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

Percentage Accurate: 58.5% → 98.6%

Time: 17.3s

Alternatives: 17

Speedup: 5.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 58.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)\\ \mathbf{if}\;x \leq -1.1 \cdot 10^{+41}:\\ \;\;\;\;\left(\left(\frac{3655.1204654076414}{x} + x \cdot 4.16438922228\right) + \frac{y - 130977.50649958357}{x \cdot x}\right) + -110.1139242984811\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+44}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)}{t_0} + \frac{z}{t_0}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{-101.7851458539211}{x} - \left(\frac{124074.40615218398 - y}{{x}^{3}} - \left(4.16438922228 + \frac{3451.550173699799}{x \cdot x}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          47.066876606
          (*
           x
           (+
            313.399215894
            (* x (+ 263.505074721 (* x (+ x 43.3400022514)))))))))
   (if (<= x -1.1e+41)
     (+
      (+
       (+ (/ 3655.1204654076414 x) (* x 4.16438922228))
       (/ (- y 130977.50649958357) (* x x)))
      -110.1139242984811)
     (if (<= x 2.6e+44)
       (*
        (+ x -2.0)
        (+
         (/
          (*
           x
           (+
            y
            (*
             x
             (+ 137.519416416 (* x (+ (* x 4.16438922228) 78.6994924154))))))
          t_0)
         (/ z t_0)))
       (*
        (+ x -2.0)
        (-
         (/ -101.7851458539211 x)
         (-
          (/ (- 124074.40615218398 y) (pow x 3.0))
          (+ 4.16438922228 (/ 3451.550173699799 (* x x))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 47.066876606 + (x * (313.399215894 + (x * (263.505074721 + (x * (x + 43.3400022514))))));
	double tmp;
	if (x <= -1.1e+41) {
		tmp = (((3655.1204654076414 / x) + (x * 4.16438922228)) + ((y - 130977.50649958357) / (x * x))) + -110.1139242984811;
	} else if (x <= 2.6e+44) {
		tmp = (x + -2.0) * (((x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))))) / t_0) + (z / t_0));
	} else {
		tmp = (x + -2.0) * ((-101.7851458539211 / x) - (((124074.40615218398 - y) / pow(x, 3.0)) - (4.16438922228 + (3451.550173699799 / (x * x)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 47.066876606d0 + (x * (313.399215894d0 + (x * (263.505074721d0 + (x * (x + 43.3400022514d0))))))
    if (x <= (-1.1d+41)) then
        tmp = (((3655.1204654076414d0 / x) + (x * 4.16438922228d0)) + ((y - 130977.50649958357d0) / (x * x))) + (-110.1139242984811d0)
    else if (x <= 2.6d+44) then
        tmp = (x + (-2.0d0)) * (((x * (y + (x * (137.519416416d0 + (x * ((x * 4.16438922228d0) + 78.6994924154d0)))))) / t_0) + (z / t_0))
    else
        tmp = (x + (-2.0d0)) * (((-101.7851458539211d0) / x) - (((124074.40615218398d0 - y) / (x ** 3.0d0)) - (4.16438922228d0 + (3451.550173699799d0 / (x * x)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 47.066876606 + (x * (313.399215894 + (x * (263.505074721 + (x * (x + 43.3400022514))))));
	double tmp;
	if (x <= -1.1e+41) {
		tmp = (((3655.1204654076414 / x) + (x * 4.16438922228)) + ((y - 130977.50649958357) / (x * x))) + -110.1139242984811;
	} else if (x <= 2.6e+44) {
		tmp = (x + -2.0) * (((x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))))) / t_0) + (z / t_0));
	} else {
		tmp = (x + -2.0) * ((-101.7851458539211 / x) - (((124074.40615218398 - y) / Math.pow(x, 3.0)) - (4.16438922228 + (3451.550173699799 / (x * x)))));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 47.066876606 + (x * (313.399215894 + (x * (263.505074721 + (x * (x + 43.3400022514))))))
	tmp = 0
	if x <= -1.1e+41:
		tmp = (((3655.1204654076414 / x) + (x * 4.16438922228)) + ((y - 130977.50649958357) / (x * x))) + -110.1139242984811
	elif x <= 2.6e+44:
		tmp = (x + -2.0) * (((x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))))) / t_0) + (z / t_0))
	else:
		tmp = (x + -2.0) * ((-101.7851458539211 / x) - (((124074.40615218398 - y) / math.pow(x, 3.0)) - (4.16438922228 + (3451.550173699799 / (x * x)))))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(x * Float64(263.505074721 + Float64(x * Float64(x + 43.3400022514)))))))
	tmp = 0.0
	if (x <= -1.1e+41)
		tmp = Float64(Float64(Float64(Float64(3655.1204654076414 / x) + Float64(x * 4.16438922228)) + Float64(Float64(y - 130977.50649958357) / Float64(x * x))) + -110.1139242984811);
	elseif (x <= 2.6e+44)
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(Float64(x * Float64(y + Float64(x * Float64(137.519416416 + Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)))))) / t_0) + Float64(z / t_0)));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(-101.7851458539211 / x) - Float64(Float64(Float64(124074.40615218398 - y) / (x ^ 3.0)) - Float64(4.16438922228 + Float64(3451.550173699799 / Float64(x * x))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 47.066876606 + (x * (313.399215894 + (x * (263.505074721 + (x * (x + 43.3400022514))))));
	tmp = 0.0;
	if (x <= -1.1e+41)
		tmp = (((3655.1204654076414 / x) + (x * 4.16438922228)) + ((y - 130977.50649958357) / (x * x))) + -110.1139242984811;
	elseif (x <= 2.6e+44)
		tmp = (x + -2.0) * (((x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))))) / t_0) + (z / t_0));
	else
		tmp = (x + -2.0) * ((-101.7851458539211 / x) - (((124074.40615218398 - y) / (x ^ 3.0)) - (4.16438922228 + (3451.550173699799 / (x * x)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(47.066876606 + N[(x * N[(313.399215894 + N[(x * N[(263.505074721 + N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.1e+41], N[(N[(N[(N[(3655.1204654076414 / x), $MachinePrecision] + N[(x * 4.16438922228), $MachinePrecision]), $MachinePrecision] + N[(N[(y - 130977.50649958357), $MachinePrecision] / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -110.1139242984811), $MachinePrecision], If[LessEqual[x, 2.6e+44], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(N[(x * N[(y + N[(x * N[(137.519416416 + N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision] + N[(z / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(-101.7851458539211 / x), $MachinePrecision] - N[(N[(N[(124074.40615218398 - y), $MachinePrecision] / N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision] - N[(4.16438922228 + N[(3451.550173699799 / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.09999999999999995e41

   1. Initial program 3.9%

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

      1. associate-*r/ 5.6%

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

      2. sub-neg 5.6%

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

      3. metadata-eval 5.6%

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

      4. *-commutative 5.6%

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

      5. fma-def 5.6%

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

      6. *-commutative 5.6%

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

      7. fma-def 5.6%

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

      8. *-commutative 5.6%

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

      9. fma-def 5.6%

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

      10. fma-def 5.6%

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

      11. *-commutative 5.6%

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

   3. Simplified 5.6%

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

   4. Taylor expanded in x around -inf 99.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} + \left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) - 110.1139242984811} \]
   5. Step-by-step derivation

      1. sub-neg 99.2%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} + \left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) + \left(-110.1139242984811\right)} \]

      2. +-commutative 99.2%

         \[\leadsto \color{blue}{\left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) + -1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)} + \left(-110.1139242984811\right) \]

      3. mul-1-neg 99.2%

         \[\leadsto \left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) + \color{blue}{\left(-\frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)}\right) + \left(-110.1139242984811\right) \]

      4. unsub-neg 99.2%

         \[\leadsto \color{blue}{\left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)} + \left(-110.1139242984811\right) \]

      5. *-commutative 99.2%

         \[\leadsto \left(\left(\color{blue}{x \cdot 4.16438922228} + 3655.1204654076414 \cdot \frac{1}{x}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      6. fma-def 99.2%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 3655.1204654076414 \cdot \frac{1}{x}\right)} - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      7. associate-*r/ 99.2%

         \[\leadsto \left(\mathsf{fma}\left(x, 4.16438922228, \color{blue}{\frac{3655.1204654076414 \cdot 1}{x}}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      8. metadata-eval 99.2%

         \[\leadsto \left(\mathsf{fma}\left(x, 4.16438922228, \frac{\color{blue}{3655.1204654076414}}{x}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      9. mul-1-neg 99.2%

         \[\leadsto \left(\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \frac{130977.50649958357 + \color{blue}{\left(-y\right)}}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      10. unsub-neg 99.2%

          \[\leadsto \left(\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \frac{\color{blue}{130977.50649958357 - y}}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      11. unpow2 99.2%

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

      12. metadata-eval 99.2%

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

   6. Simplified 99.2%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \frac{130977.50649958357 - y}{x \cdot x}\right) + -110.1139242984811} \]
   7. Step-by-step derivation

      1. fma-udef 99.2%

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

      2. *-commutative 99.2%

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

      3. div-inv 99.2%

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

      4. +-commutative 99.2%

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

      5. div-inv 99.2%

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

   8. Applied egg-rr 99.2%

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

   if -1.09999999999999995e41 < x < 2.5999999999999999e44

   1. Initial program 98.2%

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

      1. associate-*r/ 99.5%

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

      2. sub-neg 99.5%

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

      3. metadata-eval 99.5%

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

      4. *-commutative 99.5%

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

      5. fma-def 99.5%

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

      6. *-commutative 99.5%

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

      7. fma-def 99.5%

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

      8. *-commutative 99.5%

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

      9. fma-def 99.5%

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

      10. fma-def 99.5%

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

      11. *-commutative 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in z around 0 99.5%

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

   if 2.5999999999999999e44 < x

   1. Initial program 7.4%

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

      1. associate-*r/ 14.2%

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

      2. sub-neg 14.2%

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

      3. metadata-eval 14.2%

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

      4. *-commutative 14.2%

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

      5. fma-def 14.2%

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

      6. *-commutative 14.2%

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

      7. fma-def 14.2%

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

      8. *-commutative 14.2%

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

      9. fma-def 14.2%

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

      10. fma-def 14.2%

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

      11. *-commutative 14.2%

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

   3. Simplified 14.2%

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

   4. Taylor expanded in x around -inf 99.3%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(\left(-1 \cdot \frac{124074.40615218398 + -1 \cdot y}{{x}^{3}} + \left(4.16438922228 + 3451.550173699799 \cdot \frac{1}{{x}^{2}}\right)\right) - 101.7851458539211 \cdot \frac{1}{x}\right)} \]
   5. Step-by-step derivation

      1. sub-neg 99.3%

         \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(\left(-1 \cdot \frac{124074.40615218398 + -1 \cdot y}{{x}^{3}} + \left(4.16438922228 + 3451.550173699799 \cdot \frac{1}{{x}^{2}}\right)\right) + \left(-101.7851458539211 \cdot \frac{1}{x}\right)\right)} \]

      2. +-commutative 99.3%

         \[\leadsto \left(x + -2\right) \cdot \left(\color{blue}{\left(\left(4.16438922228 + 3451.550173699799 \cdot \frac{1}{{x}^{2}}\right) + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{{x}^{3}}\right)} + \left(-101.7851458539211 \cdot \frac{1}{x}\right)\right) \]

      3. mul-1-neg 99.3%

         \[\leadsto \left(x + -2\right) \cdot \left(\left(\left(4.16438922228 + 3451.550173699799 \cdot \frac{1}{{x}^{2}}\right) + \color{blue}{\left(-\frac{124074.40615218398 + -1 \cdot y}{{x}^{3}}\right)}\right) + \left(-101.7851458539211 \cdot \frac{1}{x}\right)\right) \]

      4. unsub-neg 99.3%

         \[\leadsto \left(x + -2\right) \cdot \left(\color{blue}{\left(\left(4.16438922228 + 3451.550173699799 \cdot \frac{1}{{x}^{2}}\right) - \frac{124074.40615218398 + -1 \cdot y}{{x}^{3}}\right)} + \left(-101.7851458539211 \cdot \frac{1}{x}\right)\right) \]

      5. associate-*r/ 99.3%

         \[\leadsto \left(x + -2\right) \cdot \left(\left(\left(4.16438922228 + \color{blue}{\frac{3451.550173699799 \cdot 1}{{x}^{2}}}\right) - \frac{124074.40615218398 + -1 \cdot y}{{x}^{3}}\right) + \left(-101.7851458539211 \cdot \frac{1}{x}\right)\right) \]

      6. metadata-eval 99.3%

         \[\leadsto \left(x + -2\right) \cdot \left(\left(\left(4.16438922228 + \frac{\color{blue}{3451.550173699799}}{{x}^{2}}\right) - \frac{124074.40615218398 + -1 \cdot y}{{x}^{3}}\right) + \left(-101.7851458539211 \cdot \frac{1}{x}\right)\right) \]

      7. unpow2 99.3%

         \[\leadsto \left(x + -2\right) \cdot \left(\left(\left(4.16438922228 + \frac{3451.550173699799}{\color{blue}{x \cdot x}}\right) - \frac{124074.40615218398 + -1 \cdot y}{{x}^{3}}\right) + \left(-101.7851458539211 \cdot \frac{1}{x}\right)\right) \]

      8. mul-1-neg 99.3%

         \[\leadsto \left(x + -2\right) \cdot \left(\left(\left(4.16438922228 + \frac{3451.550173699799}{x \cdot x}\right) - \frac{124074.40615218398 + \color{blue}{\left(-y\right)}}{{x}^{3}}\right) + \left(-101.7851458539211 \cdot \frac{1}{x}\right)\right) \]

      9. unsub-neg 99.3%

         \[\leadsto \left(x + -2\right) \cdot \left(\left(\left(4.16438922228 + \frac{3451.550173699799}{x \cdot x}\right) - \frac{\color{blue}{124074.40615218398 - y}}{{x}^{3}}\right) + \left(-101.7851458539211 \cdot \frac{1}{x}\right)\right) \]

      10. associate-*r/ 99.3%

          \[\leadsto \left(x + -2\right) \cdot \left(\left(\left(4.16438922228 + \frac{3451.550173699799}{x \cdot x}\right) - \frac{124074.40615218398 - y}{{x}^{3}}\right) + \left(-\color{blue}{\frac{101.7851458539211 \cdot 1}{x}}\right)\right) \]

      11. metadata-eval 99.3%

          \[\leadsto \left(x + -2\right) \cdot \left(\left(\left(4.16438922228 + \frac{3451.550173699799}{x \cdot x}\right) - \frac{124074.40615218398 - y}{{x}^{3}}\right) + \left(-\frac{\color{blue}{101.7851458539211}}{x}\right)\right) \]

      12. distribute-neg-frac 99.3%

          \[\leadsto \left(x + -2\right) \cdot \left(\left(\left(4.16438922228 + \frac{3451.550173699799}{x \cdot x}\right) - \frac{124074.40615218398 - y}{{x}^{3}}\right) + \color{blue}{\frac{-101.7851458539211}{x}}\right) \]

      13. metadata-eval 99.3%

          \[\leadsto \left(x + -2\right) \cdot \left(\left(\left(4.16438922228 + \frac{3451.550173699799}{x \cdot x}\right) - \frac{124074.40615218398 - y}{{x}^{3}}\right) + \frac{\color{blue}{-101.7851458539211}}{x}\right) \]

   6. Simplified 99.3%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+41}:\\ \;\;\;\;\left(\left(\frac{3655.1204654076414}{x} + x \cdot 4.16438922228\right) + \frac{y - 130977.50649958357}{x \cdot x}\right) + -110.1139242984811\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+44}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)} + \frac{z}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{-101.7851458539211}{x} - \left(\frac{124074.40615218398 - y}{{x}^{3}} - \left(4.16438922228 + \frac{3451.550173699799}{x \cdot x}\right)\right)\right)\\ \end{array} \]

Alternative 2: 97.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)}\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;\frac{y}{x \cdot x}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+289}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\frac{3655.1204654076414}{x} + x \cdot 4.16438922228\right) + \frac{y - 130977.50649958357}{x \cdot x}\right) + -110.1139242984811\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (/
          (*
           (- x 2.0)
           (+
            z
            (*
             x
             (+
              y
              (*
               x
               (+
                137.519416416
                (* x (+ (* x 4.16438922228) 78.6994924154))))))))
          (+
           47.066876606
           (*
            x
            (+
             313.399215894
             (* x (+ 263.505074721 (* x (+ x 43.3400022514))))))))))
   (if (<= t_0 (- INFINITY))
     (/ y (* x x))
     (if (<= t_0 5e+289)
       t_0
       (+
        (+
         (+ (/ 3655.1204654076414 x) (* x 4.16438922228))
         (/ (- y 130977.50649958357) (* x x)))
        -110.1139242984811)))))

C

double code(double x, double y, double z) {
	double t_0 = ((x - 2.0) * (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))))))) / (47.066876606 + (x * (313.399215894 + (x * (263.505074721 + (x * (x + 43.3400022514)))))));
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = y / (x * x);
	} else if (t_0 <= 5e+289) {
		tmp = t_0;
	} else {
		tmp = (((3655.1204654076414 / x) + (x * 4.16438922228)) + ((y - 130977.50649958357) / (x * x))) + -110.1139242984811;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = ((x - 2.0) * (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))))))) / (47.066876606 + (x * (313.399215894 + (x * (263.505074721 + (x * (x + 43.3400022514)))))));
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = y / (x * x);
	} else if (t_0 <= 5e+289) {
		tmp = t_0;
	} else {
		tmp = (((3655.1204654076414 / x) + (x * 4.16438922228)) + ((y - 130977.50649958357) / (x * x))) + -110.1139242984811;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((x - 2.0) * (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))))))) / (47.066876606 + (x * (313.399215894 + (x * (263.505074721 + (x * (x + 43.3400022514)))))))
	tmp = 0
	if t_0 <= -math.inf:
		tmp = y / (x * x)
	elif t_0 <= 5e+289:
		tmp = t_0
	else:
		tmp = (((3655.1204654076414 / x) + (x * 4.16438922228)) + ((y - 130977.50649958357) / (x * x))) + -110.1139242984811
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(x - 2.0) * Float64(z + Float64(x * Float64(y + Float64(x * Float64(137.519416416 + Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)))))))) / Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(x * Float64(263.505074721 + Float64(x * Float64(x + 43.3400022514))))))))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = Float64(y / Float64(x * x));
	elseif (t_0 <= 5e+289)
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(Float64(3655.1204654076414 / x) + Float64(x * 4.16438922228)) + Float64(Float64(y - 130977.50649958357) / Float64(x * x))) + -110.1139242984811);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((x - 2.0) * (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))))))) / (47.066876606 + (x * (313.399215894 + (x * (263.505074721 + (x * (x + 43.3400022514)))))));
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = y / (x * x);
	elseif (t_0 <= 5e+289)
		tmp = t_0;
	else
		tmp = (((3655.1204654076414 / x) + (x * 4.16438922228)) + ((y - 130977.50649958357) / (x * x))) + -110.1139242984811;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(x - 2.0), $MachinePrecision] * N[(z + N[(x * N[(y + N[(x * N[(137.519416416 + N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(47.066876606 + N[(x * N[(313.399215894 + N[(x * N[(263.505074721 + N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], N[(y / N[(x * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+289], t$95$0, N[(N[(N[(N[(3655.1204654076414 / x), $MachinePrecision] + N[(x * 4.16438922228), $MachinePrecision]), $MachinePrecision] + N[(N[(y - 130977.50649958357), $MachinePrecision] / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -110.1139242984811), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 4.5%

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

      1. associate-*r/ 20.3%

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

      2. sub-neg 20.3%

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

      3. metadata-eval 20.3%

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

      4. *-commutative 20.3%

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

      5. fma-def 20.3%

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

      6. *-commutative 20.3%

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

      7. fma-def 20.3%

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

      8. *-commutative 20.3%

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

      9. fma-def 20.3%

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

      10. fma-def 20.3%

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

      11. *-commutative 20.3%

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

   3. Simplified 20.3%

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

   4. Taylor expanded in y around inf 20.3%

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

   5. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{\frac{y}{{x}^{2}}} \]
   6. Step-by-step derivation

      1. unpow2 100.0%

         \[\leadsto \frac{y}{\color{blue}{x \cdot x}} \]

   7. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{y}{x \cdot x}} \]

   if -inf.0 < (/.f64 (*.f64 (-.f64 x 2) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000)) < 5.00000000000000031e289

   1. Initial program 99.5%

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

   if 5.00000000000000031e289 < (/.f64 (*.f64 (-.f64 x 2) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000))

   1. Initial program 0.2%

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

      1. associate-*r/ 5.8%

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

      2. sub-neg 5.8%

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

      3. metadata-eval 5.8%

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

      4. *-commutative 5.8%

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

      5. fma-def 5.8%

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

      6. *-commutative 5.8%

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

      7. fma-def 5.8%

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

      8. *-commutative 5.8%

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

      9. fma-def 5.8%

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

      10. fma-def 5.8%

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

      11. *-commutative 5.8%

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

   3. Simplified 5.8%

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

   4. Taylor expanded in x around -inf 98.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} + \left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) - 110.1139242984811} \]
   5. Step-by-step derivation

      1. sub-neg 98.2%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} + \left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) + \left(-110.1139242984811\right)} \]

      2. +-commutative 98.2%

         \[\leadsto \color{blue}{\left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) + -1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)} + \left(-110.1139242984811\right) \]

      3. mul-1-neg 98.2%

         \[\leadsto \left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) + \color{blue}{\left(-\frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)}\right) + \left(-110.1139242984811\right) \]

      4. unsub-neg 98.2%

         \[\leadsto \color{blue}{\left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)} + \left(-110.1139242984811\right) \]

      5. *-commutative 98.2%

         \[\leadsto \left(\left(\color{blue}{x \cdot 4.16438922228} + 3655.1204654076414 \cdot \frac{1}{x}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      6. fma-def 98.2%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 3655.1204654076414 \cdot \frac{1}{x}\right)} - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      7. associate-*r/ 98.2%

         \[\leadsto \left(\mathsf{fma}\left(x, 4.16438922228, \color{blue}{\frac{3655.1204654076414 \cdot 1}{x}}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      8. metadata-eval 98.2%

         \[\leadsto \left(\mathsf{fma}\left(x, 4.16438922228, \frac{\color{blue}{3655.1204654076414}}{x}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      9. mul-1-neg 98.2%

         \[\leadsto \left(\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \frac{130977.50649958357 + \color{blue}{\left(-y\right)}}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      10. unsub-neg 98.2%

          \[\leadsto \left(\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \frac{\color{blue}{130977.50649958357 - y}}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      11. unpow2 98.2%

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

      12. metadata-eval 98.2%

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

   6. Simplified 98.2%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \frac{130977.50649958357 - y}{x \cdot x}\right) + -110.1139242984811} \]
   7. Step-by-step derivation

      1. fma-udef 98.2%

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

      2. *-commutative 98.2%

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

      3. div-inv 98.2%

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

      4. +-commutative 98.2%

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

      5. div-inv 98.2%

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

   8. Applied egg-rr 98.2%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)} \leq -\infty:\\ \;\;\;\;\frac{y}{x \cdot x}\\ \mathbf{elif}\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)} \leq 5 \cdot 10^{+289}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\frac{3655.1204654076414}{x} + x \cdot 4.16438922228\right) + \frac{y - 130977.50649958357}{x \cdot x}\right) + -110.1139242984811\\ \end{array} \]

Alternative 3: 98.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)\\ \mathbf{if}\;x \leq -2.15 \cdot 10^{+44} \lor \neg \left(x \leq 1.7 \cdot 10^{+44}\right):\\ \;\;\;\;\left(\left(\frac{3655.1204654076414}{x} + x \cdot 4.16438922228\right) + \frac{y - 130977.50649958357}{x \cdot x}\right) + -110.1139242984811\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)}{t_0} + \frac{z}{t_0}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          47.066876606
          (*
           x
           (+
            313.399215894
            (* x (+ 263.505074721 (* x (+ x 43.3400022514)))))))))
   (if (or (<= x -2.15e+44) (not (<= x 1.7e+44)))
     (+
      (+
       (+ (/ 3655.1204654076414 x) (* x 4.16438922228))
       (/ (- y 130977.50649958357) (* x x)))
      -110.1139242984811)
     (*
      (+ x -2.0)
      (+
       (/
        (*
         x
         (+
          y
          (* x (+ 137.519416416 (* x (+ (* x 4.16438922228) 78.6994924154))))))
        t_0)
       (/ z t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = 47.066876606 + (x * (313.399215894 + (x * (263.505074721 + (x * (x + 43.3400022514))))));
	double tmp;
	if ((x <= -2.15e+44) || !(x <= 1.7e+44)) {
		tmp = (((3655.1204654076414 / x) + (x * 4.16438922228)) + ((y - 130977.50649958357) / (x * x))) + -110.1139242984811;
	} else {
		tmp = (x + -2.0) * (((x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))))) / t_0) + (z / 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 = 47.066876606d0 + (x * (313.399215894d0 + (x * (263.505074721d0 + (x * (x + 43.3400022514d0))))))
    if ((x <= (-2.15d+44)) .or. (.not. (x <= 1.7d+44))) then
        tmp = (((3655.1204654076414d0 / x) + (x * 4.16438922228d0)) + ((y - 130977.50649958357d0) / (x * x))) + (-110.1139242984811d0)
    else
        tmp = (x + (-2.0d0)) * (((x * (y + (x * (137.519416416d0 + (x * ((x * 4.16438922228d0) + 78.6994924154d0)))))) / t_0) + (z / t_0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 47.066876606 + (x * (313.399215894 + (x * (263.505074721 + (x * (x + 43.3400022514))))));
	double tmp;
	if ((x <= -2.15e+44) || !(x <= 1.7e+44)) {
		tmp = (((3655.1204654076414 / x) + (x * 4.16438922228)) + ((y - 130977.50649958357) / (x * x))) + -110.1139242984811;
	} else {
		tmp = (x + -2.0) * (((x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))))) / t_0) + (z / t_0));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 47.066876606 + (x * (313.399215894 + (x * (263.505074721 + (x * (x + 43.3400022514))))))
	tmp = 0
	if (x <= -2.15e+44) or not (x <= 1.7e+44):
		tmp = (((3655.1204654076414 / x) + (x * 4.16438922228)) + ((y - 130977.50649958357) / (x * x))) + -110.1139242984811
	else:
		tmp = (x + -2.0) * (((x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))))) / t_0) + (z / t_0))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(x * Float64(263.505074721 + Float64(x * Float64(x + 43.3400022514)))))))
	tmp = 0.0
	if ((x <= -2.15e+44) || !(x <= 1.7e+44))
		tmp = Float64(Float64(Float64(Float64(3655.1204654076414 / x) + Float64(x * 4.16438922228)) + Float64(Float64(y - 130977.50649958357) / Float64(x * x))) + -110.1139242984811);
	else
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(Float64(x * Float64(y + Float64(x * Float64(137.519416416 + Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)))))) / t_0) + Float64(z / t_0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 47.066876606 + (x * (313.399215894 + (x * (263.505074721 + (x * (x + 43.3400022514))))));
	tmp = 0.0;
	if ((x <= -2.15e+44) || ~((x <= 1.7e+44)))
		tmp = (((3655.1204654076414 / x) + (x * 4.16438922228)) + ((y - 130977.50649958357) / (x * x))) + -110.1139242984811;
	else
		tmp = (x + -2.0) * (((x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))))) / t_0) + (z / t_0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(47.066876606 + N[(x * N[(313.399215894 + N[(x * N[(263.505074721 + N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -2.15e+44], N[Not[LessEqual[x, 1.7e+44]], $MachinePrecision]], N[(N[(N[(N[(3655.1204654076414 / x), $MachinePrecision] + N[(x * 4.16438922228), $MachinePrecision]), $MachinePrecision] + N[(N[(y - 130977.50649958357), $MachinePrecision] / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -110.1139242984811), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(N[(x * N[(y + N[(x * N[(137.519416416 + N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision] + N[(z / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.14999999999999991e44 or 1.7e44 < x

   1. Initial program 5.6%

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

      1. associate-*r/ 9.8%

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

      2. sub-neg 9.8%

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

      3. metadata-eval 9.8%

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

      4. *-commutative 9.8%

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

      5. fma-def 9.8%

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

      6. *-commutative 9.8%

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

      7. fma-def 9.8%

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

      8. *-commutative 9.8%

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

      9. fma-def 9.8%

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

      10. fma-def 9.8%

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

      11. *-commutative 9.8%

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

   3. Simplified 9.8%

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

   4. Taylor expanded in x around -inf 99.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} + \left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) - 110.1139242984811} \]
   5. Step-by-step derivation

      1. sub-neg 99.2%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} + \left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) + \left(-110.1139242984811\right)} \]

      2. +-commutative 99.2%

         \[\leadsto \color{blue}{\left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) + -1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)} + \left(-110.1139242984811\right) \]

      3. mul-1-neg 99.2%

         \[\leadsto \left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) + \color{blue}{\left(-\frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)}\right) + \left(-110.1139242984811\right) \]

      4. unsub-neg 99.2%

         \[\leadsto \color{blue}{\left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)} + \left(-110.1139242984811\right) \]

      5. *-commutative 99.2%

         \[\leadsto \left(\left(\color{blue}{x \cdot 4.16438922228} + 3655.1204654076414 \cdot \frac{1}{x}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      6. fma-def 99.2%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 3655.1204654076414 \cdot \frac{1}{x}\right)} - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      7. associate-*r/ 99.2%

         \[\leadsto \left(\mathsf{fma}\left(x, 4.16438922228, \color{blue}{\frac{3655.1204654076414 \cdot 1}{x}}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      8. metadata-eval 99.2%

         \[\leadsto \left(\mathsf{fma}\left(x, 4.16438922228, \frac{\color{blue}{3655.1204654076414}}{x}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      9. mul-1-neg 99.2%

         \[\leadsto \left(\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \frac{130977.50649958357 + \color{blue}{\left(-y\right)}}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      10. unsub-neg 99.2%

          \[\leadsto \left(\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \frac{\color{blue}{130977.50649958357 - y}}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      11. unpow2 99.2%

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

      12. metadata-eval 99.2%

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

   6. Simplified 99.2%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \frac{130977.50649958357 - y}{x \cdot x}\right) + -110.1139242984811} \]
   7. Step-by-step derivation

      1. fma-udef 99.2%

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

      2. *-commutative 99.2%

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

      3. div-inv 99.2%

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

      4. +-commutative 99.2%

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

      5. div-inv 99.2%

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

   8. Applied egg-rr 99.2%

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

   if -2.14999999999999991e44 < x < 1.7e44

   1. Initial program 98.2%

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

      1. associate-*r/ 99.5%

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

      2. sub-neg 99.5%

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

      3. metadata-eval 99.5%

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

      4. *-commutative 99.5%

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

      5. fma-def 99.5%

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

      6. *-commutative 99.5%

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

      7. fma-def 99.5%

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

      8. *-commutative 99.5%

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

      9. fma-def 99.5%

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

      10. fma-def 99.5%

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

      11. *-commutative 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in z around 0 99.5%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+44} \lor \neg \left(x \leq 1.7 \cdot 10^{+44}\right):\\ \;\;\;\;\left(\left(\frac{3655.1204654076414}{x} + x \cdot 4.16438922228\right) + \frac{y - 130977.50649958357}{x \cdot x}\right) + -110.1139242984811\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)} + \frac{z}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)}\right)\\ \end{array} \]

Alternative 4: 96.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+32} \lor \neg \left(x \leq 4.2 \cdot 10^{+26}\right):\\ \;\;\;\;\left(\left(\frac{3655.1204654076414}{x} + x \cdot 4.16438922228\right) + \frac{y - 130977.50649958357}{x \cdot x}\right) + -110.1139242984811\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + \left(x \cdot x\right) \cdot \left(x + 43.3400022514\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.8e+32) (not (<= x 4.2e+26)))
   (+
    (+
     (+ (/ 3655.1204654076414 x) (* x 4.16438922228))
     (/ (- y 130977.50649958357) (* x x)))
    -110.1139242984811)
   (/
    (*
     (- x 2.0)
     (+
      z
      (*
       x
       (+
        y
        (* x (+ 137.519416416 (* x (+ (* x 4.16438922228) 78.6994924154))))))))
    (+ 47.066876606 (* x (+ 313.399215894 (* (* x x) (+ x 43.3400022514))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.8e+32) || !(x <= 4.2e+26)) {
		tmp = (((3655.1204654076414 / x) + (x * 4.16438922228)) + ((y - 130977.50649958357) / (x * x))) + -110.1139242984811;
	} else {
		tmp = ((x - 2.0) * (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))))))) / (47.066876606 + (x * (313.399215894 + ((x * x) * (x + 43.3400022514)))));
	}
	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 <= (-1.8d+32)) .or. (.not. (x <= 4.2d+26))) then
        tmp = (((3655.1204654076414d0 / x) + (x * 4.16438922228d0)) + ((y - 130977.50649958357d0) / (x * x))) + (-110.1139242984811d0)
    else
        tmp = ((x - 2.0d0) * (z + (x * (y + (x * (137.519416416d0 + (x * ((x * 4.16438922228d0) + 78.6994924154d0)))))))) / (47.066876606d0 + (x * (313.399215894d0 + ((x * x) * (x + 43.3400022514d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.8e+32) || !(x <= 4.2e+26)) {
		tmp = (((3655.1204654076414 / x) + (x * 4.16438922228)) + ((y - 130977.50649958357) / (x * x))) + -110.1139242984811;
	} else {
		tmp = ((x - 2.0) * (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))))))) / (47.066876606 + (x * (313.399215894 + ((x * x) * (x + 43.3400022514)))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.8e+32) or not (x <= 4.2e+26):
		tmp = (((3655.1204654076414 / x) + (x * 4.16438922228)) + ((y - 130977.50649958357) / (x * x))) + -110.1139242984811
	else:
		tmp = ((x - 2.0) * (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))))))) / (47.066876606 + (x * (313.399215894 + ((x * x) * (x + 43.3400022514)))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.8e+32) || !(x <= 4.2e+26))
		tmp = Float64(Float64(Float64(Float64(3655.1204654076414 / x) + Float64(x * 4.16438922228)) + Float64(Float64(y - 130977.50649958357) / Float64(x * x))) + -110.1139242984811);
	else
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(z + Float64(x * Float64(y + Float64(x * Float64(137.519416416 + Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)))))))) / Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(Float64(x * x) * Float64(x + 43.3400022514))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.8e+32) || ~((x <= 4.2e+26)))
		tmp = (((3655.1204654076414 / x) + (x * 4.16438922228)) + ((y - 130977.50649958357) / (x * x))) + -110.1139242984811;
	else
		tmp = ((x - 2.0) * (z + (x * (y + (x * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))))))) / (47.066876606 + (x * (313.399215894 + ((x * x) * (x + 43.3400022514)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.8e+32], N[Not[LessEqual[x, 4.2e+26]], $MachinePrecision]], N[(N[(N[(N[(3655.1204654076414 / x), $MachinePrecision] + N[(x * 4.16438922228), $MachinePrecision]), $MachinePrecision] + N[(N[(y - 130977.50649958357), $MachinePrecision] / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -110.1139242984811), $MachinePrecision], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(z + N[(x * N[(y + N[(x * N[(137.519416416 + N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(47.066876606 + N[(x * N[(313.399215894 + N[(N[(x * x), $MachinePrecision] * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7999999999999998e32 or 4.2000000000000002e26 < x

   1. Initial program 9.5%

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

      1. associate-*r/ 15.1%

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

      2. sub-neg 15.1%

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

      3. metadata-eval 15.1%

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

      4. *-commutative 15.1%

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

      5. fma-def 15.1%

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

      6. *-commutative 15.1%

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

      7. fma-def 15.1%

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

      8. *-commutative 15.1%

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

      9. fma-def 15.1%

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

      10. fma-def 15.1%

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

      11. *-commutative 15.1%

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

   3. Simplified 15.1%

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

   4. Taylor expanded in x around -inf 97.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} + \left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) - 110.1139242984811} \]
   5. Step-by-step derivation

      1. sub-neg 97.7%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} + \left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) + \left(-110.1139242984811\right)} \]

      2. +-commutative 97.7%

         \[\leadsto \color{blue}{\left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) + -1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)} + \left(-110.1139242984811\right) \]

      3. mul-1-neg 97.7%

         \[\leadsto \left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) + \color{blue}{\left(-\frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)}\right) + \left(-110.1139242984811\right) \]

      4. unsub-neg 97.7%

         \[\leadsto \color{blue}{\left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)} + \left(-110.1139242984811\right) \]

      5. *-commutative 97.7%

         \[\leadsto \left(\left(\color{blue}{x \cdot 4.16438922228} + 3655.1204654076414 \cdot \frac{1}{x}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      6. fma-def 97.7%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 3655.1204654076414 \cdot \frac{1}{x}\right)} - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      7. associate-*r/ 97.7%

         \[\leadsto \left(\mathsf{fma}\left(x, 4.16438922228, \color{blue}{\frac{3655.1204654076414 \cdot 1}{x}}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      8. metadata-eval 97.7%

         \[\leadsto \left(\mathsf{fma}\left(x, 4.16438922228, \frac{\color{blue}{3655.1204654076414}}{x}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      9. mul-1-neg 97.7%

         \[\leadsto \left(\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \frac{130977.50649958357 + \color{blue}{\left(-y\right)}}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      10. unsub-neg 97.7%

          \[\leadsto \left(\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \frac{\color{blue}{130977.50649958357 - y}}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      11. unpow2 97.7%

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

      12. metadata-eval 97.7%

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

   6. Simplified 97.7%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \frac{130977.50649958357 - y}{x \cdot x}\right) + -110.1139242984811} \]
   7. Step-by-step derivation

      1. fma-udef 97.7%

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

      2. *-commutative 97.7%

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

      3. div-inv 97.7%

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

      4. +-commutative 97.7%

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

      5. div-inv 97.7%

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

   8. Applied egg-rr 97.7%

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

   if -1.7999999999999998e32 < x < 4.2000000000000002e26

   1. Initial program 99.5%

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

   2. Taylor expanded in x around inf 97.0%

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

      1. cube-mult 97.0%

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

      2. unpow2 97.0%

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

      3. distribute-rgt-out 97.0%

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

      4. +-commutative 97.0%

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

      5. unpow2 97.0%

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

   4. Simplified 97.0%

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\color{blue}{\left(x \cdot x\right) \cdot \left(x + 43.3400022514\right)} + 313.399215894\right) \cdot x + 47.066876606} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+32} \lor \neg \left(x \leq 4.2 \cdot 10^{+26}\right):\\ \;\;\;\;\left(\left(\frac{3655.1204654076414}{x} + x \cdot 4.16438922228\right) + \frac{y - 130977.50649958357}{x \cdot x}\right) + -110.1139242984811\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + \left(x \cdot x\right) \cdot \left(x + 43.3400022514\right)\right)}\\ \end{array} \]

Alternative 5: 96.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7500000000000 \lor \neg \left(x \leq 25000\right):\\ \;\;\;\;\left(\left(\frac{3655.1204654076414}{x} + x \cdot 4.16438922228\right) + \frac{y - 130977.50649958357}{x \cdot x}\right) + -110.1139242984811\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7500000000000.0) (not (<= x 25000.0)))
   (+
    (+
     (+ (/ 3655.1204654076414 x) (* x 4.16438922228))
     (/ (- y 130977.50649958357) (* x x)))
    -110.1139242984811)
   (/
    (* (- x 2.0) (+ z (* x (+ y (* x 137.519416416)))))
    (+
     47.066876606
     (*
      x
      (+ 313.399215894 (* x (+ 263.505074721 (* x (+ x 43.3400022514))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7500000000000.0) || !(x <= 25000.0)) {
		tmp = (((3655.1204654076414 / x) + (x * 4.16438922228)) + ((y - 130977.50649958357) / (x * x))) + -110.1139242984811;
	} else {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * (313.399215894 + (x * (263.505074721 + (x * (x + 43.3400022514)))))));
	}
	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 <= (-7500000000000.0d0)) .or. (.not. (x <= 25000.0d0))) then
        tmp = (((3655.1204654076414d0 / x) + (x * 4.16438922228d0)) + ((y - 130977.50649958357d0) / (x * x))) + (-110.1139242984811d0)
    else
        tmp = ((x - 2.0d0) * (z + (x * (y + (x * 137.519416416d0))))) / (47.066876606d0 + (x * (313.399215894d0 + (x * (263.505074721d0 + (x * (x + 43.3400022514d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7500000000000.0) || !(x <= 25000.0)) {
		tmp = (((3655.1204654076414 / x) + (x * 4.16438922228)) + ((y - 130977.50649958357) / (x * x))) + -110.1139242984811;
	} else {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * (313.399215894 + (x * (263.505074721 + (x * (x + 43.3400022514)))))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7500000000000.0) or not (x <= 25000.0):
		tmp = (((3655.1204654076414 / x) + (x * 4.16438922228)) + ((y - 130977.50649958357) / (x * x))) + -110.1139242984811
	else:
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * (313.399215894 + (x * (263.505074721 + (x * (x + 43.3400022514)))))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7500000000000.0) || !(x <= 25000.0))
		tmp = Float64(Float64(Float64(Float64(3655.1204654076414 / x) + Float64(x * 4.16438922228)) + Float64(Float64(y - 130977.50649958357) / Float64(x * x))) + -110.1139242984811);
	else
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(z + Float64(x * Float64(y + Float64(x * 137.519416416))))) / Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(x * Float64(263.505074721 + Float64(x * Float64(x + 43.3400022514))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -7500000000000.0) || ~((x <= 25000.0)))
		tmp = (((3655.1204654076414 / x) + (x * 4.16438922228)) + ((y - 130977.50649958357) / (x * x))) + -110.1139242984811;
	else
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * (313.399215894 + (x * (263.505074721 + (x * (x + 43.3400022514)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7500000000000.0], N[Not[LessEqual[x, 25000.0]], $MachinePrecision]], N[(N[(N[(N[(3655.1204654076414 / x), $MachinePrecision] + N[(x * 4.16438922228), $MachinePrecision]), $MachinePrecision] + N[(N[(y - 130977.50649958357), $MachinePrecision] / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -110.1139242984811), $MachinePrecision], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(z + N[(x * N[(y + N[(x * 137.519416416), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(47.066876606 + N[(x * N[(313.399215894 + N[(x * N[(263.505074721 + N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.5e12 or 25000 < x

   1. Initial program 15.7%

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

      1. associate-*r/ 20.9%

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

      2. sub-neg 20.9%

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

      3. metadata-eval 20.9%

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

      4. *-commutative 20.9%

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

      5. fma-def 20.9%

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

      6. *-commutative 20.9%

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

      7. fma-def 20.9%

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

      8. *-commutative 20.9%

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

      9. fma-def 20.9%

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

      10. fma-def 20.9%

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

      11. *-commutative 20.9%

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

   3. Simplified 20.9%

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

   4. Taylor expanded in x around -inf 95.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} + \left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) - 110.1139242984811} \]
   5. Step-by-step derivation

      1. sub-neg 95.7%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} + \left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) + \left(-110.1139242984811\right)} \]

      2. +-commutative 95.7%

         \[\leadsto \color{blue}{\left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) + -1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)} + \left(-110.1139242984811\right) \]

      3. mul-1-neg 95.7%

         \[\leadsto \left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) + \color{blue}{\left(-\frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)}\right) + \left(-110.1139242984811\right) \]

      4. unsub-neg 95.7%

         \[\leadsto \color{blue}{\left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)} + \left(-110.1139242984811\right) \]

      5. *-commutative 95.7%

         \[\leadsto \left(\left(\color{blue}{x \cdot 4.16438922228} + 3655.1204654076414 \cdot \frac{1}{x}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      6. fma-def 95.7%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 3655.1204654076414 \cdot \frac{1}{x}\right)} - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      7. associate-*r/ 95.7%

         \[\leadsto \left(\mathsf{fma}\left(x, 4.16438922228, \color{blue}{\frac{3655.1204654076414 \cdot 1}{x}}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      8. metadata-eval 95.7%

         \[\leadsto \left(\mathsf{fma}\left(x, 4.16438922228, \frac{\color{blue}{3655.1204654076414}}{x}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      9. mul-1-neg 95.7%

         \[\leadsto \left(\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \frac{130977.50649958357 + \color{blue}{\left(-y\right)}}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      10. unsub-neg 95.7%

          \[\leadsto \left(\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \frac{\color{blue}{130977.50649958357 - y}}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      11. unpow2 95.7%

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

      12. metadata-eval 95.7%

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

   6. Simplified 95.7%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \frac{130977.50649958357 - y}{x \cdot x}\right) + -110.1139242984811} \]
   7. Step-by-step derivation

      1. fma-udef 95.7%

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

      2. *-commutative 95.7%

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

      3. div-inv 95.7%

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

      4. +-commutative 95.7%

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

      5. div-inv 95.7%

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

   8. Applied egg-rr 95.7%

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

   if -7.5e12 < x < 25000

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 98.1%

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

      1. *-commutative 98.1%

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

   4. Simplified 98.1%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7500000000000 \lor \neg \left(x \leq 25000\right):\\ \;\;\;\;\left(\left(\frac{3655.1204654076414}{x} + x \cdot 4.16438922228\right) + \frac{y - 130977.50649958357}{x \cdot x}\right) + -110.1139242984811\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)}\\ \end{array} \]

Alternative 6: 93.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1800 \lor \neg \left(x \leq 5600\right):\\ \;\;\;\;\left(\left(\frac{3655.1204654076414}{x} + x \cdot 4.16438922228\right) + \frac{y - 130977.50649958357}{x \cdot x}\right) + -110.1139242984811\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{z}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)} + 0.0212463641547976 \cdot \left(x \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1800.0) (not (<= x 5600.0)))
   (+
    (+
     (+ (/ 3655.1204654076414 x) (* x 4.16438922228))
     (/ (- y 130977.50649958357) (* x x)))
    -110.1139242984811)
   (*
    (+ x -2.0)
    (+
     (/
      z
      (+
       47.066876606
       (*
        x
        (+ 313.399215894 (* x (+ 263.505074721 (* x (+ x 43.3400022514))))))))
     (* 0.0212463641547976 (* x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1800.0) || !(x <= 5600.0)) {
		tmp = (((3655.1204654076414 / x) + (x * 4.16438922228)) + ((y - 130977.50649958357) / (x * x))) + -110.1139242984811;
	} else {
		tmp = (x + -2.0) * ((z / (47.066876606 + (x * (313.399215894 + (x * (263.505074721 + (x * (x + 43.3400022514)))))))) + (0.0212463641547976 * (x * y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1800.0d0)) .or. (.not. (x <= 5600.0d0))) then
        tmp = (((3655.1204654076414d0 / x) + (x * 4.16438922228d0)) + ((y - 130977.50649958357d0) / (x * x))) + (-110.1139242984811d0)
    else
        tmp = (x + (-2.0d0)) * ((z / (47.066876606d0 + (x * (313.399215894d0 + (x * (263.505074721d0 + (x * (x + 43.3400022514d0)))))))) + (0.0212463641547976d0 * (x * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1800.0) || !(x <= 5600.0)) {
		tmp = (((3655.1204654076414 / x) + (x * 4.16438922228)) + ((y - 130977.50649958357) / (x * x))) + -110.1139242984811;
	} else {
		tmp = (x + -2.0) * ((z / (47.066876606 + (x * (313.399215894 + (x * (263.505074721 + (x * (x + 43.3400022514)))))))) + (0.0212463641547976 * (x * y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1800.0) or not (x <= 5600.0):
		tmp = (((3655.1204654076414 / x) + (x * 4.16438922228)) + ((y - 130977.50649958357) / (x * x))) + -110.1139242984811
	else:
		tmp = (x + -2.0) * ((z / (47.066876606 + (x * (313.399215894 + (x * (263.505074721 + (x * (x + 43.3400022514)))))))) + (0.0212463641547976 * (x * y)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1800.0) || !(x <= 5600.0))
		tmp = Float64(Float64(Float64(Float64(3655.1204654076414 / x) + Float64(x * 4.16438922228)) + Float64(Float64(y - 130977.50649958357) / Float64(x * x))) + -110.1139242984811);
	else
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(z / Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(x * Float64(263.505074721 + Float64(x * Float64(x + 43.3400022514)))))))) + Float64(0.0212463641547976 * Float64(x * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1800.0) || ~((x <= 5600.0)))
		tmp = (((3655.1204654076414 / x) + (x * 4.16438922228)) + ((y - 130977.50649958357) / (x * x))) + -110.1139242984811;
	else
		tmp = (x + -2.0) * ((z / (47.066876606 + (x * (313.399215894 + (x * (263.505074721 + (x * (x + 43.3400022514)))))))) + (0.0212463641547976 * (x * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1800.0], N[Not[LessEqual[x, 5600.0]], $MachinePrecision]], N[(N[(N[(N[(3655.1204654076414 / x), $MachinePrecision] + N[(x * 4.16438922228), $MachinePrecision]), $MachinePrecision] + N[(N[(y - 130977.50649958357), $MachinePrecision] / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -110.1139242984811), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(z / N[(47.066876606 + N[(x * N[(313.399215894 + N[(x * N[(263.505074721 + N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.0212463641547976 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1800 or 5600 < x

   1. Initial program 16.4%

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

      1. associate-*r/ 21.5%

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

      2. sub-neg 21.5%

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

      3. metadata-eval 21.5%

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

      4. *-commutative 21.5%

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

      5. fma-def 21.5%

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

      6. *-commutative 21.5%

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

      7. fma-def 21.5%

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

      8. *-commutative 21.5%

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

      9. fma-def 21.5%

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

      10. fma-def 21.5%

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

      11. *-commutative 21.5%

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

   3. Simplified 21.5%

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

   4. Taylor expanded in x around -inf 95.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} + \left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) - 110.1139242984811} \]
   5. Step-by-step derivation

      1. sub-neg 95.5%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} + \left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) + \left(-110.1139242984811\right)} \]

      2. +-commutative 95.5%

         \[\leadsto \color{blue}{\left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) + -1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)} + \left(-110.1139242984811\right) \]

      3. mul-1-neg 95.5%

         \[\leadsto \left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) + \color{blue}{\left(-\frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)}\right) + \left(-110.1139242984811\right) \]

      4. unsub-neg 95.5%

         \[\leadsto \color{blue}{\left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)} + \left(-110.1139242984811\right) \]

      5. *-commutative 95.5%

         \[\leadsto \left(\left(\color{blue}{x \cdot 4.16438922228} + 3655.1204654076414 \cdot \frac{1}{x}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      6. fma-def 95.5%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 3655.1204654076414 \cdot \frac{1}{x}\right)} - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      7. associate-*r/ 95.5%

         \[\leadsto \left(\mathsf{fma}\left(x, 4.16438922228, \color{blue}{\frac{3655.1204654076414 \cdot 1}{x}}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      8. metadata-eval 95.5%

         \[\leadsto \left(\mathsf{fma}\left(x, 4.16438922228, \frac{\color{blue}{3655.1204654076414}}{x}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      9. mul-1-neg 95.5%

         \[\leadsto \left(\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \frac{130977.50649958357 + \color{blue}{\left(-y\right)}}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      10. unsub-neg 95.5%

          \[\leadsto \left(\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \frac{\color{blue}{130977.50649958357 - y}}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      11. unpow2 95.5%

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

      12. metadata-eval 95.5%

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

   6. Simplified 95.5%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \frac{130977.50649958357 - y}{x \cdot x}\right) + -110.1139242984811} \]
   7. Step-by-step derivation

      1. fma-udef 95.5%

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

      2. *-commutative 95.5%

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

      3. div-inv 95.5%

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

      4. +-commutative 95.5%

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

      5. div-inv 95.5%

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

   8. Applied egg-rr 95.5%

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

   if -1800 < x < 5600

   1. Initial program 99.6%

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

      1. associate-*r/ 99.6%

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

      2. sub-neg 99.6%

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

      3. metadata-eval 99.6%

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

      4. *-commutative 99.6%

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

      5. fma-def 99.6%

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

      6. *-commutative 99.6%

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

      7. fma-def 99.6%

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

      8. *-commutative 99.6%

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

      9. fma-def 99.6%

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

      10. fma-def 99.6%

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

      11. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around 0 99.6%

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

   5. Taylor expanded in x around 0 89.8%

      \[\leadsto \left(x + -2\right) \cdot \left(\color{blue}{0.0212463641547976 \cdot \left(y \cdot x\right)} + \frac{z}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1800 \lor \neg \left(x \leq 5600\right):\\ \;\;\;\;\left(\left(\frac{3655.1204654076414}{x} + x \cdot 4.16438922228\right) + \frac{y - 130977.50649958357}{x \cdot x}\right) + -110.1139242984811\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{z}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)} + 0.0212463641547976 \cdot \left(x \cdot y\right)\right)\\ \end{array} \]

Alternative 7: 92.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.19 \lor \neg \left(x \leq 4.2 \cdot 10^{-9}\right):\\ \;\;\;\;\left(\left(\frac{3655.1204654076414}{x} + x \cdot 4.16438922228\right) + \frac{y - 130977.50649958357}{x \cdot x}\right) + -110.1139242984811\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + x \cdot \left(y \cdot 0.0212463641547976 - z \cdot 0.14147091005106402\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.19) (not (<= x 4.2e-9)))
   (+
    (+
     (+ (/ 3655.1204654076414 x) (* x 4.16438922228))
     (/ (- y 130977.50649958357) (* x x)))
    -110.1139242984811)
   (*
    (+ x -2.0)
    (+
     (* z 0.0212463641547976)
     (* x (- (* y 0.0212463641547976) (* z 0.14147091005106402)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.19) || !(x <= 4.2e-9)) {
		tmp = (((3655.1204654076414 / x) + (x * 4.16438922228)) + ((y - 130977.50649958357) / (x * x))) + -110.1139242984811;
	} else {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) - (z * 0.14147091005106402))));
	}
	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 <= (-0.19d0)) .or. (.not. (x <= 4.2d-9))) then
        tmp = (((3655.1204654076414d0 / x) + (x * 4.16438922228d0)) + ((y - 130977.50649958357d0) / (x * x))) + (-110.1139242984811d0)
    else
        tmp = (x + (-2.0d0)) * ((z * 0.0212463641547976d0) + (x * ((y * 0.0212463641547976d0) - (z * 0.14147091005106402d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.19) || !(x <= 4.2e-9)) {
		tmp = (((3655.1204654076414 / x) + (x * 4.16438922228)) + ((y - 130977.50649958357) / (x * x))) + -110.1139242984811;
	} else {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) - (z * 0.14147091005106402))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.19) or not (x <= 4.2e-9):
		tmp = (((3655.1204654076414 / x) + (x * 4.16438922228)) + ((y - 130977.50649958357) / (x * x))) + -110.1139242984811
	else:
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) - (z * 0.14147091005106402))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.19) || !(x <= 4.2e-9))
		tmp = Float64(Float64(Float64(Float64(3655.1204654076414 / x) + Float64(x * 4.16438922228)) + Float64(Float64(y - 130977.50649958357) / Float64(x * x))) + -110.1139242984811);
	else
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(z * 0.0212463641547976) + Float64(x * Float64(Float64(y * 0.0212463641547976) - Float64(z * 0.14147091005106402)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -0.19) || ~((x <= 4.2e-9)))
		tmp = (((3655.1204654076414 / x) + (x * 4.16438922228)) + ((y - 130977.50649958357) / (x * x))) + -110.1139242984811;
	else
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) - (z * 0.14147091005106402))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.19], N[Not[LessEqual[x, 4.2e-9]], $MachinePrecision]], N[(N[(N[(N[(3655.1204654076414 / x), $MachinePrecision] + N[(x * 4.16438922228), $MachinePrecision]), $MachinePrecision] + N[(N[(y - 130977.50649958357), $MachinePrecision] / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -110.1139242984811), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(z * 0.0212463641547976), $MachinePrecision] + N[(x * N[(N[(y * 0.0212463641547976), $MachinePrecision] - N[(z * 0.14147091005106402), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.19 or 4.20000000000000039e-9 < x

   1. Initial program 19.4%

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

      1. associate-*r/ 24.3%

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

      2. sub-neg 24.3%

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

      3. metadata-eval 24.3%

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

      4. *-commutative 24.3%

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

      5. fma-def 24.3%

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

      6. *-commutative 24.3%

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

      7. fma-def 24.3%

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

      8. *-commutative 24.3%

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

      9. fma-def 24.3%

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

      10. fma-def 24.3%

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

      11. *-commutative 24.3%

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

   3. Simplified 24.3%

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

   4. Taylor expanded in x around -inf 92.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} + \left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) - 110.1139242984811} \]
   5. Step-by-step derivation

      1. sub-neg 92.6%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} + \left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) + \left(-110.1139242984811\right)} \]

      2. +-commutative 92.6%

         \[\leadsto \color{blue}{\left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) + -1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)} + \left(-110.1139242984811\right) \]

      3. mul-1-neg 92.6%

         \[\leadsto \left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) + \color{blue}{\left(-\frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)}\right) + \left(-110.1139242984811\right) \]

      4. unsub-neg 92.6%

         \[\leadsto \color{blue}{\left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)} + \left(-110.1139242984811\right) \]

      5. *-commutative 92.6%

         \[\leadsto \left(\left(\color{blue}{x \cdot 4.16438922228} + 3655.1204654076414 \cdot \frac{1}{x}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      6. fma-def 92.6%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 3655.1204654076414 \cdot \frac{1}{x}\right)} - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      7. associate-*r/ 92.6%

         \[\leadsto \left(\mathsf{fma}\left(x, 4.16438922228, \color{blue}{\frac{3655.1204654076414 \cdot 1}{x}}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      8. metadata-eval 92.6%

         \[\leadsto \left(\mathsf{fma}\left(x, 4.16438922228, \frac{\color{blue}{3655.1204654076414}}{x}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      9. mul-1-neg 92.6%

         \[\leadsto \left(\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \frac{130977.50649958357 + \color{blue}{\left(-y\right)}}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      10. unsub-neg 92.6%

          \[\leadsto \left(\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \frac{\color{blue}{130977.50649958357 - y}}{{x}^{2}}\right) + \left(-110.1139242984811\right) \]

      11. unpow2 92.6%

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

      12. metadata-eval 92.6%

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

   6. Simplified 92.6%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \frac{130977.50649958357 - y}{x \cdot x}\right) + -110.1139242984811} \]
   7. Step-by-step derivation

      1. fma-udef 92.6%

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

      2. *-commutative 92.6%

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

      3. div-inv 92.6%

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

      4. +-commutative 92.6%

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

      5. div-inv 92.6%

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

   8. Applied egg-rr 92.6%

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

   if -0.19 < x < 4.20000000000000039e-9

   1. Initial program 99.6%

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

      1. associate-*r/ 99.7%

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

      2. sub-neg 99.7%

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

      3. metadata-eval 99.7%

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

      4. *-commutative 99.7%

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

      5. fma-def 99.6%

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

      6. *-commutative 99.6%

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

      7. fma-def 99.6%

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

      8. *-commutative 99.6%

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

      9. fma-def 99.6%

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

      10. fma-def 99.6%

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

      11. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 92.3%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(0.0212463641547976 \cdot z + \left(0.0212463641547976 \cdot y - 0.14147091005106402 \cdot z\right) \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.19 \lor \neg \left(x \leq 4.2 \cdot 10^{-9}\right):\\ \;\;\;\;\left(\left(\frac{3655.1204654076414}{x} + x \cdot 4.16438922228\right) + \frac{y - 130977.50649958357}{x \cdot x}\right) + -110.1139242984811\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + x \cdot \left(y \cdot 0.0212463641547976 - z \cdot 0.14147091005106402\right)\right)\\ \end{array} \]

Alternative 8: 89.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -21000000000:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{elif}\;x \leq 44:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + x \cdot \left(y \cdot 0.0212463641547976 - z \cdot 0.14147091005106402\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{\frac{5.86923874282773}{x} + \left(0.24013125253755718 - \frac{55.572073733743466}{x \cdot x}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -21000000000.0)
   (/ (+ x -2.0) (+ 0.24013125253755718 (/ 5.86923874282773 x)))
   (if (<= x 44.0)
     (*
      (+ x -2.0)
      (+
       (* z 0.0212463641547976)
       (* x (- (* y 0.0212463641547976) (* z 0.14147091005106402)))))
     (/
      (+ x -2.0)
      (+
       (/ 5.86923874282773 x)
       (- 0.24013125253755718 (/ 55.572073733743466 (* x x))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -21000000000.0) {
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x));
	} else if (x <= 44.0) {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) - (z * 0.14147091005106402))));
	} else {
		tmp = (x + -2.0) / ((5.86923874282773 / x) + (0.24013125253755718 - (55.572073733743466 / (x * x))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-21000000000.0d0)) then
        tmp = (x + (-2.0d0)) / (0.24013125253755718d0 + (5.86923874282773d0 / x))
    else if (x <= 44.0d0) then
        tmp = (x + (-2.0d0)) * ((z * 0.0212463641547976d0) + (x * ((y * 0.0212463641547976d0) - (z * 0.14147091005106402d0))))
    else
        tmp = (x + (-2.0d0)) / ((5.86923874282773d0 / x) + (0.24013125253755718d0 - (55.572073733743466d0 / (x * x))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -21000000000.0) {
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x));
	} else if (x <= 44.0) {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) - (z * 0.14147091005106402))));
	} else {
		tmp = (x + -2.0) / ((5.86923874282773 / x) + (0.24013125253755718 - (55.572073733743466 / (x * x))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -21000000000.0:
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x))
	elif x <= 44.0:
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) - (z * 0.14147091005106402))))
	else:
		tmp = (x + -2.0) / ((5.86923874282773 / x) + (0.24013125253755718 - (55.572073733743466 / (x * x))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -21000000000.0)
		tmp = Float64(Float64(x + -2.0) / Float64(0.24013125253755718 + Float64(5.86923874282773 / x)));
	elseif (x <= 44.0)
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(z * 0.0212463641547976) + Float64(x * Float64(Float64(y * 0.0212463641547976) - Float64(z * 0.14147091005106402)))));
	else
		tmp = Float64(Float64(x + -2.0) / Float64(Float64(5.86923874282773 / x) + Float64(0.24013125253755718 - Float64(55.572073733743466 / Float64(x * x)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -21000000000.0)
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x));
	elseif (x <= 44.0)
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) - (z * 0.14147091005106402))));
	else
		tmp = (x + -2.0) / ((5.86923874282773 / x) + (0.24013125253755718 - (55.572073733743466 / (x * x))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -21000000000.0], N[(N[(x + -2.0), $MachinePrecision] / N[(0.24013125253755718 + N[(5.86923874282773 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 44.0], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(z * 0.0212463641547976), $MachinePrecision] + N[(x * N[(N[(y * 0.0212463641547976), $MachinePrecision] - N[(z * 0.14147091005106402), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] / N[(N[(5.86923874282773 / x), $MachinePrecision] + N[(0.24013125253755718 - N[(55.572073733743466 / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.1e10

   1. Initial program 14.1%

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

      1. associate-/l* 17.0%

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

      2. sub-neg 17.0%

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

      3. metadata-eval 17.0%

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

      4. fma-def 17.0%

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

      5. fma-def 17.0%

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

      6. fma-def 17.0%

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

      7. fma-def 17.0%

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

      8. fma-def 17.0%

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

      9. fma-def 17.0%

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

      10. fma-def 17.0%

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

   3. Simplified 17.0%

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

   4. Taylor expanded in x around inf 85.0%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718 + 5.86923874282773 \cdot \frac{1}{x}}} \]
   5. Step-by-step derivation

      1. associate-*r/ 85.0%

         \[\leadsto \frac{x + -2}{0.24013125253755718 + \color{blue}{\frac{5.86923874282773 \cdot 1}{x}}} \]

      2. metadata-eval 85.0%

         \[\leadsto \frac{x + -2}{0.24013125253755718 + \frac{\color{blue}{5.86923874282773}}{x}} \]

   6. Simplified 85.0%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718 + \frac{5.86923874282773}{x}}} \]

   if -2.1e10 < x < 44

   1. Initial program 99.6%

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

      1. associate-*r/ 99.6%

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

      2. sub-neg 99.6%

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

      3. metadata-eval 99.6%

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

      4. *-commutative 99.6%

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

      5. fma-def 99.6%

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

      6. *-commutative 99.6%

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

      7. fma-def 99.6%

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

      8. *-commutative 99.6%

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

      9. fma-def 99.6%

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

      10. fma-def 99.6%

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

      11. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 89.6%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(0.0212463641547976 \cdot z + \left(0.0212463641547976 \cdot y - 0.14147091005106402 \cdot z\right) \cdot x\right)} \]

   if 44 < x

   1. Initial program 19.8%

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

      1. associate-/l* 27.0%

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

      2. sub-neg 27.0%

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

      3. metadata-eval 27.0%

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

      4. fma-def 27.0%

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

      5. fma-def 27.0%

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

      6. fma-def 27.0%

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

      7. fma-def 27.0%

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

      8. fma-def 27.0%

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

      9. fma-def 27.0%

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

      10. fma-def 27.0%

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

   3. Simplified 27.0%

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

   4. Taylor expanded in x around inf 88.9%

      \[\leadsto \frac{x + -2}{\color{blue}{\left(0.24013125253755718 + 5.86923874282773 \cdot \frac{1}{x}\right) - 55.572073733743466 \cdot \frac{1}{{x}^{2}}}} \]
   5. Step-by-step derivation

      1. +-commutative 88.9%

         \[\leadsto \frac{x + -2}{\color{blue}{\left(5.86923874282773 \cdot \frac{1}{x} + 0.24013125253755718\right)} - 55.572073733743466 \cdot \frac{1}{{x}^{2}}} \]

      2. associate--l+ 88.9%

         \[\leadsto \frac{x + -2}{\color{blue}{5.86923874282773 \cdot \frac{1}{x} + \left(0.24013125253755718 - 55.572073733743466 \cdot \frac{1}{{x}^{2}}\right)}} \]

      3. associate-*r/ 88.9%

         \[\leadsto \frac{x + -2}{\color{blue}{\frac{5.86923874282773 \cdot 1}{x}} + \left(0.24013125253755718 - 55.572073733743466 \cdot \frac{1}{{x}^{2}}\right)} \]

      4. metadata-eval 88.9%

         \[\leadsto \frac{x + -2}{\frac{\color{blue}{5.86923874282773}}{x} + \left(0.24013125253755718 - 55.572073733743466 \cdot \frac{1}{{x}^{2}}\right)} \]

      5. associate-*r/ 88.9%

         \[\leadsto \frac{x + -2}{\frac{5.86923874282773}{x} + \left(0.24013125253755718 - \color{blue}{\frac{55.572073733743466 \cdot 1}{{x}^{2}}}\right)} \]

      6. metadata-eval 88.9%

         \[\leadsto \frac{x + -2}{\frac{5.86923874282773}{x} + \left(0.24013125253755718 - \frac{\color{blue}{55.572073733743466}}{{x}^{2}}\right)} \]

      7. unpow2 88.9%

         \[\leadsto \frac{x + -2}{\frac{5.86923874282773}{x} + \left(0.24013125253755718 - \frac{55.572073733743466}{\color{blue}{x \cdot x}}\right)} \]

   6. Simplified 88.9%

      \[\leadsto \frac{x + -2}{\color{blue}{\frac{5.86923874282773}{x} + \left(0.24013125253755718 - \frac{55.572073733743466}{x \cdot x}\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -21000000000:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{elif}\;x \leq 44:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + x \cdot \left(y \cdot 0.0212463641547976 - z \cdot 0.14147091005106402\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{\frac{5.86923874282773}{x} + \left(0.24013125253755718 - \frac{55.572073733743466}{x \cdot x}\right)}\\ \end{array} \]

Alternative 9: 76.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{elif}\;x \leq 13.5:\\ \;\;\;\;\frac{z \cdot \left(x - 2\right)}{47.066876606 + x \cdot 313.399215894}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{\frac{5.86923874282773}{x} + \left(0.24013125253755718 - \frac{55.572073733743466}{x \cdot x}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -8.5e-16)
   (/ (+ x -2.0) (+ 0.24013125253755718 (/ 5.86923874282773 x)))
   (if (<= x 13.5)
     (/ (* z (- x 2.0)) (+ 47.066876606 (* x 313.399215894)))
     (/
      (+ x -2.0)
      (+
       (/ 5.86923874282773 x)
       (- 0.24013125253755718 (/ 55.572073733743466 (* x x))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.5e-16) {
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x));
	} else if (x <= 13.5) {
		tmp = (z * (x - 2.0)) / (47.066876606 + (x * 313.399215894));
	} else {
		tmp = (x + -2.0) / ((5.86923874282773 / x) + (0.24013125253755718 - (55.572073733743466 / (x * x))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-8.5d-16)) then
        tmp = (x + (-2.0d0)) / (0.24013125253755718d0 + (5.86923874282773d0 / x))
    else if (x <= 13.5d0) then
        tmp = (z * (x - 2.0d0)) / (47.066876606d0 + (x * 313.399215894d0))
    else
        tmp = (x + (-2.0d0)) / ((5.86923874282773d0 / x) + (0.24013125253755718d0 - (55.572073733743466d0 / (x * x))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.5e-16) {
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x));
	} else if (x <= 13.5) {
		tmp = (z * (x - 2.0)) / (47.066876606 + (x * 313.399215894));
	} else {
		tmp = (x + -2.0) / ((5.86923874282773 / x) + (0.24013125253755718 - (55.572073733743466 / (x * x))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -8.5e-16:
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x))
	elif x <= 13.5:
		tmp = (z * (x - 2.0)) / (47.066876606 + (x * 313.399215894))
	else:
		tmp = (x + -2.0) / ((5.86923874282773 / x) + (0.24013125253755718 - (55.572073733743466 / (x * x))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -8.5e-16)
		tmp = Float64(Float64(x + -2.0) / Float64(0.24013125253755718 + Float64(5.86923874282773 / x)));
	elseif (x <= 13.5)
		tmp = Float64(Float64(z * Float64(x - 2.0)) / Float64(47.066876606 + Float64(x * 313.399215894)));
	else
		tmp = Float64(Float64(x + -2.0) / Float64(Float64(5.86923874282773 / x) + Float64(0.24013125253755718 - Float64(55.572073733743466 / Float64(x * x)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -8.5e-16)
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x));
	elseif (x <= 13.5)
		tmp = (z * (x - 2.0)) / (47.066876606 + (x * 313.399215894));
	else
		tmp = (x + -2.0) / ((5.86923874282773 / x) + (0.24013125253755718 - (55.572073733743466 / (x * x))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -8.5e-16], N[(N[(x + -2.0), $MachinePrecision] / N[(0.24013125253755718 + N[(5.86923874282773 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 13.5], N[(N[(z * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] / N[(47.066876606 + N[(x * 313.399215894), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] / N[(N[(5.86923874282773 / x), $MachinePrecision] + N[(0.24013125253755718 - N[(55.572073733743466 / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.5000000000000001e-16

   1. Initial program 17.9%

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

      1. associate-/l* 20.6%

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

      2. sub-neg 20.6%

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

      3. metadata-eval 20.6%

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

      4. fma-def 20.6%

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

      5. fma-def 20.6%

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

      6. fma-def 20.6%

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

      7. fma-def 20.6%

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

      8. fma-def 20.6%

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

      9. fma-def 20.6%

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

      10. fma-def 20.6%

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

   3. Simplified 20.6%

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

   4. Taylor expanded in x around inf 81.4%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718 + 5.86923874282773 \cdot \frac{1}{x}}} \]
   5. Step-by-step derivation

      1. associate-*r/ 81.4%

         \[\leadsto \frac{x + -2}{0.24013125253755718 + \color{blue}{\frac{5.86923874282773 \cdot 1}{x}}} \]

      2. metadata-eval 81.4%

         \[\leadsto \frac{x + -2}{0.24013125253755718 + \frac{\color{blue}{5.86923874282773}}{x}} \]

   6. Simplified 81.4%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718 + \frac{5.86923874282773}{x}}} \]

   if -8.5000000000000001e-16 < x < 13.5

   1. Initial program 99.6%

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

      1. associate-*r/ 99.7%

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

      2. sub-neg 99.7%

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

      3. metadata-eval 99.7%

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

      4. *-commutative 99.7%

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

      5. fma-def 99.6%

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

      6. *-commutative 99.6%

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

      7. fma-def 99.7%

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

      8. *-commutative 99.7%

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

      9. fma-def 99.7%

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

      10. fma-def 99.7%

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

      11. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 65.4%

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

   5. Taylor expanded in x around 0 65.4%

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

      1. *-commutative 65.4%

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

   7. Simplified 65.4%

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

   if 13.5 < x

   1. Initial program 21.0%

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

      1. associate-/l* 28.1%

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

      2. sub-neg 28.1%

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

      3. metadata-eval 28.1%

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

      4. fma-def 28.1%

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

      5. fma-def 28.1%

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

      6. fma-def 28.1%

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

      7. fma-def 28.1%

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

      8. fma-def 28.1%

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

      9. fma-def 28.1%

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

      10. fma-def 28.1%

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

   3. Simplified 28.1%

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

   4. Taylor expanded in x around inf 87.7%

      \[\leadsto \frac{x + -2}{\color{blue}{\left(0.24013125253755718 + 5.86923874282773 \cdot \frac{1}{x}\right) - 55.572073733743466 \cdot \frac{1}{{x}^{2}}}} \]
   5. Step-by-step derivation

      1. +-commutative 87.7%

         \[\leadsto \frac{x + -2}{\color{blue}{\left(5.86923874282773 \cdot \frac{1}{x} + 0.24013125253755718\right)} - 55.572073733743466 \cdot \frac{1}{{x}^{2}}} \]

      2. associate--l+ 87.7%

         \[\leadsto \frac{x + -2}{\color{blue}{5.86923874282773 \cdot \frac{1}{x} + \left(0.24013125253755718 - 55.572073733743466 \cdot \frac{1}{{x}^{2}}\right)}} \]

      3. associate-*r/ 87.7%

         \[\leadsto \frac{x + -2}{\color{blue}{\frac{5.86923874282773 \cdot 1}{x}} + \left(0.24013125253755718 - 55.572073733743466 \cdot \frac{1}{{x}^{2}}\right)} \]

      4. metadata-eval 87.7%

         \[\leadsto \frac{x + -2}{\frac{\color{blue}{5.86923874282773}}{x} + \left(0.24013125253755718 - 55.572073733743466 \cdot \frac{1}{{x}^{2}}\right)} \]

      5. associate-*r/ 87.7%

         \[\leadsto \frac{x + -2}{\frac{5.86923874282773}{x} + \left(0.24013125253755718 - \color{blue}{\frac{55.572073733743466 \cdot 1}{{x}^{2}}}\right)} \]

      6. metadata-eval 87.7%

         \[\leadsto \frac{x + -2}{\frac{5.86923874282773}{x} + \left(0.24013125253755718 - \frac{\color{blue}{55.572073733743466}}{{x}^{2}}\right)} \]

      7. unpow2 87.7%

         \[\leadsto \frac{x + -2}{\frac{5.86923874282773}{x} + \left(0.24013125253755718 - \frac{55.572073733743466}{\color{blue}{x \cdot x}}\right)} \]

   6. Simplified 87.7%

      \[\leadsto \frac{x + -2}{\color{blue}{\frac{5.86923874282773}{x} + \left(0.24013125253755718 - \frac{55.572073733743466}{x \cdot x}\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{elif}\;x \leq 13.5:\\ \;\;\;\;\frac{z \cdot \left(x - 2\right)}{47.066876606 + x \cdot 313.399215894}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{\frac{5.86923874282773}{x} + \left(0.24013125253755718 - \frac{55.572073733743466}{x \cdot x}\right)}\\ \end{array} \]

Alternative 10: 76.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-16} \lor \neg \left(x \leq 4.2 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(x - 2\right)}{47.066876606 + x \cdot 313.399215894}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8.5e-16) (not (<= x 4.2e-9)))
   (/ (+ x -2.0) (+ 0.24013125253755718 (/ 5.86923874282773 x)))
   (/ (* z (- x 2.0)) (+ 47.066876606 (* x 313.399215894)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.5e-16) || !(x <= 4.2e-9)) {
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x));
	} else {
		tmp = (z * (x - 2.0)) / (47.066876606 + (x * 313.399215894));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-8.5d-16)) .or. (.not. (x <= 4.2d-9))) then
        tmp = (x + (-2.0d0)) / (0.24013125253755718d0 + (5.86923874282773d0 / x))
    else
        tmp = (z * (x - 2.0d0)) / (47.066876606d0 + (x * 313.399215894d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.5e-16) || !(x <= 4.2e-9)) {
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x));
	} else {
		tmp = (z * (x - 2.0)) / (47.066876606 + (x * 313.399215894));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8.5e-16) or not (x <= 4.2e-9):
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x))
	else:
		tmp = (z * (x - 2.0)) / (47.066876606 + (x * 313.399215894))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8.5e-16) || !(x <= 4.2e-9))
		tmp = Float64(Float64(x + -2.0) / Float64(0.24013125253755718 + Float64(5.86923874282773 / x)));
	else
		tmp = Float64(Float64(z * Float64(x - 2.0)) / Float64(47.066876606 + Float64(x * 313.399215894)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -8.5e-16) || ~((x <= 4.2e-9)))
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x));
	else
		tmp = (z * (x - 2.0)) / (47.066876606 + (x * 313.399215894));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8.5e-16], N[Not[LessEqual[x, 4.2e-9]], $MachinePrecision]], N[(N[(x + -2.0), $MachinePrecision] / N[(0.24013125253755718 + N[(5.86923874282773 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] / N[(47.066876606 + N[(x * 313.399215894), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.5000000000000001e-16 or 4.20000000000000039e-9 < x

   1. Initial program 20.6%

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

      1. associate-/l* 25.4%

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

      2. sub-neg 25.4%

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

      3. metadata-eval 25.4%

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

      4. fma-def 25.5%

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

      5. fma-def 25.4%

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

      6. fma-def 25.4%

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

      7. fma-def 25.4%

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

      8. fma-def 25.4%

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

      9. fma-def 25.4%

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

      10. fma-def 25.4%

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

   3. Simplified 25.4%

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

   4. Taylor expanded in x around inf 83.2%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718 + 5.86923874282773 \cdot \frac{1}{x}}} \]
   5. Step-by-step derivation

      1. associate-*r/ 83.2%

         \[\leadsto \frac{x + -2}{0.24013125253755718 + \color{blue}{\frac{5.86923874282773 \cdot 1}{x}}} \]

      2. metadata-eval 83.2%

         \[\leadsto \frac{x + -2}{0.24013125253755718 + \frac{\color{blue}{5.86923874282773}}{x}} \]

   6. Simplified 83.2%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718 + \frac{5.86923874282773}{x}}} \]

   if -8.5000000000000001e-16 < x < 4.20000000000000039e-9

   1. Initial program 99.6%

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

      1. associate-*r/ 99.7%

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

      2. sub-neg 99.7%

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

      3. metadata-eval 99.7%

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

      4. *-commutative 99.7%

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

      5. fma-def 99.6%

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

      6. *-commutative 99.6%

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

      7. fma-def 99.6%

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

      8. *-commutative 99.6%

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

      9. fma-def 99.6%

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

      10. fma-def 99.6%

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

      11. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around inf 66.4%

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

   5. Taylor expanded in x around 0 66.4%

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

      1. *-commutative 66.4%

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

   7. Simplified 66.4%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-16} \lor \neg \left(x \leq 4.2 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(x - 2\right)}{47.066876606 + x \cdot 313.399215894}\\ \end{array} \]

Alternative 11: 76.3% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-16} \lor \neg \left(x \leq 4.2 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8.5e-16) (not (<= x 4.2e-9)))
   (/ (+ x -2.0) (+ 0.24013125253755718 (/ 5.86923874282773 x)))
   (/ (+ x -2.0) (/ 47.066876606 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.5e-16) || !(x <= 4.2e-9)) {
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x));
	} else {
		tmp = (x + -2.0) / (47.066876606 / 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 <= (-8.5d-16)) .or. (.not. (x <= 4.2d-9))) then
        tmp = (x + (-2.0d0)) / (0.24013125253755718d0 + (5.86923874282773d0 / x))
    else
        tmp = (x + (-2.0d0)) / (47.066876606d0 / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.5e-16) || !(x <= 4.2e-9)) {
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x));
	} else {
		tmp = (x + -2.0) / (47.066876606 / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8.5e-16) or not (x <= 4.2e-9):
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x))
	else:
		tmp = (x + -2.0) / (47.066876606 / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8.5e-16) || !(x <= 4.2e-9))
		tmp = Float64(Float64(x + -2.0) / Float64(0.24013125253755718 + Float64(5.86923874282773 / x)));
	else
		tmp = Float64(Float64(x + -2.0) / Float64(47.066876606 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -8.5e-16) || ~((x <= 4.2e-9)))
		tmp = (x + -2.0) / (0.24013125253755718 + (5.86923874282773 / x));
	else
		tmp = (x + -2.0) / (47.066876606 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8.5e-16], N[Not[LessEqual[x, 4.2e-9]], $MachinePrecision]], N[(N[(x + -2.0), $MachinePrecision] / N[(0.24013125253755718 + N[(5.86923874282773 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] / N[(47.066876606 / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.5000000000000001e-16 or 4.20000000000000039e-9 < x

   1. Initial program 20.6%

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

      1. associate-/l* 25.4%

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

      2. sub-neg 25.4%

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

      3. metadata-eval 25.4%

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

      4. fma-def 25.5%

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

      5. fma-def 25.4%

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

      6. fma-def 25.4%

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

      7. fma-def 25.4%

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

      8. fma-def 25.4%

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

      9. fma-def 25.4%

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

      10. fma-def 25.4%

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

   3. Simplified 25.4%

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

   4. Taylor expanded in x around inf 83.2%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718 + 5.86923874282773 \cdot \frac{1}{x}}} \]
   5. Step-by-step derivation

      1. associate-*r/ 83.2%

         \[\leadsto \frac{x + -2}{0.24013125253755718 + \color{blue}{\frac{5.86923874282773 \cdot 1}{x}}} \]

      2. metadata-eval 83.2%

         \[\leadsto \frac{x + -2}{0.24013125253755718 + \frac{\color{blue}{5.86923874282773}}{x}} \]

   6. Simplified 83.2%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718 + \frac{5.86923874282773}{x}}} \]

   if -8.5000000000000001e-16 < x < 4.20000000000000039e-9

   1. Initial program 99.6%

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

      1. associate-/l* 99.4%

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

      2. sub-neg 99.4%

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

      3. metadata-eval 99.4%

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

      4. fma-def 99.4%

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

      5. fma-def 99.4%

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

      6. fma-def 99.4%

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

      7. fma-def 99.4%

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

      8. fma-def 99.4%

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

      9. fma-def 99.4%

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

      10. fma-def 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 66.2%

      \[\leadsto \frac{x + -2}{\color{blue}{\frac{47.066876606}{z}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-16} \lor \neg \left(x \leq 4.2 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606}{z}}\\ \end{array} \]

Alternative 12: 76.3% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -21000000000:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228 + \left(\frac{3655.1204654076414}{x} - 110.1139242984811\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -21000000000.0)
   (/ (+ x -2.0) 0.24013125253755718)
   (if (<= x 2.0)
     (* z -0.0424927283095952)
     (+ (* x 4.16438922228) (- (/ 3655.1204654076414 x) 110.1139242984811)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -21000000000.0) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= 2.0) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = (x * 4.16438922228) + ((3655.1204654076414 / x) - 110.1139242984811);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-21000000000.0d0)) then
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    else if (x <= 2.0d0) then
        tmp = z * (-0.0424927283095952d0)
    else
        tmp = (x * 4.16438922228d0) + ((3655.1204654076414d0 / x) - 110.1139242984811d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -21000000000.0) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= 2.0) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = (x * 4.16438922228) + ((3655.1204654076414 / x) - 110.1139242984811);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -21000000000.0:
		tmp = (x + -2.0) / 0.24013125253755718
	elif x <= 2.0:
		tmp = z * -0.0424927283095952
	else:
		tmp = (x * 4.16438922228) + ((3655.1204654076414 / x) - 110.1139242984811)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -21000000000.0)
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	elseif (x <= 2.0)
		tmp = Float64(z * -0.0424927283095952);
	else
		tmp = Float64(Float64(x * 4.16438922228) + Float64(Float64(3655.1204654076414 / x) - 110.1139242984811));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -21000000000.0)
		tmp = (x + -2.0) / 0.24013125253755718;
	elseif (x <= 2.0)
		tmp = z * -0.0424927283095952;
	else
		tmp = (x * 4.16438922228) + ((3655.1204654076414 / x) - 110.1139242984811);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -21000000000.0], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision], If[LessEqual[x, 2.0], N[(z * -0.0424927283095952), $MachinePrecision], N[(N[(x * 4.16438922228), $MachinePrecision] + N[(N[(3655.1204654076414 / x), $MachinePrecision] - 110.1139242984811), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.1e10

   1. Initial program 14.1%

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

      1. associate-/l* 17.0%

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

      2. sub-neg 17.0%

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

      3. metadata-eval 17.0%

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

      4. fma-def 17.0%

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

      5. fma-def 17.0%

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

      6. fma-def 17.0%

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

      7. fma-def 17.0%

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

      8. fma-def 17.0%

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

      9. fma-def 17.0%

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

      10. fma-def 17.0%

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

   3. Simplified 17.0%

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

   4. Taylor expanded in x around inf 84.6%

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

   if -2.1e10 < x < 2

   1. Initial program 99.6%

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

      1. associate-*r/ 99.6%

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

      2. sub-neg 99.6%

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

      3. metadata-eval 99.6%

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

      4. *-commutative 99.6%

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

      5. fma-def 99.6%

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

      6. *-commutative 99.6%

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

      7. fma-def 99.6%

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

      8. *-commutative 99.6%

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

      9. fma-def 99.6%

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

      10. fma-def 99.6%

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

      11. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 63.7%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]
   5. Step-by-step derivation

      1. *-commutative 63.7%

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

   6. Simplified 63.7%

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

   if 2 < x

   1. Initial program 21.0%

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

      1. associate-*r/ 28.1%

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

      2. sub-neg 28.1%

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

      3. metadata-eval 28.1%

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

      4. *-commutative 28.1%

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

      5. fma-def 28.1%

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

      6. *-commutative 28.1%

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

      7. fma-def 28.1%

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

      8. *-commutative 28.1%

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

      9. fma-def 28.1%

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

      10. fma-def 28.1%

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

      11. *-commutative 28.1%

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

   3. Simplified 28.1%

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

   4. Taylor expanded in x around inf 87.0%

      \[\leadsto \color{blue}{\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - 110.1139242984811} \]
   5. Step-by-step derivation

      1. associate--l+ 87.0%

         \[\leadsto \color{blue}{4.16438922228 \cdot x + \left(3655.1204654076414 \cdot \frac{1}{x} - 110.1139242984811\right)} \]

      2. div-inv 87.0%

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

   6. Applied egg-rr 87.0%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -21000000000:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228 + \left(\frac{3655.1204654076414}{x} - 110.1139242984811\right)\\ \end{array} \]

Alternative 13: 76.1% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -21000000000 \lor \neg \left(x \leq 4.2 \cdot 10^{-9}\right):\\ \;\;\;\;x \cdot 4.16438922228 - 110.1139242984811\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -21000000000.0) (not (<= x 4.2e-9)))
   (- (* x 4.16438922228) 110.1139242984811)
   (* z -0.0424927283095952)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -21000000000.0) || !(x <= 4.2e-9)) {
		tmp = (x * 4.16438922228) - 110.1139242984811;
	} else {
		tmp = z * -0.0424927283095952;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-21000000000.0d0)) .or. (.not. (x <= 4.2d-9))) then
        tmp = (x * 4.16438922228d0) - 110.1139242984811d0
    else
        tmp = z * (-0.0424927283095952d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -21000000000.0) || !(x <= 4.2e-9)) {
		tmp = (x * 4.16438922228) - 110.1139242984811;
	} else {
		tmp = z * -0.0424927283095952;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -21000000000.0) or not (x <= 4.2e-9):
		tmp = (x * 4.16438922228) - 110.1139242984811
	else:
		tmp = z * -0.0424927283095952
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -21000000000.0) || !(x <= 4.2e-9))
		tmp = Float64(Float64(x * 4.16438922228) - 110.1139242984811);
	else
		tmp = Float64(z * -0.0424927283095952);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -21000000000.0) || ~((x <= 4.2e-9)))
		tmp = (x * 4.16438922228) - 110.1139242984811;
	else
		tmp = z * -0.0424927283095952;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -21000000000.0], N[Not[LessEqual[x, 4.2e-9]], $MachinePrecision]], N[(N[(x * 4.16438922228), $MachinePrecision] - 110.1139242984811), $MachinePrecision], N[(z * -0.0424927283095952), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1e10 or 4.20000000000000039e-9 < x

   1. Initial program 18.8%

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

      1. associate-*r/ 23.8%

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

      2. sub-neg 23.8%

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

      3. metadata-eval 23.8%

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

      4. *-commutative 23.8%

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

      5. fma-def 23.8%

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

      6. *-commutative 23.8%

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

      7. fma-def 23.8%

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

      8. *-commutative 23.8%

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

      9. fma-def 23.8%

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

      10. fma-def 23.8%

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

      11. *-commutative 23.8%

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

   3. Simplified 23.8%

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

   4. Taylor expanded in x around inf 84.4%

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

   if -2.1e10 < x < 4.20000000000000039e-9

   1. Initial program 99.6%

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

      1. associate-*r/ 99.7%

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

      2. sub-neg 99.7%

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

      3. metadata-eval 99.7%

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

      4. *-commutative 99.7%

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

      5. fma-def 99.6%

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

      6. *-commutative 99.6%

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

      7. fma-def 99.6%

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

      8. *-commutative 99.6%

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

      9. fma-def 99.6%

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

      10. fma-def 99.6%

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

      11. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 64.6%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]
   5. Step-by-step derivation

      1. *-commutative 64.6%

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

   6. Simplified 64.6%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -21000000000 \lor \neg \left(x \leq 4.2 \cdot 10^{-9}\right):\\ \;\;\;\;x \cdot 4.16438922228 - 110.1139242984811\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \end{array} \]

Alternative 14: 76.2% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -21000000000:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-9}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228 - 110.1139242984811\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -21000000000.0)
   (/ (+ x -2.0) 0.24013125253755718)
   (if (<= x 4.2e-9)
     (* z -0.0424927283095952)
     (- (* x 4.16438922228) 110.1139242984811))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -21000000000.0) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= 4.2e-9) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = (x * 4.16438922228) - 110.1139242984811;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-21000000000.0d0)) then
        tmp = (x + (-2.0d0)) / 0.24013125253755718d0
    else if (x <= 4.2d-9) then
        tmp = z * (-0.0424927283095952d0)
    else
        tmp = (x * 4.16438922228d0) - 110.1139242984811d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -21000000000.0) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else if (x <= 4.2e-9) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = (x * 4.16438922228) - 110.1139242984811;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -21000000000.0:
		tmp = (x + -2.0) / 0.24013125253755718
	elif x <= 4.2e-9:
		tmp = z * -0.0424927283095952
	else:
		tmp = (x * 4.16438922228) - 110.1139242984811
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -21000000000.0)
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	elseif (x <= 4.2e-9)
		tmp = Float64(z * -0.0424927283095952);
	else
		tmp = Float64(Float64(x * 4.16438922228) - 110.1139242984811);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -21000000000.0)
		tmp = (x + -2.0) / 0.24013125253755718;
	elseif (x <= 4.2e-9)
		tmp = z * -0.0424927283095952;
	else
		tmp = (x * 4.16438922228) - 110.1139242984811;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -21000000000.0], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision], If[LessEqual[x, 4.2e-9], N[(z * -0.0424927283095952), $MachinePrecision], N[(N[(x * 4.16438922228), $MachinePrecision] - 110.1139242984811), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.1e10

   1. Initial program 14.1%

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

      1. associate-/l* 17.0%

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

      2. sub-neg 17.0%

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

      3. metadata-eval 17.0%

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

      4. fma-def 17.0%

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

      5. fma-def 17.0%

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

      6. fma-def 17.0%

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

      7. fma-def 17.0%

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

      8. fma-def 17.0%

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

      9. fma-def 17.0%

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

      10. fma-def 17.0%

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

   3. Simplified 17.0%

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

   4. Taylor expanded in x around inf 84.6%

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

   if -2.1e10 < x < 4.20000000000000039e-9

   1. Initial program 99.6%

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

      1. associate-*r/ 99.7%

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

      2. sub-neg 99.7%

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

      3. metadata-eval 99.7%

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

      4. *-commutative 99.7%

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

      5. fma-def 99.6%

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

      6. *-commutative 99.6%

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

      7. fma-def 99.6%

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

      8. *-commutative 99.6%

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

      9. fma-def 99.6%

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

      10. fma-def 99.6%

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

      11. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 64.6%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]
   5. Step-by-step derivation

      1. *-commutative 64.6%

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

   6. Simplified 64.6%

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

   if 4.20000000000000039e-9 < x

   1. Initial program 23.3%

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

      1. associate-*r/ 30.1%

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

      2. sub-neg 30.1%

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

      3. metadata-eval 30.1%

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

      4. *-commutative 30.1%

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

      5. fma-def 30.1%

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

      6. *-commutative 30.1%

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

      7. fma-def 30.2%

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

      8. *-commutative 30.2%

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

      9. fma-def 30.2%

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

      10. fma-def 30.2%

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

      11. *-commutative 30.2%

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

   3. Simplified 30.2%

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

   4. Taylor expanded in x around inf 84.3%

      \[\leadsto \color{blue}{4.16438922228 \cdot x - 110.1139242984811} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -21000000000:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-9}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228 - 110.1139242984811\\ \end{array} \]

Alternative 15: 76.1% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -21000000000:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -21000000000.0)
   (* x 4.16438922228)
   (if (<= x 2.0) (* z -0.0424927283095952) (* x 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -21000000000.0) {
		tmp = x * 4.16438922228;
	} else if (x <= 2.0) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-21000000000.0d0)) then
        tmp = x * 4.16438922228d0
    else if (x <= 2.0d0) then
        tmp = z * (-0.0424927283095952d0)
    else
        tmp = x * 4.16438922228d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -21000000000.0) {
		tmp = x * 4.16438922228;
	} else if (x <= 2.0) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -21000000000.0:
		tmp = x * 4.16438922228
	elif x <= 2.0:
		tmp = z * -0.0424927283095952
	else:
		tmp = x * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -21000000000.0)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 2.0)
		tmp = Float64(z * -0.0424927283095952);
	else
		tmp = Float64(x * 4.16438922228);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -21000000000.0)
		tmp = x * 4.16438922228;
	elseif (x <= 2.0)
		tmp = z * -0.0424927283095952;
	else
		tmp = x * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -21000000000.0], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 2.0], N[(z * -0.0424927283095952), $MachinePrecision], N[(x * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1e10 or 2 < x

   1. Initial program 17.6%

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

      1. associate-*r/ 22.6%

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

      2. sub-neg 22.6%

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

      3. metadata-eval 22.6%

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

      4. *-commutative 22.6%

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

      5. fma-def 22.6%

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

      6. *-commutative 22.6%

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

      7. fma-def 22.6%

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

      8. *-commutative 22.6%

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

      9. fma-def 22.6%

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

      10. fma-def 22.6%

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

      11. *-commutative 22.6%

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

   3. Simplified 22.6%

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

   4. Taylor expanded in x around inf 84.9%

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

      1. *-commutative 84.9%

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

   6. Simplified 84.9%

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

   if -2.1e10 < x < 2

   1. Initial program 99.6%

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

      1. associate-*r/ 99.6%

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

      2. sub-neg 99.6%

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

      3. metadata-eval 99.6%

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

      4. *-commutative 99.6%

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

      5. fma-def 99.6%

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

      6. *-commutative 99.6%

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

      7. fma-def 99.6%

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

      8. *-commutative 99.6%

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

      9. fma-def 99.6%

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

      10. fma-def 99.6%

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

      11. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 63.7%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]
   5. Step-by-step derivation

      1. *-commutative 63.7%

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

   6. Simplified 63.7%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -21000000000:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

Alternative 16: 2.2% accurate, 12.3× speedup

Math

\[\begin{array}{l} \\ x \cdot -0.3407596943375357 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x -0.3407596943375357))

C

double code(double x, double y, double z) {
	return x * -0.3407596943375357;
}

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 * (-0.3407596943375357d0)
end function

Java

public static double code(double x, double y, double z) {
	return x * -0.3407596943375357;
}

Python

def code(x, y, z):
	return x * -0.3407596943375357

Julia

function code(x, y, z)
	return Float64(x * -0.3407596943375357)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * -0.3407596943375357;
end

Wolfram

code[x_, y_, z_] := N[(x * -0.3407596943375357), $MachinePrecision]

Derivation

1. Initial program 57.3%

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

   1. associate-/l* 59.8%

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

   2. sub-neg 59.8%

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

   3. metadata-eval 59.8%

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

   4. fma-def 59.8%

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

   5. fma-def 59.8%

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

   6. fma-def 59.8%

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

   7. fma-def 59.8%

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

   8. fma-def 59.8%

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

   9. fma-def 59.8%

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

   10. fma-def 59.8%

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

3. Simplified 59.8%

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

4. Taylor expanded in x around inf 46.1%

   \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718 + 5.86923874282773 \cdot \frac{1}{x}}} \]
5. Step-by-step derivation

   1. associate-*r/ 46.1%

      \[\leadsto \frac{x + -2}{0.24013125253755718 + \color{blue}{\frac{5.86923874282773 \cdot 1}{x}}} \]

   2. metadata-eval 46.1%

      \[\leadsto \frac{x + -2}{0.24013125253755718 + \frac{\color{blue}{5.86923874282773}}{x}} \]

6. Simplified 46.1%

   \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718 + \frac{5.86923874282773}{x}}} \]

7. Taylor expanded in x around 0 2.2%

   \[\leadsto \color{blue}{-0.3407596943375357 \cdot x} \]
8. Step-by-step derivation

   1. *-commutative 2.2%

      \[\leadsto \color{blue}{x \cdot -0.3407596943375357} \]

9. Simplified 2.2%

   \[\leadsto \color{blue}{x \cdot -0.3407596943375357} \]

10. Final simplification 2.2%

    \[\leadsto x \cdot -0.3407596943375357 \]

Alternative 17: 44.8% accurate, 12.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 57.3%

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

   1. associate-*r/ 59.9%

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

   2. sub-neg 59.9%

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

   3. metadata-eval 59.9%

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

   4. *-commutative 59.9%

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

   5. fma-def 59.9%

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

   6. *-commutative 59.9%

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

   7. fma-def 59.9%

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

   8. *-commutative 59.9%

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

   9. fma-def 59.9%

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

   10. fma-def 59.9%

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

   11. *-commutative 59.9%

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

3. Simplified 59.9%

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

4. Taylor expanded in x around inf 45.6%

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

   1. *-commutative 45.6%

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

6. Simplified 45.6%

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

7. Final simplification 45.6%

   \[\leadsto x \cdot 4.16438922228 \]

Developer target: 98.7% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023185 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C"
  :precision binary64

  :herbie-target
  (if (< x -3.326128725870005e+62) (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811) (if (< x 9.429991714554673e+55) (* (/ (- x 2.0) 1.0) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (+ (* 263.505074721 x) (+ (* 43.3400022514 (* x x)) (* x (* x x)))) 313.399215894) x) 47.066876606))) (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811)))

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