000000}{553822718361107519809} \cdot y\right) - \frac{137519416416}{23533438303}\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 98.7%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.3041881842569256, y, -5.843575199059173\right), x, -0.0424927283095952 \cdot y\right), x, -0.0424927283095952 \cdot z\right) \]

   9. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\frac{-1000000000}{23533438303} \cdot y, x, \frac{-1000000000}{23533438303} \cdot z\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 93.5%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.03 \lor \neg \left(x \leq 2\right):\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.0424927283095952 \cdot y, x, -0.0424927283095952 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 79.0% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.225 \lor \neg \left(x \leq 1.65 \cdot 10^{-9}\right):\\ \;\;\;\;4.16438922228 \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-5.843575199059173 \cdot x, x, -0.0424927283095952 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.225) (not (<= x 1.65e-9)))
   (* 4.16438922228 (- x 2.0))
   (fma (* -5.843575199059173 x) x (* -0.0424927283095952 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.225) || !(x <= 1.65e-9)) {
		tmp = 4.16438922228 * (x - 2.0);
	} else {
		tmp = fma((-5.843575199059173 * x), x, (-0.0424927283095952 * z));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.225) || !(x <= 1.65e-9))
		tmp = Float64(4.16438922228 * Float64(x - 2.0));
	else
		tmp = fma(Float64(-5.843575199059173 * x), x, Float64(-0.0424927283095952 * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.225], N[Not[LessEqual[x, 1.65e-9]], $MachinePrecision]], N[(4.16438922228 * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(-5.843575199059173 * x), $MachinePrecision] * x + N[(-0.0424927283095952 * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.225000000000000006 or 1.65000000000000009e-9 < x

   1. Initial program 18.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. 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 20.5%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 91.4%

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

   if -0.225000000000000006 < x < 1.65000000000000009e-9

   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

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z + x \cdot \left(\left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \left(\frac{-131752537360500000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)\right)\right)\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)} \]

   5. Applied rewrites 98.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(0.28294182010212804, z, \mathsf{fma}\left(\mathsf{fma}\left(0.23789659216289816, z, \mathsf{fma}\left(-6.658593866711955, \mathsf{fma}\left(0.28294182010212804, z, \mathsf{fma}\left(-2, y, z\right) \cdot 0.0212463641547976\right), \mathsf{fma}\left(0.0212463641547976, y, -5.843575199059173\right)\right)\right), x, \mathsf{fma}\left(-2, y, z\right) \cdot 0.0212463641547976\right)\right), x, -0.0424927283095952 \cdot z\right)} \]

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\frac{-1000000000}{23533438303} \cdot y + x \cdot \left(\left(\frac{500000000}{23533438303} \cdot y + \frac{156699607947000000000}{553822718361107519809} \cdot y\right) - \frac{137519416416}{23533438303}\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 98.1%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.3041881842569256, y, -5.843575199059173\right), x, -0.0424927283095952 \cdot y\right), x, -0.0424927283095952 \cdot z\right) \]

   9. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(\frac{-137519416416}{23533438303} \cdot x, x, \frac{-1000000000}{23533438303} \cdot z\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 71.4%

       \[\leadsto \mathsf{fma}\left(-5.843575199059173 \cdot x, x, -0.0424927283095952 \cdot z\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.225 \lor \neg \left(x \leq 1.65 \cdot 10^{-9}\right):\\ \;\;\;\;4.16438922228 \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-5.843575199059173 \cdot x, x, -0.0424927283095952 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 89.2% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.03:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\mathsf{fma}\left(-0.0424927283095952 \cdot y, x, -0.0424927283095952 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot \left(x - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.03)
   (* 4.16438922228 x)
   (if (<= x 2.0)
     (fma (* -0.0424927283095952 y) x (* -0.0424927283095952 z))
     (* 4.16438922228 (- x 2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.03) {
		tmp = 4.16438922228 * x;
	} else if (x <= 2.0) {
		tmp = fma((-0.0424927283095952 * y), x, (-0.0424927283095952 * z));
	} else {
		tmp = 4.16438922228 * (x - 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.03)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 2.0)
		tmp = fma(Float64(-0.0424927283095952 * y), x, Float64(-0.0424927283095952 * z));
	else
		tmp = Float64(4.16438922228 * Float64(x - 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.03], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 2.0], N[(N[(-0.0424927283095952 * y), $MachinePrecision] * x + N[(-0.0424927283095952 * z), $MachinePrecision]), $MachinePrecision], N[(4.16438922228 * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.029999999999999999

   1. Initial program 15.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing
   3. 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 19.4%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 92.0

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

   7. Applied rewrites 92.0%

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

   if -0.029999999999999999 < x < 2

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z + x \cdot \left(\left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \left(\frac{-131752537360500000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)\right)\right)\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)} \]

   5. Applied rewrites 99.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(0.28294182010212804, z, \mathsf{fma}\left(\mathsf{fma}\left(0.23789659216289816, z, \mathsf{fma}\left(-6.658593866711955, \mathsf{fma}\left(0.28294182010212804, z, \mathsf{fma}\left(-2, y, z\right) \cdot 0.0212463641547976\right), \mathsf{fma}\left(0.0212463641547976, y, -5.843575199059173\right)\right)\right), x, \mathsf{fma}\left(-2, y, z\right) \cdot 0.0212463641547976\right)\right), x, -0.0424927283095952 \cdot z\right)} \]

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\frac{-1000000000}{23533438303} \cdot y + x \cdot \left(\left(\frac{500000000}{23533438303} \cdot y + \frac{156699607947000000000}{553822718361107519809} \cdot y\right) - \frac{137519416416}{23533438303}\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 98.7%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.3041881842569256, y, -5.843575199059173\right), x, -0.0424927283095952 \cdot y\right), x, -0.0424927283095952 \cdot z\right) \]

   9. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\frac{-1000000000}{23533438303} \cdot y, x, \frac{-1000000000}{23533438303} \cdot z\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 93.5%

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

   if 2 < x

   1. Initial program 21.9%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing
   3. 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 21.9%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 90.7%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.03:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\mathsf{fma}\left(-0.0424927283095952 \cdot y, x, -0.0424927283095952 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot \left(x - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 76.8% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0295:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 14500:\\ \;\;\;\;\left(0.0212463641547976 \cdot z\right) \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot \left(x - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.0295)
   (* 4.16438922228 x)
   (if (<= x 14500.0)
     (* (* 0.0212463641547976 z) (- x 2.0))
     (* 4.16438922228 (- x 2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.0295) {
		tmp = 4.16438922228 * x;
	} else if (x <= 14500.0) {
		tmp = (0.0212463641547976 * z) * (x - 2.0);
	} else {
		tmp = 4.16438922228 * (x - 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-0.0295d0)) then
        tmp = 4.16438922228d0 * x
    else if (x <= 14500.0d0) then
        tmp = (0.0212463641547976d0 * z) * (x - 2.0d0)
    else
        tmp = 4.16438922228d0 * (x - 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.0295) {
		tmp = 4.16438922228 * x;
	} else if (x <= 14500.0) {
		tmp = (0.0212463641547976 * z) * (x - 2.0);
	} else {
		tmp = 4.16438922228 * (x - 2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.0295:
		tmp = 4.16438922228 * x
	elif x <= 14500.0:
		tmp = (0.0212463641547976 * z) * (x - 2.0)
	else:
		tmp = 4.16438922228 * (x - 2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.0295)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 14500.0)
		tmp = Float64(Float64(0.0212463641547976 * z) * Float64(x - 2.0));
	else
		tmp = Float64(4.16438922228 * Float64(x - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.0295)
		tmp = 4.16438922228 * x;
	elseif (x <= 14500.0)
		tmp = (0.0212463641547976 * z) * (x - 2.0);
	else
		tmp = 4.16438922228 * (x - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.0295], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 14500.0], N[(N[(0.0212463641547976 * z), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], N[(4.16438922228 * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.029499999999999998

   1. Initial program 15.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing
   3. 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 19.4%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 92.0

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

   7. Applied rewrites 92.0%

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

   if -0.029499999999999998 < x < 14500

   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. 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 99.7%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 66.1

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

   7. Applied rewrites 66.1%

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

   if 14500 < x

   1. Initial program 20.3%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. 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 20.3%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 92.5%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0295:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 14500:\\ \;\;\;\;\left(0.0212463641547976 \cdot z\right) \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot \left(x - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 76.8% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0295:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-9}:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot \left(x - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.0295)
   (* 4.16438922228 x)
   (if (<= x 1.65e-9) (* -0.0424927283095952 z) (* 4.16438922228 (- x 2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.0295) {
		tmp = 4.16438922228 * x;
	} else if (x <= 1.65e-9) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = 4.16438922228 * (x - 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-0.0295d0)) then
        tmp = 4.16438922228d0 * x
    else if (x <= 1.65d-9) then
        tmp = (-0.0424927283095952d0) * z
    else
        tmp = 4.16438922228d0 * (x - 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.0295) {
		tmp = 4.16438922228 * x;
	} else if (x <= 1.65e-9) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = 4.16438922228 * (x - 2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.0295:
		tmp = 4.16438922228 * x
	elif x <= 1.65e-9:
		tmp = -0.0424927283095952 * z
	else:
		tmp = 4.16438922228 * (x - 2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.0295)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 1.65e-9)
		tmp = Float64(-0.0424927283095952 * z);
	else
		tmp = Float64(4.16438922228 * Float64(x - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.0295)
		tmp = 4.16438922228 * x;
	elseif (x <= 1.65e-9)
		tmp = -0.0424927283095952 * z;
	else
		tmp = 4.16438922228 * (x - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.0295], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 1.65e-9], N[(-0.0424927283095952 * z), $MachinePrecision], N[(4.16438922228 * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.029499999999999998

   1. Initial program 15.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing
   3. 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 19.4%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 92.0

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

   7. Applied rewrites 92.0%

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

   if -0.029499999999999998 < x < 1.65000000000000009e-9

   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

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

      1. lower-*.f64 66.9

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

   5. Applied rewrites 66.9%

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

   if 1.65000000000000009e-9 < x

   1. Initial program 23.4%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   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 23.4%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 89.1%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0295:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-9}:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot \left(x - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 76.6% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0295 \lor \neg \left(x \leq 2.15 \cdot 10^{-16}\right):\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.0295) (not (<= x 2.15e-16)))
   (* 4.16438922228 x)
   (* -0.0424927283095952 z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.0295) || !(x <= 2.15e-16)) {
		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 <= (-0.0295d0)) .or. (.not. (x <= 2.15d-16))) 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 <= -0.0295) || !(x <= 2.15e-16)) {
		tmp = 4.16438922228 * x;
	} else {
		tmp = -0.0424927283095952 * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.0295) or not (x <= 2.15e-16):
		tmp = 4.16438922228 * x
	else:
		tmp = -0.0424927283095952 * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.0295) || !(x <= 2.15e-16))
		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 <= -0.0295) || ~((x <= 2.15e-16)))
		tmp = 4.16438922228 * x;
	else
		tmp = -0.0424927283095952 * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.0295], N[Not[LessEqual[x, 2.15e-16]], $MachinePrecision]], N[(4.16438922228 * x), $MachinePrecision], N[(-0.0424927283095952 * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.029499999999999998 or 2.1499999999999999e-16 < x

   1. Initial program 19.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing
   3. 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 21.8%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 89.9

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

   7. Applied rewrites 89.9%

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

   if -0.029499999999999998 < x < 2.1499999999999999e-16

   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

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

      1. lower-*.f64 67.4

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

   5. Applied rewrites 67.4%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0295 \lor \neg \left(x \leq 2.15 \cdot 10^{-16}\right):\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 45.7% accurate, 13.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 62.7%

   \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
2. Add Preprocessing
3. 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 63.8%

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

5. Taylor expanded in x around inf

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

   1. lower-*.f64 43.4

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

7. Applied rewrites 43.4%

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

8. Final simplification 43.4%

   \[\leadsto 4.16438922228 \cdot x \]
9. 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 2024324 
(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)))